4.2.1 PLASMAS

The term plasma was apparently coined by Irving Langmuir in 1929 (Ref. 1) to describe the behavior of ionized gases in high-current vacuum tubes. It was soon realized that plasmas exhibited a behavior different from simple ideal (or nonideal) un-ionized gases, and were obviously distinct from condensed liquid and solid states of matter. For these reasons plasmas were termed a rare fourth state of matter. On a cosmic scale, however, considering the northern lights, stars, and interstellar hydrogen, it has been claimed that 99% of matter in the universe exists in plasma form; on this basis solids and liquids are actually the rare states of matter. Science fiction movies containing spectacular lightning discharges and glittering advertising signs employing neon lighting provided early vehicles for displaying the mysterious attributes of plasmas. Nitriding of steel surfaces in order to harden them, and fluorescent lighting based on mercury discharges, were among the early widespread applications capitalizing on this strange state of matter.

A plasma may be broadly defined as aquasineutral gas that exhibits a collective behavior in the presence of applied electromagnetic fields. Plasmas are weakly ionized gases consisting of a collection of electrons, ions, and neutral atomic and molecular species. This definition is broad enough to encompass the spectrum of space and man-made plasmas extending from stars, solar winds and coronas, and the earth’s ionosphere to the regime of high-pressure arcs, shock tubes, and fusion reactors. These space and laboratory created plasmas broadly differ in the density n(number per cm³) of charged species. In the former rarified environments, n is typically less than 10⁷cm⁻³, whereas experimentally, densities approaching 10²⁰ cm⁻³ in magnitude have been realized in the latter man-made high-pressure plasmas. In between these extremes are the glow discharges and arcs with which this book is primarily concerned. These plasmas with ion densities ranging from ∼ 10⁸ cm⁻³ to ∼10¹⁴ cm⁻³ are the ones exploited in the industrial plasma-processing applications we shall consider.

4.2.2 THE TOWNSEND DISCHARGE

We have seen that application of a sufficiently high DC voltage between metal electrodes immersed in a low-pressure gas initiates a discharge. What is the mechanism that converts the initially insulating gas into an electrically conducting medium? This is the first question that must be addressed in order to understand the nature of such gaseous conducting media or plasmas. In essence, the discharge reflects a gaseous breakdown that may be viewed as the analog of dielectric breakdown in insulating solids; there dielectrics conduct electricity at critical applied voltages. In gases the process begins when a stray electron near the cathode carrying an initial current i₀ is accelerated toward the anode by the applied electric field (). After gaining sufficient energy the electron collides with a neutral gas atom (A) converting it into a positively charged ion (A⁺). During this impact ionization process, charge conservation indicates that two electrons are released, i.e.,

     (4-1)

These are accelerated and now bombard two additional neutral gas atoms, generating more ions and electrons, and so on. Meanwhile, the electric field drives ions in the opposite direction where they collide with the cathode, ejecting, among other particles, secondary electrons. These now also undergo charge multiplication. The effect snowballs until a sufficiently large avalanche current ultimately causes the gas to breakdown.

In order for breakdown to occur, the distance (d) between electrodes must be large enough to allow electrons to incrementally gain the requisite energy for an ionization cascade. Also, the electrodes must be wide enough to prevent the loss of electrons or ions through sideways diffusion out of the interelectrode space. The Townsend equation, whose derivation will be left for the reader in Exercise 1, is written as

     (4-2)

This equation reveals that the discharge current (i) rises dramatically from i₀ because of the combined effects of impact ionization and secondary-electron generation. These processes are respectively defined by constants α and γ_e. Known as the Townsend ionization coefficient, α represents the probability per unit length of ionization occurring during an electron-gas atom collision. Quantity γ_e is the Townsend secondary-electron emission coefficient and is defined as the number of secondary electrons emitted at the cathode per incident ion. For an electron of chargeq traveling a distance λ, the probability of reaching the ionization potential V_i is exp — (V_i/qλ), so that

     (4-3)

We may associate λ with the intercollision distance or mean free path in a gas. Since Eq. 2-5 reveals that λ ∼ P⁻¹, we expect α to be a function of the system pressure.

Breakdown is assumed to occur when the denominator in Eq. 4-2 is equal to zero, i.e., γ_e(exp αd − 1) = 1, for then the current is infinite. From this condition plus Eqs. 4-3 and 2-5, the critical breakdown field and voltage can be calculated with a bit of algebra and expressed in terms of a product of pressure and interelectrode spacing. The result, known as Paschen’s Law, is expressed by

     (4-4)

where A and B are constants.

The Paschen curve, a plot of V_B vs Pd, is shown in Fig. 4-2 for a number of gases. At low values of Pd there are few electron–ion collisions and the secondary electron yield is too low to sustain ionization in the discharge. On the other hand, at high pressures there are frequent collisions, and since electrons do not acquire sufficient energy to ionize gas atoms, the discharge is quenched. Thus at either extreme, ion generation rates are low and high voltages are required to sustain the discharge. In between, at typically a few hundred to a thousand volts, the discharge is self-sustaining. This means that for each electron at the cathode, exp(αd) electrons reach the anode, and the net effect of the collisions is to produce a new electron at the cathode. Practically, however, in most sputtering discharges the Pd product is well to the left of the minimum value.

Figure 4-2 Paschen curves for a number of gases.

(From A. von Engel, Ionized Gases. Oxford University Press, Oxford, 1965. Reprinted with permission.)

4.2.3 TYPES AND STRUCTURES OF DISCHARGES

It is instructive to follow the progress of a glow discharge in a low-pressure gas using a high-impedance DC power supply (Ref. 2). In the regime just considered, known as the Townsend discharge, a tiny current flows initially due to the small number of charge carriers in the system. With charge multiplication, the current increases rapidly, but the voltage, limited by the output impedance of the power supply, remains constant. Eventually, when enough electrons produce sufficient ions to regenerate the same number of initial electrons, the discharge becomes self-sustaining. The gas begins to glow now and the voltage drops accompanied by a sharp rise in current. At this point normal glow occurs. Initially, ion bombardment of the cathode is not uniform but concentrated near the cathode edges or at other surface irregularities. As more power is applied, the bombardment increasingly spreads over the entire surface until a nearly uniform current density is achieved. A further increase in power results in both higher voltage and cathode current-density levels. The abnormal discharge regime has now been entered and this is the operative domain for sputtering and other discharge processes such as plasma etching.

At still higher currents, the cathode gets hotter. Now thermionic emission of electrons exceeds that of secondary-electron emission and low-voltage arcs propagate. Arcs have been defined (Ref. 3) as gas or vapor discharges where the cathode voltage drop is of the order of the minimum ionizing or excitation potential. Furthermore, the arc is a self-sustained discharge that supports high currents by providing its own mechanism for electron emission from negative or positive electrodes. A number of commercial PVD processes rely on arcs. This subject will therefore be deferred to the end of Chapter 5 so that the intervening treatment of plasma physics and processing can form the basis for a discussion of these arc-deposition methods.

Returning to the DC discharge we note that there is a progression of alternating dark and luminous regions between the cathode and anode, as shown in Fig. 4-3. Although the general structure of the discharge has been known for a long time the microscopic details of charge distributions, behavior, and interactions within these regions are not totally understood. The Aston dark space is very thin and contains both low energy electrons and high energy positive ions, each moving in opposite directions. Beyond it thecathode glow appears as a highly luminous layer that envelops and clings to the cathode. De-excitation of positive ions through neutralization is the probable mechanism of light emission here.

Figure 4-3 Structure of a DC glow discharge with corresponding potential, electric field, charge, and current distributions.

Next to appear is the important Crookes or cathode dark space where some electrons are energized to the point where they begin to impact-ionize neutrals; other lower energy electrons impact neutrals without ion production. Because there is relatively little ionization this region is dark. Most of the discharge voltage is dropped across the cathode dark space, also commonly referred to as the cathode sheath. The resulting electric field serves to accelerate ions toward their eventual collision with the cathode. Next in line is the negative glow. Here the visible emission is apparently due to interactions between assorted secondary electrons and neutrals with attendant excitation and de-excitation. Beyond lie the Faraday dark space, the positive column, and finally the anode. During sputtering the substrate is typically placed inside the negative glow before the Faraday dark space so that the latter as well as the positive column do not normally appear.

When a DC voltage V is applied between the anode and cathode the electric potential distribution, unlike the case for a simple vacuum capacitor, is highly nonlinear with distance x; similarly, the electric field is not constant. Furthermore, the deviations are most pronounced near the electrodes. These characteristics stem from the complex distribution of charge near electrodes and within the plasma, and the resultant currents they produce. After considering aspects of plasma physics contained in Section 4.3, some causes of these puzzling electrical responses may, hopefully, be clarified.

4.3.1 PLASMA SPECIES

Let us now consider the interior of the plasma, i.e., a partially ionized gas composed of respective densities of electrons (n_e), ions (n_i), and neutral gas species (n₀). Electrons and ions have more or less independent velocity distributions with electrons possessing far higher velocities than ions. The plasma is electrically neutral when averaged over all the particles contained within so that n_e = n_i = n. Collisions between neutral gas species essentially cause them to execute random Brownian motion. However, the applied electric field disrupts this haphazard motion because of ionization. If the density of charged particles is high enough compared with the dimensions of the plasma, significant coulombic interaction exists among particles. This interaction enables the charged species to flow in a fluid-like fashion that determines many of the plasma properties.

The degree of gas ionization (f_i) is defined by

     (4-5)

and typically has a magnitude of ∼ 10⁻⁴ in the glow discharges used in thin-film processing. Therefore, at pressures of ∼ 10 millitorr, Fig. 2-2 based on the ideal gas law indicates a gas density of n₀ ∼ 10¹⁴ cm⁻³; hence the electron and ion densities will be about 10¹⁰ cm⁻³ each at 25°C. In high density plasmas, f_i can reach 10⁻² and charge densities more than 10¹² cm⁻³.

4.3.2 PARTICLE ENERGIES AND TEMPERATURES

Measurements on glow discharges yield electron energies (E_e) that span the range 1 to 10 eVwith 2 eV being a typical average value for calculation purposes. The effective or characteristic temperature T associated with a given energy E is simply given by T = E/k_B, where k_B is the Boltzmann constant. Substituting E_e=2 eV, we find that electrons have an astoundingly high temperature T_e of some 23,000 K. However, because there are so few of them, their heat content is small and the chamber walls do not heat appreciably. Neutral gas atoms or molecules and ions are far less energetic; the former have energies of only 0.025 eV (or T₀ = 293 K) and the latter, energies of ∼ 0.04 eV (orT_i = 500 K). Ions have higher energies than neutrals because they acquire energy from theapplied electric field.

In addition, there may be excited species at temperature T_ex with energy E_ex. Neutral molecules may become excited by virtue of acquired energy that is partitioned into translational as well as internal vibrational and rotational modes of motion; for each of these modes there is a corresponding characteristic temperature. For example, in a nitrogen gas plasma at several torr, T_e may be over 12,000 K and T₀ due to molecular translation is ∼ 1000 K, while equivalent temperatures for vibrational (T_v) and rotational (T_ro) modes are ∼3800 K and 2800 K, respectively (Ref. 7). Higher plasma pressures tend to narrow this overall disparity in temperature.

Thermodynamic equilibrium in the system implies that all of the temperatures are equilibrated, i.e., T_e = T₀ = T_i = T_ex = T_r = T_w, where T_r and T_w are the radiation and chamber wall temperatures, respectively. Since this condition is never met in our low-pressure glow discharges, we speak of a nonequilibrium or cold plasma. Plasmas types are often differentiated on the basis of the electron energy and temperature. For example, T_e for glow discharges is greater than that for flames but considerably less than that for fusion plasmas.

4.3.3 MOTION OF PLASMA SPECIES: CURRENTS AND DIFFUSION

Since surfaces (e.g., targets, substrates) are immersed in the plasma, they are bombarded by the species present. Simple kinetic theory of gases helps us understand what happens. The neutral particle flux can be calculated from Eq. 2-8. Unlike neutrals however, charged particle impingement results in an effective electrical current density (j) given by the product of the particle flux () and the charge (q) transported, where the factor of reflects that fraction of the random motion that is directed at the planar surface. Therefore,

     (4-6)

where n and are the charged species concentration and mean velocity. To compare the behavior of different species we take (Eq. 2-3b). In the case of electrons, m_e = 9.1 × 10⁻²⁸ g, and if we assumeT_e = 23,000K,υ_e = 9.5 × 10₇ cm/s; similarly, for typical Ar ions υ_i = 5.2 × 10⁴ cm/s. Furthermore, if n_e = n_i = 10¹⁰/³, j_e ∼ 38 mA/cm² and j_i = 21μA/cm². The implication of this simple calculation is that an isolated surface within the plasma charges negatively initially because of the greater electron bombardment. Subsequently, additional electrons are repelled while positive ions are attracted. Therefore, the surface continues to charge negatively at a decreasing rate until the electron flux equals the ion flux and there is no net current.

We now consider the mobility (μ) of charged species in the presence of an applied electric field . The mobility is defined as the velocity per unit electric field or . Using Newton’s law,

     (4-7)

where q isthe species charge. The second term on the right reflects a kind of frictional drag particles experience during motion because of their collisions with other particles. When the particle collides, it essentially loses its directed motion. It is common to set [δυ/δt]_coll = υν, where ν is the collision frequency, a factor assumed for simplicity to be constant. In the steady state, dv/dt = 0 and . Typical mobilities for gaseous ions at 1 torr and 273 K range from ∼4 × 10² cm²/V-s (for Xe⁺) to 1.1 × 10⁴ cm²/V-s (for H⁺).

A second kinetic effect involving species motion in plasmas is diffusion, a phenomenon governed by Fick’s Law (Eq. 1-22). When migrating species move under the simultaneous influence of two driving forces, i.e., diffusion in a concentration gradient (dn/dx) and drift in the applied electric field, we may write for the respective electron and ion particle fluxes,

     (4-8)

     (4-9)

To maintain charge neutrality in the region under consideration it is assumed that J_e = J_i = J, and n_e = n_i = n. By equating Eqs. 4-8 and 4-9,

     (4-10)

Therefore, it is apparent that an electric field develops because the difference in electron and ion diffusivities produces a separation of charge. Physically, more electrons than ions tend to leave the plasma, establishing an electric field that hinders further electron loss but at the same time enhances ion motion. Because of the coupled electron and ion motions we can assign (see Exercise 2) an effective ambipolar diffusion coefficient D_a to describe the effect, i.e.,

     (4-11)

The magnitude of D_a lies somewhere between those ofD_i and D_e so that both ions and electrons diffuse faster than intrinsic ions do.

4.3.4 ELECTRON MOTION IN COMBINED ELECTRIC AND MAGNETIC FIELDS

4.3.4.1 Parallel Fields

Let us now examine what happens when a magnetic field of strength B is superimposed parallel to the electric field between the target and substrate. Charged particles within the dual field environment experience the well-known Lorentz force in addition to electric field force, i.e.,

     (4-12)

where q, m, and υ are the electron charge, mass, and velocity, respectively. First consider the case where B and are parallel as shown in Fig. 4-4a. Only electrons will be considered because as we have already seen, their dynamical behavior controls glow-discharge processes. When electrons are emitted exactly normal to the target surface or parallel to both B and , then υ × B vanishes; electrons are only influenced by the field and simply accelerate toward the anode, gaining kinetic energy in the process. If, however,, and the electron is launched with velocity υ at an angle θ with respect to the uniform B field between electrodes (Fig. 4-4b), it experiences a force qυBsinθ in a direction perpendicular to B. The electron now executes a circular motion whose radius r is determined by a balance of the centrifugal (m(υsinθ)²/r) and Lorentz forces involved, i.e.,

Figure 4-4 Effect of and B on electron motion. (a) Linear electron trajectory when . (b) Helical orbit of constant pitch when B ≠0, . (c) Helical orbit of variable pitch when . (d) Cycloidal electron motion on cathode when .

A spiral electron motion ensues and in corkscrew fashion the electron returns to the same radial position around the axis of the field lines. 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 and uniform and B fields is somewhat more complex (Fig. 4-4c). Helical motion with constant radius occurs, but because of electron acceleration in the field the pitch of the helix lengthens with time. Time-varying fields complicate matters further and electron spirals of variable radius can occur. Clearly magnetic fields prolong the electron residence time in the discharge and enhance the probability of ion collisions.

4.3.5 COLLECTIVE CHARGE EFFECTS

4.3.6 AC EFFECTS IN PLASMAS

It is instructive to analyze the kinetic behavior of electrons in an AC discharge in order to appreciate how plasmas are sustained. After all, it is not obvious that, in their to and fro motion in the field, electrons would absorb and gain sufficient energy to cause enhanced ionization of neutrals. Assuming no collisions with neutrals, the resultant harmonic motion of the electrons resembles the oscillations of a spring. Therefore we may write

     (4-19)

where x, m_e, and q are the electronic displacement, mass, and charge, respectively, and t is the time. Furthermore, the electric field is equal to sinωt, with and Ω the field amplitude and circular frequency, respectively. From this basic equation and its solution it is a simple matter to show that the maximum electron displacement amplitude x₀ and energy E₀ are given by

     (4-20)

and

     (4-21)

We may now estimate what field strength is required to ionize argon, whose ionization energy (E₀) is 15.7 eV. For the commonly employed radio frequency 13.56 MHz (ω = 2π × 13.56 × 10⁶Hz), is calculated to be 11.5 V/cm, an easily attainable field in typical plasma reactors. No power is absorbed in the collisionless harmonic motion of electrons, however. But when the electrons undergo inelastic collisions their motion is randomized and power is effectively absorbed from the RF source. Even smaller values of can produce ionization if, after electron–gas collisions, the reversal in electron velocity coincides with the changing electric-field direction. Through such effects RF discharges are more efficient than their DC counterparts in promoting ionization.

The question arises of how to generate AC discharges. Interestingly, provided the frequency is high enough, reactors can be built without interior plate electrodes as shown schematically in Fig. 4-5. For example, a coil wrapped around a tubular reactor can inductively couple power to the gas inside ionizing it. So, too, can capacitor plates on the outside; in such a case we speak of capacitive coupling. Such electrodeless reactors have been used for etching films. However, for the deposition of films by RF sputtering, internal cathode targets are required (Section 5.2.4).

Figure 4-5 Inductively and capacitively coupled tubular RF plasma reactors.

4.3.7 ELECTRODE SHEATHS

We have already seen that immersion of a floating electrode into a plasma causes it to charge negatively because of the disparity (in mass, velocity, and energy) between electrons and ions. As a consequence, in a glow discharge we can expect that both the anode and cathode surfaces will be at a negative floating potential (V_f) relative to the plasma potential (V_p). Of course, application of the large external negative potential alters the situation, but the voltage distribution in the DC glow discharge shown in Fig. 4-6 (also Fig. 4-3) can be qualitatively understood in these terms. In essence a Debye-like, positive space charge layer shields the negative surface; we now speak of a plasma sheath of potential V_s (V_s = V_p − V_f) that envelops the electrode and repels electrons. As noted earlier, the lower electron density in the sheath means less ionization and excitation of neutrals. Hence, there is less luminosity there than in the glow itself and the sheath appears dark. Large electric fields are restricted to the sheath regions. It is at the sheath–plasma interface that ions begin to accelerate on their way to the target during sputtering. The plasma itself is not at a potential intermediate between that of the electrodes but is typically some ∼ 15 volts positive with respect to the anode. In essence the chamber walls charge negatively by the same mechanism that the electrodes do, leaving the plasma at positive potential V_p.

Figure 4-6 Voltage distribution across DC glow discharge. Note cathode sheath is wider than anode sheath.

It is not difficult to quantitatively sketch the magnitude of the potential energy barrier q(V_p − V_f) electrons face in moving from the plasma to the cathode surface through the sheath. The number of electrons () that can gain enough energy to surmount this barrier is given by

     (4-22)

A Maxwell–Boltzmann-type expression of this kind is ubiquitous in describing the probability that a species will exceed a given energy barrier; thus, represents the fractional probability of success in acquiring the requisite energy. After accounting for the electrical flux balance between electrons and ions, the equation

     (4-23)

has been derived. Since m_i is 3–4 orders of magnitude higher than m_e, the sheath potential will be several times the electron temperature in eV, e.g., ∼ 10eV.

Ion current flow through the cathode sheath is an important issue because all thin-film processing in plasmas depends on it. In this regard the interesting question arises as to whether ion motion in the sheath occurs in a “free-fall,” collisionless manner, or through “mobility limited” motion involving repeated collisions with other gas species. Thus for voltage V applied across a sheath of thickness d_s, two different formulas govern the current density (j) through it, namely,

     (4-24)

and

     (4-25)

It turns out that Eq. 4-24, also known as the Child–Langmuir equation, better describes the measured cathode-current characteristics; this is certainly true at low pressures where few collisions are likely.

The sheath dark space is sometimes visible with the unaided eye and is therefore considerably larger than calculated Debye lengths of ∼ 100μm. This means that a large planar surface behaves differently from a point charge when both are immersed in plasmas. Instead of electrons shielding a point charge, bipolar diffusion of both electrons and ions is required to shield an electrode, and this physically broadens the sheath dimensions. A useful formula (Ref. 5) suggests that the relation between d_s and λ_D is

     (4-26)

where constant a ranges between at higher pressures and at lower pressures. Thus, d_s is typically tens of times larger than λ_D.

4.4.1 COLLISION PROCESSES

Collisions are either elastic or inelastic depending on whether the internal energy of the colliding species is preserved or not. In an elastic collision, exemplified by the billiard-ball analogy of elementary physics and depicted in Fig. 4-7a, only kinetic energy is exchanged; we speak of conservation of both momentum and translational kinetic energy. On the other hand the potential energy basically resides within the electronic structure of the colliding entities; increases in potential energy are manifested by ionization or other excitation processes. In an elastic collision no atomic excitation occurs and potential energy is conserved. This is why only kinetic energy is considered in the calculation. The well-known result for the elastic binary collision between a moving particle of mass M₁ and an initially stationary particle of mass M₂ is

Figure 4-7 Models of (a) elastic and (b) inelastic collisions between moving (1) and stationary (2) particles of masses M₁ and M₂, respectively.

     (4-27)

We assume collision occurs at an angle θ defined by the initial trajectory of M₁ and the line joining the mass centers at contact. The quantity 4 M₁M₂/(M₁+ M₂)², known as the energy transfer function γ, represents the ratio of the kinetic energy (E₂) acquired by M₂ relative to the kinetic energy (E₁) of M₁. When M₁=M₂, γ has a value of 1, i.e., after collision the moving projectile is brought to a halt and all of its energy is efficiently transferred to M₂, which speeds away. When, however,M₁ « M₂ reflecting, say, a collision between a moving electron and a stationary nitrogen molecule, then the energy transfer function is ∼ 4M₁/M₂ and has a typical value of ∼ 10⁻⁴. Very little kinetic energy is transferred in the elastic collision between the electron and nitrogen molecule. This same formula albeit with modification is incorporated in theories used to describe ion collisions with surface atoms that ultimately result in the ejection of atoms (sputtering).

Now consider inelastic collisions (Fig. 4-7b). The change in internal energy, ΔU, of the struck particle must now be accounted for under the condition requiring conservation of total energy. It is left as an exercise for the reader to demonstrate that the maximum fraction of kinetic energy transferred is given by (Ref. 4)

     (4-28)

where ν₁ is the initial velocity of particle 1. For the inelastic collision between an electron and nitrogen molecule, ΔU/[½M₁ν²₁] ∼ 1, when cos θ = 1. Therefore, in contrast to an elastic collision, virtually all of an electron’s kinetic energy can be transferred to the heavier species in the inelastic collision.

4.4.2 CROSS-SECTIONS

In Section 2.2.2 the collision diameter d_c was introduced in connection with mean free paths (λ_mfp) of colliding gas atoms or molecules in a reduced-pressure environment. The plasmas we will deal with have a sufficient number of gas-phase atoms, molecules, and ions so that collisions and reactions involving these species occur with some frequency. To quantitatively deal with these processes we first define the collision cross-section σ_c, a circular area of magnitude πd²_c, that reflects the probability of interaction or collision between particles (Refs. 4, 5). The larger σ_c is, the greater is the chance that other particles will encounter it. If the concentration of the gas species is n (number/cm³), then the preceding quantities are related by

     (4-29)

Although both λ_mfp and σ₀ characterize collisions, λ_mfp is usually reserved for elastic collisions. On the other hand σ_c has broader applicability because it characterizes inelastic collisions as well.

As an example of a collision process let us consider ionization of an inert noble gas atom due to electron impact. Ionization cross sections, σ_e, for such gases are plotted as a function of E in Fig. 4-8. Units of σ_e are in 8.88 × 10⁻¹⁷ cm², which corresponds to the circular area associated with the Bohr radius (a₀), i.e., a₀= 0.53 × 10⁻⁸ cm. The ionization energy thresh old(E_th) is the minimum energy required to eject the most weakly bound electron; typically, E_th is 15–20 eV. Because no ionization occurs for electrons impacting with energy (E) below E_th, the ionization cross section σ_e is zero. As E rises so does because a greater number of accessible electron levels means an increasingly greater ionization probability. A maximum is reached at E values of ∼ 100 eV, after which σ_e declines.

Figure 4-8 Total ionization cross sections for various gases plotted as a function of energy.

(From S. C. Brown, Basic Data of Plasma Physics, 2nd ed. MIT, Cambridge, MA, 1967. Reprinted with the permission of The MIT Press.)

In addition to ionization of atoms or molecules, inelastic collisions by electrons may also lead to internal vibrational and rotational excitation of these species with cross sections given by σ_v and σ_r, respectively (Refs. 4, 7). Attachment and dissociation reactions characterized by σ_a and σ_d may also occur. It is common to add the various σ to σ_e and define a total cross-section σ_T for the reaction process, i.e., σ_T = σ_e + σ_v + σ_r + σ_a + σ_d + ^{. .}. Each constituent cross section contributes its particular energy dependence so the overall variation of σ_T vs E is very complex. The overall value σ_T is applicable when describing plasma reactions in a macroscopic sense.

4.4.3 PLASMA CHEMISTRY

Thus far we have primarily considered inert-gas plasmas and physical interactions. Now we turn our attention to far more complex plasmas that contain multicomponent species in assorted activated states. These undergo the kinds of chemical reactions that occur in the plasma-enhanced etching and chemical vapor deposition processes discussed in Chapters 5 and 6, respectively. A brief summary of the rich diversity of inelastic collisions and reactions that occur in the gas phase is given in Table 4-1, where both generic examples and actual reactions are noted. In addition to electron collisions listed first, ion–neutral as well as excited or metastable ion–excited and excited atom–neutral collisions also occur. Evidence for these uncommon gas-phase species and reactions has accumulated through real-time monitoring of discharges by mass as well as light-emission spectroscopy. As a result, a remarkable picture of plasma chemistry has emerged. For example, a noble gas such as Ar when ionized loses an electron and resembles Cl electronically as well as chemically.

Table 4-1 Chemical Reactions in Plasmas

A. Electron collisions
Type	Generic reaction	Example reaction
Ionizatione	e− + A → A++2e−	e− + O → O++2e−
	e− + A2 → A+ + 2e−	e− + O2 → O+2 + 2e−
Recombinatione	e− + A+ → A	e− + O+ → O
Attachmente	e− + A → A−	e− + F → F−
	e− + AB → AB−
Excitatione
	e− + AB → (AB)* + e−
Dissociationec	e− + AB → A* + B* + e−
Dissociative	e− + AB → A + B+ + 2e−
ionization
Dissociative attachment	e−+ A2 → A+ + A− + e−	e− + N2 → N+ + N− + e−
attachment

Simple associations and comparisons with traditional gas-phase chemistry disguise the complexity of plasma reactions. Our first inclination may be to think that plasmas represent a tractable perturbation on traditional gas or gas–solid chemistry. But unlike the several hundred degrees K characteristic of ordinary or free atoms and molecules, electron temperatures are tens of thousands of kelvins. Under these conditions activated and charged atomic and molecular species and compounds are created. These participate in homogeneous gas-phase chemical reactions that are not driven thermally but rather by the energetics of the discharge; this means they occur by nonthermal and nonequilibrium processes. In addition, there are the plasma-modified gas-solid or heterogeneous reactions txo contend with. These possess their peculiar collection of active reactants, modified surfaces, and resultant metastable and stable products.

In conclusion, plasma reactions are not in equilibrium and react in complex ways that confound thermodynamic and kinetic descriptions of them.

4.4.4 CHEMICAL REACTION RATES

For convenience we have divided chemical reactions in plasmas into two categories, i.e., electron–atom (or–molecule) and molecule–molecule. Of the two, the latter reactions are perhaps more readily understood in terms of classical chemical reaction rate theory. Consider, for example, the bimolecular reaction, A + B → P (products). We may then write (Ref. 5)

     (4-30)

where concentrations of the involved species are denoted by n. Rate constant k_AB(T) is expected to be thermally activated, i.e.,k_AB(T) = k₀ exp − (E/k_BT), with k₀ and E characteristic constants of the reaction. Plasma-etching reactions have been analyzed (Ref. 8) employing these concepts and the Arrhenius dependence of the rate constant conclusively demonstrated (see Section 5.4.4).

Now consider electron collision reactions generically denoted by

For this case, ionization, excitation, attachment, etc., products form at a rate given by

     (4-31)

where k(e,T) in typical units of cm³/s is the rate constant. Unlike reactions characterized by Eq. 4-30 where the neutrals or ions are close to translational equilibrium, the electron energies are well above thermal equilibrium values. Because of this k(e,T) depends strongly on the electron energy (E_e) as well as the electron-energy distribution function f(E_e). Like the velocity probability distribution function of Eq. 2-1, it is common to apprxoximate the temperature dependence of f(E_e) = (1/n_e)dn_e/dE_e by a similar Maxwell–Boltzmann-like expression. But k(e,T) is also proportional to the particular collision cross section (σ_T(E)) and electron velocity (ν_e(E)) so that by integrating over the range of energies we obtain (Ref. 5)

     (4-32)

It is well beyond the scope of this book to continue much further except to note that rate constants for many plasma reactions have been theoretically estimated. In view of the complexities involved, values of k(e,T) so determined may illuminate trends but often have limited quantitative value. Suffice it to say that plasma generated reactions generally enhance chemical-vapor deposition and film etching processes. Thus gas-phase chemical reactions will usually occur more rapidly and at lower tempertatures with benefit of plasma assist.

4.5.1 AN INTRODUCTION TO ION–SURFACE INTERACTIONS

Aside from occasional references to plasma sheaths, this chapter has been almost totally concerned with events occurring within the plasma gas phase. However, films and surfaces immersed in plasmas or exposed to impinging ions are subjected to one or more of the interactions shown schematically in Fig. 4-9. Critical to the implementation of thin-film processing, characterization of resulting films, and modification of their properties is an understanding of such ion–surface interactions. This is a large subject and the following comments and distinctions may prove helpful in guiding the reader through our treatment of it.

Figure 4-9 Depiction of energetic-particle bombardment effects on surfaces and growing films.

(From Ref. 9.)

Figure 4-10 Particle-sticking probability as a function of energy. The dashed vertical line corresponds to room-temperature thermal energy.

(From S. R. Kasi, H. Kang, C. S. Sass, and J. W. Rabalais, Surface Science Reports 10, Nos. 1/2, p. 1 (1989). Reprinted with the permission of Elsevier Science Publishers and Professor J. W. Rabalais.)

In keeping with an earlier stated objective, the remainder of this chapter will focus on the scientific principles underlying ion–surface interaction phenomena as they relate to the deposition of thin films. We focus on sputtering in this section and conclude with film modification effects in Section 4.6. The practical benefits of ion bombardment during film growth as well as etching will be better appreciated in the context of plasma processing and the issues they raise; these subjects are therefore deferred to the next chapter.

4.5.2 SPUTTERING

4.5.2.2 Sputter Yields

When the ion impact establishes a train of collision events in the target, leading to the ejection of a matrix atom, we speak of sputtering. Since sputtering is the result of momentum transfer it has been aptly likened to “atomic pool” where the ion (cue ball) breaks up the close-packed rack of atoms (billiard balls), scattering some backward (toward the player). The sputter yield S is defined as

     (4-33)

and is a measure of the efficiency of sputtering. Experimental values of S ranging from 10⁻⁵ to as high as 10³ have been reported (Ref. 11). However, a narrower two orders of magnitude range in S from 10⁻¹ to 10 characterizes most practical sputtering processes. Three regimes of sputtering have been identified, and they are schematically depicted in Fig. 4-11; much has been written on all three of these, but we shall only consider the first two regimes here.

Figure 4-11 Three energy regimes of sputtering. (a) Single knock-on (low energy), (b) linear cascade, (c) spike (high energy).

(After P. Sigmund.)

4.5.2.2.1 Single Knock-On

In this case ion–surface collisions set target atoms in motion and may simply give rise to separate knock-on events. If enough energy is transferred to target atoms, they overcome forces that bind them and sputter. The threshold energy, E_th, is the minimum energy required to do this. Typical values for E_th range from 5 to 40 eV and depend on the nature of the incident ion, and on the mass and atomic number of the target atoms. Most important, however, is the binding energy of atoms to the surface (U_s), a quantity that appears in all theoretical estimates of E_th. Typically, U_s may be assumed to be the heat of sublimation or vaporization and ranges between 2 and 5 eV. A chronological summary of these estimates is given by Malherbe (Ref. 11) together with ranges of applicability. Two of the simplest approximations include E_th = 4U_s, for 0.08 < M₁/M₂ < 1, and E_th = U_s/γ, where γ, the energy transfer function, was defined earlier (Section 4.4.1). In the last expression γ essentially magnifies the value of U_s by accounting for the fraction of the ion energy transferred in the collision. Experimentally measured values for E_th are entered in Table 4-2 for a number of metals and semiconductors.

Table 4-2 Sputtering Yield Data for Metals (Atoms/Ion) and Semiconductors (Molecules/Ion)

4.5.2.2.2 Linear Collision Cascade

At higher ion energies, one or more so-called linear collision cascades are initiated. When this happens the density of recoils is sufficiently low so that most collisions involve one moving and one stationary particle, instead of two moving particles. The result of such processes is sputtering, i.e., the ejection of target atoms. Sputtering in the linear collision-cascade regime has been theoretically modeled by many investigators, but the theory due to Sigmund (Ref. 12) is the most widely accepted and used to describe this process. This theory views S as a product of two terms, namely,

     (4-34)

where the first term, denoted by Λ, is a materials constant. It reflects properties such as U_S, the range of displaced target atoms, and the number of recoil atoms that overcome the surface barrier of the solid and escape. The second term, F_D, accounts for the energy deposited at the surface and depends on type, energy, and incident angle of the ion, as well as on target parameters. In particular, the energy loss ions suffer through repeated nuclear collisions as they traverse the target is the key factor. Specifically, F_D = αNS_n(E), where S_n(E) is defined as the nuclear stopping power and NS_n(E) is the nuclear energy loss, (dE/dz)_n; furthermore, N is the atomic density of the solid, and α(M₂/M₁, θ) can range from 0.1 to 1.4 depending on mass ratio and angle of impact, but often assumes a value between 0.2 and 0.4. The Sigmund theory provides the specific dependence of S on E for both low and high energies. At low energy

     (4-35)

However, for energies above 1 keV, Λ = 0.042/NU_s(Å/eV) and therefore,

     (4-36)

As an exercise (Ref. 13), let us calculate S for argon incident on copper in the approximation that S_n(E) is independent of energy. For Cu, NS_n = 124 eV/Å and N=8.47 × 10⁻² atoms/Å⁻³, yielding S_n=1464 eV-Ų/atom. Further, assumingU_S = 3 eV and α = 0.25, substitution in Eq. 4-36, gives S = 5.1, a value that compares with the measured value of ∼2.6.

When the energy dependence of S is required, S_n(E) must be known and in one approximation it takes the form

     (4-37)

Here Z₁ and Z₂ are the atomic numbers of the projectile and target atoms, respectively, a is the effective radius (0.1 to 0.2 Å) over which nuclear charge is screened by electrons during the collision, q is the electronic charge, and is a reduced nuclearstopping cross section, whose values have been tabulated (Refs. 12, 14).

The sputter yields for a number of metals and semiconductors are entered in Table 4-2. Readers should be aware that there is much scatter in these determinations among different investigators. For the metals, values at two different energies (0.5 keV and 1.0 keV) as well as five different inert gases (He, Ne, Ar, Kr, and Xe) are listed. It is apparent that S values typically span a range from 0.01 to 4, and increase with the mass and energy of the sputtering gas. Data on the energy dependence of the sputter yield of Al by Ar, obtained by eight different investigators over a 20-year span, are plotted in Fig. 4-12. The roughly linear rise in S with E, the peaking at approximately 10 keV, and the subsequent decline at energies above 100 keV is typical for many metals and basically reflects the energy dependence of S_n(E).

Figure 4-12 Sputter-yield values for Al as a function of energy. Letters on the plot refer to data from the following investigators: A. Yonts, Normand, and Harrison (1960); B. Fert, Colombie, and Fagot (1961); C. Laegreid and Wehner (1961); D. Robinson and Southern (1967); E. Weijsenfeld (1967); F. Oechsner (1973); G. Braun, Emmoth, and Buchta (1976); H. Okajima (1981).

(From N. Matsunami, et al., AT. Data. Nucl. Data Tables 31,1 (1984). Reprinted with the permission of Academic Press, Inc.)

One of the recent attempts to model sputtering in the linear collision cascade regime is due to Mahon and Vantomme (Ref. 15). They considered S to be a product of three factors given by

     (4-38)

This expression reflects the respective energy, spatial, and directional distribution factors that characterize the sputtering process. The first term E/E_avg is the effective number of recoiling target atoms created per incident ion penetration, where E_avg is the average energy at the practical endpoint of the cascade. Factor R_e/R_p essentially represents the ratio of the range of recoiling atoms at the surface (R_e) to the range of the projectile ion (R_p) in the target; R_p is dependent on energy loss with distance. Finally, factor ¼ reflects the fraction of atoms close to the surface, possessing the requisite energy to escape, that are traveling in the right direction. Spatial averaging of ion emission obeying a cosine distribution law is used to obtain this value.

The theory was applied to aluminum and tungsten sputtered with E = 1 keV argon ions. Upon substitution of appropriate values for the factors in Eq. 4-38, a value of S = 1.34 was obtained for Al. Proceeding in this manner the calculated values of S as a function of E were obtained and plotted in Fig. 4-13. A comparison with measured sputter yields for Al (Fig. 4-12) generally reveals good agreement. Significantly, this simplified collisional model reproduces trends in experimental data for the projectile energy, mass, and target dependence of the sputter yield.

Figure 4-13 Calculated sputter yields for aluminum and tungsten as a function of projectile energy for argon.

(From J. E. Mahan and A. Vantomme, J. Vac. Sci. Technol. A15, 1976 (1997). Reprinted with the permission of Professor J. E. Mahan.)

4.5.2.3 Sputtering of Alloys

In contrast to the fractionation of alloy melts during evaporation, with subsequent loss of deposit stoichiometry, sputtering allows for the deposition of films having the same composition as the target source. This is a primary reason for the widespread use of sputtering to deposit metal alloy films. We note, however, that each alloy component evaporates with a different vapor pressure and sputters with a different yield. Why, then, is film stoichiometry maintained during sputtering and not during evaporation? One reason is the generally much greater disparity in vapor pressures compared to the difference in sputter yields under comparable deposition conditions. Secondly, and more significantly, melts homogenize readily because of rapid atomic diffusion and convection effects in the liquid phase; during sputtering, however, minimal solid-state diffusion enables the maintenance of the required altered target surface composition.

Consider now sputtering effects (Ref. 16) on a binary-alloy target surface containing a number of A atoms (n_A) and B atoms (n_B) such that the total number is n = n_A + n_B. The target concentrations are C_A = n_A/n and C_B = n_B/n, with sputter yields S_A and S_B. Initially, the ratio of the sputtered atom fluxes (ψ) is given by

     (4-39)

If n_g sputtering gas atoms impinge on the target, the total number of A and B atoms ejected are n_gC_AS_A and n_gC_BS_B, respectively. Therefore, the target surface concentration ratio is modified to

     (4-40)

instead of C_A/C_B. If S_A > S_B, the surface is enriched in B atoms, which now begin to sputter in greater profusion, i.e.,

     (4-41)

Progressive change in the target surface composition lowers the sputtered flux ratio to the point where it is equal to C_A/C_B, which is the same as the original target composition. Simultaneously, the target surface reaches the value, which is maintained thereafter. A steady-state transfer of atoms from the bulk target to the plasma ensues resulting in stoichiometric film deposition. This state of affairs persists until the target is consumed. Conditioning of the target by sputtering a few hundred layers is required to reach steady-state conditions. As an explicit example, consider the deposition of Permalloy films having the atomic ratio 80 Ni–20 Fe from a target of this same composition. Using 1 keV Ar, the sputter yields are S_Ni = 2.2 and S_Fe = 1.3. The target surface composition is altered in the steady state to C_Ni/C_Fe = 80(1.3)/20(2.2) = 2.36, which is equivalent to 70.2Ni and 29.8 Fe.

4.5.2.4 A Potpourri of Sputtering Results and Effects

Over the years a large number of interesting experimental observations have been made with regard to sputtering effects. The influence of sputtering gas and ion energy have already been discussed. Other phenomena and results are listed next in no particular order.

1. Effect of periodic table. Sputter yields were measured for metal elements in given rows of the periodic table using 400 eV Ar ions (Ref. 17). In the sequence Zr, Nb, Mo, Ru, Pd, and Ag, there was a continuous rise in S from ∼ 0.5 to about 2.7. Similar, although smaller, increases in S were observed for those elements lying in the row between Ti and Cu, as well as the row between Ta and Au. The well-known strong inverse variation between S and sublimation energy is apparent in these results. In a similar vein, the previously noted correlation between threshold energy (E_th) and sublimation energy (U_s) has been roughly verified for many metals, i.e.,E_th 5U_s.

2. Crystallographic effects. Studies of ion-bombarded single crystals reveal that atom emission reflects the lattice symmetry. In FCC metals it has been demonstrated that atoms are preferentially ejected along the [110] direction, but ejection in [100] and [111] directions also occurs to lesser extents (Ref. 18). For BCC metals [111] is the usual direction for atom ejection. These results are consistent with the idea that whenever a beam sees a low density of projected lattice points the ions penetrate more deeply, thus reducing S. Such observations on single crystals confirmed momentum transfer as the mechanism for atomic ejection; the notion of ion-induced melting and evaporation of atoms was dispelled because preferred directions for sublimation of atoms are not observed.

3. Energy distribution of sputtered atoms. Sputtered atoms have neither zero nor very high energies; instead the distribution peaks in between at typical energies 2 to 7 eV. The number distribution of sputtered atoms as a function of energy is reminiscent of the Boltzmann distribution for gas or evaporated particle energies whose peak magnitudes cluster about the much smaller thermal value of ∼ 0.1 eV.

4. Angular distribution of sputtered atoms. As is the case for evaporation, a cosine law distribution for the emission of sputtered atoms is generally observed (Ref. 18). Slight deviations from this law have been observed depending on ion energy, metal, and degree of crystallographic texture in the target. The emission lobe is generally extended (i.e., overcosine) normal to the target for high ion energies and compressed (i.e., undercosine) at low energies.

5. Angle of ion incidence. The entire discussion of sputtering until now has assumed that ion impingement is normal to the target surface. It has been observed, however, that the sputter yield (S(θ)) depends on the angle (θ) defined between the directions of ion incidence and the target normal. Furthermore, as shown in Fig. 4-14, S(θ) is enhanced relative to S(θ = 0) such that the ratio S(θ)/S(θ = 0) is found to vary as (cos θ)⁻¹ for values of θ up to ∼ 70° (Ref. 19). Physically, shallower collision cascades create a greater density of displaced surface atoms that can be potentially sputtered. However, the inverse cosθ dependence obviously fails at glancing angles approaching 90° because the number of ions penetrating the surface drops precipitously.

6. Sputtering of compound semiconductors. Most of the previous discussion applies to metals, and with the exception of item (2) earlier, refers largely to polycrystalline targets. Sputtering effects in compound semiconductors display similar features but there are interesting differences (Ref. 11). Based on emission patterns there is evidence that these normally single-crystal targets sputter preferentially along crystalline directions at elevated temperatures, but when the targets are cooled sputtering is isotropic. Apparently, at lower temperatures the ion bombardment and radiation damage create sufficient structural defects to amorphize surface layers. At higher temperatures, amorphous regions do not form because the defects anneal out; the target remains crystalline and sputters accordingly. A transition temperature separating these sputtering regimes has been suggested in GaAs. Wide variations in S may arise from deep ion penetration or channeling along certain crystallographic directions and a complex damage distribution as a function of ion energy and flux.

7. Sputtering of molecules. Sputtering is not limited to the world of inorganic materials. Very complex organic molecules have been ejected intact into the vapor phase when electronically excited by incident photons, electrons, and ions. The process has been called “electronic” sputtering (Ref. 20). For example, with fast heavy ions (∼1 MeV) bovine insulin molecules (C₂₅₄H₃₇₇N₆₅O₇₅S₆) were emitted from a solid sample and C⁶⁰ buckyballs were ejected from a (C₂H₂F₂)_n polymer. In the latter case it has been suggested that ion-beam interaction yields a highly ionized region 0.4 nm in diameter where molecules are formed. Surrounding this out to a 2-nm diameter, large intact ions are ejected. And large neutral molecules are sputtered within a 4-nm diameter. Beyond this out to a diameter of 10 nm there is impact damage.

Figure 4-14 Sputter-yield dependence of Ag, Ta, Ti, and Al on angle of incident 1.04 keV Ar.

(From H. Oechsner, Appl. Phys. 8, 195 (1975). Reprinted with the permission of Professor H. Oechsner.)

4.6 ION BOMBARDMENT MODIFICATION OF GROWING FILMS

4.6.3.1 Surface Topography Modification

In evaporative deposition processes the evolution of surface features on growing films is very much dependent on the substrate temperature and statistical fluctuations in the impinging particle flux and subsequent atomic surface diffusion. At high temperatures, diffusion is rapid, and a typically rough, hillocky film topography that is controlled by surface energy considerations emerges. Adatom diffusion is frozen at lower temperatures, however, and film surfaces are less rough. A smoothing of the surface is also observed under simultaneous ion bombardment, as comparisons between thermally evaporated and sputtered films typically reveal. This is particularly true for low-energy (1–10 eV) ions in a low pressure plasma. For ion bombardment at higher energy we may expect breakup of surface clusters upon impingement, a process that would tend to planarize deposits.

Film smoothing and improved coverage of depressions, corners, and steps are enhanced by resputtering. The phenomenon of resputtering occurs when energetic ions cause atoms in the film deposit to sputter. It is less tightly bound atoms at atomic projections and regions of high curvature that are particularly vulnerable to resputtering under angular ion impact. The involved atoms generally land nearby where they further energize atomic diffusion and promote planarization of the film surface.

While ion flux induced surface smoothing occurs during film growth, an interesting roughening of surface topography is observed under certain conditions. Ions of moderate energy, i.e., less than 1 keV on up to tens of keV, are necessary. Under ion bombardment various micron-sized surface-structures such as cones, pyramids, ridges, ledges, pits, and faceted planes form. Sometimes quasi liquid-like and microtextured labyrinth-like features also develop. An example of cone formation on a Cu single crystal after 40 keV Ar bombardment is shown in Fig. 4-15. The term “cone formation” is used to generically categorize this class of topological phenomena. Wehner (Ref. 24) and Banks (Ref. 25) have extensively reviewed aspects of ion-beam-induced surface topography and texturing effects, including materials systems that are susceptible, processing conditions, and theories for the observed effects. Known for a half-century, cone formation has been interpreted in terms of either left-standing or real-growth models. The former model views conical projection arising from sputter-resistant impurities or intentionally deposited seed atoms (e.g., Mo) that etch or sputter at a lower rate than the surrounding surface (e.g., Cu). Sputter-yield variations as a function of ion incidence angle, nonuniform redeposition of atoms on oblique cones, and surface-diffusion effects are operative in this mechanism. The latter model likewise requires the presence of impurity seed atoms. In this case, however, they serve as nucleating sites for growth of genuine single-crystal whiskers that sprout in all crystallographic directions relative to ion incidence. The subsequent interplay among whisker growth, surface diffusion, and sputtering results in the observed cones. Cone formation is likely to be more visible on impure sputtering targets than on depositing thin films. Nevertheless, crystallographic features may be etched into a film surface if strongly anisotropic sputtering occurs.

Figure 4-15 Pyramid structures on a single-crystal Cu surface after 40 keV Ar bombardment.

From J. L. Whitton, G. Carter, and M. J. Nobes, Radiation Effects 32, 129 (1977).

4.6.3.2 Crystallography and Texture

Changes in interplanar spacings and film orientations are among the effects in this category of structural modification. Distortions from cubic to tetragonal crystal structures also occur. Expansions in the (111) lattice spacing of close to 1% have been observed in several ion-bombarded metal films (Fig. 4-16a). Interestingly, with increasing ion energy the interplanar spacing sometimes peaks and then diminishes, suggesting that gas and associated defects are first incorporated, but then partially anneal out. Similar effects were reported in an extensive study by Kuratani et al. (Ref. 26) on ion beam assisted deposition of Cr under energetic Ar ion bombardment. By either increasing ion energies or the ratio of arriving Ar (ions) to Cr (atoms), the Cr lattice constant was found to increase from 0.28845 to 0.2910 nm. The observed film surface roughening at the maximum lattice constants is apparently due to the very large internal compressive stress levels generated and the microdestruction of the lattice as a result.

Figure 4-16 (a) Lattice distortion of Ni, Pd, Ag, and Cu films grown under Ar ion bombardment of indicated energy. (b) Grain size and dislocation density of Ag films deposited at room temperature as a function of the average energy per deposited atom. The average energy is the weighted sum over ions plus atoms. Film thickness is approximately the same in all cases.

(From Ref. 21.)

Films frequently display preferred orientation, or preponderance of certain planes lying parallel to the substrate plane, in the presence of ion bombardment. For example, in metal films grown on amorphous substrates, low-index, high atomic density planes, e.g., (111), (110), often lie parallel to the film surface. A better appreciation of why such preferred orientation develops in films will emerge with an understanding of ion-beam channeling effects, a subject discussed in Section 4.6.4.2.

4.6.3.3 Grain Structure

That the microstructure of thin films can vary widely is a theme that pervades the book, and in particular, Chapter 9. When observed in plan view, typical polycrystalline thin films (if there is such a thing) appear to be roughly equiaxed with considerable variation in grain size. In cross section such films have a tilted, voided columnar structure that reflects low atom mobility and the shadowing effects of previously deposited material. It is well documented that ion bombardment generally causes a reduction of film grain size. In bulk solids, it is also known that impurity atoms segregate to grain boundaries (GBs) and associate with matrix atoms and defects located there. Incorporated gas atoms and precipitates constitute such impurities in sputtered films. Since their presence effectively pins GBs, migration of the latter are prevented and small grains result. As Fig. 4-16b shows, the grain size of Ag falls as the average energy per depositing atom rises to 40 eV/atom, but then remains constant above this value. Apparently, some structural annealing occurs at the higher energies where there is more subsurface atom penetration.

A more revealing look at ion-beam modified grain structures is evident in Fig. 4-17. Shown is a sequence of Cr films exposed to successively greater Ar/Cr ratios while maintaining a 2-keV Ar beam energy. Regardless of ratio the film structure is columnar and the columns appear to grow at various angles. At low Ar/Cr ratios the columns are narrow and short, but they widen and lengthen at large Ar/Cr values where the structure is rough and contains voids between columns.

Figure 4-17 Cross-sectional scanning electron micrographs of electron beam evaporated Cr films bombarded by 2-keV Ar ions during deposition. TR(AR/Cr) values refer to the concentration ratio of the species transported to the film surface.

(From N. Kuratani, A. Ebe, and K. Ogata, J. Vac. Sci. Technol. A19(1), 153 (2001): 155. Reprinted by permission.)

4.6.4 ION IMPLANTATION

Ion implantation, an extremely important processing technique, is primarily used to modify or alter the subsurface structure and properties of previously deposited films. Since there is a large and accessible literature on its major use in doping semiconductors, this subject will not be treated here. Similarly, high-energy ion implantation has beneficially modified the surfaces of mechanically functional components such as dies and surgical prostheses (Ref. 28). Projectile ions impinging on such components that are not reflected or adsorbed, and do not cause sputtering, are implanted. At ion energies between tens and hundreds of keV, the probability is great that ions will be buried hundreds to thousands of angstroms deep beneath the surface.

Although such energies are normally beyond the range of common ion-assisted film-deposition processes (plasma-immersion ion-implantation (Section 5.5.6) is an exception), we may, nevertheless, profitably extrapolate ion-implantation phenomena to lower energy regimes. During implantation, ions lose energy chiefly through two mechanisms, namely electronic and nuclear interactions.

Through electronic and nuclear interactions the ion energy (E) continuously decreases in a very complicated way with distance (z) traversed beneath the surface. For simplicity, the energy loss is expressed by (see Section 4.5.2.2)

     (4-42)

where S_e(E) and S_n(E) are the respective electronic and nuclear stopping powers (in units of eV-cm²), and N is the target atom density. The magnitudes of both stopping powers depend on the atomic numbers and masses of the ions as well as matrix atoms. Typically, electronic stopping results in energy losses of 5–10eV/Å as opposed to the higher losses of 10–100eV/Å for nuclear stopping. When comparing these values with typical electronic and lattice energies in solids, film modification over many angstroms can be expected.

4.6.4.1 Subsurface Compositional Change

As a result of implantation it is clear that no two ions will execute identical trajectories but will, rather, participate in some admixture of nuclear and electronic collision events. Furthermore, the collective damage and zigzag motion of ions within the matrix cause them to deviate laterally from the surface entry point. When summed over the huge number of participating ions, these factors lead to the statistical distribution of ions as a function of depth (z) shown in Fig. 4-18. The concentration of implanted ions ideally has a Gaussian depth profile given by

Figure 4-18 Gaussian distribution of implanted ions as a function of depth beneath the surface.

     (4-43)

with a peak magnitude varying directly as the fluence or dose φ of incident ions. Dose has units of number (of ions) per cm² and is related to the measured time-integrated current or charge Q deposited per unit surface area A. Specifically,

     (4-44)

where n is the number of electronic charges, q, per ion. The projected range, R_p, is the depth most ions are likely to come to rest at yielding a peak concentration of

Note that the actual distance an ion travels is greater than the depth projected normal to the target surface. This is analogous to the total distance executed in atomic random-walk jumps exceeding the net diffusional displacement. Spread in the ion range is accounted for by the term ΔR_P, the standard deviation or longitudinal “straggle” of the distribution. Similarly, ΔR_L or the lateral ion straggle is a measure of the spread in the transverse direction.