**ESE 521 The Physics of Solid State Energy Devices **

**Homework #4 **

1. A p-n abrupt junction with N_{A}=10^{17}/cm^{3} and N_{D}=5x10^{15}/cm^{3} has τ_{p}=0.1 µs and τ_{n}=0.01 µs with kT=0.026 eV, A=10^{-4} cm^{2}, n_{i}=10^{10}/cm^{3}, µ_{n}=801 cm^{2}/Vs and µ_{p}=438 cm^{2}/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} cm^{2} has a doping of N_{A}=10^{17}/cm^{3} and N_{D}=10^{15}/cm^{3}. Let µ_{n}=801 cm^{2}/Vs and τ_{n}=0.1 µs on the p-side; and let µ_{p}=477 cm^{2}/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

- 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}=10^{18}/cm^{3}and N_{D}=10^{16}/cm^{3} where E_{cr}=4x10^{5} V/cm with n_{i}=10^{10}/cm^{3} (kT =0.026 eV). Calculate:

- V
_{BR}; - the depletion width at V
- If N
_{D}=10^{17}/cm^{3}repeat part (a)

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