The diode equation for forward current in an ideal p–n junction is $$I = I_s (e^{qV/(kT)} − 1)$$ . When I ≫ I_s, which simplified expression most appropriately estimates V?

At T = 300 K, the thermal voltage V_T = kT/q is approximately which value?

A PN-junction solar cell delivers photocurrent $$I_L = 1 \text{ mA}$$ . At its maximum power point, the terminal voltage is $$V_m = 0.3 \text{ V}$$ and the thermal voltage is $$V_T = 30 \text{ mV}$$ . Assuming the one-diode model with $$I = I_L - I_0 (e^{V/V_T} - 1)$$ , what is the reverse saturation current $$I_0$$ ?

In a solar cell modeled by the single diode equation $$I = I_L − I_0 (e^{V/V_T} − 1)$$ , increasing V_T while keeping V_m fixed and I_L constant will have what qualitative effect on the required I_0 to satisfy I(V_m) = 0?

The intrinsic carrier concentration of a semiconductor is $$n_i = 2.5 \times 10^{16} m^{−3}$$ at 300 K. Electron and hole mobilities are $$μ_n = 0.15 m^{2}/V·s$$ and $$μ_p = 0.05 m^{2}/V·s$$ . Taking $$q = 1.6 \times 10^{−19} C$$ , what is the intrinsic resistivity $$ρ$$ ?

Using $$σ = q n_i (μ_n + μ_p)$$ , what is the intrinsic conductivity for the semiconductor with $$n_i = 2.5×10^{16} m^{−3}$$ , $$μ_n = 0.15 m^{2}/V·s$$ , $$μ_p = 0.05 m^{2}/V·s$$ ?

Which parameter primarily sets the exponential slope of the diode I–V characteristic in the ideal diode equation?

A germanium diode and a silicon diode have the same reverse saturation current I_s at 300 K. For the same forward current I ≫ I_s, which statement about required forward voltage is most accurate?

If the intrinsic carrier concentration n_i doubles while mobilities remain constant, how does intrinsic resistivity ρ = 1/(q n_i (μ_n+μ_p)) change?

For a diode with I_s = 10 μA at 300 K, what forward current corresponds to V = 0.238 V assuming I ≫ I_s? Use V_T = 25.9 mV.

Which element is a suitable n-type dopant when added to crystalline silicon?

In an n-type semiconductor, the donor level ED is 0.25 eV below the conduction band edge EC. Which statement best describes the position of EF if ED − EF = 0.18 eV?

Five percent of donor atoms remain neutral in an n-type semiconductor. What fraction of donor atoms are ionized?

For a donor level with degeneracy factor g = 2, which term appears in the expression for electrons occupying the donor level nd = 1 + g exp[(kT ED − EF)] Nd?

Given EC − EF = 0.25 eV and ED − EF = 0.07275 eV from VT ln(38), what is the numerical value of EC − ED?

In an extrinsic semiconductor, the hole concentration is $$p = 1.5 ni$$ where $$ni$$ is the intrinsic carrier concentration. Using mass action ( $$np = ni^2$$ ), what is the electron concentration $$n$$ ?

If equal drift currents are carried by electrons and holes (Jn = Jp) under the same electric field, which relation between mobilities holds when p = 1.5 ni and n = (ni/1.5)?

Thermal voltage VT is approximated as 20 mV at room temperature. Which expression correctly uses VT to relate ED − EF when the occupation ratio gives exp[(ED − EF)/kT] = 38?

For an intrinsic semiconductor at absolute zero (T = 0 K), which statement is correct about band occupancy?

In a non-degenerate semiconductor at 300 K, the relation between electron concentration n, the conduction band edge Ec, and the electron quasi-Fermi level EFn is $$n = N_c \exp[−(E_c − E_{Fn})/kT]$$ . If $$N_c = 10^{19} \text{ cm}^{-3}$$ and $$E_c − E_{Fn} = 0.2 \text{ eV}$$ , what is n? Use $$kT \approx 0.026 \text{ eV}$$ .

For two non-degenerate samples at the same temperature with electron densities n1 and n2 and identical Nc, the difference (Ec − EF1) − (Ec − EF2) equals kT ln(n2/n1). If n2 = 0.5 n1 and kT = 26 meV, what is (Ec − EF1) − (Ec − EF2)?

The intrinsic Fermi level Ei in a semiconductor with effective density of states Nc and Nv is offset from midgap by Δ = (kT/2) ln(Nv/Nc). If Nv = 2Nc at 300 K and kT = 26 meV, what is |Δ|?

Which statement best explains why Ei shifts toward the band with larger effective density of states?

A silicon sample at 300 K has Nd = $$5\times10^{16} cm^{-3}$$ and is uniformly illuminated with optical generation rate Gopt = $$1.5\times10^{20} cm^{-3} s^{-1}$$ . Under low-level injection, what is the steady-state excess minority hole concentration Δp0 if τp0 = $$0.1 \mu s$$ ?

After the light is turned off at t = 0, the excess minority holes in the sample of the previous question decay as Δp(t) = $$Δp0 e^{−t/τp0}$$ . With $$Δp0$$ from steady state and $$τp0 = 0.1 μs$$ , what is $$Δp at t = 0.3 μs$$ ?

For n-type silicon with Nd ≫ ni and low-level injection, which approximation is most appropriate for the majority carrier concentration n0?

Given ni = $$10^{10} cm^{-3}$$ at 300 K, Nc = $$10^{19} cm^{-3}$$ , and n = $$10^{16} cm^{-3}$$ , compute Ec − EFn using Ec − EFn = $$kT \ln(\frac{Nc}{n})$$ with $$kT = 26 meV$$ .

If Nv/Nc = 0.5 at 300 K, what is the direction of Ei shift relative to midgap and its magnitude? Use Δ = (kT/2) ln(Nv/Nc) with kT = 26 meV.

A sample has τp0 = 0.1 μs and τn0 = 0.5 μs under low-level injection. Which plot of Δp(t) correctly represents the transient after the light is turned off at t = 0?