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Mass Tranfer Model A. Mass Transfer Model Based on Experimental Measurements The following model is used to simulate SiH4/H2 discharges in a parallel plate reactor, including gas phase chemistry, mass-transfer and substrate-plasma interaction. Model Inputs: - the spatial profile of SiH4 primary dissociation, measured using Laser Induced Fluorescence measurements - the total SiH4 consumption measured using mass spectrometry Model Outputs: - the spatial distribution of radicals in the discharge - the flux of neutrals, ions, radicals towards the surface - the amorphous and microcrystalline silicon growth rate Model Formulation: The model uses the spatial distribution of the Laser Induced Fluorescence (LIF) intensity of SiH (X2Π) radicals and the total SiH4 consumption measured by mass spectrometry, in order to calculate the spatial distribution of the SiH4 electron impact dissociation rate. The distribution of the ground state SiH radicals over the interelectrode space, as measured using LIF, for different values of the applied voltage and in conditions of high dilution of SiH4 in H2 is presented in fig. 1.
Figure 1: Spatial LIF intensity distribution of SiH(X2Π) at four different peak to peak voltages (Vpp) in highly diluted SiH4 in H2 (1/150). The shape of the LIF profiles reflects the existence of the powered sheath as well as the less pronounced grounded sheath electron heating mechanisms, indicating an analogy of the spatial distribution of the LIF intensity to the distribution of the SiH4 electron induced dissociation rate.The shape of the LIF intensity distribution is determined by the mass balance of the SiH radical in the discharge and can be written
where Thus, the effective electron density for the SiH4 dissociation can be considered analogous to the LIF intensity and the rate of production of radicals at every point of the discharge space can be expressed as
where ke isthe SiH4 dissociation rate constant, ne(x) and I(x) are the electron density and the LIF intensity at point x in the discharge and ITOT the total LIF intensity. As
where kd is the product of the SiH4 dissociation rate constant and the average electron density. The term attributed to SiH4 consumption by electron impact dissociation WSiH4+e- together with the term concerning SiH4 consumption through secondary gas phase reactions Wsec are then introduced to the steady-state mass balance differential equation for the neutral species
where Dn is the diffusion coefficient of species n in the gas mixture calculated according to the Chapman-Enscog theory, u is the gas flow velocity and cn the concentration of species n. In the term Wsec are included the twenty-seven most important radical-molecule, ion-molecule and radical-radical reactions as well as the electron impact dissociation of Si2H6, Si3H8 and H2. The dissociation rates of these molecules have been calculated in accordance with SiH4 dissociation rate kd,by compensating the differences in the cross sections and the energy thresholds between these processes. The relations kd(H2)=0.08 kd(SiH4), kd(Si2H6)=2.5 kd(SiH4), kd(Si3H8)=3.5 kd(SiH4), kion(H2)=0.02 kd(SiH4) and kion(SiH4)=0.22 kd(SiH4) have been used to correlate these processes with SiH4 dissociation. Branching ratios have been adopted to express the different paths of SiH4 and Si2H6 electron induced dissociation, whereas for Si3H8 only one dissociation channel has been used. In the case of SiH4 the branching ratio of SiH4 ionization has been used (α=46%, β=36%, γ=11% and δ=7%,) , whereas the values (α1=0.91, β1=0.09) have been used for the Si2H6 dissociation channels. Ion density balance and ion chemistry are introduced in the simulation by applying the drift-diffusion approximation for the charged particles flux leading to the following modification of eq. (4):
where Di, μi are the diffusion and the mobility transport coefficient for ion i, E the effective electric field and Wionthe term accounting for the production and consumption of ion i in the discharge. For simplicity, only two kinds of ions have been included in the model (H2+ and SiH3+). The high and low field mobilities for these ions in the SiH4/H2 gas mixture are calculated according to the Langevin formulas. The diffusion coefficient Di are calculated using the Einstein relation Di= μikbTi/e, where Ti is the ion temperature that is assumed to be equal to the gas temperature. The spatial distribution of the electric field in the discharge, required for the solution of eq. (5), is also an input to the model and is always pre-calculated according to a method that is based on the electrical measurements as described in detail elsewhere. The boundary conditions required for the solution of eqs. (4) and (5) for the powered and grounded electrode are different for each specie, taking into account its probability to interact with the surfaces.Thus, for the neutral radicals (SixHy, H) the boundary condition proposed by Gallagher has been used Thus, for the neutral radicals (SixHy, H) the boundary condition proposed by Gallagher has been used
where cn is the radical concentration in a distance of one mean free path from the surface and un the radical thermal velocity. The loss probabilities βn of radicals on the surfaces, required in eq. (6), have been taken from literature. Thus, a value of β=0.5 has been used for Si2H2x+1 radicals and a value of β=0.7 for H atoms. Concerning SiH2 and H3SiSiH radicals we have followed the assumption of β=0.8 used by Perrin et al.,34 as no measurements of loss probabilities on a-Si:H and μc-Si:H surfaces are available. Disilene (H2SiSiH2)has been treated separately by assuming a lower value of β=0.4. Concerning positive ions, the ion flux towards the electrodes has been assumed to be governed by the ion drift motion in the high field powered and grounded sheaths. Thus, H2+ and SiH3+ ions in both powered and grounded electrode have to satisfy the conditions:
Namely, the density gradient of ions close to the electrodes has been set equal to zero, while the sum of the drift fluxes of both ions have to equalize the ion conduction current Ji that is calculated according to the Child-Langmuir law for collisional sheaths. Concerning the stable molecules (SiH4, H2, Si2H6 and Si3H8), which do not interact with the surfaces, and considering the production of these molecules through surface reactions, the boundary condition can be written as
where γj is the probability of radical j to recombine at the surface and produce molecule n, and βj is the total surface loss probability of radical j. The set of equations concerning the seventeen most important species was solved numerically for the entire interelectrode space using a fixed step centered finite difference scheme, whereas for the first and the last point (corresponding to the powered and the grounded electrode respectively) the boundary conditions have been solved by a forward and a backward finite difference scheme respectively. The procedure that is followed is that the value of the SiH4 dissociation rate kd is adjusted to the specific total SiH4 consumption as measured by mass spectrometry. Namely, the normalized LIF profiles are used to provide the correct shape of SiH4 dissociation in the discharge and the total SiH4 consumption to transform the normalized values into real SiH4 dissociation rate values. In addition an initial guess of the values of radical recombination probabilities γj is required in eq. (8). These recombination probabilities are not known and the most common assumption is that H, SiH3 and Si2H5 recombine only as H2, SiH4 and Si2H6 respectively. However, in the case of high deposition rates that require high radical fluxes, this assumption can lead to significant errors especially in the case of the SiH3 radical for which the relative probability to recombine as Si2H6 is enhanced, for fluxes above 1015 cm-2 s-1. Thus, in order to have a better estimation of the recombination probabilities γj required in eq. (6), surface kinetics have been treated more precisely by applying an analytical simulation of the film growth, similar to that reported by Guizot et al. Briefly, the evolution of the different surface sites due to radical-surface reactions and surface reconstruction have been taken into account and the chemical composition of the surface was evaluated by solving the balance equations for each surface site-type present:
Nine different surface sites have been considered. Namely: - dangling bond sites ºSio (θo), =SiHo(θ1) and –SiH2o(θ2) - H covered sites ºSiH(θ3), =SiH2(θ4) and -SiH3(θ5) and - SiH3 physisorpted sites ºSiHSiH3 (θ6), =SiH2SiH3(θ7) and –SiH3SiH3 (θ7) The surface and gas-surface reactions that have been taken into account in the balance equations together with the frequency, the activation energies and the probabilities of the processes are given in the database page. For the reactions between radicals and dangling bonds a unity probability has been considered, assuming no energy barrier for these processes. The same assumption was applied for the reactions of radicals with SiH3 in the physisorpted state, considering that surface acts as a third body that stabilizes the volatile products of these reactions. Surface reconstruction through Langmuir-Hinshelwood abstractions has been assumed to lead to silicon network formation rather than to the formation of dangling bond sites. The frequency and the activation energy of reconstruction between sites having a different number of bonded hydrogen atoms have been estimated from the average values of the reconstruction of similar sites. Having calculated the fraction of the different sites present on the surface, the sticking coefficient of SiH3 and the relative probability of H atoms, SiH3 and Si2H5 radicals to recombine as H2, SiH4, Si2H6, and Si3H8 can be evaluated. The system of the nine non-linear site balance equations is solved according to a modified Powel hybrid algorithm, using as input the radicals flux that result from the gas phase chemistry module with the initial guess of γj. The calculated new set of the values of γj is then returned to eq. (8) and the procedure is iterated until a convergence between the gas phase and the surface module is achieved. The main results of the combined gas-phase and surface models are the spatial concentration of each of the species in the discharge, the average value of SiH4 dissociation rate and the radical fluxes towards the powered and the deposition electrode. The deposition rate can be then calculated by summing the contribution of each of the radicals to the film growth, including silicon etching by H atoms
where p=2.26 gr/mol the mass density of μc-Si:H, m the molar mass assuming a hydrogen content of 5%, αn the number of silicon atoms in radical n, sn the sticking coefficient of radical n and γe/γΗ the ratio of the etching probability γe of a silicon atom by H atoms to the recombination probability γΗ to molecular H2. The rate constants of the gas phase reactions, the sticking probabilities and coefficients of radicals and the frequency of the surface properties that have been used in the model are summarized in the database page. The model has been applied for the investigation of the effect of the main SiH4/H2 discharge parameters (frequency, power, pressure, silane fraction in the mixture) on the microcrystalline silicon deposition rate. The most striking features are summarized below. B. Mass Transer Model Results The model has been applied to several cases for examining the effect of various discharge parameters as frequency, SiH4 partial pressure, total gas pressure and power, on the microcrystalline silicon deposition rate. A quite good agreement between experimentally measured and model predicted film growth rates, has been found for a wide range of conditions. Some of the experimental results and the model predictions are presented below: Frequency The influence of frequency in the range from 13.56 MHz to 50 MHz, on the properties of 2% silane in hydrogen 0.5 Torr discharges used for the deposition of microcrystalline silicon thin films, has been investigated. The experiments were carried out under constant power conditions 28 mW/cm2 and the mass transfer model has been applied for the investigation of the changes that are induced from the frequency variations, on the flux of radicals towards the growing surface and the deposition rate.
Figure 1 presents the radicals/ions fluxes towards the grounded electrode as predicted by the model. The flux of hydrogen atoms dominates by far silicon hydride and ion fluxes over the entire range of frequencies while it is almost tripled when increasing frequency from 13.56 MHz to 50 MHz. The enhancement of H2 dissociation to hydrogen atoms with frequency is reflected on the flux of hydrogen atoms, since under these conditions diffusion dominates the main reaction (H+SiH4) that can consume atomic hydrogen before reaching the surfaces. Concerning the flux of silicon hydrides, the increase of frequency leads to a continuous increase of all radicals reaching the surface. Silyl radical (SiH3) dominates over all other silicon containing species being ~2.5 times higher than silylene (SiH2) and about one order of magnitude higher than silicon oligomers (Si2H5, H2Si=SiH2 and H3SiSiH). This is due to the lower gas-phase reactivity of SiH3 compared to SiH2, whereas the production of Si2H5 and Si2H4 from secondary gas phase reactions is not favoured under the present conditions.
Figure 2 shows the experimental measured and the model predicted film growth rate at different driving frequencies. As shown in fig. 9, the model underestimates the deposition rate by ~25% due to the choice of a rather conservative set of sticking coefficients (database). In addition, the ion core model database that has been adopted for the branching ratio of SiH4 dissociation is most probably underestimating the production of highly sticking SiH2 radicals contributing also in the deviation of the calculated values of the deposition rate from the experimental ones. However, the model can very well reproduce the, experimentally measured, increase of about 50% between 13.56 MHz to 35 MHz and the tendency for constant film growth rate with a further increase. In fig.2, is presented also the contribution of the main radicals to the film growth. It is observed that despite the high SiH3 flux, the contribution of this radical to the calculated values of the deposition rate is only about 20%, while SiH2 contributes by more than 50%. This is a result of the quite different sticking probabilities (s) of these radicals (0.09 and 0.65 respectively). The above-mentioned increase of the hydrogen flux with frequency can also affect the sticking probability of the SiH3 radical by reducing its effective residence time in the physisorpted state.This will normally lead to a further reduction of the sticking coefficient and consequently the contribution of the radical in the film growth. Therefore, it appears that the increase of frequency will lead to an enhancement of the contribution of SiH2 to the film growth relative to SiH3.
Partial pressure The main reason for the low deposition rate of μc-Si:H is the extremely high dilution of SiH4 in H2 that induces a very low a low concentration of radicals in the discharge. Thus, the μc-Si:H growth rate for 2% SiH4 in H2 discharges at total pressures of 0.5 and 1Torr and extremely high power levels and silane depletion, leads to a deposition rate that cannot exceed 2Å /sec. On the other hand a large increase of the silane percentage can deteriorate the film crystallinity. Therefore, the effect of silane partial pressure (2%-6%) on the film growth rate has been investigated in order to avoid the undesirable transition to amorphous silicon. The driving frequency were 30 MHz, the total gas pressure 0.5 Torr and the power dissipation was maintainted constant at 48mW/cm2.The mass transfer model has been applied in these conditions and the results are shown in fig. 3 and 4.
Figure 3 presents the flux of radicals towards the grounded electrode as predicted by the model. The flux of hydrogen atoms dominates by far silicon hydride for all the silane partial pressures but decreases slightly with silane fraction. The consumption of H atoms in the gas phase through the H+SiH4 reaction that is favoured by the increase of SiH4, is responsible for this decrease. Concerning the flux of silicon hydrides, the increase of % SiH4 leads to a continuous increase of all radicals reaching the surface. Silyl radical (SiH3) dominates over all other silicon containing species being ~2.5 times higher than silylene (SiH2) and about one order of magnitude higher than silicon oligomers (Si2H5, Si2H4). This is due to the lower gas-phase reactivity of SiH3 compared to SiH2, whereas the production of Si2H5 and Si2H4 from secondary gas phase reactions is not favoured under the present low pressure conditions .
In fig. 4 is presented, the variation of deposition rate as a function of silane percentage, at conditions of constant power dissipation (48mW/cm2) in 30MHz, 0.5Torr SiH4/H2 discharges. It is observed that the film growth rate is almost doubled as the silane partial pressure increases from 10mTorr to 30mTorr. In addition, an excellent agreement between experimental values and model deposition rate predictions has been found. According to the model, the deposition rate, either for the low or for the high silane concentration, is determined from highly sticking at the surfaces-highly reactive in the gas phase radicals (SiH2, Si2H4). Contribution of radicals having low film incorporation probability (SiH3, Si2H5) increases as the fraction of silane in the gas mixture increases but in all the cases remains lower than 20% of the total deposition rate. The variation of the contribution of SixH2x+1 compared to the SixH2x radicals to the film growth as silane percentage increases, is related to their different gas-phase reactivity. SixH2x+1 have low gas-phase reactivity and thus the increase of silane concentration is expected to increase their production. In contrast SixH2x radicals undergo rather fast reactions with silane and thus the increase of silane concentration is expected to enhance their consumption, decreasing their relative contribution into film growth. This is also the reason that there is no simple one to one relation between the increase of silane concentration and deposition rate i.e. although silane concentration is tripled deposition rate is less than doubled.
"Deposition rate optimization in SiH4/H2 PECVD of hydrogenated microcrystalline silicon"
Low pressure vs high pressure - Power effect
The gas phase and surface models have been used to simulate also two rather different experimental conditions: (a) The low pressure-low silane concentration case of 0.5 Torr 2 % SiH4 in H2 discharges and (b) the high pressure-high SiH4 concentration case of 1 Torr 6 % SiH4 in H2 discharges. The frequency of 30 MHz has been used in all these experiments.
Figure 5: Variation of the SiH4 dissociation rate towards neutral radicals (z-axis) and of the % power deposition in this process (y-axis) as a function of the total power consumption at the condition of 2% SiH4 in H2 (-■-) and 6% SiH4 in H2 (-●-). The variation of the SiH4 electron induced dissociation rate kd with power as calculated from the simulation, is presented in fig. 6. The increase of the power density is followed by an enhancement of the SiH4 dissociation rate in both mixtures with kd being rather lower in the high-pressure case. It has been proved in a previous work of this group that the increase of power in pure SiH4 discharges results to an increase of the effective electron population for SiH4 dissociation whereas the increase of pressure has the opposite effect. This describes very well also the present experimental conditions of highly diluted SiH4 in H2 discharges, despite the rather different pressures and power levels.
Figure 6: Experimentally measured and model predicted film growth rate as a function of silane partial pressure for 30 MHz 0.5 Torr 2 % SiH4 in H2 discharges. The contribution of the main radicals to the film growth rate are also included.
Figure 7: Experimentally measured and model predicted film growth rate as a function of silane partial pressure for 30 MHz 1 Torr 6 % SiH4 in H2 discharges. The contribution of the main radicals to the film growth rate are also included. The differences between the two pressures as reflected in SiH4 dissociation rate, and the relative importance of secondary reactions are also reflected on the experimental measurements of the deposition rate presented in fig.6 (2 % SiH4 in H2) and fig.7 (6 % SiH4 in H2). The increase of power is followed by an increase of the deposition rate that in the case of 2 % SiH4 in H2 is limited to 1.6 Å/sec despite the rather high power density (168 mW/cm2). As in the case of SiH4 consumption, the effect of power on the deposition rate is much more pronounced in the 6 % SiH4 in H2 case reaching 7.4 Å/sec for a power density of 63 mW/cm2. The predictions of the deposition rate are also included in fig. 6,7 and a quite good agreement between model and experimental results can be observed. Bar columns in fig. 6, 7 represent the contribution of each of the radicals to the calculated values of the deposition rate. In the case of high dilution (fig.6), the contribution of SiH2 radicals dominates over the entire power range, being responsible for more than 50 % of the calculated deposition rate. The contribution of the low-sticking radicals (Si2H2x+1) is found to be in any case less than 25 % while the contribution of Si2H4 increases with power remaining however lower than 15 %. On the other hand, in the 6 % SiH4 in H2 case, the importance of SiH2 radicals is reduced to less than 25 % over the entire range of power. In this case, the contribution of Si2H2x+1 radicalsis enhanced to about 20 %-30 %, while Si2H4 radicals have been found to contribute by more than 45 %, being mainly responsible for the observed rather high values of the deposition rate.
Figure 8: Flux of the main radicals / ions / H atoms predicted by the model as a function of discharge power for 30 MHz 0.5 Torr 2 % SiH4 in H2 discharges. The different contribution of each of the radicals to the film growth between the two pressures can be understood by taking into account the changes of the composition of the radical flux reaching the growing surface, as predicted by the simulation. The fluxes of radicals, ions and H atoms are presented in fig.8 and 9 respectively as a function of the power consumed in the discharge for the 2 % SiH4 in H2 and 6 % SiH4 in H2 conditions. An increase of power is normally followed by an enhancement of the flux of all radicals and H atoms. However, this effect is stronger on H atom flux and this is related to the above-mentioned increase of both SiH4 and H2 dissociation rates. This is because two H atoms are produced per each H2 dissociative collision as well as from the SiH4+e- → SiH2+2H+e- dissociation path. In the high dilution case (fig.8), where the only path of H atoms consumption in the gas phase through the H+SiH4 reaction is not favored due to the low SiH4 density, H atoms flux is more than an order of magnitude higher than all the other species. In fact the H atoms diffusion length (Λ) in the case of 0.5 Torr 2 % SiH4 in H2 discharges is 2.5cm which is higher than the interelectrode gap (1.7 cm). Thus, hydrogen atoms produced in the discharge can easily reach the growing film surface. In the case of 1Torr 6% SiH4 in H2 (fig. 9), this diffusion length is only 0.6 cm resulting in a lower H atoms flux.
Figure 9: Flux of the main radicals / ions / H atoms predicted by the model as a function of discharge power for 30 MHz 1 Torr 6 % SiH4 in H2 discharges. Silyl (SiH3), due to its low gas phase reactivity, is the most abundant radical in the gas-phase and the main component of the radical flux to the surface in both cases. In the case of 1 Torr 6 % SiH4 in H2 the production of this radical is favored due to the enhancement of the H+SiH4 reaction and this results in a significantly higher SiH3 flux compared to the high dilution case. However, the low sticking coefficient of this radical does not allow for an analogous contribution to the film growth. To the contrary, silyl has a very important role in the increase of Si2H6 production through surfacedimerization. The flux of SiH2 radicals towards surfaces, for the 0.5 Torr 2 % SiH4 in H2 discharges (fig.8(a)), is enhanced due to the low SiH4 fraction in the gas mixture since the rather fast SiH2+SiH4 reaction database is not favored. The rate constant of the SiH2+H2 reaction is also rather low database leading to a diffusion length of 0.65 cm for the high dilution case. Thus, SiH2 radicals without participating in many gas phase reactions diffuse towards the deposition electrode and this, considering also the high SiH2 surface reactivity, leads to the very strong contribution of this radical to the film growth rate (~50 %). In the 1 Torr 6 % SiH4 in H2 discharges (fig.7), the consumption of SiH2 radical through the SiH2+SiH4 reaction becomes very important and the diffusion length of this radical falls under these conditions to 0.25 cm. Thus, the contribution of this radical to the film growth is limited in high pressure. The increase of power tends to enhance the flux of SiH2 radicals (fig.8(b)), as the depletion of silane at higher power levels prevents the consumption of SiH2. However, the enhancement of the flux of this radical remains low, leading to an analogous contribution of this radical to the film growth (< 25 %). In addition, the increase of the relative importance of the secondary gas phase reactions in the case of 6 % SiH4 in H2 gas mixture, results to an enhancement of the flux of higher radicals (Si2H5, Si2H4, fig.9). Concerning Si2H5 radicals, a low surface reactivity similar to that of the SiH3 radical has been assumed and thus its contribution to film growth is almost negligible. In contrast, Si2H4 have been considered as highly sticking radicals and are consequently easily incorporated into the film each offering two silicon atoms to the network. Thus, in this case Si2H4 appear to be the main film precursors contributing by more than 45 % to the film growth rate. More detailed analysis of the effect of discharge power under low and high pressure on microcrystalline silicon deposition process can be found in the following work: "Gas-phase and surface kinetics in Plasma Enhanced Chemical Vapor Deposition of microcrystalline silicon" E. Amanatides, S. Stamou, D. Mataras J. Appl. Phys. 90, 5786 (2001) © | ||
is the rate constant of the SiH+SiH4 reaction, 
where ne(x) the average electron density in the discharge, the previous expression can be written as
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