Samer Elatrache V-17810600 estudiante de CRF
This chapter concludes with a discussion of several PVD processes that are
more complex than the conventional ones considered up to this point. They
demonstrate the diversity of process hybridization and modification possible in
producing films with unusual properties. Ion plating, reactive evaporation, and
ion-beam-assisted deposition will be the processes considered first. In the first
two, the material deposited usually originates from a heated evaporation
source. In the third, well-characterized ion beams bombard films deposited by
evaporation or sputtering. The chapter closes with a discussion of ionized
cluster-beam deposition. This process is different from others considered in
this chapter in that film formation occurs through impingement of collective
groups of atoms from the gas phase rather than individual atoms.
Ion Plating
Ion plating, developed by Mattox (Ref. 29), refers to evaporated film deposition
processes in which the substrate is exposed to a flux of high-energy ions
capable of causing appreciable sputtering before and during film formation. A
schematic representation of a diode-type batch, ion-plating system is shown in
Fig. 3-25a. Since it is a hybrid system, provision must be made to sustain the
plasma, cause sputtering, and heat the vapor source. Prior to deposition, the
substrate, negatively biased from 2 to 5 kV, is subjected to inert-gas ion
bombardment at a pressure in the millitorr range for a time sufficient to
sputter-clean the surface and remove contaminants. Source evaporation is then
begun without interrupting the sputtering, whose rate must obviously be less
than that of the deposition rate. Once the interface between film and substrate
has formed, ion bombardment may or may not be continued. To circumvent
the relatively high system pressures associated with glow discharges, highvacuum
ion-plating systems have also been constructed. They rely on directed
ion beams targeted at the substrate. Such systems, which have been limited
thus far to research applications, are discussed in Section 3.8.3.
Perhaps the chief advantage of ion plating is the ability to promote extremely
good adhesion between the film and substrate by the ion and particle bombardment
mechanisms discussed in Section 3.7.5. A second important advantage is
the high "throwing power" when compared with vacuum evaporation. This
results from gas scattering, entrainment, and sputtering of the film, and
enables deposition in recesses and on areas remote from the source-substrate
line of sight. Relatively uniform coating of substrates with complex shapes is
thus achieved. Lastly, the quality of deposited films is frequently enhanced.
The continual bombardment of the growing film by high-energy ions or neutral
atoms and molecules serves to peen and compact it to near bulk densities.
Sputtering of loosely adhering film material, increased surface diffusion, and
reduced shadowing effects serve to suppress undesirable columnar growth.
A major use of ion plating has been to coat steel and other metals with very
hard films for use in tools and wear-resistant applications. For this purpose,
metals like Ti, Zr, Cr, and Si are electron-beam-evaporated through an Ar
plasma in the presence of reactive gases such as N, , 0, , and CH, , which are
simultaneously introduced into the system. This variant of the process is
known as reactive ion plating (RIP), and coatings of nitrides, oxides, and
carbides have been deposited in this manner.
Reactive Evaporation Processes
In reactive evaporation the evaporant metal vapor flux passes through and
reacts with a gas (at 1-30 X torr) introduced into the system to produce
compound deposits. The process has a history of evolution in which evaporation
was first carried out without ionization of the reactive gas. In the more
recent activated reactive evaporation (ARE) processes developed by Bunshah
and co-workers (Ref. 30), a plasma discharge is maintained directly within the
reaction zone between the metal source and substrate. Both the metal vapor
and reactive gases, such as 0,, N,, CH,, C,H,, etc., are, therefore, ionized
increasing their reactivity on the surface of the growing film or coating,
promoting stoichiometric compound formation. One of the process configurations
is illustrated in Fig. 3-25b, where the metal is melted by an electron
beam. A thin plasma sheath develops on top of the molten pool. Low-energy
secondary electrons from this source are drawn upward into the reaction zone
by a circular wire electrode placed above the melt biased to a positive dc
potential (20-100 V), creating a plasma-filled region extending from the
electron-beam gun to near the substrate. The ARE process is endowed with
considerable flexibility, since the substrates can be grounded, allowed to float
electrically, or biased positively or negatively. In the latter variant ARE is
quite similar to RIP. Other modifications of ARE include resistance-heated
evaporant sources coupled with a low-voltage cathode (electron) emitter-anode
assembly. Activation by dc and RF excitation has also been employed to
sustain the plasma, and transverse magnetic fields have been applied to
effectively extend plasma electron lifetimes.
Before considering the variety of compounds produced by ARE, we recall
that thermodynamic and kinetic factors are involved in their formation. The
high negative enthalpies of compound formation of oxides, nitrides, carbides,
and borides indicate no thermodynamic obstacles to chemical reaction. The
rate-controlling step in simple reactive evaporation is frequently the speed of
the chemical reaction at the reaction interface. The actual physical location of
the latter may be the substrate surface, the gas phase, the surface of the metal
evaporant pool, or a combination of these. Plasma activation generally lowers
the energy barrier for reaction by creating many excited chemical species. By
eliminating the major impediment to reaction, ARE processes are thus capable
of deposition rates of a few thousand angstroms per minute.
Ion-Beam-Assisted Deposition Processes (Ref. 31)
We noted in Section 3.7.5 that ion bombardment of biased substrates during
sputtering is a particularly effective way to modify film properties. Process
control in plasmas is somewhat haphazard, however, because the direction,
energy, and flux of the ions incident on the growing film cannot be regulated.
Ion-beam-assisted processes were invented to provide independent control of
the deposition parameters and, particularly, the characteristics of the ions
bombarding the substrate. Two main ion source configurations are employed.
In the dual-ion-beam system, one source provides the inert or reactive ion
beam to sputter a target in order to yield a flux of atoms for deposition onto
the substrate. Simultaneously, the second ion source, aimed at the substrate,
supplies the inert or reactive ion beam that bombards the depositing film.
Separate film-thickness-rate and ion-current monitors, fixed to the substrate
holder, enable the two incident beam fluxes to be independently controlled.
In the second configuration (Fig. 3-25c), an ion source is used in conjunction
with an evaporation source. The process, known as ion-assisted deposition
(IAD), combines the benefits of high film deposition rate and ion
bombardment. The energy flux and direction of the ion beam can be regulated
independently of the evaporation flux. In both configurations the ion-beam
angle of incidence is not normal to the substrate and can lead to anisotropic
film properties. Substrate rotation is, therefore, recommended if isotropy is
desired.
Broad-beam (Kaufman) ion sources, the heart of ion-beam-assisted deposition
systems, were first used as ion thrusters for space propulsion (Ref. 32).
Their efficiency has been optimized to yield high-ion-beam fluxes for given
power inputs and gas flows. They contain a discharge chamber that is raised to
a potential corresponding to the desired ion energy. Gases fed into the chamber
become ionized in the plasma, and a beam of ions is extracted and accelerated
through matching apertures in a pair of grids. Current densities of several
mA/cm2 are achieved. (Note that 1 mA/cm2 is equivalent to 6.25 x 1015
ions/cm2-sec or several monolayers per second.) The resulting beams have a
low-energy spread (typically 10 eV) and are well collimated, with divergence
angles of only a few degrees. Furthermore, the background pressure is quite
low (-
Examples of thin-film property modification as a result of IAD are given in
Table 3-8. The reader should appreciate the applicability to all classes of solids
and to a broad spectrum of properties. For the most part, ion energies are
lower than those typically involved in sputtering. Bombarding ion fluxes are
generally smaller than depositing atom fluxes. Perhaps the most promising
application of ion bombardment is the enhancement of the density and index of
refraction of optical coatings.
Ionized Cluster Beam (ICB) Deposition (Ref. 33)
The idea of employing energetic ionized clusters of atoms to deposit thin films
is due to T. Takagi. In this novel technique, vapor-phase aggregates or
clusters, thought to contain a few hundred to a few thousand atoms, are
created, ionized, and accelerated toward the substrate as depicted schematically
in Fig. 3-26. As a result of impact with the substrate, the cluster breaks apart,
releasing atoms to spread across the surface. Cluster production is, of course,
the critical step and begins with evaporation from a crucible containing a small
aperture or nozzle. The evaporant vapor pressure is much higher (10-*-10
torr) than in conventional vacuum evaporation. For cluster formation the
nozzle diameter must exceed the mean-free path of vapor atoms in the crucible.
Viscous flow of atoms escaping the nozzle then results in an adiabatic
supersonic expansion and the formation of stable cluster nuclei. Optimum
expansion further requires that the ratio of the vapor pressure in the crucible to
that in the vacuum chamber exceed lo4 to 10'.
The arrival of ionized clusters with the kinetic energy of the acceleration
voltage (0-10 kV), and neutral clusters with the kinetic energy of the nozzle
ejection velocity, affects film nucleation and growth processes in the following
ways:
1. The local temperature at the point of impact increases.
2. Surface diffusion of atoms is enhanced.
3. Activated centers for nucleation are created.
4. Coalescence of nuclei is fostered.
5. At high enough energies, the surface is sputter-cleaned, and shallow
implantation of ions may occur.
6. Chemical reactions between condensing atoms and the substrate or gas-phase
atoms are favored.
Moreover, the magnitude of these effects can be modified by altering the
extent of electron impact ionization and the accelerating voltage.
Virtually all classes of film materials have been deposited by ICB (and
variant reactive process versions), including pure metals, alloys, intermetallic
compounds, semiconductors, oxides, nitrides, carbides, halides, and organic
compounds. Special attributes of ICB-prepared films worth noting are strong
adhesion to the substrate, smooth surfaces, elimination of columnar growth
morphology, low-temperature growth, controllable crystal structures, and,
importantly, very high quality single-crystal growth (epitaxial films). Large Au
film mirrors for CO, lasers, ohmic metal contacts to Si and Gap, electromigration-
(Section 8.4) resistant A1 films, and epitaxial Si, GaAs, Gap, and InSb
films deposited at low temperatures are some examples indicative of the
excellent properties of ICB films. Among the advantages of ICB deposition are
vacuum cleanliness (- lo-' torr in the chamber) of evaporation and energetic
ion bombardment of the substrate, two normally mutually exclusive features.
In addition, the interaction of slowly moving clusters with the substrate is
confined, limiting the amount of damage to both the growing film and
substrate. Despite the attractive features of ICB, the formation of clusters and
their role in film formation are not well understood. Recent research (Ref. 34),
however, clearly indicates that the total number of atoms agglomerated in large
metal clusters is actually very small (only 1 in lo4) and that only a fraction of
large clusters is ionized. The total energy brought to the film surface by
ionized clusters is, therefore, quite small. Rather, it appears that individual
atomic ions, which are present in much greater profusion than are ionized
clusters, are the dominant vehicle for transporting energy and momentum to
the growing film. In this respect, ICB deposition belongs to the class of
processes deriving benefits from the ion-beam-assisted film growth mechanisms
previously discussed.
domingo, 21 de marzo de 2010
Magnetron Sputtering
Samer Elatrache V-17810600 estudiante de CRF
Electron Motion in Parallel Electric and Magnetic Fields. Let
us now examine what happens when a magnetic field of strength B is
superimposed on the electric field 8 between the target and substrate. Such a
situation arises in magnetron sputtering as well as in certain plasma etching
configurations. Electrons within the dual field environment experience the
well-known Lorentz force in addition to electric field force, i.e.,
m dv
dt
F = - - - -q(g+ v X B),
where q, m and u are the electron charge, mass, and velocity, respectively
First consider the case where B and 8 are parallel as shown in Fig. 3-20a.
When electrons are emitted exactly normal to the target surface and parallel to
both fields, then v x B vanishes; electrons are only influenced by the 8 field,
which accelerates them toward the anode. Next consider the case where the 8
field is neglected but B is still applied as shown in Fig. 3-20b. If an electron is
launched from the cathode with velocity u at angle 8 with respect to B, it
experiences a force quB sin 8 in a direction perpendicular to B. The electron
now orbits in a circular motion with a radius r that is determined by a balance
of the centrifugal (m(v sin 8 ) * / r ) and Lorentz forces involved, i.e., r =
mu sin 8 /qB. The electron motion is helical; in corkscrew fashion it spirals
down the axis of the discharge with constant velocity u cos 8. If the magnetic
field were not present, such off-axis electrons would tend to migrate out of the
discharge and be lost at the walls.
The case where electrons are launched at an angle to parallel, uniform
and B fields is somewhat more complex. Corkscrew motion with constant
radius occurs, but because of electron acceleration in the 8 field, the pitch of
the helix lengthens with time (Fig. 3-2Oc). Time varying fields complicate
matters further and electron spirals of variable radius can occur. Clearly
magnetic fields prolong the electron residence time in the plasma and thus
enhance the probability of ion collisions. This leads to larger discharge
currents and increased sputter deposition rates. Comparable discharges in a
simple diode-sputtering configuration operate at higher currents and pressures,
Therefore, applied magnetic fields have the desirable effect of reducing
electron bombardment of substrates and extending the operating vacuum range
Perpendicular Electric and M8gnetiC Fields. In magnetrons,
electrons ideally do not even reach the anode but are trapped near the target,
enhancing the ionizing efficiency there. This is accomplished by employing a
magnetic field oriented parallel to the target and perpendicular to the electric
field, as shown schematically in Fig. 3-21. Practically, this is achieved by
placing bar or horseshoe magnets behind the target. Therefore, the magnetic
field lines first emanate normal to the target, then bend with a component
parallel to the target surface (this is the magnetron component) and finally
return, completing the magnetic circuit. Electrons emitted from the cathode are
initially accelerated toward the anode, executing a helical motion in the
process; but when they encounter the region of the parallel magnetic field, they
are bent in an orbit back to the target in very much the same way that electrons
are deflected toward the hearth in an e-gun evaporator. By solving the coupled
differential equations resulting from the three components of Eq. 3-39, we
readily see that the parameric equations of motion are where y and x are the distances above and along the target, and w, = qE/m.
These equations describe a cycloidal motion that the electrons execute within
the cathode dark space where both fields are present. If, however, electrons
stray into the negative glow region where the 8 field is small, the electrons
describe a circular motion before collisions may drive them back into the dark
space or forward toward the anode. By suitable orientation of target magnets, a
"race track" can be defined where the electrons hop around at high speed.
Target erosion by sputtering occurs within this track because ionization of the
working gas is most intense above it.
Magnetron sputtering is presently the most widely commercially practiced
sputtering method. The chief reason for its success is the high deposition rates
achieved (e.g., up to 1 pm/min for Al). These are typically an order of
magnitude higher than rates attained by conventional sputtering techniques.
Popular sputtering configurations utilize planar, toroidal (rectangular cross
section), and toroidal-conical (trapezoidal cross section) targets (Le., the
S-gun). In commercial planar magnetron sputtering systems, the substrate
plane translates past the parallel facing target through interlocked vacuum
chambers to allow for semicontinuous coating operations. The circular
(toridal-conical) target, on the other hand, is positioned centrally within the
chamber, creating a deposition geometry approximating that of the analogous
planar (ring) evaporation source. In this manner wafers on a planetary substrate
holder can be coated as uniformly as with e-gun sources.
Reactive Sputtering
In reactive sputtering, thin films of compounds are deposited on substrates by
sputtering from metallic targets in the presence of a reactive gas, usually mixed
with the inert working gas (invariably Ar). The most common compounds
reactively sputtered (and the reactive gases employed) are briefly listed:
1. Oxides (oxygen)-Al,O,, In,O,, SnO,, SO,, Ta,O,
2. Nitrides (nitrogen, ammonia)-TaN, TiN, AlN, Si,N,
3. Carbides (methane, acetylene, propane)-Tic, WC, Sic
4. Sulfides (H,S)-CdS, CuS, ZnS
5. Oxycarbides and oxynitrides of Ti, Ta, Al, and Si
Irrespective of which of these materials is considered, during reactive
sputtering the resulting film is either a solid solution alloy of the target metal
doped with the reactive element (e.g., TaN,,,,), a compound (e.g., TiN), or
some mixture of the two. Westwood (Ref. 25) has provided a useful way to
visualize the conditions required to yield alloys or compounds. These two
regimes are distinguished in Fig. 3-22a, illustrating the generic hysteresis
curve for the total system pressure (P) as a function of the flow rate of
reactive gas (Q,) into the system. First, however, consider the dotted line
representing the variation of P with flow rate of an inert sputtering gas (Q,).
Clearly, as Qi increases, P increases because of the constant pumping speed
(see Eq. 2-16). An example of this characteristic occurs during Ar gas
sputtering of Ta. Now consider what happens when reactive N, gas is
introduced into the system. As Q, increases from Q,(O), the system pressure
essentially remains at the initial value Po because N, reacts with Ta and is
removed from the gas phase. But beyond a critical flow rate QF, the system
pressure jumps to the new value P,. If no reactive sputtering took place, P
would be somewhat higher (i.e., P3). Once the equilibrium value of P is
established, subsequent changes in Q, cause P to increase or decrease linearly
as shown. As Q, decreases sufficiently, P again reaches the initial pressure.
The hysteresis behavior represents two stable states of the system with a
rapid transition between them. In state A there is little change in pressure,
while for state B the pressure varies linearly with Q,. Clearly, all of the
reactive gas is incorporated into the deposited film in state A-the doped metal
and the atomic ratio of reactive gas dopant to sputtered metal increases with
Q,. The transition from state A to state B is triggered by compound formation
on the metal target. Since ion-induced secondary electron emission is usually
much higher for compounds than for metals, Ohm's law suggests that the
plasma impedance is effectively lower in state B than in state A. This effect is
reflected in the hysteresis of the target voltage with reactive gas flow rate, as
schematically depicted in Fig. 3-22b.
The choice of whether to employ compound targets and sputter directly or
sputter reactively is not always clear. If reactive sputtering is selected, then
there is the option of using simple dc diode, RF, or magnetron configurations.
Many considerations go into making these choices. and we will address some
of them in turn.
Target Purity. It is easier to manufacture high-purity metal targets
than to make high-purity compound targets. Since hot pressed and sintered
compound powders cannot be consolidated to theoretical bulk densities, incorporation
of gases, porosity, and impurities is unavoidable. Film purity using
elemental targets is high, particularly since high-purity reactive gases are
commercially available.
Deposition Rates. Sputter rates of metals drop dramatically when
compounds form on the targets. Decreases in deposition rate well in excess of
50% occur because of the lower sputter yield of compounds relative to metals.
The effect is very much dependent on reactive gas pressure. In dc discharges,
sputtering is effectively halted at very high gas pressures, but the limits are
also influenced by the applied power. Conditioning of the target in pure Ar is
required to restore the pure metal surface and desired deposition rates. Where
high deposition rates are a necessity, the reactive sputtering mode of choice is
either dc or RF magnetron.
Stoichiometry and Properties. Considerable variation in the
composition and properties of reactively sputtered films is possible, depending
on operating conditions. The case of tantalum nitride is worth considering in
this regard. One of the first electronic applications of reactive sputtering
involved deposition of TaN resistors employing dc diode sputtering at voltages
of 3-5 kV, and pressures of about 30 x torr. The dependence of the
resistivity of "tantalum nitride" films is shown in Fig. 3-23, where either Ta,
Ta,N, TaN, or combinations of these form as a function of N, partial
pressure. Color changes accompany the varied film stoichiometries. For
example, in the case of titanium nitride films, the metallic color of Ti gives
way to a light gold, then a rose, and finally a brown color with increasing
nitrogen partial pressure.
Electron Motion in Parallel Electric and Magnetic Fields. Let
us now examine what happens when a magnetic field of strength B is
superimposed on the electric field 8 between the target and substrate. Such a
situation arises in magnetron sputtering as well as in certain plasma etching
configurations. Electrons within the dual field environment experience the
well-known Lorentz force in addition to electric field force, i.e.,
m dv
dt
F = - - - -q(g+ v X B),
where q, m and u are the electron charge, mass, and velocity, respectively
First consider the case where B and 8 are parallel as shown in Fig. 3-20a.
When electrons are emitted exactly normal to the target surface and parallel to
both fields, then v x B vanishes; electrons are only influenced by the 8 field,
which accelerates them toward the anode. Next consider the case where the 8
field is neglected but B is still applied as shown in Fig. 3-20b. If an electron is
launched from the cathode with velocity u at angle 8 with respect to B, it
experiences a force quB sin 8 in a direction perpendicular to B. The electron
now orbits in a circular motion with a radius r that is determined by a balance
of the centrifugal (m(v sin 8 ) * / r ) and Lorentz forces involved, i.e., r =
mu sin 8 /qB. The electron motion is helical; in corkscrew fashion it spirals
down the axis of the discharge with constant velocity u cos 8. If the magnetic
field were not present, such off-axis electrons would tend to migrate out of the
discharge and be lost at the walls.
The case where electrons are launched at an angle to parallel, uniform
and B fields is somewhat more complex. Corkscrew motion with constant
radius occurs, but because of electron acceleration in the 8 field, the pitch of
the helix lengthens with time (Fig. 3-2Oc). Time varying fields complicate
matters further and electron spirals of variable radius can occur. Clearly
magnetic fields prolong the electron residence time in the plasma and thus
enhance the probability of ion collisions. This leads to larger discharge
currents and increased sputter deposition rates. Comparable discharges in a
simple diode-sputtering configuration operate at higher currents and pressures,
Therefore, applied magnetic fields have the desirable effect of reducing
electron bombardment of substrates and extending the operating vacuum range
Perpendicular Electric and M8gnetiC Fields. In magnetrons,
electrons ideally do not even reach the anode but are trapped near the target,
enhancing the ionizing efficiency there. This is accomplished by employing a
magnetic field oriented parallel to the target and perpendicular to the electric
field, as shown schematically in Fig. 3-21. Practically, this is achieved by
placing bar or horseshoe magnets behind the target. Therefore, the magnetic
field lines first emanate normal to the target, then bend with a component
parallel to the target surface (this is the magnetron component) and finally
return, completing the magnetic circuit. Electrons emitted from the cathode are
initially accelerated toward the anode, executing a helical motion in the
process; but when they encounter the region of the parallel magnetic field, they
are bent in an orbit back to the target in very much the same way that electrons
are deflected toward the hearth in an e-gun evaporator. By solving the coupled
differential equations resulting from the three components of Eq. 3-39, we
readily see that the parameric equations of motion are where y and x are the distances above and along the target, and w, = qE/m.
These equations describe a cycloidal motion that the electrons execute within
the cathode dark space where both fields are present. If, however, electrons
stray into the negative glow region where the 8 field is small, the electrons
describe a circular motion before collisions may drive them back into the dark
space or forward toward the anode. By suitable orientation of target magnets, a
"race track" can be defined where the electrons hop around at high speed.
Target erosion by sputtering occurs within this track because ionization of the
working gas is most intense above it.
Magnetron sputtering is presently the most widely commercially practiced
sputtering method. The chief reason for its success is the high deposition rates
achieved (e.g., up to 1 pm/min for Al). These are typically an order of
magnitude higher than rates attained by conventional sputtering techniques.
Popular sputtering configurations utilize planar, toroidal (rectangular cross
section), and toroidal-conical (trapezoidal cross section) targets (Le., the
S-gun). In commercial planar magnetron sputtering systems, the substrate
plane translates past the parallel facing target through interlocked vacuum
chambers to allow for semicontinuous coating operations. The circular
(toridal-conical) target, on the other hand, is positioned centrally within the
chamber, creating a deposition geometry approximating that of the analogous
planar (ring) evaporation source. In this manner wafers on a planetary substrate
holder can be coated as uniformly as with e-gun sources.
Reactive Sputtering
In reactive sputtering, thin films of compounds are deposited on substrates by
sputtering from metallic targets in the presence of a reactive gas, usually mixed
with the inert working gas (invariably Ar). The most common compounds
reactively sputtered (and the reactive gases employed) are briefly listed:
1. Oxides (oxygen)-Al,O,, In,O,, SnO,, SO,, Ta,O,
2. Nitrides (nitrogen, ammonia)-TaN, TiN, AlN, Si,N,
3. Carbides (methane, acetylene, propane)-Tic, WC, Sic
4. Sulfides (H,S)-CdS, CuS, ZnS
5. Oxycarbides and oxynitrides of Ti, Ta, Al, and Si
Irrespective of which of these materials is considered, during reactive
sputtering the resulting film is either a solid solution alloy of the target metal
doped with the reactive element (e.g., TaN,,,,), a compound (e.g., TiN), or
some mixture of the two. Westwood (Ref. 25) has provided a useful way to
visualize the conditions required to yield alloys or compounds. These two
regimes are distinguished in Fig. 3-22a, illustrating the generic hysteresis
curve for the total system pressure (P) as a function of the flow rate of
reactive gas (Q,) into the system. First, however, consider the dotted line
representing the variation of P with flow rate of an inert sputtering gas (Q,).
Clearly, as Qi increases, P increases because of the constant pumping speed
(see Eq. 2-16). An example of this characteristic occurs during Ar gas
sputtering of Ta. Now consider what happens when reactive N, gas is
introduced into the system. As Q, increases from Q,(O), the system pressure
essentially remains at the initial value Po because N, reacts with Ta and is
removed from the gas phase. But beyond a critical flow rate QF, the system
pressure jumps to the new value P,. If no reactive sputtering took place, P
would be somewhat higher (i.e., P3). Once the equilibrium value of P is
established, subsequent changes in Q, cause P to increase or decrease linearly
as shown. As Q, decreases sufficiently, P again reaches the initial pressure.
The hysteresis behavior represents two stable states of the system with a
rapid transition between them. In state A there is little change in pressure,
while for state B the pressure varies linearly with Q,. Clearly, all of the
reactive gas is incorporated into the deposited film in state A-the doped metal
and the atomic ratio of reactive gas dopant to sputtered metal increases with
Q,. The transition from state A to state B is triggered by compound formation
on the metal target. Since ion-induced secondary electron emission is usually
much higher for compounds than for metals, Ohm's law suggests that the
plasma impedance is effectively lower in state B than in state A. This effect is
reflected in the hysteresis of the target voltage with reactive gas flow rate, as
schematically depicted in Fig. 3-22b.
The choice of whether to employ compound targets and sputter directly or
sputter reactively is not always clear. If reactive sputtering is selected, then
there is the option of using simple dc diode, RF, or magnetron configurations.
Many considerations go into making these choices. and we will address some
of them in turn.
Target Purity. It is easier to manufacture high-purity metal targets
than to make high-purity compound targets. Since hot pressed and sintered
compound powders cannot be consolidated to theoretical bulk densities, incorporation
of gases, porosity, and impurities is unavoidable. Film purity using
elemental targets is high, particularly since high-purity reactive gases are
commercially available.
Deposition Rates. Sputter rates of metals drop dramatically when
compounds form on the targets. Decreases in deposition rate well in excess of
50% occur because of the lower sputter yield of compounds relative to metals.
The effect is very much dependent on reactive gas pressure. In dc discharges,
sputtering is effectively halted at very high gas pressures, but the limits are
also influenced by the applied power. Conditioning of the target in pure Ar is
required to restore the pure metal surface and desired deposition rates. Where
high deposition rates are a necessity, the reactive sputtering mode of choice is
either dc or RF magnetron.
Stoichiometry and Properties. Considerable variation in the
composition and properties of reactively sputtered films is possible, depending
on operating conditions. The case of tantalum nitride is worth considering in
this regard. One of the first electronic applications of reactive sputtering
involved deposition of TaN resistors employing dc diode sputtering at voltages
of 3-5 kV, and pressures of about 30 x torr. The dependence of the
resistivity of "tantalum nitride" films is shown in Fig. 3-23, where either Ta,
Ta,N, TaN, or combinations of these form as a function of N, partial
pressure. Color changes accompany the varied film stoichiometries. For
example, in the case of titanium nitride films, the metallic color of Ti gives
way to a light gold, then a rose, and finally a brown color with increasing
nitrogen partial pressure.
SPUTTERINPGR OCESSES
Samer Elatrache V-17810600 estudiante de CRF
For convenience we divide sputtering processes into four cateogories: (1) dc,
(2) RF, (3) magnetron, (4) reactive. We recognize, however, that there are
important variants within each category (e.g., dc bias) and even hybrids
between categories (e.g., reactive RF). Targets of virtually all important
materials are commercially available for use in these sputtering processes. A
selected number of target compositions representing the important classes
of solids, together with typical sputtering applications for each are listed in
Table 3-6.
In general, the metal and alloy targets are fabricated by melting either in
vacuum or under protective atmospheres, followed by thermomechanical processing.
Refractory alloy targets (e.g., Ti-W) are hot-pressed via the powder
metallurgy route. Similarly, nonmetallic targets are generally prepared by
hot-pressing of powders. The elemental and metal targets tend to have purities
of 99.99% or better, whereas those of the nonmetals are generally less pure,
with a typical upper purity limit of 99.9%. In addition, less than theoretical
densities are achieved during powder processing. These metallurgical realities
are sometimes reflected in emission of particulates, release of trapped gases,
nonuniform target erosion, and deposited films of inferior quality. Targets are
available in a variety of shapes (e.g., disks, toroids, plates, etc.) and sizes.
Prior to use, they must be bonded to a cooled backing plate to avoid thermal
cracking. Metal-filled epoxy cements of high thermal conductivity are employed
for this purpose.
DC Sputtering
Virtually everything mentioned in the chapter so far has dealt with dc sputtering,
also known as diode or cathodic sputtering. There is no need to further
discuss the system configuration (Fig. 3-13), the discharge environment (Section
3.5), the ion-surface interactions (Section 3.6. l), or intrinsic sputter
yields (Section 3.6.2). It is worthwhile, however, to note how the relative film
deposition rate depends on the sputtering pressure and current variables. At
low pressures, the cathode sheath is wide and ions are produced far from the
target; their chances of being lost to the walls are great. The mean-free
electron path between collisions is large, and electrons collected by the anode
are not replenished by ion-impact-induced cathode secondary emission. Therefore,
ionization efficiencies are low, and self-sustained discharges cannot be
maintained below about 10 mtorr. As the pressure is increased at a fixed
voltage, the electron mean-free path is decreased, more ions are generated, and
larger currents flow. But if the pressure is too high, the sputtered atoms
undergo increased collisional scattering and are not efficiently deposited. The
trade-offs in these opposing trends are shown in Fig. 3-18, and optimum
operating conditions are shaded in. In general, the deposition rate is proportional
to the power consumed, or to the square of the current density, and
inversely dependent on the electrode spacing.
RF Sputtering
RF sputtering was invented as a means of depositing insulating thin films.
Suppose we wish to produce thin SiO, films and attempt to use a quartz disk
0.1 cm thick as the target in a conventional dc sputtering system. For quartz
p = 10l6 Q-cm. To draw a current density J of 1 mA/cm2, the cathode needs
a voltage V = 0.1 p J. Substitution gives an impossibly high value of 10l2 V,
which indicates why dc sputtering will not work. If we set a convenient level
of I/ = 100 V, it means that a target with a resistivity exceeding lo6 Q-cm
could not be dc-sputtered.
Now consider what happens when an ac signal is applied to the electrodes.
Below about 50 kHz, ions are sufficiently mobile to establish a complete
discharge at each electrode on each half-cycle. Direct current sputtering
conditions essentially prevail at both electrodes, which alternately behave as
cathodes and anodes. Above 50 kHz two important effects occur. Electrons
oscillating in the glow region acquire enough energy to cause ionizing collisions,
reducing the need for secondary electrons to sustain the discharge.
Secondly, RF voltages can be coupled through any kind of impedance so that
the electrodes need not be conductors. This makes it possible to sputter any
material irrespective of its resistivity. Typical RF frequencies employed range
from 5 to 30 MHz. However, 13.56 MHz has been reserved for plasma
processing by the Federal Communications Commission and is widely used.
RF sputtering essentially works because the target self-biases to a negative
potential. Once this happens, it behaves like a dc target where positive ion
bombardment sputters away atoms for subsequent deposition. Negative target
bias is a consequence of the fact that electrons are considerably more mobile
than ions and have little difficulty in following the periodic change in the
electric field. In Fig. 3-13b we depict an RF sputtering system schematically,where the target is capacitively coupled to the RF generator. The disparity in
electron and ion mobilities means that isolated positively charged electrodes
draw more electron current than comparably isolated negatively charged
electrodes draw positive ion current. For this reason the discharge currentvoltage
characteristics are asymmetric and resemble those of a leaky rectifier
or diode. This is indicated in Fig. 3-19, and even though it applies to a dc
discharge, it helps to explain the concept of self-bias at RF electrodes.
As the pulsating RF signal is applied to the target, a large initial electron
current is drawn during the positive half of the cycle. However, only a small
ion current flows during the second half of the cycle. This would enable a net
current averaged over a complete cycle to be different from zero; but this
cannot happen because no charge can be transferred through the capacitor.
Therefore, the operating point on the characteristic shifts to a negative voltage
-the target bias-and no net current flows.
The astute reader will realize that since ac electricity is involved, both
electrodes should sputter. This presents a potential problem because the
resultant film may be contaminated as a consequence. For sputtering from only
one electrode, the sputter target must be an insulator and be capacitively
coupled to the RF generator. The equivalent circuit of the sputtering system
can be thought of as two series capacitors-one at the target sheath region, the
other at the substrate-with the applied voltage divided between them. Since
capacitive reactance is inversely proportional to the capacitance or area, more
voltage will be dropped across the capacitor of a smaller surface area.
Therefore, for efficient sputtering the area of the target electrode should be
small compared with the total area of the other, or directly coupled, electrode.
In practice, this electrode consists of the substrate stage and system ground,
but it also includes baseplates, chamber walls, etc. It has been shown that the
ratio of the voltage across the sheath at the (small) capacitively coupled
electrode (V,) to that across the (large) directly coupled electrode V.
For convenience we divide sputtering processes into four cateogories: (1) dc,
(2) RF, (3) magnetron, (4) reactive. We recognize, however, that there are
important variants within each category (e.g., dc bias) and even hybrids
between categories (e.g., reactive RF). Targets of virtually all important
materials are commercially available for use in these sputtering processes. A
selected number of target compositions representing the important classes
of solids, together with typical sputtering applications for each are listed in
Table 3-6.
In general, the metal and alloy targets are fabricated by melting either in
vacuum or under protective atmospheres, followed by thermomechanical processing.
Refractory alloy targets (e.g., Ti-W) are hot-pressed via the powder
metallurgy route. Similarly, nonmetallic targets are generally prepared by
hot-pressing of powders. The elemental and metal targets tend to have purities
of 99.99% or better, whereas those of the nonmetals are generally less pure,
with a typical upper purity limit of 99.9%. In addition, less than theoretical
densities are achieved during powder processing. These metallurgical realities
are sometimes reflected in emission of particulates, release of trapped gases,
nonuniform target erosion, and deposited films of inferior quality. Targets are
available in a variety of shapes (e.g., disks, toroids, plates, etc.) and sizes.
Prior to use, they must be bonded to a cooled backing plate to avoid thermal
cracking. Metal-filled epoxy cements of high thermal conductivity are employed
for this purpose.
DC Sputtering
Virtually everything mentioned in the chapter so far has dealt with dc sputtering,
also known as diode or cathodic sputtering. There is no need to further
discuss the system configuration (Fig. 3-13), the discharge environment (Section
3.5), the ion-surface interactions (Section 3.6. l), or intrinsic sputter
yields (Section 3.6.2). It is worthwhile, however, to note how the relative film
deposition rate depends on the sputtering pressure and current variables. At
low pressures, the cathode sheath is wide and ions are produced far from the
target; their chances of being lost to the walls are great. The mean-free
electron path between collisions is large, and electrons collected by the anode
are not replenished by ion-impact-induced cathode secondary emission. Therefore,
ionization efficiencies are low, and self-sustained discharges cannot be
maintained below about 10 mtorr. As the pressure is increased at a fixed
voltage, the electron mean-free path is decreased, more ions are generated, and
larger currents flow. But if the pressure is too high, the sputtered atoms
undergo increased collisional scattering and are not efficiently deposited. The
trade-offs in these opposing trends are shown in Fig. 3-18, and optimum
operating conditions are shaded in. In general, the deposition rate is proportional
to the power consumed, or to the square of the current density, and
inversely dependent on the electrode spacing.
RF Sputtering
RF sputtering was invented as a means of depositing insulating thin films.
Suppose we wish to produce thin SiO, films and attempt to use a quartz disk
0.1 cm thick as the target in a conventional dc sputtering system. For quartz
p = 10l6 Q-cm. To draw a current density J of 1 mA/cm2, the cathode needs
a voltage V = 0.1 p J. Substitution gives an impossibly high value of 10l2 V,
which indicates why dc sputtering will not work. If we set a convenient level
of I/ = 100 V, it means that a target with a resistivity exceeding lo6 Q-cm
could not be dc-sputtered.
Now consider what happens when an ac signal is applied to the electrodes.
Below about 50 kHz, ions are sufficiently mobile to establish a complete
discharge at each electrode on each half-cycle. Direct current sputtering
conditions essentially prevail at both electrodes, which alternately behave as
cathodes and anodes. Above 50 kHz two important effects occur. Electrons
oscillating in the glow region acquire enough energy to cause ionizing collisions,
reducing the need for secondary electrons to sustain the discharge.
Secondly, RF voltages can be coupled through any kind of impedance so that
the electrodes need not be conductors. This makes it possible to sputter any
material irrespective of its resistivity. Typical RF frequencies employed range
from 5 to 30 MHz. However, 13.56 MHz has been reserved for plasma
processing by the Federal Communications Commission and is widely used.
RF sputtering essentially works because the target self-biases to a negative
potential. Once this happens, it behaves like a dc target where positive ion
bombardment sputters away atoms for subsequent deposition. Negative target
bias is a consequence of the fact that electrons are considerably more mobile
than ions and have little difficulty in following the periodic change in the
electric field. In Fig. 3-13b we depict an RF sputtering system schematically,where the target is capacitively coupled to the RF generator. The disparity in
electron and ion mobilities means that isolated positively charged electrodes
draw more electron current than comparably isolated negatively charged
electrodes draw positive ion current. For this reason the discharge currentvoltage
characteristics are asymmetric and resemble those of a leaky rectifier
or diode. This is indicated in Fig. 3-19, and even though it applies to a dc
discharge, it helps to explain the concept of self-bias at RF electrodes.
As the pulsating RF signal is applied to the target, a large initial electron
current is drawn during the positive half of the cycle. However, only a small
ion current flows during the second half of the cycle. This would enable a net
current averaged over a complete cycle to be different from zero; but this
cannot happen because no charge can be transferred through the capacitor.
Therefore, the operating point on the characteristic shifts to a negative voltage
-the target bias-and no net current flows.
The astute reader will realize that since ac electricity is involved, both
electrodes should sputter. This presents a potential problem because the
resultant film may be contaminated as a consequence. For sputtering from only
one electrode, the sputter target must be an insulator and be capacitively
coupled to the RF generator. The equivalent circuit of the sputtering system
can be thought of as two series capacitors-one at the target sheath region, the
other at the substrate-with the applied voltage divided between them. Since
capacitive reactance is inversely proportional to the capacitance or area, more
voltage will be dropped across the capacitor of a smaller surface area.
Therefore, for efficient sputtering the area of the target electrode should be
small compared with the total area of the other, or directly coupled, electrode.
In practice, this electrode consists of the substrate stage and system ground,
but it also includes baseplates, chamber walls, etc. It has been shown that the
ratio of the voltage across the sheath at the (small) capacitively coupled
electrode (V,) to that across the (large) directly coupled electrode V.
Cinetica de los materiales!
Samer Elatrache, V-17810600 estudiante de CRF
Macroscopic Transport
Whenever a material system is not in thermodynamic equilibrium, driving
forces arise naturally to push it toward equilibrium. Such a situation can occur,
for example, when the free energy of a microscopic system varies from point
to point because of compositional inhomogeneities. The resulting atomic
concentration gradients generate time-dependent, mass-transport effects that
reduce free-energy variations in the system. Manifestations of such processes
include phase transformations, recrystallization, compound growth, and degradation
phenomena in both bulk and thin-film systems. In solids, mass transport
is accomplished by diffusion, which may be defined as the migration of an
atomic or molecular species within a given matrix under the influence of a
concentration gradient. Fick established the phenomenological connection
between concentration gradients and the resultant diffusional transport through
the equation
dC
dx
J = -D- (1-21)
The minus sign occurs because the vectors representing the concentration
gradient dC/& and atomic flux J are oppositely directed. Thus an increasing
concentration in the positive x direction induces mass flow in the negative x
direction, and vice versa. The units of C are typically atoms/cm3. The
diffusion coefficient D, which has units of cm2/sec, is characteristic of both
the diffusing species and the matrix in which transport occurs. The extent of
observable diffusion effects depends on the magnitude of D. As we shall later
note, D increases in exponential fashion with temperature according to a
Maxwell-Boltzmann relation; Le.,
D = Doexp - E,/RT, ( 1-22)
where Do is a constant and RT has the usual meaning. The activation energy
for diffusion is ED (cal/mole) .
Solid-state diffusion is generally a slow process, and concentration changes
occur over long periods of time; the steady-state condition in which concentrations
are time-independent rarely occurs in bulk solids. Therefore, during
one-dimensional diffusion, the mass flux across plane x of area A exceeds
that which flows across plane x + dx. Atoms will accumulate with time in the
volume A dx, and this is expressed by
dJ dJ dc ( dx ) dx dt
J A - J + - d x A = - - A d x = - A d x . (1-23)
Substituting Eq. 1-21 and assuming that D is a constant independent of C or x
gives
ac( X , t ) a2cX( , t )
=D
at a x2
( 1-24)
The non-steady-state heat conduction equation is identical if temperature is
substituted for C and the thermal diffusivity for D. Many solutions for both
diffusion and heat conduction problems exist for media of varying geometries,
constrained by assorted initial and boundary conditions. They can be found in
the books by Carslaw and Jaeger, and by Crank, listed in the bibliography.
Since complex solutions to Eq. 1-24 will be discussed on several occasions
(e.g., in Chapters 8, 9, and 13), we introduce simpler applications here.
Consider an initially pure thick film into which some solute diffuses from
the surface. If the film dimensions are very large compared with the extent of
diffusion, the situation can be physically modeled by the following conditions
C(x,O) = 0 at t = 0 ( 1 -25a)
C(o0, t ) = 0 at x = 03 for t > 0. (1-25b)
The second boundary condition that must be specified has to do with the nature
of the diffusant distribution maintained at the film surface x = 0. Two simple
cases can be distinguished. In the first, a thick layer of diffusant provides an
essentially limitless supply of atoms maintaining a constant surface concentration
Co for all time. In the second case, a very thin layer of diffusant provides
an instantaneous source So of surface atoms per unit area. Here the surface
concentration diminishes with time as atoms diffuse into the underlying film.
These two cases are respectively described by
c(0, t ) = c,
lmcx(, t )d x = so
is a tabulated function of only the upper limit or argument x / 2 f i .
Normalized concentration profiles for the Gaussian and Erfc solutions
are shown in Fig. 1-15. It is of interest to calculate how these distributions
spread with time. For the erfc solution, the diffusion front at the arbitrary
concentration of C(x, t)/C, = 1/2 moves parabolically with time as x =
2merfc-'(1/2) or x = 0 . 9 6 m . When becomes large compared
with the film dimensions, the assumption of an infinite matrix is not valid and
the solutions do not strictly hold. The film properties may also change
appreciably due to interdiffusion. To limit the latter and ensure the integrity of
films, D should be kept small, which in effect means the maintenance of low
temperatures. This subject will be discussed further in Chapter 8.
Atomistic Considerations
Macroscopic changes in composition during diffusion are the result of the
random motion of countless individual atoms unaware of the concentration
gradient they have helped establish. On a microscopic level, it is sufficient to
explain how atoms execute individual jumps from one lattice site to another,
for through countless repetitions of unit jumps macroscopic changes occur.
Consider Fig. 1-16a, showing neighboring lattice planes spaced a distance a,
apart within a region where an atomic concentration gradient exists. If there
are n, atoms per unit area of plane 1, then at plane 2, n2 = n, + (dn /dx)
where we have taken the liberty of assigning a continuum behavior at discrete
planes. Each atom vibrates about its equilibrium position with a characteristic
lattice frequency v, typically lOI3 sec -'. Very few vibrational cycles have
sufficient amplitude to cause the atom to actually jump into an adjoining lattice
position, thus executing a direct atomic interchange. This process would be
greatly encouraged, however, if there were neighboring vacant sites. The
fraction of vacant lattice sites was previously given by eCEflkT(s ee Eq. 1-3).
In addition, the diffusing atom must acquire sufficient energy to push the
surrounding atoms apart so that it can squeeze past and land in the so-called
activated state shown in Fig. 1-16b. This step is the precursor to the downhill
jump of the atom into the vacancy. The number of times per second that an
atom successfully reaches the activated state is ve-'JIkT, where ci is the
vacancy jump or migration energy per atom. Here the Boltzmann factor may
be interpreted as the fraction of all sites in the crystal that have an activated
state configuration. The atom fluxes from plane 1 to 2 and from plane 2 to 1
are then, respectively logarithm of the rate is plotted on the ordinate and the reciprocal of the
absolute temperature is plotted along the abscissa. The slope of the resulting
line is then equal to - ED / R , from which the characteristic activation energy
can be extracted.
The discussion to this point is applicable to motion of both impurity and
matrix atoms. In the latter case we speak of self-diffusion. For matrix atoms
there are driving forces other than concentration gradients that often result in
transport of matter. Examples are forces due to stress fields, electric fields,
and interfacial energy gradients. To visualize their effect, consider neighboring
atomic positions in a crystalline solid where no fields are applied. The free
energy of the system has the periodicity of the lattice and varies schematically,
as shown in Fig. 1-17a. Imposition of an external field now biases the system
such that the free energy is lower in site 2 relative to 1 by an amount 2 AG. A
free-energy gradient exists in the system that lowers the energy barrier to
motion from 1 -+ 2 and raises it from 2 -+ 1.
Macroscopic Transport
Whenever a material system is not in thermodynamic equilibrium, driving
forces arise naturally to push it toward equilibrium. Such a situation can occur,
for example, when the free energy of a microscopic system varies from point
to point because of compositional inhomogeneities. The resulting atomic
concentration gradients generate time-dependent, mass-transport effects that
reduce free-energy variations in the system. Manifestations of such processes
include phase transformations, recrystallization, compound growth, and degradation
phenomena in both bulk and thin-film systems. In solids, mass transport
is accomplished by diffusion, which may be defined as the migration of an
atomic or molecular species within a given matrix under the influence of a
concentration gradient. Fick established the phenomenological connection
between concentration gradients and the resultant diffusional transport through
the equation
dC
dx
J = -D- (1-21)
The minus sign occurs because the vectors representing the concentration
gradient dC/& and atomic flux J are oppositely directed. Thus an increasing
concentration in the positive x direction induces mass flow in the negative x
direction, and vice versa. The units of C are typically atoms/cm3. The
diffusion coefficient D, which has units of cm2/sec, is characteristic of both
the diffusing species and the matrix in which transport occurs. The extent of
observable diffusion effects depends on the magnitude of D. As we shall later
note, D increases in exponential fashion with temperature according to a
Maxwell-Boltzmann relation; Le.,
D = Doexp - E,/RT, ( 1-22)
where Do is a constant and RT has the usual meaning. The activation energy
for diffusion is ED (cal/mole) .
Solid-state diffusion is generally a slow process, and concentration changes
occur over long periods of time; the steady-state condition in which concentrations
are time-independent rarely occurs in bulk solids. Therefore, during
one-dimensional diffusion, the mass flux across plane x of area A exceeds
that which flows across plane x + dx. Atoms will accumulate with time in the
volume A dx, and this is expressed by
dJ dJ dc ( dx ) dx dt
J A - J + - d x A = - - A d x = - A d x . (1-23)
Substituting Eq. 1-21 and assuming that D is a constant independent of C or x
gives
ac( X , t ) a2cX( , t )
=D
at a x2
( 1-24)
The non-steady-state heat conduction equation is identical if temperature is
substituted for C and the thermal diffusivity for D. Many solutions for both
diffusion and heat conduction problems exist for media of varying geometries,
constrained by assorted initial and boundary conditions. They can be found in
the books by Carslaw and Jaeger, and by Crank, listed in the bibliography.
Since complex solutions to Eq. 1-24 will be discussed on several occasions
(e.g., in Chapters 8, 9, and 13), we introduce simpler applications here.
Consider an initially pure thick film into which some solute diffuses from
the surface. If the film dimensions are very large compared with the extent of
diffusion, the situation can be physically modeled by the following conditions
C(x,O) = 0 at t = 0 ( 1 -25a)
C(o0, t ) = 0 at x = 03 for t > 0. (1-25b)
The second boundary condition that must be specified has to do with the nature
of the diffusant distribution maintained at the film surface x = 0. Two simple
cases can be distinguished. In the first, a thick layer of diffusant provides an
essentially limitless supply of atoms maintaining a constant surface concentration
Co for all time. In the second case, a very thin layer of diffusant provides
an instantaneous source So of surface atoms per unit area. Here the surface
concentration diminishes with time as atoms diffuse into the underlying film.
These two cases are respectively described by
c(0, t ) = c,
lmcx(, t )d x = so
is a tabulated function of only the upper limit or argument x / 2 f i .
Normalized concentration profiles for the Gaussian and Erfc solutions
are shown in Fig. 1-15. It is of interest to calculate how these distributions
spread with time. For the erfc solution, the diffusion front at the arbitrary
concentration of C(x, t)/C, = 1/2 moves parabolically with time as x =
2merfc-'(1/2) or x = 0 . 9 6 m . When becomes large compared
with the film dimensions, the assumption of an infinite matrix is not valid and
the solutions do not strictly hold. The film properties may also change
appreciably due to interdiffusion. To limit the latter and ensure the integrity of
films, D should be kept small, which in effect means the maintenance of low
temperatures. This subject will be discussed further in Chapter 8.
Atomistic Considerations
Macroscopic changes in composition during diffusion are the result of the
random motion of countless individual atoms unaware of the concentration
gradient they have helped establish. On a microscopic level, it is sufficient to
explain how atoms execute individual jumps from one lattice site to another,
for through countless repetitions of unit jumps macroscopic changes occur.
Consider Fig. 1-16a, showing neighboring lattice planes spaced a distance a,
apart within a region where an atomic concentration gradient exists. If there
are n, atoms per unit area of plane 1, then at plane 2, n2 = n, + (dn /dx)
where we have taken the liberty of assigning a continuum behavior at discrete
planes. Each atom vibrates about its equilibrium position with a characteristic
lattice frequency v, typically lOI3 sec -'. Very few vibrational cycles have
sufficient amplitude to cause the atom to actually jump into an adjoining lattice
position, thus executing a direct atomic interchange. This process would be
greatly encouraged, however, if there were neighboring vacant sites. The
fraction of vacant lattice sites was previously given by eCEflkT(s ee Eq. 1-3).
In addition, the diffusing atom must acquire sufficient energy to push the
surrounding atoms apart so that it can squeeze past and land in the so-called
activated state shown in Fig. 1-16b. This step is the precursor to the downhill
jump of the atom into the vacancy. The number of times per second that an
atom successfully reaches the activated state is ve-'JIkT, where ci is the
vacancy jump or migration energy per atom. Here the Boltzmann factor may
be interpreted as the fraction of all sites in the crystal that have an activated
state configuration. The atom fluxes from plane 1 to 2 and from plane 2 to 1
are then, respectively logarithm of the rate is plotted on the ordinate and the reciprocal of the
absolute temperature is plotted along the abscissa. The slope of the resulting
line is then equal to - ED / R , from which the characteristic activation energy
can be extracted.
The discussion to this point is applicable to motion of both impurity and
matrix atoms. In the latter case we speak of self-diffusion. For matrix atoms
there are driving forces other than concentration gradients that often result in
transport of matter. Examples are forces due to stress fields, electric fields,
and interfacial energy gradients. To visualize their effect, consider neighboring
atomic positions in a crystalline solid where no fields are applied. The free
energy of the system has the periodicity of the lattice and varies schematically,
as shown in Fig. 1-17a. Imposition of an external field now biases the system
such that the free energy is lower in site 2 relative to 1 by an amount 2 AG. A
free-energy gradient exists in the system that lowers the energy barrier to
motion from 1 -+ 2 and raises it from 2 -+ 1.
Termodinamica de los materiales!
Samer Elatrache V-17810600 Estudiante de CRF
Thermodynamics is definite about events that are impossible. It will say, for
example, that reactions or processes are thermodynamically impossible. Thus,
gold films do not oxidize and atoms do not normally diffuse up a concentration
gradient. On the other hand, thermodynamics is noncommittal about permissi-
reactions and processes. Thus, even though reactions are thermodynamically
favored, they may not occur in practice. Films of silica glass should
revert to crystalline form at room temperature according to thermodynamics,
but the solid-state kinetics are so sluggish that for all practical purposes
amorphous SiO, is stable. A convenient measure of the extent of reaction
feasibility is the free-energy function G defined as
G = H - TS, (1-5)
where H is the enthalpy, S the entropy, and T the absolute temperature.
Thus, if a system changes from some initial (i) to final (9 state at constant
temperature due to a chemical reaction or physical process, a free-energy
change AG = G, - C, occurs given by
AG = AH - TAS,
where AH and AS are the corresponding enthalpy and entropy changes. A
consequence of the second law of thermodynamics is that spontaneous reactions
occur at constant temperature and pressure when AG < 0. This condition
implies that systems will naturally tend to minimize their free energy and
successively proceed from a value G, to a still lower, more negative value G,
until it is no longer possible to reduce G further. When this happens, AG = 0.
The system has achieved equilibrium, and there is no longer a driving force for
change.
On the other hand, for a process that cannot occur, AG > 0. Note that
neither the sign of AH nor of AS taken individually determines reaction
direction; rather it is the sign of the combined function AG that is crucial.
Thus, during condensation of a vapor to form a solid film, AS < 0 because
fewer atomic configurations exist in the solid. The decrease in enthalpy,
however, more than offsets that in entropy, and the net change in AG is
negative.
The concept of minimization of free energy as a criterion for both stability in
a system and forward change in a reaction or process is a central theme in
materials science. The following discussion will develop concepts of thermodynamics
used in the analysis of chemical reactions and phase diagrams. Subsequent
applications will be made to such topics as chemical vapor deposition,
interdiffusion, and reactions in thin films.
Chemical Reactions
The general chemical reaction involving substances A, B, and C in equilibrium
is
aA + bB * cC.
The free-energy change of the reaction is given by
AG = c G ~- uGA - bG,, (1-8)
where a, b, and c are the stoichiometric coefficients. It is customary to denote
the free energy of individual reactant or product atomic or molecular species
by
Gi = G,o + RTIn ai. (1-9)
G,o is the free energy of the species in its reference or standard state. For
solids this is usually the stable pure material at 1 atm at a given temperature.
The activity ai may be viewed as an effective thermodynamic concentration
and reflects the change in free energy of the species when it is not in its
standard state. Substitution of Eq. 1-9 into Eq. 1-8 yields
I
a;
a:.; '
AG = AG" -k RT In- (1-10)
where AG' = cGG - aGi - bGi. If the system is now in equilibrium,
AG = 0 and ai is the equilibrium value ai(eg)T. hus,
or
O = A G o + R T l n ( L1 4 ( e 4 l ) }
'A(,)
-AGO = RTln K,
(1-1 1)
(1-12)
where the equilibrium constant K is defined by the quantity in braces.
Equation 1-12 is one of the most frequently used equations in chemical
thermodynamics and will be helpful in analyzing CVD reactions.
Combining Eqs. 1-10 and 1-11 gives
Each term a, / ai(eg)r epresents a supersaturation of the species if it exceeds 1,
and a subsaturation if it is less than 1. Thus, if there is a supersaturation of
reactants and a subsaturation of products, AG < 0. The reaction proceeds
spontaneously as written with a driving force proportional to the magnitude of
AG. For many practical cases the ai differ little from the standard-state
activities, which are taken to be unity. Therefore, in such a case Eq. 1-10
yields
AG = AGO
Quantitative information on the feasibility of chemical reactions is thus
provided by values of AGO, and these are tabulated in standard references on
thermodynamic data. The reader should be aware that although much of the
data are the result of measurement, some values are inferred from various
connecting thermodynamic laws and relationships. Thus, even though the
vapor pressure of tungsten at room temperature cannot be directly measured,
its value is nevertheless "known." In addition, the data deal with equilibrium
conditions only, and many reactions are subject to overriding kinetic limitations
despite otherwise favorable free-energy considerations.
A particularly useful representation of AGO data for formation of metal
oxides as a function of temperature is shown in Fig. 1-10 and is known as an
Ellingham diagram. As an example of its use, consider two oxides of importance
in thin-film technology, SiO, and A,O, , with corresponding oxidation
reactions
Si + 0, + SiO, ; AGiio2, (1-15a)
(4/3)A + 0, + (2/3)A1,O3; AGi12~. , (1-15b)
Through elimination of 0, the reaction
(4/3)AI + S~O, + (2/3)~l,0, + Si (1-16)
results, where AGO = AGAz0, - AGiio2. Since the AGO- T curve for Al,O,
is more negative or lower than that for SiO,, the reaction is thermodynamically
favored as written. At 400 O C , for example, AG" for Eq. 1-16 is
- 233 - (- 180) = - 53 kcal/mole. Therefore, Al films tend to reduce SiO,
films, leaving free Si behind, a fact observed in early field effect transistor
structures. This was one reason for the replacement of Al film gate electrodes
by polycrystalline Si fdms. As a generalization then, the metal of an oxide that
has a more negative AGO than a second oxide will reduce the latter and be
oxidized in the process. Further consideration of Eqs. 1-12 and 1-15b indicates
that
)2/3 AG
( aAl,03 = exp - -. K =(aAYl 3pO2 RT
The A1,0, and A1 may be considered to exist in pure standard states with unity
activities while the activity of 0, is taken to be its partial pressure Po,.
Therefore, AGO = RT In Po,. If Al were evaporated from a crucible to
produce a film, then the value of Po, in equilibrium with both Al and A1203
can be calculated at any temperature when AGO is known. If the actual oxygen
partial pressure exceeds the equilibrium pressure, then A1 ought to oxidize. If
the reverse is true, AZO, would be reduced to Al. At lo00 'C, AGO = -202
Phase Diagrams
The most widespread method for representing the conditions of chemical
equilibrium for inorganic systems as a function of initial composition, temperature,
and pressure is through the use of phase diagrams. By phases we not only
mean the solid, liquid, and gaseous states of pure elements and compounds but
a material of variable yet homogeneous composition, such as an alloy, is also a
phase. Although phase diagrams generally contain a wealth of thermodynamic
information on systems in equilibrium, they can readily be interpreted without
resorting to complex thermodynamic laws, functions, or equations. They have
been experimentally determined for many systems by numerous investigators
over the years and provide an invaluable guide when synthesizing materials.
There are a few simple rules for analyzing phase diagrams. The most
celebrated of these is the Gibbs phase rule, which, though deceptively simple,
is arguably the most important linear algebraic equation in physical science. It
can be written as
f = n + 2 - 4, (1-18)
where n is the number of components (i.e., different atomic species), 4 is the
number of phases, and f is the number of degrees of freedom or variance in
the system. The number of intensive variables that can be independently varied
without changing the phase equilibrium is equal to f.
One-Component System. As an application to a one-component
system, consider the P- T diagram given for carbon in Fig. 1-1 1. Shown are
the regions of stability for different phases of carbon as a function of pressure
and temperature. Within the broad areas, the single phases diamond and
graphite are stable. Both P and T variables can be independently varied to a
greater or lesser extent without leaving the single-phase field. This is due to the
phase rule, which gives f = 1 + 2 - 1 = 2. Those states that lie on any of
the lines of the diagram represent two-phase equilibria. Now f = 1 + 2 - 2
= 1. This means, for example, that in order to change but maintain the
equilibrium along the diamond-graphite line, only one variable, either T or
P, can be independently varied; the corresponding variables P or T must
change in a dependent fashion. At a point where three phases coexist (not
shown), f = 0. Any change of T or P will destroy the three-phase equilib-
rium, leaving instead either one or two phases. The diagram suggests that
pressures between lo4 to lo5 bars (- 1O,O00-100,000 atm) are required to
transform graphite into diamond. In addition, excessively high temperatures
(- 2000 K) are required to make the reaction proceed at appreciable rates. It
is exciting, therefore, that diamond thin films have been deposited by decomposing
methane in a microwave plasma at low pressure and temperature, thus
avoiding the almost prohibitive pressure-temperature regime required for bulk
diamond synthesis.
Thermodynamics is definite about events that are impossible. It will say, for
example, that reactions or processes are thermodynamically impossible. Thus,
gold films do not oxidize and atoms do not normally diffuse up a concentration
gradient. On the other hand, thermodynamics is noncommittal about permissi-
reactions and processes. Thus, even though reactions are thermodynamically
favored, they may not occur in practice. Films of silica glass should
revert to crystalline form at room temperature according to thermodynamics,
but the solid-state kinetics are so sluggish that for all practical purposes
amorphous SiO, is stable. A convenient measure of the extent of reaction
feasibility is the free-energy function G defined as
G = H - TS, (1-5)
where H is the enthalpy, S the entropy, and T the absolute temperature.
Thus, if a system changes from some initial (i) to final (9 state at constant
temperature due to a chemical reaction or physical process, a free-energy
change AG = G, - C, occurs given by
AG = AH - TAS,
where AH and AS are the corresponding enthalpy and entropy changes. A
consequence of the second law of thermodynamics is that spontaneous reactions
occur at constant temperature and pressure when AG < 0. This condition
implies that systems will naturally tend to minimize their free energy and
successively proceed from a value G, to a still lower, more negative value G,
until it is no longer possible to reduce G further. When this happens, AG = 0.
The system has achieved equilibrium, and there is no longer a driving force for
change.
On the other hand, for a process that cannot occur, AG > 0. Note that
neither the sign of AH nor of AS taken individually determines reaction
direction; rather it is the sign of the combined function AG that is crucial.
Thus, during condensation of a vapor to form a solid film, AS < 0 because
fewer atomic configurations exist in the solid. The decrease in enthalpy,
however, more than offsets that in entropy, and the net change in AG is
negative.
The concept of minimization of free energy as a criterion for both stability in
a system and forward change in a reaction or process is a central theme in
materials science. The following discussion will develop concepts of thermodynamics
used in the analysis of chemical reactions and phase diagrams. Subsequent
applications will be made to such topics as chemical vapor deposition,
interdiffusion, and reactions in thin films.
Chemical Reactions
The general chemical reaction involving substances A, B, and C in equilibrium
is
aA + bB * cC.
The free-energy change of the reaction is given by
AG = c G ~- uGA - bG,, (1-8)
where a, b, and c are the stoichiometric coefficients. It is customary to denote
the free energy of individual reactant or product atomic or molecular species
by
Gi = G,o + RTIn ai. (1-9)
G,o is the free energy of the species in its reference or standard state. For
solids this is usually the stable pure material at 1 atm at a given temperature.
The activity ai may be viewed as an effective thermodynamic concentration
and reflects the change in free energy of the species when it is not in its
standard state. Substitution of Eq. 1-9 into Eq. 1-8 yields
I
a;
a:.; '
AG = AG" -k RT In- (1-10)
where AG' = cGG - aGi - bGi. If the system is now in equilibrium,
AG = 0 and ai is the equilibrium value ai(eg)T. hus,
or
O = A G o + R T l n ( L1 4 ( e 4 l ) }
'A(,)
-AGO = RTln K,
(1-1 1)
(1-12)
where the equilibrium constant K is defined by the quantity in braces.
Equation 1-12 is one of the most frequently used equations in chemical
thermodynamics and will be helpful in analyzing CVD reactions.
Combining Eqs. 1-10 and 1-11 gives
Each term a, / ai(eg)r epresents a supersaturation of the species if it exceeds 1,
and a subsaturation if it is less than 1. Thus, if there is a supersaturation of
reactants and a subsaturation of products, AG < 0. The reaction proceeds
spontaneously as written with a driving force proportional to the magnitude of
AG. For many practical cases the ai differ little from the standard-state
activities, which are taken to be unity. Therefore, in such a case Eq. 1-10
yields
AG = AGO
Quantitative information on the feasibility of chemical reactions is thus
provided by values of AGO, and these are tabulated in standard references on
thermodynamic data. The reader should be aware that although much of the
data are the result of measurement, some values are inferred from various
connecting thermodynamic laws and relationships. Thus, even though the
vapor pressure of tungsten at room temperature cannot be directly measured,
its value is nevertheless "known." In addition, the data deal with equilibrium
conditions only, and many reactions are subject to overriding kinetic limitations
despite otherwise favorable free-energy considerations.
A particularly useful representation of AGO data for formation of metal
oxides as a function of temperature is shown in Fig. 1-10 and is known as an
Ellingham diagram. As an example of its use, consider two oxides of importance
in thin-film technology, SiO, and A,O, , with corresponding oxidation
reactions
Si + 0, + SiO, ; AGiio2, (1-15a)
(4/3)A + 0, + (2/3)A1,O3; AGi12~. , (1-15b)
Through elimination of 0, the reaction
(4/3)AI + S~O, + (2/3)~l,0, + Si (1-16)
results, where AGO = AGAz0, - AGiio2. Since the AGO- T curve for Al,O,
is more negative or lower than that for SiO,, the reaction is thermodynamically
favored as written. At 400 O C , for example, AG" for Eq. 1-16 is
- 233 - (- 180) = - 53 kcal/mole. Therefore, Al films tend to reduce SiO,
films, leaving free Si behind, a fact observed in early field effect transistor
structures. This was one reason for the replacement of Al film gate electrodes
by polycrystalline Si fdms. As a generalization then, the metal of an oxide that
has a more negative AGO than a second oxide will reduce the latter and be
oxidized in the process. Further consideration of Eqs. 1-12 and 1-15b indicates
that
)2/3 AG
( aAl,03 = exp - -. K =(aAYl 3pO2 RT
The A1,0, and A1 may be considered to exist in pure standard states with unity
activities while the activity of 0, is taken to be its partial pressure Po,.
Therefore, AGO = RT In Po,. If Al were evaporated from a crucible to
produce a film, then the value of Po, in equilibrium with both Al and A1203
can be calculated at any temperature when AGO is known. If the actual oxygen
partial pressure exceeds the equilibrium pressure, then A1 ought to oxidize. If
the reverse is true, AZO, would be reduced to Al. At lo00 'C, AGO = -202
Phase Diagrams
The most widespread method for representing the conditions of chemical
equilibrium for inorganic systems as a function of initial composition, temperature,
and pressure is through the use of phase diagrams. By phases we not only
mean the solid, liquid, and gaseous states of pure elements and compounds but
a material of variable yet homogeneous composition, such as an alloy, is also a
phase. Although phase diagrams generally contain a wealth of thermodynamic
information on systems in equilibrium, they can readily be interpreted without
resorting to complex thermodynamic laws, functions, or equations. They have
been experimentally determined for many systems by numerous investigators
over the years and provide an invaluable guide when synthesizing materials.
There are a few simple rules for analyzing phase diagrams. The most
celebrated of these is the Gibbs phase rule, which, though deceptively simple,
is arguably the most important linear algebraic equation in physical science. It
can be written as
f = n + 2 - 4, (1-18)
where n is the number of components (i.e., different atomic species), 4 is the
number of phases, and f is the number of degrees of freedom or variance in
the system. The number of intensive variables that can be independently varied
without changing the phase equilibrium is equal to f.
One-Component System. As an application to a one-component
system, consider the P- T diagram given for carbon in Fig. 1-1 1. Shown are
the regions of stability for different phases of carbon as a function of pressure
and temperature. Within the broad areas, the single phases diamond and
graphite are stable. Both P and T variables can be independently varied to a
greater or lesser extent without leaving the single-phase field. This is due to the
phase rule, which gives f = 1 + 2 - 1 = 2. Those states that lie on any of
the lines of the diagram represent two-phase equilibria. Now f = 1 + 2 - 2
= 1. This means, for example, that in order to change but maintain the
equilibrium along the diamond-graphite line, only one variable, either T or
P, can be independently varied; the corresponding variables P or T must
change in a dependent fashion. At a point where three phases coexist (not
shown), f = 0. Any change of T or P will destroy the three-phase equilib-
rium, leaving instead either one or two phases. The diagram suggests that
pressures between lo4 to lo5 bars (- 1O,O00-100,000 atm) are required to
transform graphite into diamond. In addition, excessively high temperatures
(- 2000 K) are required to make the reaction proceed at appreciable rates. It
is exciting, therefore, that diamond thin films have been deposited by decomposing
methane in a microwave plasma at low pressure and temperature, thus
avoiding the almost prohibitive pressure-temperature regime required for bulk
diamond synthesis.
union de los materiales
Samer Elatrache V-17810600 estudiante de CRF
Widely spaced isolated atoms condense to form solids due to the energy
reduction accompanying bond formation. Thus, if N atoms of type A in the
gas phase (8) combine to form a solid (s), the binding energy Eb is released
according to the equation
NA, + NA, -k Eb.
Energy Eb must be supplied to reverse the equation and decompose the solid.
The more stable the solid, the higher is its binding energy. It has become the
custom to picture the process of bonding by considering the energetics within
and between atoms as the interatomic distance progressively shrinks. In each
isolated atom, the electron energy levels are discrete, as shown on the
right-hand side of Fig. 1-8a. As the atoms approach one another, the individual
levels split, as a consequence of an extension of the Pauli exclusion principle,
to a collective solid; namely, no two electrons can exist in the same quantum
state. Level splitting and broadening occur first for the valence or outer
electrons, since their electron clouds are the first to overlap. During atomic
attraction, electrons populate these lower energy levels, reducing the overall
energy of the solid. With further dimensional shrinkage, the overlap increases
and the inner charge clouds begin to interact. Ion-core overlap now results in
strong repulsive forces between atoms, raising the system energy. A compromise
is reached at the equilibrium interatomic distance in the solid where the
system energy is minimized. At equilibrium, some of the levels have broadened
into bands of energy levels. The bands span different ranges of energy,
depending on the atoms and specific electron levels involved. Sometimes as in
metals, bands of high energy overlap. Insulators and semiconductors have
energy gaps of varying width between bands where electron states are not
allowed. The whys and hows of energy-level splitting, band structure evolution,
and implications with regard to property behavior are perhaps the most
fundamental and difficult questions in solid-state physics. We briefly return to
the subject of electron-band structure after introducing the classes of solids.
An extension of the ideas expressed in Fig. 1-8a is commonly made by
simplifying the behavior to atoms as a whole, in which case the potential
energy of interaction V(r) is plotted as a function of interatomic distance r in
Fig. 1-8b. The generalized behavior shown is common for all classes of solid
materials, regardless of the type of bonding or crystal structure. Although the
mathematical forms of the attractive or repulsive portions are complex, a
number of qualitative features of these curves are not difficult to understand.
For example, the energy at the equilibrium spacing r = a, is the binding
energy. Solids with high melting points tend to have high values of Eb. The
curvature of the potential energy is a measure of the elastic stiffness of the
solid. To see this, we note that around a, the potential energy is approximately
harmonic or parabolic. Therefore, V(r) = (1/2)K,r2, where K, is related to
the spring constant (or elastic modulus). Narrow wells of high curvature are
associated with large values of K,, broad wells of low curvature with small
values of K, . Since the force F between atoms is given by F = - dV/dr,
F = - Ksrr which has its counterpart in Hooke's law-i.e., that stress is
linearly proportional to strain. Thus, in solids with high K, values, correspondingly
larger stresses develop under loading. Interestingly, a purely
parabolic behavior for I/ implies a material with a coefficient of thermal
expansion equal to zero. In real materials, therefore, some asymmetry or
anharmonicity in V(r) exists.
For the most part, atomic behavior within a thin solid film can also be
described by a V(r)-r curve similar to that for the bulk solid. The surface
atoms are less tightly bound, however, which is reflected by the dotted line
behavior in Fig. 1-8b. The difference between the energy minima for surface
and bulk atoms is a measure of the surface energy of the solid. From the
previous discussion, surface layers would tend to be less stiff and melt at lower
temperatures than the bulk. Slight changes in equilibrium atomic spacing or
lattice parameter at surfaces may also be expected.
Despite apparent similarities, there are many distinctions between the four
important types of solid-state bonding and the properties they induce. A
discussion of these individual bonding categories follows.
Metallic
The so-called metallic bond occurs in metals and alloys. In metals the outer
valence electrons of each atom form part of a collective free-electron cloud or
gas that permeates the entire lattice. Even though individual electron-electron
interactions are repulsive, there is sufficient electrostatic attraction between the
free-electron gas and the positive ion cores to cause bonding.
What distinguishes metals from all other solids is the ability of the electrons
to respond readily to applied electric fields, thermal gradients, and incident
light. This gives rise to high electrical and thermal conductivities as well as
high reflectivities. Interestingly, comparable properties are observed in liquid
metals, indicating that aspects of metallic bonding and the free-electron model
are largely preserved even in the absence of a crystal structure. Metallic
electrical resistivities typically ranging from lop5 to ohm-cm should be
contrasted with the much, much larger values possessed by other classes of
solids.
Furthermore, the temperature coefficient of resistivity is positive. Metals
thus become poorer electrical conductors as the temperature is raised. The
reverse is true for all other classes of solids. The conductivity of pure metals is
always reduced with low levels of impurity alloying, which is also contrary to
the usual behavior in other solids. The effect of both temperature and alloying
element additions on metallic conductivity is to increase electron scattering,
which in effect reduces the net component of electron motion in the direction
of the applied electric field. On the other hand, in ionic and semiconductor
solids production of more charge carriers is the result of higher temperatures
and solute additions.
The bonding electrons are not localized between atoms; thus, metals are said
to have nondirectional bonds. This causes atoms to slide by each other and
plastically deform more readily than is the case, for example, in covalent
solids, which have directed atomic bonds.
Examples of thin-metal-film applications include A1 contacts and interconnections
in integrated circuits, and ferromagnetic alloys for data storage
applications. Metal films are also used in mirrors, in optical systems, and as
decorative coatings of various components and packaging materials.
tonic
Ionic bonding occurs in compounds composed of strongly electropositive
elements (metals) and strongly electronegative elements (nonmetals). The
alkali halides (NaCl, LiF, etc.) are the most unambiguous examples of
ionically bonded solids. In other compounds, such as oxides, sulfides, and
many of the more complex salts of inorganic chemistry (e.g., nitrates, sulfates,
etc.), the predominant, but not necessarily exclusive, mode of bonding is ionic
in character. In the rock-salt structure of NaC1, for example, there is an
alternating three-dimensional checkerboard array of positively charged cations
and negatively charged anions. Charge transfer from the 3s electron level of
Na to the 3p level of C1 creates a single isolated NaCl molecule. In the solid,
however, the transferred charge is distributed uniformly among nearest neighbors.
Thus, there is no preferred directional character in the ionic bond since
the electrostatic forces between spherically symmetric inert gaslike ions is
independent of orientation.
Much success has been attained in determining the bond energies in alkali
halides without resorting to quantum mechanical calculation. The alternating
positive and negative ionic charge array suggests that Coulombic pair interac
tions are the cause of the attractive part of the interatomic potential, which
varies simply as - 1 / r. Ionic solids are characterized by strong electrostatic
bonding forces and, thus, relatively high binding energies and melting points.
They are poor conductors of electricity because the energy required to transfer
electrons from anions to cations is prohibitively large. At high temperatures,
however, the charged ions themselves can migrate in an electric field, resulting
in limited electrical conduction. Typical resistivities for such materials can
range from lo6 to 1015 ohm-cm.
Among the ionic compounds employed in thin-film technology are MgF,,
ZnS, and CeF,, which are used in antireflection coatings on optical components.
Assorted thin-film oxides and oxide mixtures such as Y,Fe,O,, ,
Y3Al,01,, and LiNbO, are employed in components for integrated optics.
Transparent electrical conductors such as In,O,-SnO, glasses, which serve as
heating elements in window defrosters on cars as well as electrical contacts
over the light exposed surfaces of solar cells, have partial ionic character.
Covalent
Covalent bonding occurs in elemental as well as compound solids. The
outstanding examples are the elemental semiconductors Si, Ge, and diamond,
and the 111-V compound semiconductors such as GaAs and InP. Whereas
elements at the extreme ends of the periodic table are involved in ionic
bonding, covalent bonds are frequently formed between elements in neighboring
columns. The strong directional bonds characteristic of the group IV
elements are due to the hybridization or mixing of the s and p electron wave
functions into a set of orbitals which have high electron densities emanating
from the atom in a tetrahedral fashion. A pair of electrons contributed by
neighboring atoms makes a covalent bond, and four such shared electron pairs
complete the bonding requirements.
Covalent solids are strongly bonded hard materials with relatively high
melting points. Despite the great structural stability of semiconductors, relatively
modest thermal stimulation is sufficient to release electrons from filled
valence bonding states into unfilled electron states. We speak of electrons
being promoted from the valence band to the conduction band, a process that
increases the conductivity of the solid. Small dopant additions of group 111
elements like B and In as well as group V elements like P and As take up
regular or substitutional lattice positions within Si and Ge. The bonding
requirements are then not quite met for group III elements, which are one
electron short of a complete octet. An electron deficiency or hole is thus
created in the valence band.
For each group V dopant an excess of one electron beyond the bonding octet
can be promoted into the conduction band. As the name implies, semiconductors
lie between metals and insulators insofar as their ability to conduct
electricity is concerned. Typical semiconductor resistivities range from 10-
to lo5 ohm-cm. Both temperature and level of doping are very influential in
altering the conductivity of semiconductors. Ionic solids are similar in this
regard.
The controllable spatial doping of semiconductors over very small lateral
and transverse dimensions is a critical requirement in processing integrated
circuits. Thin-film technology is thus simultaneously practiced in three dimensions
in these materials. Similarly, there is a great necessity to deposit
compound semiconductor thin films in a variety of optical device applications.
Other largely covalent materials such as Sic, Tic, and BN have found coating
applications where hard, wear-resistant surfaces are required. They are usually
deposited by chemical vapor deposition methods and will be discussed at length
in Chapter 12.
van der Waals Forces
A large group of solid materials are held together by weak molecular forces.
This so-called van der Waals bonding is due to dipole-dipole charge interactions
between molecules that, though electrically neutral, have regions possessing
a net positive or negative charge distribution. Organic molecules such as
methane and inert gas atoms are weakly bound together in the solid by these
charges. Such solids have low melting points and are mechanically weak. Thin
polymer films used as photoresists or for sealing and encapsulation purposes
contain molecules that are typically bonded by van der Waals' forces.
Widely spaced isolated atoms condense to form solids due to the energy
reduction accompanying bond formation. Thus, if N atoms of type A in the
gas phase (8) combine to form a solid (s), the binding energy Eb is released
according to the equation
NA, + NA, -k Eb.
Energy Eb must be supplied to reverse the equation and decompose the solid.
The more stable the solid, the higher is its binding energy. It has become the
custom to picture the process of bonding by considering the energetics within
and between atoms as the interatomic distance progressively shrinks. In each
isolated atom, the electron energy levels are discrete, as shown on the
right-hand side of Fig. 1-8a. As the atoms approach one another, the individual
levels split, as a consequence of an extension of the Pauli exclusion principle,
to a collective solid; namely, no two electrons can exist in the same quantum
state. Level splitting and broadening occur first for the valence or outer
electrons, since their electron clouds are the first to overlap. During atomic
attraction, electrons populate these lower energy levels, reducing the overall
energy of the solid. With further dimensional shrinkage, the overlap increases
and the inner charge clouds begin to interact. Ion-core overlap now results in
strong repulsive forces between atoms, raising the system energy. A compromise
is reached at the equilibrium interatomic distance in the solid where the
system energy is minimized. At equilibrium, some of the levels have broadened
into bands of energy levels. The bands span different ranges of energy,
depending on the atoms and specific electron levels involved. Sometimes as in
metals, bands of high energy overlap. Insulators and semiconductors have
energy gaps of varying width between bands where electron states are not
allowed. The whys and hows of energy-level splitting, band structure evolution,
and implications with regard to property behavior are perhaps the most
fundamental and difficult questions in solid-state physics. We briefly return to
the subject of electron-band structure after introducing the classes of solids.
An extension of the ideas expressed in Fig. 1-8a is commonly made by
simplifying the behavior to atoms as a whole, in which case the potential
energy of interaction V(r) is plotted as a function of interatomic distance r in
Fig. 1-8b. The generalized behavior shown is common for all classes of solid
materials, regardless of the type of bonding or crystal structure. Although the
mathematical forms of the attractive or repulsive portions are complex, a
number of qualitative features of these curves are not difficult to understand.
For example, the energy at the equilibrium spacing r = a, is the binding
energy. Solids with high melting points tend to have high values of Eb. The
curvature of the potential energy is a measure of the elastic stiffness of the
solid. To see this, we note that around a, the potential energy is approximately
harmonic or parabolic. Therefore, V(r) = (1/2)K,r2, where K, is related to
the spring constant (or elastic modulus). Narrow wells of high curvature are
associated with large values of K,, broad wells of low curvature with small
values of K, . Since the force F between atoms is given by F = - dV/dr,
F = - Ksrr which has its counterpart in Hooke's law-i.e., that stress is
linearly proportional to strain. Thus, in solids with high K, values, correspondingly
larger stresses develop under loading. Interestingly, a purely
parabolic behavior for I/ implies a material with a coefficient of thermal
expansion equal to zero. In real materials, therefore, some asymmetry or
anharmonicity in V(r) exists.
For the most part, atomic behavior within a thin solid film can also be
described by a V(r)-r curve similar to that for the bulk solid. The surface
atoms are less tightly bound, however, which is reflected by the dotted line
behavior in Fig. 1-8b. The difference between the energy minima for surface
and bulk atoms is a measure of the surface energy of the solid. From the
previous discussion, surface layers would tend to be less stiff and melt at lower
temperatures than the bulk. Slight changes in equilibrium atomic spacing or
lattice parameter at surfaces may also be expected.
Despite apparent similarities, there are many distinctions between the four
important types of solid-state bonding and the properties they induce. A
discussion of these individual bonding categories follows.
Metallic
The so-called metallic bond occurs in metals and alloys. In metals the outer
valence electrons of each atom form part of a collective free-electron cloud or
gas that permeates the entire lattice. Even though individual electron-electron
interactions are repulsive, there is sufficient electrostatic attraction between the
free-electron gas and the positive ion cores to cause bonding.
What distinguishes metals from all other solids is the ability of the electrons
to respond readily to applied electric fields, thermal gradients, and incident
light. This gives rise to high electrical and thermal conductivities as well as
high reflectivities. Interestingly, comparable properties are observed in liquid
metals, indicating that aspects of metallic bonding and the free-electron model
are largely preserved even in the absence of a crystal structure. Metallic
electrical resistivities typically ranging from lop5 to ohm-cm should be
contrasted with the much, much larger values possessed by other classes of
solids.
Furthermore, the temperature coefficient of resistivity is positive. Metals
thus become poorer electrical conductors as the temperature is raised. The
reverse is true for all other classes of solids. The conductivity of pure metals is
always reduced with low levels of impurity alloying, which is also contrary to
the usual behavior in other solids. The effect of both temperature and alloying
element additions on metallic conductivity is to increase electron scattering,
which in effect reduces the net component of electron motion in the direction
of the applied electric field. On the other hand, in ionic and semiconductor
solids production of more charge carriers is the result of higher temperatures
and solute additions.
The bonding electrons are not localized between atoms; thus, metals are said
to have nondirectional bonds. This causes atoms to slide by each other and
plastically deform more readily than is the case, for example, in covalent
solids, which have directed atomic bonds.
Examples of thin-metal-film applications include A1 contacts and interconnections
in integrated circuits, and ferromagnetic alloys for data storage
applications. Metal films are also used in mirrors, in optical systems, and as
decorative coatings of various components and packaging materials.
tonic
Ionic bonding occurs in compounds composed of strongly electropositive
elements (metals) and strongly electronegative elements (nonmetals). The
alkali halides (NaCl, LiF, etc.) are the most unambiguous examples of
ionically bonded solids. In other compounds, such as oxides, sulfides, and
many of the more complex salts of inorganic chemistry (e.g., nitrates, sulfates,
etc.), the predominant, but not necessarily exclusive, mode of bonding is ionic
in character. In the rock-salt structure of NaC1, for example, there is an
alternating three-dimensional checkerboard array of positively charged cations
and negatively charged anions. Charge transfer from the 3s electron level of
Na to the 3p level of C1 creates a single isolated NaCl molecule. In the solid,
however, the transferred charge is distributed uniformly among nearest neighbors.
Thus, there is no preferred directional character in the ionic bond since
the electrostatic forces between spherically symmetric inert gaslike ions is
independent of orientation.
Much success has been attained in determining the bond energies in alkali
halides without resorting to quantum mechanical calculation. The alternating
positive and negative ionic charge array suggests that Coulombic pair interac
tions are the cause of the attractive part of the interatomic potential, which
varies simply as - 1 / r. Ionic solids are characterized by strong electrostatic
bonding forces and, thus, relatively high binding energies and melting points.
They are poor conductors of electricity because the energy required to transfer
electrons from anions to cations is prohibitively large. At high temperatures,
however, the charged ions themselves can migrate in an electric field, resulting
in limited electrical conduction. Typical resistivities for such materials can
range from lo6 to 1015 ohm-cm.
Among the ionic compounds employed in thin-film technology are MgF,,
ZnS, and CeF,, which are used in antireflection coatings on optical components.
Assorted thin-film oxides and oxide mixtures such as Y,Fe,O,, ,
Y3Al,01,, and LiNbO, are employed in components for integrated optics.
Transparent electrical conductors such as In,O,-SnO, glasses, which serve as
heating elements in window defrosters on cars as well as electrical contacts
over the light exposed surfaces of solar cells, have partial ionic character.
Covalent
Covalent bonding occurs in elemental as well as compound solids. The
outstanding examples are the elemental semiconductors Si, Ge, and diamond,
and the 111-V compound semiconductors such as GaAs and InP. Whereas
elements at the extreme ends of the periodic table are involved in ionic
bonding, covalent bonds are frequently formed between elements in neighboring
columns. The strong directional bonds characteristic of the group IV
elements are due to the hybridization or mixing of the s and p electron wave
functions into a set of orbitals which have high electron densities emanating
from the atom in a tetrahedral fashion. A pair of electrons contributed by
neighboring atoms makes a covalent bond, and four such shared electron pairs
complete the bonding requirements.
Covalent solids are strongly bonded hard materials with relatively high
melting points. Despite the great structural stability of semiconductors, relatively
modest thermal stimulation is sufficient to release electrons from filled
valence bonding states into unfilled electron states. We speak of electrons
being promoted from the valence band to the conduction band, a process that
increases the conductivity of the solid. Small dopant additions of group 111
elements like B and In as well as group V elements like P and As take up
regular or substitutional lattice positions within Si and Ge. The bonding
requirements are then not quite met for group III elements, which are one
electron short of a complete octet. An electron deficiency or hole is thus
created in the valence band.
For each group V dopant an excess of one electron beyond the bonding octet
can be promoted into the conduction band. As the name implies, semiconductors
lie between metals and insulators insofar as their ability to conduct
electricity is concerned. Typical semiconductor resistivities range from 10-
to lo5 ohm-cm. Both temperature and level of doping are very influential in
altering the conductivity of semiconductors. Ionic solids are similar in this
regard.
The controllable spatial doping of semiconductors over very small lateral
and transverse dimensions is a critical requirement in processing integrated
circuits. Thin-film technology is thus simultaneously practiced in three dimensions
in these materials. Similarly, there is a great necessity to deposit
compound semiconductor thin films in a variety of optical device applications.
Other largely covalent materials such as Sic, Tic, and BN have found coating
applications where hard, wear-resistant surfaces are required. They are usually
deposited by chemical vapor deposition methods and will be discussed at length
in Chapter 12.
van der Waals Forces
A large group of solid materials are held together by weak molecular forces.
This so-called van der Waals bonding is due to dipole-dipole charge interactions
between molecules that, though electrically neutral, have regions possessing
a net positive or negative charge distribution. Organic molecules such as
methane and inert gas atoms are weakly bound together in the solid by these
charges. Such solids have low melting points and are mechanically weak. Thin
polymer films used as photoresists or for sealing and encapsulation purposes
contain molecules that are typically bonded by van der Waals' forces.
defectos
samer elatrache v-17810600 estudiante de CRF
The picture of a perfect crystal structure repeating a particular geometric
pattern of atoms without interruption or mistake is somewhat exaggerated.
Although there are materials-carefully grown silicon single crystals, for
example-that have virtually perfect crystallographic structures extending over
macroscopic dimensions, this is not generally true in bulk materials. In thin
crystalline films the presence of defects not only serves to disrupt the geometric
regularity of the lattice on a microscopic level, it also significantly
influences many film properties, such as chemical reactivity, electrical conduction,
and mechanical behavior. The structural defects briefly considered in this
section are grain boundaries, dislocations, and vacancies.
Grain Boundaries
Grain boundaries are surface or area defects that constitute the interface
between two single-crystal grains of different crystallographic orientation. The
atomic bonding, in particular grains, terminates at the grain boundary where
more loosely bound atoms prevail. Like atoms on surfaces, they are necessarily
more energetic than those within the grain interior. This causes the grain
boundary to be a heterogeneous region where various atomic reactions and
processes, such as solid-state diffusion and phase transformation, precipitation,
corrosion, impurity segregation, and mechanical relaxation, are favored or
accelerated. In addition, electronic transport in metals is impeded through
increased scattering at grain boundaries, which also serve as charge recombination
centers in semiconductors. Grain sizes in films are typically from 0.01 to
1.0 pm in dimension and are smaller, by a factor of more than 100, than
common grain sizes in bulk materials. For this reason, thin films tend to be
more reactive than their bulk counterparts. The fraction of atoms associated
with grain boundaries is approximately 2 a / I , where a is the atomic dimension
and 1 is the grain size. For 1 = loo0 A, this corresponds to about 5 in 1OOO.
Grain morphology and orientation in addition to size control are not only
important objectives in bulk materials but are quite important in thin-film
technology. Indeed a major goal in microelectronic applications is to eliminate
grain boundaries altogether through epitaxial growth of single-crystal semiconductor
films onto oriented single-crystal substrates. Many special techniques
involving physical and chemical vapor deposition methods are employed in this
effort, which continues to be a major focus of activity in semiconductor
technology.
Dislocations
Dislocations are line defects that bear a definite crystallographic relationship to
the lattice. The two fundamental types of dislocations-the edge and the screw
-are shown in Fig. 1-6 and are represented by the symbol I . The edge
dislocation results from wedging in an extra row of atoms; the screw dislocation
requires cutting followed by shearing of the perfect crystal lattice. The
geometry of a crystal containing a dislocation is such that when a simple closed
traverse is attempted about the crystal axis in the surrounding lattice, there is a
closure failure; i.e., one finally amves at a lattice site displaced from the
starting position by a lattice vector, the so-called Burgers vector b. The
individual cubic cells representing the original undeformed crystal lattice are
now distorted somewhat in the presence of dislocations. Therefore, even
without application of external forces on the crystal, a state of internal stress
exists around each dislocation. Furthermore, the stresses differ around edge
and screw dislocations because the lattice distortions differ. Close to the
dislocation axis the stresses are high, but they fall off with distance ( r )
according to a 1 / r dependence.
Dislocations are important because they have provided a model to help
explain a great variety of mechanical phenomena and properties in all classes
of crystalline solids. An early application was the important process of plastic
deformation, which occurs after a material is loaded beyond its limit of elastic
response. In the plastic range, specific planes shear in specific directions
relative to each other much as a deck of cards shear from a rectangular prism
to a parallelepiped. Rather than have rows of atoms undergo a rigid group
displacement to produce the slip offset step at the surface, the same amount of
plastic deformation can be achieved with less energy expenditure. This alternative
mechanism requires that dislocations undulate through the crystal, making
and breaking bonds on the slip plane until a slip step is produced, as shown in
Fig. 1-7a. Dislocations thus help explain why metals are weak and can be
deformed at low stress levels. Paradoxically, dislocations can also explain why
metals work-harden or get stronger when they are deformed. These explanations
require the presence of dislocations in great profusion. In fact, a density
of as many 10l2 dislocation lines threading 1 cm2 of surface area has been
observed in highly deformed metals. Many deposited polycrystalline metal thin
films also have high dislocation densities. Some dislocations are stacked
vertically, giving rise to so-called small-angle grain boundaries (Fig. 1-7b).
The superposition of externally applied forces and internal stress fields of
individual or groups of dislocations, arrayed in a complex three-dimensional
network, sometimes makes it more difficult for them to move and for the
lattice to deform easily.
The role dislocations play in thin films is varied. As an example, consider
the deposition of atoms onto a single-crystal substrate in order to grow an
epitaxial single-crystal film. If the lattice parameter in the film and substrate
differ, then some geometric accommodation in bonding may be required at the
interface, resulting in the formation of interfacial dislocations. The latter are
unwelcome defects particularly if films of high crystalline perfection are
required. For this reason, a good match of lattice parameters is sought for
epitaxial growth. Substrate steps and dislocations should also be eliminated
where possible prior to growth. If the substrate has screw dislocations emerging
normal to the surface, depositing atoms may perpetuate the extension of the
dislocation spiral into the growing film. Like grain boundaries in semiconductors,
dislocations can be sites of charge recombination or generation as a result
of uncompensated "dangling bonds. " Film stress, thermally induced mechanical
relaxation processes, and diffusion in films are all influenced by dislocations.
Vacancies
The last type of defect considered is the vacancy. Vacancies are point defects
that simply arise when lattice sites are unoccupied by atoms. Vacancies form
because the energy required to remove atoms from interior sites and place
them on the surface is not particularly high. This low energy, coupled with the
increase in the statistical entropy of mixing vacancies among lattice sites, gives
rise to a thermodynamic probability that an appreciable number of vacancies
will exist, at least at elevated temperature. The fraction f of total sites that will
be unoccupied as a function of temperature T is predicted to be approximately
reflecting the statistical thermodynamic nature of vacancy formation. Noting
that k is the gas constant and is typically 1 eV/atom gives f = lop5 at
loo0 K.
Vacancies are to be contrasted with dislocations, which are not thermodynamic
defects. Because dislocation lines are oriented along specific crystallographic
directions, their statistical entropy is low. Coupled with a high
formation energy due to the many atoms involved, thermodynamics would
predict a dislocation content of less than one per crystal. Thus, although it is
possible to create a solid devoid of dislocations, it is impossible to eliminate
vacancies.
Vacancies play an important role in all processes related to solid-state
diffusion, including recrystallization, grain growth, sintering, and phase transformations.
In semiconductors, vacancies are electrically neutral as well as
charged and can be associated with dopant atoms. This leads to a variety of
normal and anomalous diffusional doping effects
The picture of a perfect crystal structure repeating a particular geometric
pattern of atoms without interruption or mistake is somewhat exaggerated.
Although there are materials-carefully grown silicon single crystals, for
example-that have virtually perfect crystallographic structures extending over
macroscopic dimensions, this is not generally true in bulk materials. In thin
crystalline films the presence of defects not only serves to disrupt the geometric
regularity of the lattice on a microscopic level, it also significantly
influences many film properties, such as chemical reactivity, electrical conduction,
and mechanical behavior. The structural defects briefly considered in this
section are grain boundaries, dislocations, and vacancies.
Grain Boundaries
Grain boundaries are surface or area defects that constitute the interface
between two single-crystal grains of different crystallographic orientation. The
atomic bonding, in particular grains, terminates at the grain boundary where
more loosely bound atoms prevail. Like atoms on surfaces, they are necessarily
more energetic than those within the grain interior. This causes the grain
boundary to be a heterogeneous region where various atomic reactions and
processes, such as solid-state diffusion and phase transformation, precipitation,
corrosion, impurity segregation, and mechanical relaxation, are favored or
accelerated. In addition, electronic transport in metals is impeded through
increased scattering at grain boundaries, which also serve as charge recombination
centers in semiconductors. Grain sizes in films are typically from 0.01 to
1.0 pm in dimension and are smaller, by a factor of more than 100, than
common grain sizes in bulk materials. For this reason, thin films tend to be
more reactive than their bulk counterparts. The fraction of atoms associated
with grain boundaries is approximately 2 a / I , where a is the atomic dimension
and 1 is the grain size. For 1 = loo0 A, this corresponds to about 5 in 1OOO.
Grain morphology and orientation in addition to size control are not only
important objectives in bulk materials but are quite important in thin-film
technology. Indeed a major goal in microelectronic applications is to eliminate
grain boundaries altogether through epitaxial growth of single-crystal semiconductor
films onto oriented single-crystal substrates. Many special techniques
involving physical and chemical vapor deposition methods are employed in this
effort, which continues to be a major focus of activity in semiconductor
technology.
Dislocations
Dislocations are line defects that bear a definite crystallographic relationship to
the lattice. The two fundamental types of dislocations-the edge and the screw
-are shown in Fig. 1-6 and are represented by the symbol I . The edge
dislocation results from wedging in an extra row of atoms; the screw dislocation
requires cutting followed by shearing of the perfect crystal lattice. The
geometry of a crystal containing a dislocation is such that when a simple closed
traverse is attempted about the crystal axis in the surrounding lattice, there is a
closure failure; i.e., one finally amves at a lattice site displaced from the
starting position by a lattice vector, the so-called Burgers vector b. The
individual cubic cells representing the original undeformed crystal lattice are
now distorted somewhat in the presence of dislocations. Therefore, even
without application of external forces on the crystal, a state of internal stress
exists around each dislocation. Furthermore, the stresses differ around edge
and screw dislocations because the lattice distortions differ. Close to the
dislocation axis the stresses are high, but they fall off with distance ( r )
according to a 1 / r dependence.
Dislocations are important because they have provided a model to help
explain a great variety of mechanical phenomena and properties in all classes
of crystalline solids. An early application was the important process of plastic
deformation, which occurs after a material is loaded beyond its limit of elastic
response. In the plastic range, specific planes shear in specific directions
relative to each other much as a deck of cards shear from a rectangular prism
to a parallelepiped. Rather than have rows of atoms undergo a rigid group
displacement to produce the slip offset step at the surface, the same amount of
plastic deformation can be achieved with less energy expenditure. This alternative
mechanism requires that dislocations undulate through the crystal, making
and breaking bonds on the slip plane until a slip step is produced, as shown in
Fig. 1-7a. Dislocations thus help explain why metals are weak and can be
deformed at low stress levels. Paradoxically, dislocations can also explain why
metals work-harden or get stronger when they are deformed. These explanations
require the presence of dislocations in great profusion. In fact, a density
of as many 10l2 dislocation lines threading 1 cm2 of surface area has been
observed in highly deformed metals. Many deposited polycrystalline metal thin
films also have high dislocation densities. Some dislocations are stacked
vertically, giving rise to so-called small-angle grain boundaries (Fig. 1-7b).
The superposition of externally applied forces and internal stress fields of
individual or groups of dislocations, arrayed in a complex three-dimensional
network, sometimes makes it more difficult for them to move and for the
lattice to deform easily.
The role dislocations play in thin films is varied. As an example, consider
the deposition of atoms onto a single-crystal substrate in order to grow an
epitaxial single-crystal film. If the lattice parameter in the film and substrate
differ, then some geometric accommodation in bonding may be required at the
interface, resulting in the formation of interfacial dislocations. The latter are
unwelcome defects particularly if films of high crystalline perfection are
required. For this reason, a good match of lattice parameters is sought for
epitaxial growth. Substrate steps and dislocations should also be eliminated
where possible prior to growth. If the substrate has screw dislocations emerging
normal to the surface, depositing atoms may perpetuate the extension of the
dislocation spiral into the growing film. Like grain boundaries in semiconductors,
dislocations can be sites of charge recombination or generation as a result
of uncompensated "dangling bonds. " Film stress, thermally induced mechanical
relaxation processes, and diffusion in films are all influenced by dislocations.
Vacancies
The last type of defect considered is the vacancy. Vacancies are point defects
that simply arise when lattice sites are unoccupied by atoms. Vacancies form
because the energy required to remove atoms from interior sites and place
them on the surface is not particularly high. This low energy, coupled with the
increase in the statistical entropy of mixing vacancies among lattice sites, gives
rise to a thermodynamic probability that an appreciable number of vacancies
will exist, at least at elevated temperature. The fraction f of total sites that will
be unoccupied as a function of temperature T is predicted to be approximately
reflecting the statistical thermodynamic nature of vacancy formation. Noting
that k is the gas constant and is typically 1 eV/atom gives f = lop5 at
loo0 K.
Vacancies are to be contrasted with dislocations, which are not thermodynamic
defects. Because dislocation lines are oriented along specific crystallographic
directions, their statistical entropy is low. Coupled with a high
formation energy due to the many atoms involved, thermodynamics would
predict a dislocation content of less than one per crystal. Thus, although it is
possible to create a solid devoid of dislocations, it is impossible to eliminate
vacancies.
Vacancies play an important role in all processes related to solid-state
diffusion, including recrystallization, grain growth, sintering, and phase transformations.
In semiconductors, vacancies are electrically neutral as well as
charged and can be associated with dopant atoms. This leads to a variety of
normal and anomalous diffusional doping effects
estructura: The Materials Science of Thin Films
Samer Elatrache V-17810600 estudiante de CRF
Crystalline Solids
Many solid materials possess an ordered internal crystal structure despite
external appearances that are not what we associate with the term crystalline-
Le., clear, transparent, faceted, etc. Actual crystal structures can be
imagined to arise from a three-dimensional array of points geometrically and
repetitively distributed in space such that each point has identical surroundings.
There are only 14 ways to arrange points in space having this property, and the
resulting point arrays are known as Bravais lattices. They are shown in Fig.
1-1 with lines intentionally drawn in to emphasize the symmetry of the lattice.
Only a single cell for each lattice is reproduced here, and the point array
actually stretches in an endlessly repetitive fashion in all directions. If an atom
or group of two or more atoms is now placed at each Bravais lattice point, a
physically real crystal structure emerges. Thus, if individual copper atoms
populated every point of a face-centered cubic (FCC) lattice whose cube edge
dimension, or so-called lattice parameter, were 3.615 A, the material known as metallic copper would be generated; and similarly for other types of lattices
and atoms.
The reader should realize that just as there are no lines in actual crystals,
there are no spheres. Each sphere in the Cu crystal structure represents the
atomic nucleus surrounded by a complement of 28 core electrons [i.e., (1s)'
(2s)* ( 2 ~()3~~ ()3~~ (3)d)~'O I and a portion of the free-electron gas contributed
by 4s electrons. Furthermore, these spheres must be imagined to touch in
certain crystallographic directions, and their packing is rather dense. In FCC
structures the atom spheres touch along the direction of the face diagonals,
i.e., [110], but not along the face edge directions, i.e., [lOO]. This means that
the planes containing the three face diagonals shown in Fig. 1-2a, i.e., the
(111) plane, are close-packed. On this plane the atoms touch each other in
much the same way as a racked set of billiard balls on a pool table. All other
planes in the FCC structure are less densely packed and thus contain fewer
atoms per unit area.
Placement of two identical silicon atoms at each FCC point would result in
the formation of the diamond cubic silicon structure (Fig. 1-2c), whereas the
rock-salt structure (Fig. 1-2b) is generated if sodium-chlorine groups were
substituted for each lattice point. In both cases the positions and orientation of
the two atoms in question must be preserved from point to point.
In order to quantitatively identify atomic positions as well as planes and
directions in crystals, simple concepts of coordinate geometry are utilized.
First, orthogonal axes are arbitrarily positioned with respect to a cubic lattice
(e.g., FCC) such that each point can now be identified by three coordinates
If the center of the coordinate axes is taken as x = 0, y = 0,
z = 0, or (0, 0, O), then the coordinates of other nearest equivalent cube comer
points are (1,0,0) (0, 1,O) (1,0,0), etc. In this framework the two Si atoms
referred to earlier, situated at the center of the coordinate axes, would occupy
the (0, 0,O) and (1/4,1/4,1/4) positions. Subsequent repetitions of this
oriented pair of atoms at each FCC lattice point generate the diamond cubic
structure in which each Si atom has four nearest neighbors arranged in a
tetrahedral configuration. Similarly, substitution of the motif (0, 0,O) Ga and
(1/4, 1/4, 1/4) As for each point of the FCC lattice would result in the zinc
blende GaAs crystal structure (Fig. 1-2d).
Specific crystal planes and directions are frequently noteworthy because
phenomena such as crystal growth, chemical reactivity, defect incorporation,
deformation, and assorted properties are not isotropic or the same on all planes
and in all directions. Therefore, it is important to be able to identify accurately
and distinguish crystallographic planes and directions. A simple recipe for
identifying a given plane in the cubic system is the following:
1. Determine the intercepts of the plane on the three crystal axes in number of
2. Take reciprocals of those numbers.
3. Reduce these reciprocals to smallest integers by clearing fractions.
The result is a triad of numbers known as the Miller indices for the plane in
question, i.e., (h, k, l ) . Several planes with identifying Miller indices are
indicated in Fig. 1-3. Note that a negative index is indicated above the integer
with a minus sign.
Crystallographic directions shown in Fig. 1-3 are determined by the components
of the vector connecting any two lattice points lying along the direction.
If the coordinates of these points are u1 , ul, w1 and u,, u,, w2, then the
components of the direction vector are u1 - u2, u1 - u , , w1 - w,. When
reduced to smallest integer numbers, they are placed within brackets and are
known as the Miller indices for the direction, Le., [hkl]. In this notation
the direction cosines for the given directions are h / d h 2 + k2 + 1 2 ,
k / d h 2 + k2 + 1 2 , l / d h 2 + k2 + 1'. Thus, the angle a between any two
directions [ h, , k, , 11] and [ h, , k, , /2] is given by the vector dot product
h,h, + k,k2 + / ] 1 2
Jh: + k: + 1: d h ; + ki + /;
cos Q = (1-1)
Two other useful relationships in the crystallography of cubic systems are
given without proof.
1. The Miller indices of the direction normal to the (hkl) plane are [ hkl].
2. The spacing between individual (hkl) planes is a = a , / d h 2 + k2 + 1 2 ,
where a, is the lattice parameter.
As an illustrative example, we shall calculate the angle between any two
neighboring tetrahedral bonds in the diamond cubic lattice. The bonds lie along
[ 11 11-type directions that are specifically taken here to be [i 'i 11 and [l 1 11.
Therefore, by Eq. 1-1,
1
3
cos a = ( I ) ( - 1) + I ( - 1) + (1)(1) = -- and
d 1 2 + 1, + l2 J( - 1)2 + (- 1)2 + l2
a = 109.5".
These two bond directions lie in a common (110)-type crystal plane. The
precise indices of this plane must be 010) or (1iO). This can be seen by noting
that the dot product between each bond vector and the vector normal to the
plane in which they lie must vanish.
We close this brief discussion with some experimental evidence in support of
the internal crystalline structure of solids. X-ray diffraction methods have very
convincingly supplied this evidence by exploiting the fact that the spacing
between atoms is comparable to the wavelength (A) of X-rays. This results in
easily detected emitted beams of high intensity along certain directions when
incident X-rays impinge at critical diffraction angles (8). Under these conditions
the well-known Bragg relation
nX = 2asin8 (1-2)
holds, where n is an integer.
In bulk solids large diffraction effects occur at many values of 8. In thin
films, however, very few atoms are present to scatter X-rays into the diffracted
beam when 8 is large. For this reason the intensities of the diffraction lines or
spots will be unacceptably small unless the incident beam strikes the film
surface at a near-glancing angle. This, in effect, makes the film look thicker.
Such X-ray techniques for examination of thin films have been developed and
will be discussed in Chapter 6. A drawback of thin films relative to bulk solids
is the long counting times required to generate enough signal for suitable
diffraction patterns. This thickness limitation in thin films is turned into great
advantage, however, in the transmission electron microscope. Here electrons
must penetrate through the material under observation, and this can occur only
in thin films or specially thinned specimens. The short wavelength of the
electrons employed enables high-resolution imaging of the lattice structure as
well as diffraction effects to be observed. As an example, consider the
remarkable electron micrograph of Fig. 1-4, showing atom positions in a thin
film of cobalt silicide grown with perfect crystalline registry (epitaxially) on a
silicon wafer. The silicide film- substrate was mechanically and chemically
thinned normal to the original film plane to make the cross section visible.
Such evidence should leave no doubt as to the internal crystalline nature of
solids.
Crystalline Solids
Many solid materials possess an ordered internal crystal structure despite
external appearances that are not what we associate with the term crystalline-
Le., clear, transparent, faceted, etc. Actual crystal structures can be
imagined to arise from a three-dimensional array of points geometrically and
repetitively distributed in space such that each point has identical surroundings.
There are only 14 ways to arrange points in space having this property, and the
resulting point arrays are known as Bravais lattices. They are shown in Fig.
1-1 with lines intentionally drawn in to emphasize the symmetry of the lattice.
Only a single cell for each lattice is reproduced here, and the point array
actually stretches in an endlessly repetitive fashion in all directions. If an atom
or group of two or more atoms is now placed at each Bravais lattice point, a
physically real crystal structure emerges. Thus, if individual copper atoms
populated every point of a face-centered cubic (FCC) lattice whose cube edge
dimension, or so-called lattice parameter, were 3.615 A, the material known as metallic copper would be generated; and similarly for other types of lattices
and atoms.
The reader should realize that just as there are no lines in actual crystals,
there are no spheres. Each sphere in the Cu crystal structure represents the
atomic nucleus surrounded by a complement of 28 core electrons [i.e., (1s)'
(2s)* ( 2 ~()3~~ ()3~~ (3)d)~'O I and a portion of the free-electron gas contributed
by 4s electrons. Furthermore, these spheres must be imagined to touch in
certain crystallographic directions, and their packing is rather dense. In FCC
structures the atom spheres touch along the direction of the face diagonals,
i.e., [110], but not along the face edge directions, i.e., [lOO]. This means that
the planes containing the three face diagonals shown in Fig. 1-2a, i.e., the
(111) plane, are close-packed. On this plane the atoms touch each other in
much the same way as a racked set of billiard balls on a pool table. All other
planes in the FCC structure are less densely packed and thus contain fewer
atoms per unit area.
Placement of two identical silicon atoms at each FCC point would result in
the formation of the diamond cubic silicon structure (Fig. 1-2c), whereas the
rock-salt structure (Fig. 1-2b) is generated if sodium-chlorine groups were
substituted for each lattice point. In both cases the positions and orientation of
the two atoms in question must be preserved from point to point.
In order to quantitatively identify atomic positions as well as planes and
directions in crystals, simple concepts of coordinate geometry are utilized.
First, orthogonal axes are arbitrarily positioned with respect to a cubic lattice
(e.g., FCC) such that each point can now be identified by three coordinates
If the center of the coordinate axes is taken as x = 0, y = 0,
z = 0, or (0, 0, O), then the coordinates of other nearest equivalent cube comer
points are (1,0,0) (0, 1,O) (1,0,0), etc. In this framework the two Si atoms
referred to earlier, situated at the center of the coordinate axes, would occupy
the (0, 0,O) and (1/4,1/4,1/4) positions. Subsequent repetitions of this
oriented pair of atoms at each FCC lattice point generate the diamond cubic
structure in which each Si atom has four nearest neighbors arranged in a
tetrahedral configuration. Similarly, substitution of the motif (0, 0,O) Ga and
(1/4, 1/4, 1/4) As for each point of the FCC lattice would result in the zinc
blende GaAs crystal structure (Fig. 1-2d).
Specific crystal planes and directions are frequently noteworthy because
phenomena such as crystal growth, chemical reactivity, defect incorporation,
deformation, and assorted properties are not isotropic or the same on all planes
and in all directions. Therefore, it is important to be able to identify accurately
and distinguish crystallographic planes and directions. A simple recipe for
identifying a given plane in the cubic system is the following:
1. Determine the intercepts of the plane on the three crystal axes in number of
2. Take reciprocals of those numbers.
3. Reduce these reciprocals to smallest integers by clearing fractions.
The result is a triad of numbers known as the Miller indices for the plane in
question, i.e., (h, k, l ) . Several planes with identifying Miller indices are
indicated in Fig. 1-3. Note that a negative index is indicated above the integer
with a minus sign.
Crystallographic directions shown in Fig. 1-3 are determined by the components
of the vector connecting any two lattice points lying along the direction.
If the coordinates of these points are u1 , ul, w1 and u,, u,, w2, then the
components of the direction vector are u1 - u2, u1 - u , , w1 - w,. When
reduced to smallest integer numbers, they are placed within brackets and are
known as the Miller indices for the direction, Le., [hkl]. In this notation
the direction cosines for the given directions are h / d h 2 + k2 + 1 2 ,
k / d h 2 + k2 + 1 2 , l / d h 2 + k2 + 1'. Thus, the angle a between any two
directions [ h, , k, , 11] and [ h, , k, , /2] is given by the vector dot product
h,h, + k,k2 + / ] 1 2
Jh: + k: + 1: d h ; + ki + /;
cos Q = (1-1)
Two other useful relationships in the crystallography of cubic systems are
given without proof.
1. The Miller indices of the direction normal to the (hkl) plane are [ hkl].
2. The spacing between individual (hkl) planes is a = a , / d h 2 + k2 + 1 2 ,
where a, is the lattice parameter.
As an illustrative example, we shall calculate the angle between any two
neighboring tetrahedral bonds in the diamond cubic lattice. The bonds lie along
[ 11 11-type directions that are specifically taken here to be [i 'i 11 and [l 1 11.
Therefore, by Eq. 1-1,
1
3
cos a = ( I ) ( - 1) + I ( - 1) + (1)(1) = -- and
d 1 2 + 1, + l2 J( - 1)2 + (- 1)2 + l2
a = 109.5".
These two bond directions lie in a common (110)-type crystal plane. The
precise indices of this plane must be 010) or (1iO). This can be seen by noting
that the dot product between each bond vector and the vector normal to the
plane in which they lie must vanish.
We close this brief discussion with some experimental evidence in support of
the internal crystalline structure of solids. X-ray diffraction methods have very
convincingly supplied this evidence by exploiting the fact that the spacing
between atoms is comparable to the wavelength (A) of X-rays. This results in
easily detected emitted beams of high intensity along certain directions when
incident X-rays impinge at critical diffraction angles (8). Under these conditions
the well-known Bragg relation
nX = 2asin8 (1-2)
holds, where n is an integer.
In bulk solids large diffraction effects occur at many values of 8. In thin
films, however, very few atoms are present to scatter X-rays into the diffracted
beam when 8 is large. For this reason the intensities of the diffraction lines or
spots will be unacceptably small unless the incident beam strikes the film
surface at a near-glancing angle. This, in effect, makes the film look thicker.
Such X-ray techniques for examination of thin films have been developed and
will be discussed in Chapter 6. A drawback of thin films relative to bulk solids
is the long counting times required to generate enough signal for suitable
diffraction patterns. This thickness limitation in thin films is turned into great
advantage, however, in the transmission electron microscope. Here electrons
must penetrate through the material under observation, and this can occur only
in thin films or specially thinned specimens. The short wavelength of the
electrons employed enables high-resolution imaging of the lattice structure as
well as diffraction effects to be observed. As an example, consider the
remarkable electron micrograph of Fig. 1-4, showing atom positions in a thin
film of cobalt silicide grown with perfect crystalline registry (epitaxially) on a
silicon wafer. The silicide film- substrate was mechanically and chemically
thinned normal to the original film plane to make the cross section visible.
Such evidence should leave no doubt as to the internal crystalline nature of
solids.
Hisotira de materials scince of thin films
Samer Elatrache V. 17810600 estudiante de CRF
Thin-film technology is simultaneously one of the oldest arts and one of the
newest sciences. Involvement with thin films dates to the metal ages of
antiquity. Consider the ancient craft of gold beating, which has been practiced
continuously for at least four millenia. Gold's great malleability enables it to be
hammered into leaf of extraordinary thinness while its beauty and resistance to
chemical degradation have earmarked its use for durable ornamentation and
protection purposes. The Egyptians appear to have been the earliest practitioners
of the art of gold beating and gilding. Many magnificent examples of
statuary, royal crowns, and coffin cases which have survived intact attest to the
level of skill achieved. The process involves initial mechanical rolling followed
by many stages of beating and sectioning composite structures consisting of
gold sandwiched between layers of vellum, parchment, and assorted animal
skins. Leaf samples from Luxor dating to the Eighteenth Dynasty (1567-1320
B.C.) measured 0.3 microns in thickness. As a frame of reference for the
reader, the human hair is about 75 microns in diameter. Such leaf was
carefully applied and bonded to smoothed wax or resin-coated wood surfaces
in a mechanical (cold) gilding process. From Egypt the art spread as indicated
by numerous accounts of the use of gold leaf in antiquity.
Today, gold leaf can be machine-beaten to 0.1 micron and to 0.05 micron
when beaten by a skilled craftsman. In this form it is invisible sideways and
quite readily absorbed by the skin. It is no wonder then that British gold
beaters were called upon to provide the first metal specimens to be observed
in the transmission electron microscope. Presently, gold leaf is used to decorate
such diverse structures and objects as statues, churches, public buildings,
tombstones, furniture, hand-tooled leather, picture frames and, of course,
illuminated manuscripts.
Thin-film technologies related to gold beating, but probably not as old, are
mercury and fire gilding. Used to decorate copper or bronze statuary, the cold
mercury process involved carefully smoothing and polishing the metal surface,
after which mercury was rubbed into it. Some copper dissolved in the
mercury, forming a very thin amalgam film that left the surface shiny and
smooth as a mirror. Gold leaf was then pressed onto the surface cold and
bonded to the mercury-rich adhesive. Alternately, gold was directly amalgamated
with mercury, applied, and the excess mercury was then driven off by
heating, leaving a film of gold behind. Fire gilding was practiced well into the
nineteenth century despite the grave health risk due to mercury vapor. The
hazard to workers finally became intolerable and provided the incentive to
develop alternative processes, such as electroplating.
The history of gold beating and gilding is replete with experimentation and
process development in diverse parts of the ancient world. Practitioners were
concerned with the purity and cost of the gold, surface preparation, the
uniformity of the applied films, adhesion to the substrate, reactions between
and among the gold, mercury, copper, bronze (copper-tin), etc., process
safety, color, optical appearance, durability of the final coating, and competitive
coating technologies. As we shall see in the ensuing pages, modem
thin-film technology addresses these same generic issues, albeit with a great
compression of time. And although science is now in the ascendancy, there is
still much room for art.
Thin-film technology is simultaneously one of the oldest arts and one of the
newest sciences. Involvement with thin films dates to the metal ages of
antiquity. Consider the ancient craft of gold beating, which has been practiced
continuously for at least four millenia. Gold's great malleability enables it to be
hammered into leaf of extraordinary thinness while its beauty and resistance to
chemical degradation have earmarked its use for durable ornamentation and
protection purposes. The Egyptians appear to have been the earliest practitioners
of the art of gold beating and gilding. Many magnificent examples of
statuary, royal crowns, and coffin cases which have survived intact attest to the
level of skill achieved. The process involves initial mechanical rolling followed
by many stages of beating and sectioning composite structures consisting of
gold sandwiched between layers of vellum, parchment, and assorted animal
skins. Leaf samples from Luxor dating to the Eighteenth Dynasty (1567-1320
B.C.) measured 0.3 microns in thickness. As a frame of reference for the
reader, the human hair is about 75 microns in diameter. Such leaf was
carefully applied and bonded to smoothed wax or resin-coated wood surfaces
in a mechanical (cold) gilding process. From Egypt the art spread as indicated
by numerous accounts of the use of gold leaf in antiquity.
Today, gold leaf can be machine-beaten to 0.1 micron and to 0.05 micron
when beaten by a skilled craftsman. In this form it is invisible sideways and
quite readily absorbed by the skin. It is no wonder then that British gold
beaters were called upon to provide the first metal specimens to be observed
in the transmission electron microscope. Presently, gold leaf is used to decorate
such diverse structures and objects as statues, churches, public buildings,
tombstones, furniture, hand-tooled leather, picture frames and, of course,
illuminated manuscripts.
Thin-film technologies related to gold beating, but probably not as old, are
mercury and fire gilding. Used to decorate copper or bronze statuary, the cold
mercury process involved carefully smoothing and polishing the metal surface,
after which mercury was rubbed into it. Some copper dissolved in the
mercury, forming a very thin amalgam film that left the surface shiny and
smooth as a mirror. Gold leaf was then pressed onto the surface cold and
bonded to the mercury-rich adhesive. Alternately, gold was directly amalgamated
with mercury, applied, and the excess mercury was then driven off by
heating, leaving a film of gold behind. Fire gilding was practiced well into the
nineteenth century despite the grave health risk due to mercury vapor. The
hazard to workers finally became intolerable and provided the incentive to
develop alternative processes, such as electroplating.
The history of gold beating and gilding is replete with experimentation and
process development in diverse parts of the ancient world. Practitioners were
concerned with the purity and cost of the gold, surface preparation, the
uniformity of the applied films, adhesion to the substrate, reactions between
and among the gold, mercury, copper, bronze (copper-tin), etc., process
safety, color, optical appearance, durability of the final coating, and competitive
coating technologies. As we shall see in the ensuing pages, modem
thin-film technology addresses these same generic issues, albeit with a great
compression of time. And although science is now in the ascendancy, there is
still much room for art.
The Materials Science of Thin Films
Samer Elatrache V-17810600 estudiante de CRF
Thin-film science and technology play a crucial role in the high-tech industries
that will bear the main burden of future American competitiveness. While the
major exploitation of thin films has been in microelectronics, there are
numerous and growing applications in communications, optical electronics,
coatings of all kinds, and in energy generation and conservation strategies. A
great many sophisticated analytical instruments and techniques, largely developed
to characterize thin films and surfaces, have already become indispensable
in virtually every scientific endeavor irrespective of discipline. When I
was called upon to offer a course on thin films, it became a genuine source of
concern to me that there were no suitable textbooks available on this unquestionably
important topic. This book, written with a materials science flavor, is
a response to this need. It is intended for
1.
2.
3.
Science and engineering students in advanced undergraduate or first-year
graduate level courses on thin films
Participants in industrial in-house courses or short courses offered by
professional societies
Mature scientists and engineers switching career directions who require an
overview of the field.
Readers should be reasonably conversant with introductory college chemistry
and physics and possess a passive cultural familiarity with topics commonly
treated in undergraduate physical chemistry and modem physics courses.
It is worthwhile to briefly elaborate on this book's title and the connection
between thin films and the broader discipline of materials science and engineering.
A dramatic increase in our understanding of the fundamental nature of
materials throughout much of the twentieth century has led to the development
of materials science and engineering. This period witnessed the emergence of
polymeric, nuclear, and electronic materials, new roles for metals and ceramics,
and the development of reliable methods to process these materials in bulk
and thin-film form. Traditional educational approaches to the study of materials
have stressed structure-property relationships in bulk solids, typically
utilizing metals, semiconductors, ceramics; and polymers, taken singly or
collectively as illustrative vehicles to convey principles. The same spirit is
adopted in this book except that thin solid films are the vehicle. In addition,
the basic theme has been expanded to include the multifaceted processingstructure-
properties-performance interactions. Thus the original science
core is preserved but enveloped by the engineering concerns of processing
and performance. Within this context, I have attempted to weave threads of
commonality among seemingly different materials and properties, as well as to
draw distinctions between materials that exhibit outwardly similiar behavior. In
particular, parallels and contrasts between films and bulk materials are recurring
themes.
An optional introductory review chapter on standard topics in materials
establishes a foundation for subsequent chapters. Following a second chapter
on vacuum science and technology, the remaining text is broadly organized
into three categories. Chapters 3 and 4 deal with the principles and practices of
film deposition from the vapor phase. Chapters 5-9 deal with the processes
and phenomena that influence the structural, chemical, and physical attributes
of films, and how to characterize them. Topics discussed include nucleation,
growth, crystal perfection, epitaxy, mass transport effects, and the role of
stress. These are the common thin-film concerns irrespective of application.
The final portion of the book (Chapters 10-14) is largely devoted to specific
film properties (electrical, magnetic, optical, mechanical) and applications, as
well as to emerging materials and processes. Although the first nine chapters
may be viewed as core subject matter, the last five chapters offer elective
topics intended to address individual interests. It is my hope that instructors
using this book will find this division of topics a useful one.
Much of the book reflects what is of current interest to the thin-film research
and development communities. Examples include chapters on chemical vapor
deposition, epitaxy, interdiffusion and reactions, metallurgical and protective
coatings, and surface modification. The field is evolving so rapidly that even
the classics of yesteryear, e.g., Maissel and Glang, Handbook of Thin Film
Technology (1970) and Chopra, Thin Film Phenomena (1969), as well as
more recent books on thin films, e.g., Pulker, Coatings on Glass (1984), and
Eckertova, Physics of Thin Films (1986), make little or no mention of these
now important subjects.
As every book must necessarily establish its boundaries, I would like to
point out the following: (1) Except for coatings (Chapter 12) where thicknesses
range from several to as much as hundreds of microns (1 micron or 1
pm = lop6 meter), the book is primarily concerned with films that are less
than 1 pm thick. (2) Only films and coatings formed from the gas phase by
physical (PVD) or chemical vapor deposition (CVD) processes are considered.
Therefore spin and dip coating, flame and plasma spraying of powders,
electrolytic deposition, etc., will not be treated. (3) The topic of polymer films
could easily justify a monograph of its own, and hence will not be discussed
here. (4) Time and space simply do not allow for development of all topics
from first principles. (Nevertheless, I have avoided using the unwelcome
phrase "It can be shown that . . . ," and have refrained from using other
textbooks or the research literature to fill in missing steps of derivations.) (5) A
single set of units (e.g., CGS, MKS, SI, etc.) has been purposely avoided to
better address the needs of a multifaceted and interdisciplinary audience.
Common usage, commercial terminology, the research literature and simple
bias and convenience have all played a role in the ecumenical display of units.
Where necessary, conversions between different systems of units are provided.
At the end of each chapter are problems of varying difficulty, and I believe a
deeper sense of the subject matter will be gained by considering them. Three
very elegant problems (Le. 9-6, -7, -8) were developed by Professor W. D.
Nix, and I thank him for their use.
By emphasizing immutable concepts, I hope this book will be spared the
specter of rapid obsolescence. However, if this book will in some small
measure help spawn new technology rendering it obsolete, it will have served a
useful function
Thin-film science and technology play a crucial role in the high-tech industries
that will bear the main burden of future American competitiveness. While the
major exploitation of thin films has been in microelectronics, there are
numerous and growing applications in communications, optical electronics,
coatings of all kinds, and in energy generation and conservation strategies. A
great many sophisticated analytical instruments and techniques, largely developed
to characterize thin films and surfaces, have already become indispensable
in virtually every scientific endeavor irrespective of discipline. When I
was called upon to offer a course on thin films, it became a genuine source of
concern to me that there were no suitable textbooks available on this unquestionably
important topic. This book, written with a materials science flavor, is
a response to this need. It is intended for
1.
2.
3.
Science and engineering students in advanced undergraduate or first-year
graduate level courses on thin films
Participants in industrial in-house courses or short courses offered by
professional societies
Mature scientists and engineers switching career directions who require an
overview of the field.
Readers should be reasonably conversant with introductory college chemistry
and physics and possess a passive cultural familiarity with topics commonly
treated in undergraduate physical chemistry and modem physics courses.
It is worthwhile to briefly elaborate on this book's title and the connection
between thin films and the broader discipline of materials science and engineering.
A dramatic increase in our understanding of the fundamental nature of
materials throughout much of the twentieth century has led to the development
of materials science and engineering. This period witnessed the emergence of
polymeric, nuclear, and electronic materials, new roles for metals and ceramics,
and the development of reliable methods to process these materials in bulk
and thin-film form. Traditional educational approaches to the study of materials
have stressed structure-property relationships in bulk solids, typically
utilizing metals, semiconductors, ceramics; and polymers, taken singly or
collectively as illustrative vehicles to convey principles. The same spirit is
adopted in this book except that thin solid films are the vehicle. In addition,
the basic theme has been expanded to include the multifaceted processingstructure-
properties-performance interactions. Thus the original science
core is preserved but enveloped by the engineering concerns of processing
and performance. Within this context, I have attempted to weave threads of
commonality among seemingly different materials and properties, as well as to
draw distinctions between materials that exhibit outwardly similiar behavior. In
particular, parallels and contrasts between films and bulk materials are recurring
themes.
An optional introductory review chapter on standard topics in materials
establishes a foundation for subsequent chapters. Following a second chapter
on vacuum science and technology, the remaining text is broadly organized
into three categories. Chapters 3 and 4 deal with the principles and practices of
film deposition from the vapor phase. Chapters 5-9 deal with the processes
and phenomena that influence the structural, chemical, and physical attributes
of films, and how to characterize them. Topics discussed include nucleation,
growth, crystal perfection, epitaxy, mass transport effects, and the role of
stress. These are the common thin-film concerns irrespective of application.
The final portion of the book (Chapters 10-14) is largely devoted to specific
film properties (electrical, magnetic, optical, mechanical) and applications, as
well as to emerging materials and processes. Although the first nine chapters
may be viewed as core subject matter, the last five chapters offer elective
topics intended to address individual interests. It is my hope that instructors
using this book will find this division of topics a useful one.
Much of the book reflects what is of current interest to the thin-film research
and development communities. Examples include chapters on chemical vapor
deposition, epitaxy, interdiffusion and reactions, metallurgical and protective
coatings, and surface modification. The field is evolving so rapidly that even
the classics of yesteryear, e.g., Maissel and Glang, Handbook of Thin Film
Technology (1970) and Chopra, Thin Film Phenomena (1969), as well as
more recent books on thin films, e.g., Pulker, Coatings on Glass (1984), and
Eckertova, Physics of Thin Films (1986), make little or no mention of these
now important subjects.
As every book must necessarily establish its boundaries, I would like to
point out the following: (1) Except for coatings (Chapter 12) where thicknesses
range from several to as much as hundreds of microns (1 micron or 1
pm = lop6 meter), the book is primarily concerned with films that are less
than 1 pm thick. (2) Only films and coatings formed from the gas phase by
physical (PVD) or chemical vapor deposition (CVD) processes are considered.
Therefore spin and dip coating, flame and plasma spraying of powders,
electrolytic deposition, etc., will not be treated. (3) The topic of polymer films
could easily justify a monograph of its own, and hence will not be discussed
here. (4) Time and space simply do not allow for development of all topics
from first principles. (Nevertheless, I have avoided using the unwelcome
phrase "It can be shown that . . . ," and have refrained from using other
textbooks or the research literature to fill in missing steps of derivations.) (5) A
single set of units (e.g., CGS, MKS, SI, etc.) has been purposely avoided to
better address the needs of a multifaceted and interdisciplinary audience.
Common usage, commercial terminology, the research literature and simple
bias and convenience have all played a role in the ecumenical display of units.
Where necessary, conversions between different systems of units are provided.
At the end of each chapter are problems of varying difficulty, and I believe a
deeper sense of the subject matter will be gained by considering them. Three
very elegant problems (Le. 9-6, -7, -8) were developed by Professor W. D.
Nix, and I thank him for their use.
By emphasizing immutable concepts, I hope this book will be spared the
specter of rapid obsolescence. However, if this book will in some small
measure help spawn new technology rendering it obsolete, it will have served a
useful function
domingo, 14 de marzo de 2010
ION-BEAM MODIFICATION PHENOMENA AND APPLICATIONS
Ion-Beam Mixing
Ion-beam mixing phenomena deal with compositional and structural changes in a two- or multiple-component system under the influence of ion radiation. The effect commonly occurs during sputteríng and results in changes in surface composition during depth profiling anaJysis by SIMS and AES techniques. For example, consider a thin film of A on substrate B bombarded by a beam of inert-gas ions. Typically, the ion range (/?) exceeds the escape depth of the sputtered A atoms. If R does not exceed the thickness of A, then only A atoms sputter. If, after some sputteríng, R now extends into the substrate región, the atomic displacements and interdiffusion that occur within colusión cascades will cause A and B to intermix. The mixing occurs locally at the interface and eventually links with other similarly intermixed zones to créate a continuous ion-beam mixed layer. Now B atoms also enter the stream of sputtered atoms because the combination of continued surface erosión and interfacial broaden-ing, due to ion mixing, has brought them closer to the surface.
Through the use of high-energy ion beams, mixing reactions occur over substantial dimensions. Films can, therefore, be effectively alloyed with sub-strates and layered, but normally immiscible films can be homogenized with the assistance of ion implantation. As an example, consider the multiple-layer structure consisting of alternating Au and Co films. According to the phase diagram, these elements do not dissolve in each other; but they form a uniform metastable solid solution under a flux of 3 x 1015 Xe ions/cm2 at an energy of 300 keV. Colusión cascades, ballistic effects of recoils, and defect migration during room-temperature irradiation all con¬tribute, in a complex way, to the observed mixing.
In suicides, equilibrium as well as metastable phases have been observed after mixing. Experiment has shown that the suicide thickness is both dose-and ion-species-dependent. At the same energy and dose, more mixing occurs the heavier the ion. In metal film systems, extended solubility is virtually always observed, metastable phase formation is a frequent occurrence, and amorphous phases occasionally form at cryogenic temperatures.
Modification of Mechanically Functional Surfaces
By enhancing the ability of surfaces to resist plástic deformation, the benefits of reduced wear, less tendency to surface cracking, and greater dimensional stability are effected. In recent years there has been considerable research on the use of ion implantation to realize these desirable ends. For the case of steel, the implantation of light interstitial ions, such as nitrogen, boron, and carbón, yields considerable improvement in wear and fatigue resistance. The reason is due to the elastic interaction between dislocations and undersized interstitials; this results in their mutual attractíon and the segregation of the atoms to the defects. Long known in metallurgical circles, the interaction occurs even at room temperature and is quite effective in pinning dislocations, thus restrictíng their motion. In addition, iron nitrides, carbides, borides, etc., form when the limited solubilities of the interstitial atoms are locally exceeded; these precipí-tales are also effective barriers to dislocation movement. Since surface damage processes depend on plástic flow of surface layers, the importance of limiting dislocation motion is apparent.
An altérnate approach to improving the wear resistance of surfaces through the deposition of hard coatings was addressed at length. It is instructive to compare this approach with that of ion implantation. Although CVD deposits manage to conformally coat external as well as internal surfaces, ion implantation is limited by geometry to line-of-sight processing. CVD coatings are bonded to the substrate across an interfacial región, which is frequently a source of adhesión difficulty; on the other hand, ion-implantation modified layers are not subject to adhesión problems because no sharp inter-face exists. Since CVD deposition is conducted at elevated temperatures, the substrate is frequently heat-affected and sometimes softened in the process; ion implantation only modifies a very thin surface layer, leaving the remainder of the substrate unaffected. Lastly, thick CVD coatings several microns thick imply less stringent substrate smoothness requirements than for ion-implanta-tion processing. The latter is the only practical method available for modifying precisión surfaces while preserving extreme dimensional tolerances. Clearly, ion implantation is only cost-effective for high-value added components, such as surgical implants or dies.
The issue of the effective surface depth modified by ion implantation is an interesting one. It has been observed that ion implantation effects persist well beyond the shallow depth of the projected ion range. Implanted atoms are frequently observed considerably deeper within the substrate than can be accounted for by the geometry of wear tracks. The cause has been attributed to the generation of fresh dislocation networks that effectively trap and drag atoms deeper below the damaged surface layers. Frictional wear is also accompanied by temperature increases of as much as 600-700 °C at contacting asperities. Migration of mobile impurities is thus encouraged, especially where the dislocation density is high. Such effects provide an unexpected wear protection bonus for ion-implanted surfaces.
A number of industrial applications involving wear reduction by means of ion implantation methods is Usted in Table 13-2. Hardness and resistance to adhesive and abrasive wear are the attributes required of the assorted cutting, mechanical forming, and molding tools. In steel matrices nitrogen is a favored interstitial ion, and implanted cobalt has been explored as a means of modify-ing tungsten carbide tools. Typical doses are well into the 1017/cm2 range and impart two- to fivefold decreases in wear rate with corresponding increases in tool life. Specific examples of ion-implantation modified tools and components.
A totally different application which nevertheless exploits the benefits of enhanced hardness and reduced wear involves metallic surgical implants. Tens of thousands of titanium alloy (Ti-6 wt%-Al-4 wt% V) hip and lcnee replace-ment prostheses have already been ion-implanted with nitrogen resulting in improved tribological properties. In service, the implant moves in contact with a high-molecular-weight polyethylene mating socket, so that wear of this couple is of concern. Apparently, the formation of hard TiOz particles results in abrasión of the unimplanted alloy surface during use. Implantation produces a surface containing hard titanium nitride precipitates that effectively resists such wear. Part of the improvement in properties may be attributable to the enhanced corrosión resistance ion-implanted surfaces exhibit. High defect concentrations promote thickening of air-formed oxide films and enhance chemical homogenization of the underlying metal. The former effect affords an added measure of surface passivation and protection, and the latter helps eliminate localized galvanic corrosión. Lastly, note that there are no practica! alternatives to modifying the surface properties of orthopedic prostheses. Unlike tools whose surfaces can tolérate CVD or PVD coatings, chemical biocompatibility with contac'ting body fluids places severe restrictions on the surface composition of surgical implants.
Ronellys Flores---CRF---libro the materials science of thin films
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