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14 Gain in Semiconductors EE 47410

# 14 Gain in Semiconductors EE 47410 - Gain in Semiconductors...

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Unformatted text preview: Gain in Semiconductors Recombination in Semiconductors Energy and Momentum are conserved in radiative recombination in pure direct energy gap semiconductors. E a- E b = h ν k b + k photon = k a How do we describe gain in a semiconductor where there is a “continuum” of states? h h h Density of States Review: Density of States in a Solid Electrons can be treated QM as waves where Ψ (r,t) describes probability amplitude to find particle in r at t. Probability per unit volume is Ψ Ψ = | Ψ| 2 . For an electron with effective mass m*, the wave function Ψ ∼ e ikr and . Therefore in a solid of dimension a * b * c, the electron wavefunction propagation vector, k, is quantized. 2 2 * 2 k E m = h a b c 3 2 , , m, n, q are integers , , Volume of a state in k space is . abc Volume of phase space enclosed in a shell 4 of radius k and thickness k is . 8 The number of state x y z x y z n m q k k k a b c k k k a b c k dk π π π π π π π π = = = ⇒ ∆ = ∆ = ∆ = ∆ 2 2 3/2 * 3 3 s / volume / unit k in dk ( ) includes a factor of 2 for spin. 1 2 ( ) 2 k dk k dk m E dE EdE ρ π ρ π = ⇒ = h dk k x k y k z Density of States 2 2 * * 3/2 2 2 * 3/2 2 2 for states in the conduction band, 2 2 1 and ( ) ( ) 2 2 1 and ( ) ( ) 2 c c c cond c v val v k E E m m E dE E E dE m E dE E EdE ρ π ρ π- = =- =- h h h E E c E v ρ (E) probability Equilibrium and NonEquilibrium Statistics...
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14 Gain in Semiconductors EE 47410 - Gain in Semiconductors...

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