ECE 440
Homework VII
Spring 2006
Due: Wednesday, February 22, 2006
1.
The donor profile of a silicon sample is shown below. Assume that the majority carrier
mobility can be obtained from Fig. 323, and the sample is at thermal equilibrium at 300 K.
(a) Determine the diffusion coefficients for majority carriers at points A, B and C,
respectively.
(b) Find the majority carrier diffusion current densities along the cross sections at points A, B
and C, respectively. Indicate not only the magnitude but also the direction.
(c)
Find an expression for the builtin electric field
E
(x) at equilibrium over the range
from x= 1μm to x=3 μm.
(d)
Sketch a band diagram such as in Fig. 415 over the range from x= 1μm to x=3 μm
and indicate the direction of
E
.
2.
A bar of silicon has a donor doping profile of n(x) = N
o
exp{Ax
2
} where A is a constant.
Derive an expressing for the builtin electric field as a function of x. If A = 5.6 x 10
7
/cm
2
,
determine the position at which the electric field is 10
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 Spring '11
 Leburton
 builtin electric field, excess electron concentration, maximum electron diffusion

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