244 CHAPTER 5. SEMICONDUCTOR JUNCTIONS
Problem 5.20 To fabricate very high-quality ohmic contacts on a large-bandgap material
one often deposits a heavily doped low-bandgap material. For example, to make ann-type
ohmic contact on GaAs, one may depositn+InAs.Discusswhythiswouldhelpto
improve the resistance of the contact.
Problem 5.21Consider aW-nSi Schottky barrier on silicon doped at 1018 and
1020 cm−^3. Calculate the tunneling probability of electrons for electrons with energies
near the conduction band in the two doping cases.
Problem 5.22 A (001) Si-SiO 2 interface has∼ 1011 cm−^2 interface states. Assume that
each state corresponds to one defective bond at the interface. Calculate the fraction of
defective bonds for the interface.
Problem 5.23 Calculate the sheet resistance of a 0.5μm thick poly film dopedn-type at
1019 cm−^3. This film is used to form a resistor of width 20μm and length 0.1 cm.
Calculate the resistance of the contact if the electron mobility is 150 cm^2 /V·s.
Problem 5.24 The measured value ofΔECfor the AlGaAs/GaAs system is
approximately 0 .6ΔEG. However, electron affinity rules predict a different value for
ΔEC. Show, using band diagrams and potential profiles, that an interfacial dipole present
at the AlGaAs/GaAs interface can explain this. Discuss bothn-AlGaAs/n-GaAs and
n-AlGaAs/p-GaAs junctions.
Problem 5.25 Consider four differentn-p+Al 0. 3 Ga 0. 7 As/GaAs heterojunctions with
ND=10^17 andNA=5× 1018. The AlGaAs in these junctions is graded fromx=0to
x=0. 3 overXGrade=0(abrupt),XGrade= 100A, ̊ XGrade= 300A, and ̊
XGrade=1μm.
(a) Calculate and plot the energy band diagrams for the above four cases.
(b) When a forward bias is applied, how will the minority carrier current ratio
In−GaAs/Ip−AlGaAsvary in these four heterojunctions? Which one would you use as the
base-emitter junction in ann-p-nHBT?
Assume the dielectric constant of AlGaAs to be the same as that of GaAs.
Problem 5.26In an attempt to increase the collector breakdown voltage of an
n-AlInAs/p-GaInAs/i-GaInAs/n+-GaInAs HBT, I replace the i-GaInAs collector with
i-InP. Unfortunately, this introduced a potential barrier in the conduction band of
ΔEC=0. 2 eV. I decide to linearly grade the barrier over a distance of 50nm for GaInAs
(Eg=0. 7 eV)toInP(Eg=1. 4 eV). Design the electrostatics so that there is no barrier to
electron from over the graded region. Assume thatEF=EVin the p base andEF=EC
in the n+ subcollector. How would the desing change if I decided to grade the region
parabolically as shown in figure 5.15.
