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The following model is used to simulate SiH
- the spatial profile of SiH - the total SiH
- the spatial distribution of radicals in the discharge - the flux of neutrals, ions, radicals towards the surface - the amorphous and microcrystalline silicon growth rate
The model uses the spatial distribution of the Laser Induced Fluorescence (LIF) intensity of SiH (X
Figure 1: Spatial LIF intensity distribution of SiH(X 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 SiH (1) where is the rate constant of the SiH+SiH Thus, the effective electron density for the SiH (2) where k As where n (3) where k The term attributed to SiH (4) where D In the term W 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): (5) where μ are the diffusion and the mobility transport coefficient for ion _{i}i, E the effective electric field and Wthe term accounting for the production and consumption of ion _{ion}i in the discharge. For simplicity, only two kinds of ions have been included in the model (H and _{2}^{+}SiH). The high and low field mobilities for these ions in the SiH_{3}^{+}_{4}/H_{2} gas mixture are calculated according to the Langevin formulas. The diffusion coefficient D are calculated using the Einstein relation _{i}D, where _{i}= μ_{i}k_{b}T_{i}/eT 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._{i}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 (Si Thus, for the neutral radicals (S (6) where u the radical thermal velocity. The loss probabilities _{n}β of radicals on the surfaces, required in eq. (6), have been taken from literature. Thus, a value of _{n}β=0.5 has been used for Si_{2}H_{2x+1 }radicals and a value of β=0.7 for H atoms. Concerning SiH_{2} and H_{3}SiSiH 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 (H_{2}SiSiH_{2})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, SiH ions in both powered and grounded electrode have to satisfy the conditions:_{3}^{+}
(7) 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 Concerning the stable molecules (SiH (8) where j to recombine at the surface and produce molecule n, and β is the total surface loss probability of radical _{j}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 SiH _{4} consumption as measured by mass spectrometry. Namely, the normalized LIF profiles are used to provide the correct shape of SiH_{4} dissociation in the discharge and the total SiH_{4} consumption to transform the normalized values into real SiH_{4} dissociation rate values.In addition an initial guess of the values of radical recombination probabilities _{3} and Si_{2}H_{5} recombine only as H_{2}, SiH_{4} and Si_{2}H_{6} 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 SiH_{3} radical for which the relative probability to recombine as Si_{2}H_{6} is enhanced, for fluxes above 10^{15 }cm^{-2 }s^{-1}. Thus, in order to have a better estimation of the recombination probabilities γ 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 _{j}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:(9) Nine different surface sites have been considered. Namely: - dangling bond sites ºSi ^{o}(θ) and –SiH_{1}_{2}^{o}(θ)_{2}- H covered sites ºSiH( _{2}(θ) and -SiH_{4}_{3}(θ) and_{5}- SiH _{2}SiH_{3}(θ) and –SiH_{7}_{3}SiH_{3 }(θ)_{7}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 SiH Having calculated the fraction of the different sites present on the surface, the sticking coefficient of SiH 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 γ is then returned to eq. (8) and the procedure is iterated until a convergence between the gas phase and the surface module is achieved._{j}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 SiH (10) where n, s the sticking coefficient of radical _{n}n and γ the ratio of the etching probability _{e}/γ_{Η}γ of a silicon atom by H atoms to the recombination probability _{e}γ to molecular H_{Η}_{2}.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 The model has been applied for the investigation of the effect of the main SiH
The model has been applied to several cases for examining the effect of various discharge parameters as 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:
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/cm
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 H
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
The main reason for the low deposition rate of μc-Si:H is the extremely high dilution of SiH
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+SiH
In fig. 4 is presented, the variation of deposition rate as a function of silane percentage, at conditions of constant power dissipation (48mW/cm
"Deposition rate optimization in SiH
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 % SiH
The variation of the SiH
The differences between the two pressures as reflected in SiH
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 % SiH SiH dissociation path. In the high dilution case (fig.8), where the only path of H atoms consumption in the gas phase through the H+SiH_{2}+2H+e^{-}_{4} reaction is not favored due to the low SiH_{4} 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 % SiH_{4} in H_{2} 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% SiH_{4} in H_{2} (fig. 9), this diffusion length is only 0.6 cm resulting in a lower H atoms flux.
Silyl (SiH The flux of SiH In addition, the increase of the relative importance of the secondary gas phase reactions in the case of 6 % SiH
"Gas-phase and surface kinetics in Plasma Enhanced Chemical Vapor Deposition of microcrystalline silicon" E. Amanatides, S. Stamou, D. Mataras
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