## PHT.301 Physics of Semiconductor Devices31.01.2019

Problem 1
Consider a bipolar transistor.

(a) How could you determine experimentally if it is npn or pnp?

(b) Assuming the emitter-base junction can be considered a one-sided pn-junction, how could you measure the doping concentration of the base?

(c) Explain what a diffusion current is. How is the diffusion constant related to the electron mobility?

(d) How does a phototransistor work?

Problem 2

(a) Draw an $p$-channel MOSFET showing the source, drain, gate, and body contacts.

(b) Draw the depletion regions in this MOSFET when it is biased in saturation. Draw arrows indicating the direction that the electric field is pointing.

(c) Draw the band diagram (conduction band, valence band, Fermi energy), and the electric field as a function of position in a MOS capacitor with a $n$-type substrate in accumulation.

(d) How does the depletion width vary along the channel from source to drain in the saturation regime?

(e) What is the subthreshold current?

Problem 3
Consider a Schottky contact between a metal and a p-type semiconductor.

(a) Draw the band diagram (conduction band, valence band, Fermi energy) for no applied bias voltage.

(b) How do the interface states affect the band diagram?

(c) Describe the current mechanism when the diode is forward biased.

(d) How does the current mechanism change if the semiconductor is heavily doped?

(e) What voltages would you apply to bias a p-channel MESFET in saturation?

Problem 4

(a) What would have a larger reverse saturation current, a light emitting diode or a solar cell? Why?

(b) Can you use an indirect band gap semiconductor to make a solar cell? Explain why or why not.

(c) The depletion region of a solar cell has a certain thickness in the dark. What determines this thickness? What happens to the depletion width when light falls on the solar cell?

(d) What happens when a solar cell heats up? How do these changes affect the functioning of a solar cell?

 Quantity Symbol Value Units electron charge e 1.60217733 × 10-19 C speed of light c 2.99792458 × 108 m/s Planck's constant h 6.6260755 × 10-34 J s reduced Planck's constant $\hbar$ 1.05457266 × 10-34 J s Boltzmann's constant kB 1.380658 × 10-23 J/K electron mass me 9.1093897 × 10-31 kg Stefan-Boltzmann constant σ 5.67051 × 10-8 W m-2 K-4 Bohr radius a0 0.529177249 × 10-10 m atomic mass constant mu 1.6605402 × 10-27 kg permeability of vacuum μ0 4π × 10-7 N A-2 permittivity of vacuum ε0 8.854187817 × 10-12 F m-1 Avogado's constant NA 6.0221367 × 1023 mol-1