Quantum Theory of the Optical and Electronic Properties of Semiconductors (4th Edition)
Hartmut Haug, Stephan W. Koch
Language: English
Pages: 465
ISBN: B01JXWP31G
Format: PDF / Kindle (mobi) / ePub
This invaluable textbook presents the basic elements needed to understand and research into semiconductor physics. It deals with elementary excitations in bulk and low-dimensional semiconductors, including quantum wells, quantum wires and quantum dots. The basic principles underlying optical nonlinearities are developed, including excitonic and many-body plasma effects. Fundamentals of optical bistability, semiconductor lasers, femtosecond excitation, the optical Stark effect, the semiconductor photon echo, magneto-optic effects, as well as bulk and quantum-confined Franz-Keldysh effects, are covered. The material is presented in sufficient detail for graduate students and researchers with a general background in quantum mechanics.
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periodic potential V0 (r), we obtain Tn ψ(r) = ψ(r + Rn ) = tn ψ(r) , (3.4) where tn is a phase factor, because the electron probability distributions |ψ(r)|2 and |ψ(r + Rn )|2 have to be identical. Since the Hamiltonian H= p2 + V0 (r) 2m0 (3.5) has the full lattice symmetry, the commutator of H and Tn vanishes: [H, Tn ] = 0 . (3.6) Under this condition a complete set of functions exists which are simultaneously eigenfunctions to H and Tn : Hψλ (k, r) = Eλ ψλ (k, r) (3.7) and Tn ψλ (k,
derivative of the denominator, showing that Eq. (6.45) yields the Bose–Einstein distribution function gk = 1 eβ(Ek −µ) −1 . (6.48) Bose–Einstein distribution Generally, for Bosons we have two possible cases: i) Particle number not conserved, i.e. N = k gk = constant. In this case, µ cannot be determined from this relation, it has to be equal to zero: µ = 0. January 26, 2004 16:26 WSPC/Book Trim Size for 9in x 6in Ideal Quantum Gases book2 99 Examples for this class of Bosons are
(8.48) Inserting (8.48) into the Fourier-transform of Eq. (8.39): Vef f (q) = Vq + Vind (q) , (8.49) January 26, 2004 16:26 WSPC/Book Trim Size for 9in x 6in book2 Plasmons and Plasma Screening 139 yields Vef f (q) = Vq [1 + Vef f (q)P 1 (q, ω)] (8.50) or Vef f (q) = Vq Vq = ≡ Vs (q, ω) . 1 1 − Vq P (q, ω) (q, ω) (8.51) Here, we introduced Vs (q, ω) as the dynamically screened Coulomb potential. The dynamic dielectric function (q, ω) is given by (q, ω) = 1 − Vq P 1 (q, ω) , (8.52)
(8.48) Inserting (8.48) into the Fourier-transform of Eq. (8.39): Vef f (q) = Vq + Vind (q) , (8.49) January 26, 2004 16:26 WSPC/Book Trim Size for 9in x 6in book2 Plasmons and Plasma Screening 139 yields Vef f (q) = Vq [1 + Vef f (q)P 1 (q, ω)] (8.50) or Vef f (q) = Vq Vq = ≡ Vs (q, ω) . 1 1 − Vq P (q, ω) (q, ω) (8.51) Here, we introduced Vs (q, ω) as the dynamically screened Coulomb potential. The dynamic dielectric function (q, ω) is given by (q, ω) = 1 − Vq P 1 (q, ω) , (8.52)
− iδ ω (1.17) where P denotes the principal value of an integral under which this relation is used. We find +∞ +∞ 1 dν χ(ν) + 2πi ν − ω 2 χ(ω) = P −∞ −∞ dνχ(ν)δ(ν − ω) . (1.18) For the real and imaginary parts of the susceptibility, we obtain separately +∞ χ (ω) = P χ (ω) = −P dν χ (ν) π ν−ω −∞ +∞ −∞ (1.19) dν χ (ν) . π ν −ω (1.20) Splitting the integral into two parts 0 χ (ω) = P −∞ dν χ (ν) +P π ν −ω +∞ 0 dν χ (ν) π ν −ω (1.21) and using the relation χ (ω) = −χ (−ω), we find
