4.10. PROBLEMS 205
Problem 4.4Consider the sample discussed in problem 4.2. The diode has a diameter of
50 μm. Also calculate the charge in the depletion regions and plot the electric field profile
in the diode.
Problem 4.5An abrupt siliconp-ndiode at 300 K has a doping of
Na=10^18 cm−^3 ,Nd=10^15 cm−^3. Calculate the built-in potential and the depletion
widths in thenandpregions.
Problem 4.6AGep-ndiode hasNa=5× 1017 cm−^3 andNd=10^17 cm−^3. Calculate
the built-in voltage at 300 K. At what temperature does the built-in voltage decrease by
1%?
Problem 4.7Consider a p-n junction withNA=ND=10^17 cm−^3. When the
capacitance is measured to be twice the value expected.
The reason is an unintentional interfacial dipole between the p and n layers.
- What is the magnitude of the dipole moment?
- Draw the band diagrams of the ideal p-n junction and the non-ideal one. Include the
electric field profiles and depletion region widths.
Assume that the dipole is supported by negative and positive charges separated by a very
small distance,δ.
Problem 4.8Explain, using physical arguments, why the reverse current in ap-ndiode
does not change with bias (before breakdown). Would this be the case if the electrons and
holes had a constant mobility independent of the electric field?
Problem 4.9The diode of problem 4.3 is subjected to bias values of: (a)Vf=0.1V;(b)
Vf=0.5V;(c)Vr=1.0V;(d)Vr= 5.0 V. Calculate the depletion widths and the maximum
fieldFmunder these biases.
Problem 4.10Consider ap+nSi diode withNa=10^18 cm−^3 andNd=10^16 cm−^3 .The
hole diffusion coefficient in then-side is 10 cm^2 /s andτp=10−^7 s.Thedeviceareais
10 −^4 cm^2. Calculate the reverse saturation current and the forward current at a forward
bias of 0.8 V at 300 K.
Problem 4.11Consider ap+nsilicon diode with area 10 −^4 cm^2. The doping is given by
Na=10^18 cm−^3 andNd=10^17 cm−^3. Plot the 300 K values of the electron and hole
currentsInandIpat a forward bias of 0.8 V. Assumeτn=τp=1μs and neglect
recombination effects.Dn=20cm^2 /s andDp=10cm^2 /s.
Problem 4.12A GaAs LED has a doping profile ofNa=10^17 cm−^3 ,Nd=10^18 cm−^3 at
300 K. The minority carrier time isτn=10−^8 s;τp=5× 10 −^9 s. The electron diffusion
coefficient is 100 cm^2 s−^1 while that of the holes is 20 cm^2 s−^1. Calculate the ratio of the
electron-injected current (across the junction) to the total current.
