ESE 521 The Physics of Solid State Energy Devices

ESE 521 The Physics of Solid State Energy Devices

Homework #4

1. A p-n abrupt junction with NA=1017/cm3 and ND=5x1015/cm3 has τp=0.1 µs and τn=0.01 µs with kT=0.026 eV, A=10-4 cm2, ni=1010/cm3, µn=801 cm2/Vs and µp=438 cm2/Vs.

  • Calculate the reverse saturation current due to holes.
  • Calculate the reverse saturation current due to electrons.
  • Calculate the total reverse saturation current.
  • If VA= Vbi/2, calculate the injected minority carrier currents at the edges of the depletion region. What are the injected minority carrier concentrations at 0 and 1 µm into the bulk regions?
  • If VA= -Vbi/2, calculate the injected (depleted) minority carrier concentrations at the edges of the bulk regions? Calculate the minority carrier currents at the edges of the depletion regions.
  • At what value of VA and where in the diode will the assumption of "low-level injection" first be violated? Use the criterion of the minority carrier reaching 10% of the majority carrier concentration as the violation.

2. A silicon step junction diode with a cross-sectional area A=10-4 cm2 has a doping of NA=1017/cm3 and ND=1015/cm3. Let µn=801 cm2/Vs and τn=0.1 µs on the p-side; and let µp=477 cm2/Vs and τp=1 µs on the n-side.

  • Calculate the current through the diode at room temperature if
    • VA= -50 V
    • VA= -0.1 V, and
    • VA= 0.2 V
  • Assuming that the mobilities and lifetimes do not vary significantly with temperatures. repeat part (a) for T=500 K.
  • Summarize in your own words what has been exhibited by this problem.

3. A p+-n silicon step junction is doped NA=1018/cm3and ND=1016/cm3 where Ecr=4x105 V/cm with ni=1010/cm3 (kT =0.026 eV). Calculate:

  • VBR;
  • the depletion width at V
  • If ND=1017/cm3 repeat part (a)

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