A kinetic Monte Carlo Model of Silicon CVD Growth from a Mixed H 2 /siH 4 Gas Source
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Reaction SiH4 (g) + 2- -- SiH 3 + H 4 2H
H 2 (g) + 2-
SilH3 ±-_> -SiH 2 + H 2S l2 -- 2S___i + 2H2 (g) 2H -- H 2 (g)
)
k (s
1.0 x 101 3 1.0 x 1013
5.5 x 1015
Ea(eV) -
1.00 1.40 2.51
Table 1: Reactions and their rate coefficients for silicon (001) growth[5][6], - represents a silicon dangling bond site and (g) a gas species. The evaluation of the adsorption reaction rates is discussed in the text.
configuration dependent sticking coefficient for species i and F, is the incident particle flux. The sticking coefficient depends on the density of clean silicon dimers, Ndb, through, SRi = Ndb
ki exp(-
E( ICBTW
where Tw is the substrate (wafer) temperature. The activation energies for H2 and Sill4 adsorption are taken to be 17.3 and 3 kcal/mole respectively [4, 7]. The pre-exponential factor ki is fitted to yield sticking coefficients on a clean surface at 673K of 2 x 10 6 for molecular hydrogen and 2.5 x 10-4 for silane [4]. Incident fluxes to the surface for each gas species, Fi, are evaluated using the kinetic theory of gases expression [8],
F-
(2) N/2rmmkBTv,
where Pi and mi are the partial pressure and molecular mass of species i respectively. The validity of this expression is demonstrated in Table 2 where the kinetic theory fluxes are comn)ared to those derived from computational fluid dynamics simulations of a custom low pressure reactor. Details of the CFD calculations, which are particularly valuable for studying transient effects during complex growth procedures, will be reported in a later publication [9]. Wafer Temp. (K) 723.0 823.0 1123.0
Sill4 Flux 0.375 (0.381) 0.345 (0.350) 0.311 (0.316)
H2 1.073 0.988 0.905
Flux (1.070) (0.983) (0.903)
Table 2: Comparison of incident silane and hydrogen fluxes (in units of 10' 9 molecules/cm 2 /s) evaluated using the kinetic theory of gases (Equation 2) and from computational fluid dynamics (CFD) calculations. The CFD results are given in brackets. In both calculations the flow rates into the reactor were 376 scem H2 and 52.5 scem SiH 4. A single reaction is chosen randomly at each time step from the constructed table but weighted according to the rate of each reaction. The time clock of the simulation is then incremented, following the N-fold Way Monte Carlo approach [10], by an amount 6t = ln(r)/W where r is a random number between 0 and 1 chosen from a uniform distribution and W is the sum of reaction rates stored in the reaction table at that step. Thus, the time step in the model is variable, increasing when only slow reactions are 258
occuring and decreasing when fast processes are possible. Having chosen a reaction to occur, the system is updated accordingly, a new reaction table is constructed, and the process repeated. RESULTS The model was initially used to study the kinetics of hydrogen desorption from Si(001). To enable this, hydrogen surface diffusion along the dimer rows was added to the reaction database. Two regimes of high and low initial hydrogen coverages were modelled at a range of substrate temperatures. It was found necessary, p
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