2.14. PROBLEMS 89
Problem 2.12For long-haul optical communication, the optical transmission losses in a
fiber dictate that the optical beam must have a wavelength of either 1.3μmor1.55μm.
Which alloy combinations lattice matched to InP have a bandgap corresponding to these
wavelengths?
Problem 2.13Calculate the composition of HgxCd 1 −xTe which can be used for a night
vision detector with bandgap corresponding to a photon energy of 0.1 eV. Bandgap of
CdTe is 1.6 eVandthatofHgTeis− 0. 3 eV at low temperatures around 4 K.
Problem 2.14In the In 0. 53 Ga 0. 47 As/InP system, 40% of the bandgap discontinuity is in
the conduction band. Calculate the conduction and valence band discontinuities. Calculate
the effective bandgap of a 100A quantum well. Use the infinite potential approximation ̊
and the finite potential approximation and compare the results.
Problem 2.15In an n-type Si crystal the doping changes abruptly fromND=10^15 to
ND=10^17. Make a qualitative sketch of the band diagram. Calculate
- the built-in potential at then+/n−interface, in eV. Also calculate how much of the
band-bending occurs on each side of the junction,
- the electric field at then+/n−interface and
- the electron concentration at then+/n−interface.
AssumeT= 300K.
Problem 2.16Calculate the first and second subband energy levels for the conduction
band in a GaAs/Al 0. 3 Ga 0. 7 As quantum well as a function of well size. Assume that the
barrier height is 0.18 eV.
Problem 2.17Calculate the width of a GaAs/AlGaAs quantum well structure in which the
effective bandgap is 1.6 eV. The effective bandgap is given by
Eef fg =Eg(GaAs) +Ee 1 +Eh 1
whereEg(GaAs) is the bandgap of GaAs (= 1.5 eV) andEe 1 andE 1 hare the ground state
energies in the conduction and valence band quantum wells. Assume that
m∗e=0. 067 m 0 ,m∗hh=0. 45 m 0. The barrier heights for the conduction and valence
band well is 0.2 eV and 0.13 eV, respectively.
Problem 2.18Assume that a particular defect in silicon can be represented by a
three-dimensional quantum well of depth 1.5 eV (with reference to the conduction
bandedge). Calculate the position of the ground state of the trap level if the defect
dimensions are 5A ̊× 5 A ̊× 5 A. The electron effective mass is 0.26 ̊ m 0.
Problem 2.19A defect level in silicon produces a level at 0.5 eV below the conduction
band. Estimate the potential depth of the defect if the defect dimension is 5A ̊× 5 A ̊× 5 A. ̊
The electron mass is 0.25m 0.
