$[1\mathrm{.}0$ point$]$ Silicon epitaxial layers are commonly grown with silicon deposited from the gas

phase at the growth rate, $G_R,$ given by

$G_R=\frac{N_g}{N}(\frac{k_s{h}_g}{k_s+h_g})$

where $k_s=$ surface reaction rate constant, $h_g=$ vapor$-$phase mass$-$transfer coefficient, $N_g=$

atomic density in the gas stream, and $N=$ atomic density on the film deposited.

Using $h_g=1c\frac{m}{sec,k_5}=2{10}^6{e}^{-\frac{1\mathrm{.}2}{kT}}c\frac{m}{sec,N_g}=3{10}^{16}$ato$\frac{m}{c}{m}^3,$ and $N=5{10}^{22}$

atoms $\frac{?}{c{m}^3},$ do the following:

a$.$ Calculate the growth rate of a silicon layer from an $SiC{l}_4$ source at $1200C.$

b$.$ Find the change in growth rate if the temperature is increased by $25C.$

c$.$ Determine the temperature at which $k_s=h_g.$

d$.$ Calculate the growth rate at the temperature when $k_s=h_g$ :

e$.$ Use the plots shown in figure below to find the value of activation energy $E_A$ at the

temperature found in part $($c$)$ above.

Temperature dependence of the silicon epitaxial growth

process for four different sources. The growth rate is

surface$-$reaction limited in region A and is mass$-$transfer

limited in region B $($taken from Philips Journal of Research$).$