Question

Below image and equations describe the thermal oxidation (Deal-Grove model). Answer the questions below. $x^2 + Ax = B(t + \tau)$, $A = \frac{2D}{k}$, $B = \frac{2DC_o}{C_i}$, $\tau = \frac{d_o^2}{B} + \frac{d_o}{B/A}$ $C_o$: oxidant concentration at $SiO_2$ surface (#/cm³) $C_s$: oxidant concentration at Si surface (#/cm³) $C_i$: the number of oxidant in a unit volume of grown $SiO_2$ d (= x): $SiO_2$ thickness k: surface reaction rate constant D: diffusion coefficient $\tau$: the time required to grow $d_o$ (initial oxide thickness) a) The solution to the above equation is presented on the right. 1) $t >> A^2/4B$, $t >> \tau$ Fill in the blank A, B, C and D, which describe the growth curve. 2) $t + \tau << A^2/4B$ b) Draw the $SiO_2$ thickness vs. oxidation time graph, including very thin oxide layer.

          Below image and equations describe the thermal oxidation (Deal-Grove model). Answer the questions below.
$x^2 + Ax = B(t + \tau)$, 
$A = \frac{2D}{k}$, $B = \frac{2DC_o}{C_i}$, $\tau = \frac{d_o^2}{B} + \frac{d_o}{B/A}$
$C_o$: oxidant concentration at $SiO_2$ surface (#/cm³)
$C_s$: oxidant concentration at Si surface (#/cm³)
$C_i$: the number of oxidant in a unit volume of grown
$SiO_2$
d (= x): $SiO_2$ thickness
k: surface reaction rate constant
D: diffusion coefficient
$\tau$: the time required to grow $d_o$ (initial oxide thickness)
a) The solution to the above equation is presented on the right.
1) $t >> A^2/4B$, $t >> \tau$
Fill in the blank A, B, C and D, which describe the growth curve.
2) $t + \tau << A^2/4B$
b) Draw the $SiO_2$ thickness vs. oxidation time graph, including very thin
oxide layer.

Below image and equations describe the thermal oxidation (Deal-Grove model). Answer the questions below.
x^2 + Ax = B(t + τ),
A = (2D)/(k), B = (2DCo)/(Ci), τ = (do^2)/(B) + (do)/(B/A)
Co: oxidant concentration at SiO2 surface (#/cm³)
Cs: oxidant concentration at Si surface (#/cm³)
Ci: the number of oxidant in a unit volume of grown
SiO2
d (= x): SiO2 thickness
k: surface reaction rate constant
D: diffusion coefficient
τ: the time required to grow do (initial oxide thickness)
a) The solution to the above equation is presented on the right.
1) t >> A^2/4B, t >> τ
Fill in the blank A, B, C and D, which describe the growth curve.
2) t + τ << A^2/4B
b) Draw the SiO2 thickness vs. oxidation time graph, including very thin
oxide layer.

Added by Scott H.

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