Question

A part of the infinitely long silicon sample with
1017 cm-3 acceptors is illuminated on the left side. The illuminated
light intensity varies over time as shown in the graph. For t < 0, gop =
1021 EHP/cm3-s and, for 5μs < t < 10μs , gop = 2 x 1021 EHP/cm3-s.
Assume that tp = tn = 1 μs. Neglect any heating due to light
illumination and assume that the sample is at room temperature.
(a) (5 points) What is the electron concentration at x=0 at t=0?
(b) (8 points) What is the separation in quasi-Fermi levels (Fn-Fp) at x <
0 at t < 0.
(c) (8 points) What is the electron concentration at x=0 at t=15μs?
(d) (15 points) What is the electron concentration at x=25μm at t=3μs?
Obtain all necessary material properties from the graphs in the page 2
and 3 of this exam. Mark in the graphs and submit the graphs with
your solution.

Answer 1

x=0 at t=0 4) Given Light intensity T ti 7 X at, Tous Sus 10 cm no = 1.5x100 ci 1 Po = 10cm no² no = Po 20 2.25x10 = 2.25x10 cm For tco , 9 ho= 12 cms. In = Ep = ius. ca At Electron concentration is n - grox En 10² cms xos 10 cm? n = (b) We hatre Po for to. 17 - 3 = 10 cm los em n = 10 cm 10-3 No = 1.5x10 cm EF,- Ep = ktin () ev 0.02586 in ( 107 1.5x100

nt, not ne Eco - Ep 0.406 ev. Also, En Efy = KT ln (11) 10 0.02586 In (1.5 ev 1.5x10 En - Epi= 0.287 er. (En-EF4) + (EF - Ep) = 0.287 +0.406 En-Ep = 0.693 er c) Electron concentration at x=0 is given by we have to find not At t= 15us, Let nti is the Conc. at t= sus -5xioliti

So, not 2. 25x103 + 10sx - 5x1olixio cm 6.74 x 10 x 10² 361

nti al 2x10 cms, ames, Enclos At t= sus, 9L2 = Conc. at t=sus the is So, Let ntz the light is upto talous because these time limits. between illuminated ntz nti + 9 L2 in 6.74x100 + + 2x10 x 100 15 -3 ntz - 2x10 cm

The electron concentration at t= 15us is n = nti -t/up + taxe 15 lo + - (15-10) 170 11x70 2 x 10 xe {ite turous} 6.7 4x100 6.748102 + axloxe 6.74X102 + 2x6.748102 15 - 5 n = 2.022x10 cm

d) Electron conc. at x = 25um at t= 3us. At t=3us at x=0 the electron Concentration is : - 3x10/1x10 2-25x103 + 10sx n 4.98 x 103 cm n = Now at is : x = 25um = 25x100 cm at & zus, electron concentration the ne 11 not

2.25 x 103 cm no = 13 - 3 4.98 x 10 cm n = at Ln = unin = ✓ soixio (from graph = 28.3x18 Un = 801 m/rus P- 1x10 cm in= 2.25x100 + (4.98x103) - (85) asarid 2.25x100 +4.56x103 13 na 4.56x 103 cm