Week 9: A p-n junction and a solar cell from two levels

A p-n junction from two levels and two smart contacts (Datta Ch. 12, Figs. 12.5–12.6)

Level A (energy ε_A) talks only to contact 1, level B (ε_B = ε_A − ℏω) only to contact 2. No elastic path connects the contacts: current flows only through inelastic jumps A ↔ B caused by scatterers at temperature T₀ (Eqs. 12.6–12.7). The device is at T = 300 K. Set T₀ = T for a dark diode, T₀ = 6000 K for "sunlight". The model is solved exactly in steady state (rates in units of the contact coupling γ).

Applied voltage V = (μ₁ − μ₂)/q Scatterer (light) temperature T₀ Level spacing ℏω = ε_A − ε_B (the "band gap") Inelastic strength K / γ Dilution δ of the hot scatterers (1 = Datta's model)

symmetric contacts (Fig. 12.6b)

Short-circuit current I_sc (units qγ)–

Open-circuit voltage V_OC · Carnot ℏω(1 − T/T₀)/q + (kT/q)lnδ–

Dark slope (Eq. 12.5 with ν = 1: 59.5 mV/dec)–

At the set V: (μ_A − μ_B)/q and I–