Download Minority carrier generation by light

Minority carrier generation by light
7. März 2011
1 Problem
Light shines on silicon at 300K. The silicon is n-doped at a level of 3·1016 cm−3 . The light
generates 1019 electron-hole pairs per second per cm3 . The electron and hole lifetimes
are τn = 3µs and τp = 6µs.
1. What is the minority carrier concentration pn0 before the light is turned on?
2. What is the minority carrier concentration pn after the light is turned on?
3. After the light has been on for a long time, it is switched off. How long does it
take after the light is switched off before the minority carrier concentration reaches
1.1pn0 ?
2 Solution
In thermal equilibrium the minority carrier density in a n-type semiconductor is given
by:
pn0 =
n2i
(1.5 · 1010 cm−3 )2
=
= 7500cm−3
Nd
3 · 1016 cm−3
(1)
After turning on the light additional electron-hole pairs are generated in the semiconductor. The new minority-carrier concentration is:
pn = pn0 + Gl · τp = 7500cm−3 + 1019 s−1 cm−3 · 6µs = 6 · 1013 cm−3
(2)
After switching off the light the carrier densities will decay exponentially:
− τt
pn (t) = (pn (0) − pn0 )e
p
1.1pn0 = pn (0)e
1
− τt
+ pn0 ≈ pn (0)e
− τt
p
+ pn0
p
+ pn0
(3)
(4)
0.1pn0
− t
= e τp
pn (0)
pn (0)
t = τp · ln
0.1pn0
6 · 1013 cm−3
= 6µs · ln
0.1 · 7500cm−3
2
(5)
!
= 150.6µs
(6)