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 N_A=10¹⁷/cm³ and N_D=5x10¹⁵/cm³ has τ_p=0.1 µs and τ_n=0.01 µs with kT=0.026 eV, A=10^-4 cm², n_i=10¹⁰/cm³, µ_n=801 cm²/Vs and µ_p=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 V_A= V_bi/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 V_A= -V_bi/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 V_A 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 N_A=10¹⁷/cm³ and N_D=10¹⁵/cm³. Let µ_n=801 cm²/Vs and τ_n=0.1 µs on the p-side; and let µ_p=477 cm²/Vs and τ_p=1 µs on the n-side.

• Calculate the current through the diode at room temperature if
  • V_A= -50 V
  • V_A= -0.1 V, and
  • V_A= 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 N_A=10¹⁸/cm³and N_D=10¹⁶/cm³ where E_cr=4x10⁵ V/cm with n_i=10¹⁰/cm³ (kT =0.026 eV). Calculate:

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

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