EE2 Problem Set#4 Solutions:
Due May 03 in class
Question#1 (15 points):
A silicon wafer (N
A
=10
14
/cm
3
,
τ
n
=1 microsec, T=room
temperature) is first illuminated for a time t>>
τ
n
with light that generates G
LO
= 10
16
electronhole pairs per cm
3
sec uniformly throughout the volume of the silicon. At time
t = 0 the light intensity isredused making G
L
=G
LO
/2 for t>0. Determine
Δ
n
p
(
t
) for t>0.
The initial illumination is present for a time very much longer than the minoritycarrier lifetime.
Thus, prior to reducing the light intensity, the excess carrier concentration will have reached a
steady value Δ
n
(0) =
G
L0
τ
n
= 10
16
×
10
6
= 10
10
cm
3
(thus, lowlevel injection prevails). With the
illumination reduced, we now need to solve the minoritycarrier diffusion equation dΔ
n
/d
t
= (Δ
n
/
τ
n
) + (
G
L0
/2), where we have noted that the illumination is
uniform
throughout the sample. Since
this equation is subject to the boundary condition D
n
(0) =
G
L0
τ
n
and noting the form of the solution
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 Winter '07
 Vis
 lowlevel injection, Δn, steady state condition, minoritycarrier diffusion equation

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