# Introduction to the Physics of Semiconductor Devices

Seminar series held at the University of Pretoria by Matthias Schmidt in 2012.
Time: Wednesdays, 16:30. Venue: 5-31

Part 1: Semiconductor Properties

• Crystal Structures and Crystal growth
• How many eqivalent <110> planes exist in the fcc lattice?
• What is the atomic packing factor of the hexagonal lattice?
• Silicon crystallises in the diamond structure. The lattice constant is 0.543nm. The atomic mass of a Si atom is 28. Calculate the mass density of silicon!
• Which symmetry has the reciprocal lattice of the body centred cubic (bcc) lattice?

• Bandstructure, Charge Carrier Statistics
• Order the following semiconductors by their bandgap energy: GaSb, GaN, Ge, GaP, GaAs, and Sn. Use the results of the Kronig-Penney model!
• How will the bandgap of a semiconductor change under hydrostatic pressure?
• How many equivalent conduction band minima exist in GaAs? How many in silicon?
• What are the energy eigenstates in a one/two/three-dimensional infinite quantum well?
• Calculate the density of states in a two-dimensional quantum well!
• What is the value of kT at T=200K? (in meV)

• Optical properties
• What is an exciton? What is the consequence of the formation of excitons on the absorption spectra of a semiconductor?
• What are the energy states of an exciton?
• How can the thickness of a thin film be determined from a transmission measurement?
• How are the densities of states in the conduction band and the valence band, respectively, related to the absorption coefficient?
• How is the momentum conserved in optical transitions in indirect semiconductors?
• What is the dependence of the absorption coefficient on the photon energy (≈Eg) in a direct and an indirect semiconductor?

• Defects and Doping
• For T > 0K every solid necessarily contains (intrinsic) defects. Why?
• What is a Frenkel pair?
• What is the difference between shallow defects and deep levels?
• Write down the charge balance equation for a semiconductor containing two different types of donors and one acceptor in much lower concentration. What is the conduction type of the semiconductor?
• What is the position of the Fermi level in a compensated, non-degenerate p-type semiconductor at 0K?
• What are donor-like impurities in silicon? Give at least three examples.
• Silicon in gallium arsenide can be a donor or an acceptor. Explain why!
• How is the probability to find an electronic defect state occupied by an electron related to charge carrier capture and ionisation processes? (Differential equation, solutions for equilibrium and transient relaxation of the system into equilibrium)

Part 2: Semiconductor Devices

• Diodes
• Which types of diodes exist?
• How is the Schottky barrier height related to the positions of the Fermi levels in the metal and in the semiconductor?
• Give the expression for the current-voltage characteristics of a diode in case of thermionic emission!

• Space Charge Spectroscopy
• What is the dependence of the electric potential/electric field in the space charge region of a homogeneously doped semiconductor on the distance from the metal/semiconductor interface?
• What is the relation between the capacitance of a space charge region and the space charge region width?
• How is the DLTS signal calculated from capacitance transients?
• A DLTS spectrum measured on an n-type semiconductor contains two peaks at different temperatures. Is the defect state causing the low temperature peak energetically closer to the conduction band edge than the second state, or does the opposite hold?

• Solar Cells
• What is the solar constant? At which wavelength occures the intensity maximum in the solar spectrum?
• Why is silicon a bad choice for a solar cell material?
• Why are space charge regions needed for the generation of a photo-current?
• How can the reflection of light at the surface of the solar cell be decreased?
• Why does the solar cell efficiency decrease with increasing temperature of the cell?

• Light Emitting Diodes
• What is the advantage of using a pn heterojunction to fabricate light emitting diodes instead of a pn homojunction?
• Which materials are commonly used to make IR and red LEDs?
• Why is nitrogen doping nescessary for green GaP LEDs? How is it connected to Heisenberg's uncertainty principle?
• How can a white LED be achieved? What is the meaning of "colour temperature"?
• What is the "luminous flux" of an LED? Calculate the luminous flux of a 0.3 Watt GaAs LED (efficiency=0.7)!

• Solid State Lasers
• What is stimulated emission?
• What is Lambert-Beer's law? What is "gain"?
• How does the absorption coefficient change under "population inversion"?
• What is the design of a vertical cavity surface emitting laser (VCSEL)?
• What happens at the lasing threshold? How can the threshold be measured?
• What is a Bragg mirror? What is the relation between the thickness of the dielectic layers and the reflected wavelength?
• What is a distributed feedback laser?
• Name at least two possibilities how lasers can be tuned?
• What are "random lasing" and "whispering gallery mode lasing"?