3.10. PROBLEMS 143
Problem 3.7 The power output of a device depends upon the maximum voltage that the
device can tolerate before impact-ionization-generated carriers become significant (say
10% excess carriers). Consider a device of lengthL,over which a potentialVdrops
uniformly. What is the maximum voltage that can be tolerated by an Si and a diamond
device forL=2μmandL=0.5μm? Use the values of the critical fields given in this
chapter.
Problem 3.8 The electron concentration in a Si sample is given by
n(x)=n(0) exp(−x/Ln);x> 0
withn(0) = 10^18 cm−^3 andLn=3. 0 μm. Calculate the diffusion current density as a
function of position ifDn=35 cm^2 /s.
Problem 3.9 Consider a GaAs sample doped n-type at 1016 cm−^3 on which an
experiment is done. At timet=0an external stimulus introduces excess electrons at a
pointx=0. The excess charge is detected atx=10. 0 μm in the absence of any applied
field after 2. 5 × 10 −^9 s.
Use this information to answer the following:
- What is the diffusion coefficient of electrons?
- How much time will electrons travel (by drift) 1.0μm under an applied field of
1.0 kV/cm? Assume that the velocity–field relation is linear.
- What is the conductivity of this sample? Assume that the electron effective mass is
0.067m 0.
Problem 3.10In ap-type GaAs doped atNa=10^18 cm−^3 , electrons are injected to
produce a minority carrier concentration of 1016 cm−^3. What is the rate of photon
emission assuming that alle-hrecombination is due to photon emission? What is the
optical output power? The photon energy isω= 1.41 eV and the radiative lifetime is
1.0 ns.
Problem 3.11Calculate the electron carrier density needed to push the electron Fermi
level to the conduction bandedge in GaAs. Also calculate the hole density needed to push
the hole Fermi level to the valence bandedge. Calculate the results for 300 K and 77 K.
Problem 3.12A photodetector uses pure silicon as its active region. Calculate thedark
conductivity of the detector (i.e., conductivity when no light is shining on the detector).
Light with intensity 10−^3 W/cm^2 shines on the device. Calculate the conductivity in
presence of light.
μn = 1000 cm^2 /V·s
μp = 400 cm^2 /V·s
α =10^3 cm−^1
τr =10−^7 s
