144 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS
Problem 3.13Electrons are injected into ap−typesilicon sample at 300 K. The
electron-hole radiative lifetime is 1 ensuremathμs. The sample also has midgap traps with
a cross-section of 10−^15 cm−^2 and a density of 10^16 cm−^3. Calculate the diffusion length
for the electrons if the diffusion coefficient is 30cm^2 s−^1.
Problem 3.14Assume that silicon has a midgap impurity level with a cross-section of
10 −^14 cm^2. The radiative lifetime is given to be 1 ensuremathμsat 300 K. Calculate the
maximum impurity concentration that will ensure thatτr<τnr.
Problem 3.15When holes are injected into ann−typeohmic contact, they decay within a
few hundred angstroms. Thus one can assume that the minority charge density goes to zero
at an ohmic contact. Discuss the underlying physical reasons for this boundary condition.
Problem 3.16Electrons are injected intop−typeGaAs at 300 K. The radiative lifetime for
the electrons is 2 ns. The material has 1015 impurities with a cross-section of 10 −^14 cm^2.
Calculate the distance the injected minority charge will travel before 50% of the electrons
recombine with holes. The diffusion coefficient is 100 cm^2 /s.
Problem 3.17Electrons are injected intop−typesilicon atx=0. Calculate the fraction of
electrons that recombine within a distanceLwhereLis given by (a) 0.5μm, (b) 1.0μm,
and (c) 10.0μm. The diffusion coefficient is 30cm^2 s−^1 and the minority carrier lifetime is
10 −^7 s.
Problem 3.18Consider a Si sample of lengthL. The diffusion coefficient for electrons is
25 cm^2 s−^1 and the electron lifetime is 0.01μs. An excess electron concentration is
maintained atx=0andx=L. The excess concentrations are:
δn(x=0)=2. 0 × 1018 cm−^3 ; δn(x=L)=− 1. 0 × 1014 cm−^3
Calculate and plot the excess electron distribution fromx=0tox=L.Dothe
calculations for the following values ofL:
L =10. 0 μm
L =5. 0 μm
L =1. 0 μm
L =0. 5 μm
Note that the excess electron distribution starts out being nonlinear in space for the long
structure, butbecomeslinearbetweenthetwoboundaryvaluesfortheshortstructure.
Problem 3.19An experiment is carried out at 300 K onn-type Si doped atNd=10^17
cm−^3. The conductivity is found to be 10.0(Ω cm)−^1.
When light with a certain intensity shines on the material the conductivity changes to 11.0
(Ω cm)−^1. The light is turned off at time 0 and it is found that at time 1. 0 μsthe
conductivity is 10.5(Ω cm)−^1. The light-induced excess conductivity is found to decay as
δσ=δσ(0) exp
(
−
t
τ
)
