Texts: 4-1 (Evaluate the Fermi level separation of optically-pumped GaN crystal)
A high-quality GaN crystal is pumped by a HeCd laser, whose incident peak power P = 0.1 MW/cm². The surface is coated with an anti-reflection (AR) coating to ensure that all photons are absorbed. The laser power in bulk GaN follows Beer-Lambert's Law: P(x) = P₀ * exp(-αx), where α = 2 * 10 cm⁻¹ for 325 nm light. Assuming that every absorbed photon generates a pair of electron and hole, it creates a generation rate profile, G(x): G(x) = P(x) * α * hv.
Evaluate the carrier generation rate at the surface (x = 0) and 20 nm beneath the surface (x = 20 nm).
HeCd laser Anti-reflection coating = 325 nm
GaN N(x) = 3.39 eV
b) Suppose the effective density of states of electrons is 0.2 m⁻³, and that of holes is 1.5 m⁻³. If the excitation results in the alignment of E and E' (E' = E somewhere in the crystal), evaluate the Quasi-Fermi level separation energy, E - E'.
4-2 (Evaluate the Fermi level separation of GaN QW under pumping energies in the conduction band and valence band)
Hint:
1) For convenience, we assume the effective masses (mₑ, mₕ) of AIGaN to be the same as those in GaN in HW 4-1.
2) Assume E/E' to be 0.66.
3) E' = 0.5 eV.
b) If the quantum well (QW) is optically pumped, so the position of E matches Ec, evaluate the Quasi-Fermi level separation energy, EF - E' under pumping.
Hint:
a) Only n = 1 in the conduction band and valence band need to be considered. Evaluate Nₑ and locate E based on charge neutrality. Nₑ = Pₑ.
Evaluate Ec - Ev.
