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

Homework

Part 1: Semiconductor Properties

• Optical properties
• Calculate the Brewster angle for an air/ZnO surface for green light. (nZnO=2.2)
• Calculate the exciton binding energy (within the effective mass theory) for GaN. (meffe=0.2, meffh=0.8, ε=10)

• Defects and Doping
• Calculate the temperature-dependence of the hole density in a non-degenerate p-type semiconductor with no compensating donors. The acceptor concentration is 3x1016cm-3, Nv=1018cm-3. What is the energetic position of the Fermi level at 0K?

Part 2: Semiconductor Devices

• Diodes
• Read up Schottky's approach to calculate the capacitance of Schottky diodes (for instance Sze Physics of semiconductor devices).
• Calculate the potential distribution in a space charge region. The semiconductor shall be ZnO, meffe=0.27, ε=8.2. The potential at the interface shall be 2V and the net doping density is 1016cm-3. What is the space charge region width?
• Space Charge Spectroscopy
• Solve the differential equation for the time evolution of the probability to find an electronic defect state occupied. The state shall initially be totally occupied, q(0)=1, and relaxes into an equilibrium occupancy q(∞), whereas en=100cn. What is q(∞)? Assume that the state does not interact with the valence band.
• Solar Cells
• Determine the fill factor for the I-V characteristics of the solar cell given on the handout.
• Find out, what the difference (optimisation!) between a solar cell and a photodetector is? Literature: Sze.
• Light Emitting Diodes
• A blue InGaN LED is to be connected to a DC voltage of 12V. Which built-in voltage is to be expected (approximate value)? Calculate the nescessary series resistance if the current through the diode is 10mA!
• Calculate the opening angle of the cone under which light from an AlGaAs/GaAs/AlGas heterostructure LED (GaAs is the active layer) can be coupled out of the device! (nAlGaAs=3.5)
Hint: Fresnel formula.
• Read up about how to make white LEDs!
• Calculate the luminous flux of the sun!
• Solid State Lasers
• What is a Bragg mirror?
• Why are (at least) three electronic states needed to achieve lasing?
• A GaAs laser has an optical power of 1mW and is focussed on a spot of 1mm diametre. Calculate the photon flux!
• A AlGaAs/GaAs VCSEL has GaAs/AlAs Bragg mirrors. The refractive indices of the materials at the laser mode are nGaAs=3.538 and nAlAs=2.958. Approximately which wavelength is the laser mode? How thick are the GaAs and AlAs layers?
• Transistors
• Read up about the field effect transistor (FET). Compare the FET with a vacuum tube triode.
• CMOS
• Design a XOR gate. Use exclusively NAND gates!