Surface processes during thin-film growth

Transcription

1 Plasma Sources Sci. Technol. 9 (2000) Printed in the UK PII: S (00) Surface processes during thin-film growth Achim von Keudell Max-Planck-Institut für Plasmaphysik, Boltzmannstrasse 2, Garching, Germany Received 1 October 1999 Abstract. The growth of thin films from low-temperature plasmas plays an important role in many applications such as optical or wear-resistant layers or for the fabrication of electronic devices. Albeit of great importance, the underlying growth mechanisms responsible for film formation from low-temperature plasmas are not well known. The direct identification of a growth mechanism is often hampered by the huge complexity of the bulk plasma processes and the plasma surface interaction. The distribution of impinging species is very diverse, and ions, radicals and neutrals are interacting simultaneously with the growing film surface. A macroscopic quantity such as the growth rate can be the result of possible synergisms and anti-synergisms among a large variety of growth precursors. Due to the broad range of plasma-deposited materials as well as deposition methods, the objective of this paper is not to review them all, but to present a basic overview on the elementary surface mechanisms of radicals and ions. On the basis of these surface reactions, typical growth models will be discussed. As an example, for surface processes during thin-film growth, the current deposition models for amorphous hydrogenated carbon and silicon films are presented. Introduction The growth of thin films from low-temperature plasmas is of great interest for many applications, such as optical coatings or wear-resistant protective layers [1 3]. In the semiconductor industry many process steps involve not only etching, but also thin-film growth processes, i.e. silicon oxide growth. In low-temperature plasmas, a precursor gas is ionized and dissociated, and radicals as well as ions impinging onto the substrate lead to film growth. This enables the preparation of films with superior material properties and allows access to a wide range of stoichiometric compositions and of microstructures. However, despite this great importance in many applications, the underlying growth mechanisms are poorly understood. This is due to the complexity of the growth process: the spectrum of species arriving at the surface can be very diverse, consisting of ions, radicals and neutrals as well as electrons and highenergy photons. All these species can contribute to film formation and synergistic or anti-synergistic effects among these precursors can dominate macroscopic parameters such as growth rate or film properties. In order to identify these growth mechanisms, individual interaction mechanisms can be studied in model experiments. The interaction of ions with growing films can be studied in detail theoretically as well as experimentally. For ion energies greater than 100 ev the theoretical predictions for physical sputtering, for example, agree very well with the corresponding ion beam experiments [4]. In some cases, however, chemical effects of the interaction of impinging ions with the growing film surface can become dominant in comparison to physical effects. The interaction of radicals with surfaces can be studied in particle beam experiments. With the exact knowledge of the surface structure and of the angular and energy distribution for the incoming and outgoing species, very detailed conclusions on the interaction mechanisms can be drawn. One example is the interaction of fluorine with silicon as the elementary step in silicon etching [5]. However, in many growth plasmas the dominant precursor for film growth are larger radicals such as SiH 3, Si 2 H 5, CH 3, etc. The preparation of a well defined particle beam of these species, which is essential for this type of study, can be difficult. Therefore, only little is known on the microscopic surface mechanisms of these precursors. The objective of this paper is to introduce the basic principles of the interaction of ions, neutrals and radicals with surfaces, which are necessary for the description and understanding of typical growth models; for more details on elementary surface mechanisms, the reader should refer to standard surface science literature [6]. Furthermore, surface reactions such as abstraction or surface recombination are described here. Based on these possible reaction mechanisms, typical growth models are discussed. Finally, as an example, the growth models for the formation of amorphous hydrogenated carbon and silicon films are presented. 1. Neutral surface interactions 1.1. Adsorption Neutral species or radicals impinging onto the growing film surface can adsorb at the surface according to their /00/ $ IOP Publishing Ltd 455

2 A von Keudell Figure 1. Schematic diagram of the chemisorption and physisorption potential above a surface. For details see text. sticking coefficient s and form an adsorbate. This sticking coefficient s describes the probability for the incoming particle to loose its kinetic energy via energy transfer to the atoms of the solid and to become trapped in a bound state at the surface. This bound surface state can be a physisorbed or chemisorbed state; in the physisorbed state the binding energy is typically below 0.5 ev. The binding force is promoted via dipole dipole interactions (van-der- Waals force). In the chemisorbed state the binding energy is typically above 0.5 ev and the adsorbed species forms a chemical bond (covalent or ionic) with the substrate. The physisorbed state can represent a precursor state for the chemisorbed state. This is illustrated in figure 1 for the adsorption of a molecule A 2 to form two adsorbed atoms A by the potential curves above the surface for the molecule A 2 (a) and the atom A (b). The difference in the potential energies for A and A 2 at large distances from the surface corresponds to one half of the dissociation energy E dissociation of molecule A 2. The adsorption of a molecule A 2 can be described as follows. A 2 approaches the surface at vacuum level. Upon collision with the surface atom, it transfers its kinetic energy to the solid and thereby reduces its potential energy and becomes trapped into the physisorbed state with a binding energy E physisorption. If the cross over of the potential curve for A (b) with the potential curve for A 2 (a) is below the vacuum level, the molecule A 2 can directly dissociate and go into the chemisorbed state with a binding energy E chemisorption as two atoms A. This is called dissociative chemisorption. If this cross over is above the vacuum level, as illustrated in figure 1, the molecule A 2 can only chemisorb if it can overcome an activation barrier E act. This can occur at higher substrate temperatures via thermal activation or if the kinetic energy of the impinging molecule A 2 is large enough. In many cases, the thermal energy at room temperature is sufficient for the desorption of the physisorbed molecule back into to the gas phase via thermal activation. As a consequence, the sticking coefficient for the chemisorption of molecules at room temperature is often very small. An existing activation barrier between the physisorbed and the chemisorbed state, however, can easily be overcome by a radical, since it has a higher potential energy at large distance from the surface (see figure 1). The radical, approaching the surface, converts its potential energy into kinetic energy in the potential well above the surface. However, this radical can only go into the chemisorbed state if it can transfer this kinetic energy to the target. This is more difficult compared to the adsorption of molecules in the physisorbed state, because a larger amount of kinetic energy must be lost to the surface atoms in order to become finally trapped in the chemisorbed state, as can be seen from figure 1. The sticking coefficient for radicals is, therefore, dominated by their ability to transfer sufficient kinetic energy to the surface atoms. This transferred energy is then dissipated by the atom of the solid via phonon excitation. The energy transfer from the impinging species to the surface atom can be roughly estimated on the basis of energy and momentum conservation in the binary collisions approximation. The maximum transferable energy T max yields: 4m 1 m 2 T max = E 0 (1) (m 1 + m 2 ) 2 where E 0 denotes the kinetic energy of the incoming species upon collision with the surface atom, m 1 the mass of the projectile and m 2 is the mass of the target atom. Equation (1) shows that for a light projectile impinging on a heavy target, the transferred energy is small. Thereby the incoming species may be unable to lose enough kinetic energy to become chemisorbed, which leads to a small sticking coefficient. A typical example is the low sticking coefficient for the adsorption of atomic hydrogen on many materials. It should be mentioned, that the potential curves, as shown in figure 1, are only simplified one-dimensional representations. In general, the adsorption is described by a reaction coordinate, which corresponds to a multidimensional pathway on the potential hyper-surface above the surface for the trajectory of the incoming species, approaching from the gas phase, into the chemisorbed state on the surface. Furthermore, the exact value for a sticking coefficient is governed by the dissipation of the transferred energy in a surface collision by the excitation of phonons in the solid. Thereby, the dependence of the sticking coefficient on the kinetic energy of the incoming particle is correlated to the phonon spectrum of the solid. The adsorption of species on a surface is described in terms of the surface coverage, which corresponds to the ratio of the occupied adsorption sites n ads at the surface to the total number of available adsorption sites n 0 : = n ads /n 0. (2) Sticking coefficients can be measured in a dosing experiment: a surface is exposed to a gas at a constant pressure, resulting in a constant surface collision rate. The dose is measured in Langmuir, which corresponds to the number of particles impinging onto a surface at a pressure of 10 6 mbar in 1 s. If the sticking coefficient would be unity, approximately one monolayer ( surface atoms cm 2 ) would be deposited at a dose of 1 Langmuir. After the dosing of the surface, the resulting surface coverage of the adsorbate is measured via thermal desorption spectroscopy or other surface analysis techniques. From a modelling of the coverage as a function of the dose, the sticking coefficient can be deduced. The sticking coefficient can also be measured by modulated beam experiments. A particle beam source 456

3 Surface processes during thin-film growth Figure 2. Modelling of the film deposition inside a cavity with a surface reaction probability β = 0.9 (a) and β = 0.1 (b). Species from the discharge enter the cavity via a slit. From [8]. is used, striking a surface under ultra-high vacuum conditions, and the reflected species are monitored via mass spectrometry. A modulation of the particle beam or the entrance of the mass spectrometer is necessary to separate the signals of the background gas from the signals of the directed beam component. In these experiments, the velocity distribution of the reflected particles can also be measured using time of flight methods. These types of measurements have been successfully used for the investigation of surface reactions of radicals such as F on silicon surfaces [5]. For many growth processes, however, the dominant precursors are larger molecules, such as CH x or SiH x radicals for the growth of amorphous hydrogenated carbon (a-c:h) or amorphous hydrogenated silicon (a-si:h) films. A particle beam source for these radicals is difficult to implement, and, therefore, only little experimental data exist on the surface reactions of these growth precursors. Since it is difficult to measure the sticking coefficients for typical growth precursors directly, the surface loss probabilities are often measured instead, using lowtemperature plasmas as particle source [7 12]. The surface loss probability corresponds to the sticking coefficient plus the probability for an incoming species to react at the surface to form a volatile non-reactive product. This surface loss probability β has been investigated in methane and silane discharges, by the measurement of the decay of CH 3, respectively SiH 3, radicals in the plasma afterglow by ionization threshold mass spectrometry. In a pulsed plasma, the decay time of the density of the reactive species after switching off the discharge depends on the efficiency of the chamber walls to act as a sink for these species: (i) if the surface loss probability is large, the species do not survive many wall collisions, leading to a decay time in the order of the travel time for the reactive species from the position of their formation in the plasma to the vessel walls; (ii) if the surface loss probability is small, the species survive many wall collisions and the decay time is governed by the pumping speed of the plasma vessel. A simple modelling of this decay yields β = 10 3 for CH 3 and β = 0.25 for SiH 3 [13]. Figure 3. Modelling and experimental results for the film deposition in a cavity exposed to methane (a) and acetylene (b) discharges. From [8]. The surface loss probability can also be measured by depositing films inside a cavity, which is exposed to a discharge [7 12]. Growth precursors, emanating from the discharge, enter this cavity via a slit or a hole and build up a layer inside. From the analysis of the layer thickness profile, the surface loss probability can be determined. If the surface loss probability is high, films are only deposited in a close proximity to the entrance of the cavity, since the species cannot survive many wall collisions. If the surface loss probability is small, the species will survive many wall collisions and the deposition profile inside the cavity becomes uniform. The variation of the film thickness inside the cavity can be modelled by Monte Carlo simulations, which follow the reflections of the incoming growth precursors among the walls inside the cavity. Typical results for a cavity with a slit as the entrance geometry are shown in figure 2 for β = 0.9 and β = 0.1. It can be seen that for a high β (figure 2(a)), deposition is observed predominately on the side opposite the entrance slit, corresponding to the position of the first wall collision of the incoming species. For a small β (figure 2(b)), a uniform deposition is observed on all walls inside the cavity. If the absolute flux of growth precursors to the surface is known, the sticking coefficient can be calculated from the absolute film thickness; or, on the other hand, if the probability to form a non-reactive volatile product is known, the sticking coefficient can directly be deduced from the surface loss probability. As an example for the application of this technique, the deposition inside a cavity exposed to a hydrocarbon discharge is discussed in the following [7, 8]. Figure 3 shows the measured and modelled deposition profiles for a cavity exposed to an electron cyclotron resonance plasma from methane figure 3(a) and acetylene figure 3(b). This cavity is placed in a remote position with respect to the 457

4 A von Keudell magnetic field lines. Since the ion trajectories are confined to the magnetic field lines and the perpendicular transport is small, the influence of the ion bombardment on the deposition inside the cavity is greatly reduced and becomes negligible. The comparison with the theoretical model yields, for the deposition profile in a methane discharge, β = 0.65 ± 0.15 and in an acetylene discharge β = 0.92 ± In a methane discharge, the dominant contribution in the radical flux towards the surface consists of CH 3 radicals [14]. However, as mentioned above, the surface loss probability β for CH 3 radicals is of the order of Thereby, the neutral growth precursor responsible for film formation inside the cavity in the methane discharge cannot be the CH 3 radical. In an acetylene discharge the dominant radical should be the C 2 H radical. Therefore, one assumes that the surface loss probability of β = 0.92 corresponds to the surface reaction of C 2 H. In a methane discharge, however, larger hydrocarbon molecules are formed in the gas phase via molecule molecule or ion molecule reactions as identified by mass spectrometry [15]. These C 2 H x species in the methane discharge can efficiently contribute to growth, which is able to explain the high β value of 0.65 as measured in the experiment Surface reactions Reactive species, impinging onto a surface can react at the surface to form new species, which desorb. Two phenomenological types of reactions can be distinguished. In an Eley Rideal reaction, the incoming species A from the gas phase does not thermally equilibrate upon adsorption at the surface, but reacts directly with a surface atom B to form a new molecule AB, which desorbs. The occurrence of an Eley Rideal mechanism can be identified by several criteria. (i) The reaction obeys first-order kinetics since it is directly proportional to the flux of the incoming species A. (ii) The impinging species are not in thermal equilibrium with the surface, which leads to the hyperthermal kinetic energy of the desorbing products AB. (iii) Eley Rideal type mechanisms have often a small cross section, since the incoming species have to directly break a chemical bond at the surface to form a volatile product on the time scale of a molecular vibration ( s). In addition, this process can also be sterically hindered, resulting in a small cross section for this reaction. (iv) The reaction rate changes, when using isotopes of the reactants A or B. A good example is the abstraction of surface-bonded hydrogen/deuterium by incoming atomic hydrogen/deuterium via an Eley Rideal mechanism: the abstraction rate should be smaller in the case of D abstraction due to incoming H atoms ((i): H + D-surface H D + surface) compared to H abstraction due to incoming D atoms ((ii): D + H-surface D H + surface). In the case of an incoming D atom, the transition state (D + H-surface D H-surface) moves significantly towards the surface, due to momentum conservation. In the case of an incoming H atom, the transition state (H + D-surface H D-surface) moves only slightly towards the surface. As a consequence the interaction time for reaction (i) is smaller than for reaction (ii), resulting in a smaller cross section. The rate of an Eley Rideal reaction with cross section σ reaction for the interaction of impinging species A with flux j A with adsorbed species B with a coverage B can be written as reaction rate j A B σ reaction. (3) A typical example for this type of reaction is the abstraction of hydrogen due to incoming atomic hydrogen from amorphous hydrogenated carbon film surfaces [16]. The cross section is 0.05 Å 2, which can be compared to the typical area of a surface site of about 7 Å 2, yielding a reaction probability of for H abstraction by atomic hydrogen from a-c:h surfaces. An incoming species A can also adsorb at the surface and thermalize prior to reacting with another adsorbed species B to form the molecule AB, which desorbs. This is called a Langmuir Hinshelwood type reaction. The occurrence of such a reaction is indicated by several criteria. (i) The reaction obeys second-order kinetics and is proportional to the coverage of species A and B. (ii) The incoming species A thermalize at the surface, which leads to a kinetic energy of the desorbing molecules AB corresponding to the substrate temperature. (iii) The cross section for this reaction is large, since both species A and B react in their adsorbed states, leading to a much longer interaction time compared to an Eley Rideal type reaction. (iv) The reaction rate is insensitive to the use of isotopes for reactants A and B, since the species react in thermal equilibrium with the surface and any initial momentum of reactant A is lost during its thermalization with the surface. The rate of a Langmuir Hinshelwood reaction with cross section σ reaction for the reaction of impinging species A leading to a coverage A with adsorbed species B with a coverage B at a surface with a total number of adsorption sites n 0, can be written as: reaction rate A B σ reaction n 0. (4) In summary, the reaction rate for the adsorption of neutral growth precursors on surfaces can be estimated on the basis of the following. (i) Neutral, stable precursors in many cases have to overcome an activation barrier to transfer from the physisorbed into the chemisorbed state. Often, this activation barrier cannot be overcome by thermal activation at room temperature. However, since the potential well of the physisorbed state is shallow compared to the thermal energy at typical substrate temperatures (around room temperature), the adsorbed precursor desorbs thermally activated. As a result, stable neutral precursors are mainly reflected and their sticking coefficient is usually small. (ii) Radicalic growth precursors have a high potential energy at large distances above the surface, corresponding to the half of the dissociation energy, necessary for the formation of the radical. Upon approaching the surface the radical converts its potential energy into kinetic energy, which has to be released via energy transfer to the atoms of the solid upon impact, in order to become trapped in the chemisorbed state. This energy transfer depends on the masses of the solid target atoms and the impinging species: a heavy incoming particle can transfer more energy to a target atom compared to a light 458

5 Surface processes during thin-film growth incoming particle. As a result, the sticking coefficient increases with the mass of the incoming radical. (iii) The cross section for the direct reaction of an incoming radical with an adsorbed surface atom is usually small and depends on the type of isotope for the reactants. The cross section for the reaction of an incoming particle which adsorbs and thermalizes prior to reacting with another adsorbed particle is in general much larger. The energy distribution of the desorbing species is correlated to the kinetic energy of the incoming species plus the reaction enthalpy in the first case and is correlated to the surface temperature in the latter. These guidelines can only represent a rule of thumb for the estimation of sticking coefficients. In many systems not all of these criteria are fulfilled, since the probability for adsorption depends in detail on the multi-dimensional potential hyper-surface above the surface as well as on the angle and energy distribution of the impinging species. 2. Ion surface interactions In low-temperature plasmas, the precursor gas is dissociated and ionized, leading to a flux of ions and radicals towards the surface. The impinging ion flux can contribute to growth by the direct incorporation of the ions and by the modification of the surface. This modification can be, for example, the creation of adsorption sites for incoming neutral and radicalic growth precursors. The ion bombardment can also lead to sputtering and thereby to a reduction of the growth rate. Besides these effects on the growth rate, the ion bombardment can also govern the resulting film properties, since the stoichiometry as well as the binding structure of the growing film is modified due to the displacement of atoms inside the solid by penetrating ions. The influence of ion bombardment on thin-film growth will be discussed in the following. For further details the reader should refer to [4]. The kinetic energy of impinging ions in a lowtemperature plasma is determined by the voltage drop of the plasma sheath in front of the surface. In the case of low plasma pressures (<1 Pa), this sheath can, in general, be considered collisionless and the impinging ions have a kinetic energy corresponding to the sheath voltage plus the plasma potential. If the substrates are placed on the driven electrode of a dc discharge at low pressure, the average kinetic energy corresponds to the dc voltage plus the plasma potential. In the case of an rf discharge at low pressure, the kinetic energy corresponds to the dc self-bias plus the plasma potential. However, with decreasing rf frequency, the ions are able to follow the rf modulation, resulting in a broader distribution of the kinetic energy up to the dc self-bias plus the applied rf peak voltage. In the case of high pressure (>10 Pa), the ion energy distribution is also modified by collisions and charge exchange reactions in the sheath, leading to a very broad distribution of the kinetic energy of the impinging particles. It should be kept in mind that the collision and charge exchange reactions in the sheath produce fast neutrals, which also bombard the surface, where they lead to almost identical reactions as ions with the same energy. Incoming ions are neutralized upon approaching the surface and transfer their kinetic energy to the target atoms of the solid. This energy loss occurs due to nuclear and electronic stopping. The nuclear stopping of the projectile occurs due to momentum and energy transfer in collisions with the target atoms. In the binary collision approximation, which is a good approximation for ion energy of a few tens of electronvolts, the transferred energy in a single collision is determined by the masses of the collision partners m 1 and m 2, the kinetic energy of the impinging particle E 0 and scattering angle ϑ of the target atom in the laboratory system. The energy, transferred to the target atom yields, in the laboratory system [4], m 1 m 2 T = E 0 (m 1 + m 2 ) (cos ϑ f 2 sin 2 ϑ) 2 (5) 2 f 2 = (v 1 /v 1) 2 with v 1 and v 1 are, respectively, the velocities of the projectile before and after the collision in the centre of mass system. The maximum energy is transferred for a scattering angle of ϑ = π, corresponding to f = 1, and equation (5) reduces to equation (1). The nuclear stopping is the dominant loss mechanism for typical ion energies in thin-film growth processes (approximately several hundred electronvolts). The cross section for the scattering of a projectile with mass m 1, charge Z 1 and velocity v 0 at the Coulomb potential of the target atoms with mass m 2 and charge Z 2 is described by the Rutherford scattering formula. The differential cross section dσ for the scattering in a solid angle d is given in the centre of mass system with a scattering angle ϑ by ( dσ d = b2 sin ϑ ) 4 with b = Z 1Z 2 e πε 0 E E = 1 m 1 m 2 2 v2 0 (6) (m 1 + m 2 ) with e the electron charge and ε 0 the dielectric constant. In general, the Coulomb potential is screened by the electrons of the solid, which leads to a modified scattering formula. The differential cross section for scattering at the Coulomb potential is large for small scattering angles and approximately proportional to 1/E 2. Consequently, the cross section for large-angle scattering decreases with E, which implies a smaller energy transfer in a collision at high projectile energies. The electronic stopping occurs due to the electronic excitation along the ion trajectory in the solid. This electronic energy loss can be estimated by the Bethe-Bloch formula and is for low ion velocities (less than several kiloelectronvolts) proportional to the velocity of the projectile in the solid and independent of the projectile mass. In most deposition plasmas the typical ion energy is small and, therefore, the electronic energy loss is not considered in the following. A quantitative comparison of the energy losses for different projectile ions in a-c:h films can be found in [36]. The consecutive collisions of an impinging particle leads to a collision cascade in the solid. During this collision cascade, the projectile loses its energy, according to the 459

6 A von Keudell energy transfer, which is determined by the kinetic energy of the projectile and the scattering angle in equation (5). In every collision, energy is transferred to the target atoms. If this transferred energy is above the threshold for displacement, the target atom is released from its network site. If this displaced atom cannot recombine with the created empty network site it remains as an interstitial in the solid, leading to the formation of a Frenkel pair (defect and interstitial). If this target atom, however, is at the surface and the transferred energy is above the surface binding energy, the target atom can leave the solid, leading to physical sputtering. This surface binding energy E SB is of the order of the sublimation energy of the solid. The threshold for physical sputtering can roughly be estimated by the assumption that an incoming particle with mass m 1 has to inverse its momentum and to transfer its kinetic energy to a target atom with mass m 2. This gives the threshold for physical sputtering for light projectiles on heavy targets, i.e. [17] E threshold = E SB 1 γ(1 γ) with γ = 4m 1m 2 (m 1 + m 2 ) 2. (7) The ion bombardment of a solid can be modelled by the computer code TRIM ( transport of ions in matter ) [4], which is based on the modelling of the trajectory of the projectile in the solid as consecutive binary collisions between a projectile and target atoms. For the scattering potentials, screened Coulomb potentials are used and the surface binding energies are tabulated for many materials. This surface binding energy represents an adjustable parameter for the TRIM code and is determined from the comparison of modelling results with the corresponding ion beam experiments. It is generally claimed that the TRIM code is only valid for high ion energies (>100 ev). However, since the necessary energy transfer to a surface atom in a collision cascade for physical sputtering is in the range of a few electronvolts, the TRIM code has to be able to model the trajectory of the projectile in the solid accurately down to this kinetic energy. The good agreement between the TRIM modelling and the measured sputtering yields justifies this conclusion. As a consequence, the modelling by the TRIM code should also be valid for low projectile energies, down to about 10 ev. The only limitation in comparison of the TRIM results with experimental data, however, is the fact that sputtering yields, in particular, for low-energy ions can be dominated by chemical effects. As an example, the theoretical yields for the physical sputtering and the experimental yields for the interaction of hydrogen-, deuterium-, helium- and carbon-ions with graphite are shown in figure 4 [18]. It can be seen that the sputtering yields for graphite increase with increasing projectile mass from H to C, according to the improved energy transfer (equation (5)). The threshold for the physical sputtering of graphite decreases with increasing projectile mass from H to C. Furthermore, the sputtering yield decreases at higher projectile energies. This can be explained as follows: ions impinging onto the surface lose their kinetic energy only via electronic energy loss or small-angle scattering in the near surface layers. The large-angle scattering occurs only in deeper layers of the target, when the kinetic energy of the projectiles is small due to nuclear and electronic stopping Figure 4. Modelling results for physical sputtering (full curves) and experimental results (full and open points) for the interaction of hydrogen-, deuterium-, helium- and carbon-ions with graphite. From [18]. on the way from the surface into the solid. This largeangle scattering implies a large energy transfer to the target atoms, leading to their displacement. These displaced target atoms, however, are created in deeper layers in the solid and not directly at the surface. As a consequence, the total sputtering yield is small for high projectile energies. Finally, figure 4 shows that no threshold for sputtering is observed for the sputtering of carbon by H + and D + ions. This can be explained by the fact that at low ion energies, chemical effects become dominant, leading to the chemical sputtering of the target, which cannot be modelled by the TRIM code. At high energies, however, the chemical effects are of minor importance and the sputtering can be very well described by the TRIM modelling. Ion bombardment during thin-film growth from lowtemperature plasmas plays a dominant role for many applications. (i) Physical sputtering by ion bombardment is used in deposition systems where sputtering of solid targets in an argon plasma is used to produce volatile growth precursors. These sputtered precursors can then produce thin films on a substrate which is placed in front of the sputter target. A typical example is the preparation of thin metallic films. In reactive magnetron sputtering (RMS), a reactive gas is added to the argon discharge. As an example, TiN films are prepared from a titanium sputter target by adding N 2 to the argon discharge. For details see [19 21]. (ii) In most growth processes, the sputtering of the growing film surface itself is not desired, since it reduces the effective growth rate or may deteriorate the quality of the material due to the formation of defects at the surface or in the bulk. For example, the production of device quality a-si:h films requires the prevention of any bombardment with highenergy particles, since the ion-induced defects otherwise act as recombination centres for the electron transport in the material. Consequently, the substrates for a-si:h film growth are placed on the grounded electrode of a rf discharge reactor [2]. (iii) For the preparation of amorphous hydrogenated carbon films, however, ion bombardment is essential 460

7 Surface processes during thin-film growth to produce dense films with superior material qualities. This is explained by the subplantation model [22, 23]. Ions with kinetic energies above about 90 ev have a penetration range of a few angstroms, leading to their subplantation beneath the first monolayers. Due to the incorporation of carbon atoms at interstitial network sites, compressive stress evolves, which favours the formation of a dense sp 3 -hybridized network. By depositing films from mono-energetic carbon ions, amorphous sp 3 -coordinated carbon films can be prepared with a density and hardness close to that of diamond. (iv) Ion bombardment creates defects at the growing film surface due to sputtering or displacement of surface atoms. These open bonds can act as adsorption sites for incoming radicals. This leads to ion radical synergism, since the effective sticking coefficient for radicals is enhanced by the ion bombardment. This ion radical synergism for the adsorption of CH 3 radicals on amorphous hydrogenated carbon film surfaces has been proposed in a number of growth models for a-c:h film growth [30, 32, 35]. A nice confirmation of this ion radical synergism was found by Shiratani et al [13]. They measured the decay time of CH 3 radicals in the afterglow of a methane rf discharge using ionization threshold mass spectrometry. It was observed that the decay of CH 3 radicals after switching off the rf CH 4 discharge is characterized by two time constants corresponding to the two surface loss probabilities of 10 2 and This was explained by the fact that immediately after stopping the discharge, the ion bombardment disappears on the time scale of the confinement time for the ions in the discharge (approximately microseconds). The radicals, however, have a much longer confinement time. Immediately after the disappearance of the ions, only radicals are therefore present in the afterglow. The ion bombardment during plasma exposure creates dangling bonds at the surface. At these dangling bonds, the radicals, present in the afterglow, can adsorb more easily than at an undisturbed surface, leading to an enhanced surface reaction probability of Since no ion bombardment is present in the afterglow, these chemisorption sites are consumed by the adsorption of the radicals. After the complete saturation of all the dangling bonds, a surface loss probability of 10 3 is measured, corresponding to the reactivity of CH 3 with a hydrogen saturated surface. A similar example for the occurrence of ion neutral synergisms exist for the etching of silicon in CF 4 discharges [5]. The influence of the ion bombardment on thin-film growth is summarized as follows. (i) An impinging ion leads to defects at the growing film surface due to the displacement or sputtering of target atoms. This displacement depends on the energy transfer in a collision and, thereby, on the masses of the projectile and target atoms. A large displacement yield is obtained, if the mass of the projectile matches the mass of the target atoms. (ii) The threshold for physical sputtering depends on the surface binding energy of the solid. Part of the momentum of the incoming ion has to be reversed by collisions in order to transfer kinetic energy to a surface atom that is directed away from the surface. This surface atom might then be able to overcome the surface binding energy and to be released from the solid. (iii) With the increasing kinetic energy of the projectile, the impinging species penetrate deeper into the solid and nuclear stopping becomes only dominant at the end of the range. As a consequence, the maximum of the energy transfer and therefore the maximum number of displacements occurs further inside the solid. (iv) The ion-induced formation of defects at the film surface can create adsorption sites for incoming radicals. This leads to ion radical synergisms during film growth. These are only qualitative arguments and many of these effects can be quantified by computer codes like TRIM. However, for low ion energies or complex molecular ions, molecular dynamic simulations of the ion solid interactions are the appropriate approach. Molecular dynamic calculations, however, are at present limited to small model systems and short time scales (approximately picoseconds), which is much too short for typical time scales of thin-film growth (seconds to minutes). 3. Growth models In the following, we will discuss several growth models, which combine the microscopic surface reactions of neutrals, radicals and ions at the growing film surface in order to explain the macroscopic growth rate Growth via direct adsorption The growth of thin films is often described by rate equations for the adsorption of species from the gas phase or the plasma. Rate equations are set up for each adsorbed species. The simplest case is the adsorption of species from the gas phase directly at the surface. The growth rate, expressed in chemisorbed atoms per area and time gives growth rate j species σ adsorption n 0. (8) Here the growth rate is proportional to the flux of growth precursors j species towards the surface multiplied by the cross section for chemisorption σ adsorption multiplied by the total number of adsorption sites n 0. A typical example is the growth of thin metallic films using magnetron discharges, as mentioned above. The dependence on the substrate temperature is only weak, since the sticking coefficient for metal atoms is very high due to their strong chemisorption potential. In some cases, the chemisorption sites might be consumed by the adsorption of growth precursors. This can be included by introducing the coverage of adsorption sites and the probability to chemisorb at an unoccupied adsorption site p 0. The total probability for chemisorption then gives p = p 0 (1 ). (9) The macroscopic growth rate might also be diminished due to a simultaneous chemical etching by reactive species impinging onto the growing film surface or due to physical 461

8 A von Keudell sputtering by ion bombardment. Both effects can simply be incorporated by etch rate = j etchant σ etching n 0 and sputtering rate = j ions Y(E) (10) with j etchant describing the flux of reactive etching precursors, σ etching the cross section for etching, j ions the ion flux towards the surface with energy E and Y(E) the energy-dependent sputtering yield Growth via an adsorbed layer If a precursor state is involved prior to chemisorption, an adsorbed layer model for film growth is used. Species, impinging onto the growing film surface, adsorb into a weakly-adsorbed state. In this surface state, they might be able to diffuse on the surface and to find an open bond at the surface at which they chemisorb. On the other hand, they can return to the gas phase via thermal desorption. The residence time τ in the weakly-adsorbed state is described by the Frenkel equation [6] ( τ = τ 0 exp E ) act. (11) kt Here τ 0 describes the smallest possible residence time in the weakly-adsorbed state and corresponds to the inverse of the vibrational frequency of the surface bond, which is of the order of s. E act is the activation energy for the thermal desorption, k is the Boltzmann constant, T is the substrate temperature. The adsorbed layer model can be expressed by rate equations. The density of precursors n ads in the weakly-adsorbed state is given by dn ads dt = jσ ads n 0 (1 ) n 0 τ. (12) The growth precursors with a flux j adsorb into the weaklyadsorbed state at an empty site with a cross section σ ads. The total number of surface sites is n 0. The coverage in the weakly-adsorbed state corresponds to = n ads /n 0. The term n 0 /τ defines the temperature-dependent desorption rate of weakly-adsorbed species. These precursors can be transformed into the chemisorbed state with a time constant τ chemisorption. The growth rate yields, therefore, n 0 growth rate = (13) τ chemisorption and equation (12) modifies to dn ads dt = jσ ads n 0 (1 ) n 0 τ n 0 τ chemisorption. (14) This model yields a temperature-dependent growth rate: if the substrate temperature increases, the rate of thermal desorption from the weakly-adsorbed state increases (see equations (11) and (12)) leading to a decrease of. Consequently, the growth rate decreases, because it is directly proportional to the coverage in the weakly-adsorbed state. This is typical for epitaxial growth of crystalline silicon [24]. Figure 5. Variation of the probability for adsorption via an intermediate hot-precursor state. κ 1 describes the number of surface sites and precursor samples prior to chemisorption. For details see text. The growth precursors adsorb on terraces on the surface and diffuse to surface steps, where they are trapped, promoting film growth. At a high surface temperature, the thermal desorption becomes too rapid, compared with the time the precursors need to reach the chemisorption sites at these surface steps via surface diffusion. As a consequence, the growth rate decreases with increasing substrate temperature. Further surface reactions, such as the etching of the growing film as well as the etching of the weakly-adsorbed state, can be described in a similar way to equation (10) Growth via a hot-precursor state Impinging species, adsorbing into a weakly-adsorbed state, may not be able to thermalize with the surface upon impact, but diffuse on the surface as hot precursors [25]. This has several consequences for the interpretation of the macroscopic growth rate. The surface diffusion in the hotprecursor state can be incorporated into the adsorbed layer growth model in the following way. A growth precursor adsorbs into the hot-precursors state at position 1. This growth precursor can chemisorb with a probability p a at an empty chemisorption site, it can desorb as thermally activated with probability p b, or it can diffuse to a neighbouring surface site with a probability p c. The probabilities at surface site 1 depending on the coverage,, of occupied chemisorption sites give [25] p a1 = (1 )p a p b1 = p b p c1 = 1 p a1 p b1. (15) The probability for chemisorption after the species have diffused to a neighbouring site 2 is p a2 = p c1 (1 )p a = (1 p a1 p b )(1 )p a = (1 (1 )p a p b )(1 )p a. (16) This leads to an iteration. The total probability for chemisorption is given by p( ) = p 0 (1+ 1 κ ) 1 with κ = p b p a + p b (17) 462

9 Surface processes during thin-film growth with p 0 the probability for an incoming species to chemisorb on the surface for = 0. The inverse of parameter κ corresponds to the average number of surface sites the precursor samples prior to chemisorption. A small κ corresponds to a large number of surface sites, which are sampled prior to chemisorption and thereby to fast surface diffusion and vice versa. Ifκ is equal to one, the probability of equation (17) reduces to p( ) = p 0 (1 ). This case describes the simple surface site limited adsorption, as introduced by (9). The dependence of p( ) on the parameter κ is shown in figure 5. It can be seen that for small values of κ, p remains large even at a high occupation of chemisorption sites. This indicates that the total probability to chemisorb is not significantly lowered due to the consumption of surface sites, since the growth precursors are still able to find an open site at the surface via fast surface diffusion. Only if the mean distance between unoccupied surface sites drops significantly at larger coverages, the total probability to find an unoccupied chemisorption decreases. A typical example for adsorption via a hot-precursor state is the adsorption of atomic hydrogen on the hydrogen-terminated silicon surface [26 29]. Summarizing, the macroscopic growth rate can be described by several growth models on the basis of microscopic surface mechanisms. Examples of growth models and the underlying microscopic growth mechanisms are discussed in the next section. 4. Examples 4.1. Growth of a-c:h films The growth of a-c:h films is investigated for a large variety of deposition plasmas and preparation methods. One fundamental observation is the fact that with increasing substrate temperature, the growth rate decreases. According to the growth models, as introduced above, it has been assumed that the growth of these films occurs via a weaklyadsorbed precursor state in order to account for the universal temperature dependence of the deposition rate [30 35]. Furthermore, it has been assumed that the dominant growth precursor is the CH 3 radical, since it contributes predominantly to the impinging radical flux towards the surface [14]. It is known that the sticking coefficient of these radicals on hydrogen-terminated surfaces is in the range of 10 3 in the absence of any ion bombardment [13]. In order to explain a significant growth rate by adsorption of CH 3 radicals, open bonds at the surface have to be present, which can act as chemisorption sites for incoming CH 3 radicals. These open bonds can be created by the additional ion bombardment during growth [30, 35, 36]. Thereby, CH 3 radicals at first adsorb in a weakly-adsorbed state and reside on the surface until they desorb via thermal activation or chemisorb at a dangling bond produced by impinging ions. The corresponding adsorbed layer model yields a growth rate, which decreases with increasing substrate temperature due to the decreasing coverage of weakly-adsorbed CH 3 growth precursors. At higher substrate temperatures, growth occurs only due to the incorporation of ions. The rate equations for the weakly-adsorbed state and the growth rate Figure 6. Hydrogen content and growth rate for films deposited at various substrate temperatures from a methane discharge at the floating potential. From [32]. are dn ads dt = χ CH3 j CH3 (1 ) n 0 τ n 0j ions σ cross linking (18) growth rate = n 0 j ions σ cross linking + j ions (19) with j CH3 and j ion being the flux of CH 3 radicals and ions towards the surface, n 0 is the total number of adsorption sites, χ CH3 is the probability for adsorption of CH 3 into the weaklyadsorbed state, σ cross linking is the cross section for the creation of dangling bonds due to the ion bombardment followed by the chemisorption of the weakly-adsorbed precursors and τ is the residence time in the weakly-adsorbed state. This model was compared to the measurement of the growth rate in an ECR plasma from methane [32], which is shown in figure 6: at low substrate temperatures the growth rate decreases, due to the decreasing coverage of CH 3 growth precursors, and remains constant at higher substrate temperatures due to the temperature-independent incorporation of ions. In low-temperature plasmas from methane, however, atomic hydrogen is produced via dissociation of the hydrocarbon source gas. This atomic hydrogen leads to the etching of the hydrocarbon films, which depends on the substrate temperature and the microstructure of the films [31]. From a direct comparison of the temperature-dependent etching of films in hydrogen plasmas with the temperaturedependent deposition of films in methane plasmas in the very same experimental set-up, it was concluded that the temperature dependence of the growth rate is not due to a temperature-dependent deposition process, but due to a temperature-dependent erosion process [31]. This is illustrated in figure 7. It can be seen that the functional behaviour of the etch rate is identical to the functional behaviour of the deposition rate. Based on this result, the adsorbed layer model was rejected as the underlying mechanism for the explanation of the temperature-dependent growth rate. A new model 463

10 A von Keudell Figure 7. Comparison of the temperature-dependent deposition from methane at the floating potential with the temperature-dependent erosion of a polymer-like C:H film from a hydrogen plasma. From [31]. is formulated, which describes the macroscopic deposition rate as the temperature-independent, constant growth rate minus a temperature-dependent etch rate. However, if one assumes that etching leads simply to an exponential decrease of the growth rate for increasing substrate temperature, the experimental data as shown in figure 6 cannot be explained: the thermally-activated re-etching of the growing film would lead to no film deposition at higher substrate temperatures, which is in contradiction to the constant growth rate at high substrate temperatures as shown in figure 6. This contradiction can be resolved by investigating the re-etching by atomic hydrogen in more detail. It was mentioned above that the etch rate not only depends on the substrate temperature, but also on the film structure. For polymer-like films, characterized by a hydrogen content of 50%, the etch rate is much larger than for hard carbon films, characterized by a hydrogen content of typically 30% [31]. The transition from a polymer-like film structure to a hard film structure can be caused by enhanced ion bombardment [37], which displaces the bonded hydrogen in the film and thereby reduces its hydrogen content, or it can be caused by the thermal release of larger hydrocarbon molecules, which reduces significantly the hydrogen content. This transition occurs at a temperature of about 550 K, which is indicated by the dramatic decrease in the hydrogen content, as shown in figure 6. This abrupt change in film properties is able to explain the dependence of the deposition rate on the substrate temperature: a constant growth rate is diminished by the temperature- and materialdependent re-etching due to atomic hydrogen. Above 550 K, the structural change in the material leads to a film, which is more resistant against the temperature-activated re-etching by atomic hydrogen. Thereby the growth rate of amorphous hydrogen has to be reformulated as growth rate = j ions + j radicals f(dangling bonds) j H f(film structure) (20) f(dangling bonds) denotes the functional behaviour of the ion-induced creation of defects at the film surface as chemisorption sites for the incoming radicalic growth precursors. This functional behaviour is predominantly dependent on the ion energy and independent of the substrate temperature. f(t substrate, film structure) denotes the functional behaviour of the etch rate on the substrate temperature and the film structure. In this model the rate of carbon incorporation is independent of the substrate temperature and is solely determined by the fluxes of radicals and ions as well as by the ability of the ions to create defects as adsorption sites for the incoming neutral growth precursors. The temperature dependence of the growth rate is solely caused by the re-etching by atomic hydrogen, depending on the flux of atomic hydrogen towards the surface and the material properties. The example of a-c:h film growth illustrates the fact that good agreement between the model and the measured macroscopic deposition rates can be misleading. With a more detailed knowledge of the underlying microscopic mechanisms, in this case the hydrogen re-etching, a more sound growth model can be formulated Growth of a-si:h films A-Si:H films are used in electronic applications such as solar cells or flat panel displays [2, 38]. These applications require a low defect density of the material. This is achieved by the incorporation of hydrogen in the growing film which efficiently saturates the open bonds in the material. Any ion bombardment would deteriorate the film quality, since the displacement of silicon or hydrogen atoms in the growing film leads to open bonds, which act as recombination centres for electron transport in the final device. The a-si:h films are, therefore, usually deposited on the grounded electrode of a rf silane discharge, in order to limit the kinetic energy of the impinging ions to the plasma potential. The dominant growth precursors in low-temperature plasmas from silane are SiH 3 radicals, if the depletion of the feed gas is in the range of 10% [39 42]. The formation of SiH 3 in the gas phase is well understood and follows at typical plasma pressures of several pascals the following reaction scheme: (i) the SiH 4 source gas is dissociated due to electron impact to form SiH 2 and two H atoms; (ii) SiH 2 reacts with SiH 4 to form Si 2 H 6, which dissociates again to form SiH 3 ; (iii) atomic hydrogen, created by the dissociation of SiH 4, also reacts with SiH 4 to form SiH 3 and H 2. The surface loss probability of SiH 3 radicals on a:si H films has been measured by several authors with various techniques to be β = 0.25 [9 12]. This surface loss probability is also independent of the substrate temperature. The growth rate is temperature independent up to 350 C, corresponding to a sticking coefficient of s = 0.1 and increases by a factor of 2.5 above this temperature, corresponding to a sticking coefficient of s = 0.25 [10]. It is believed that the growth of a-si:h films is due to the adsorption of SiH 3 radicals at dangling bonds on the surface. This can explain the increase of the growth rate at 350 C: below 350 C, the surface of the a-si:h film is hydrogen terminated and incoming atomic hydrogen or SiH 3 radicals 464