Consider a quantum well with a directbandgap semiconductor w

Consider a quantum well with a direct-bandgap semiconductor whose electron and hole effective masses are both equal to 0.5 m_0. The interband transition energy from m = 1 to n = 1 is 1eV. The well width is 10 nm. What is the maximum optical gain of the semiconductor when the separation of the quasi-Fermi levels is 52 meV above the transition energy? Assume T = 0 K. What is the spectral width of the optical gain? What are the electron and hole concentrations for the condition in (a)?

Solution

maximum optical gain is,

        alpha = C₀[m₀/6]*E_p*rho

here, C₀ = 7.762X109 m²/kg, Ep = 24 eV

Hence, alpha = 2.95x10⁴ cm^-1

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width is, w = dF - Eg = 52 meV

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Electron fermi-levels is, 1/2 of dF -Eg, that is 26 meV

So, electron concentration, N = [{m_e / pi*h_bar²*Lz}*26 meV] = 5.423x10¹⁸ cm^-3

       Hole concentration        P = N = 5.423x10¹⁸ cm^-3