By Lok C. Lew Yan Voon
This publication offers a close exposition of the formalism and alertness of k.p concept for either bulk and nanostructured semiconductors. For bulk crystals, this can be the 1st time the entire significant strategies for deriving the most well-liked Hamiltonians were supplied in a single position. For nanostructures, this can be the 1st time the Burt-Foreman concept has been made available. hence, the reader will achieve a transparent figuring out of the k.p technique, can have an specific directory of many of the Hamiltonians in a constant notation for his or her use, and a suite of consultant effects. furthermore, the reader can derive a very good realizing of the digital constitution of semiconductors.
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Additional resources for The k p Method: Electronic Properties of Semiconductors
There are no matrix elements with δ1l− and δ2l− , where δ1l− , δ2l− , δ3l− ∼ x, y, z: yz| p y |y I C2y yz| p y |x I C2z = 0, = 0, but yz| p y |z = 0. 28 3 Perturbation Theory – Valence Band Similarly, let H2 ≡ 2 m 20 l | yz| p y |ε3l− |2 . , (yz)a − (yz)a ]; except for operations with inversion, the Let Γ25 matrix elements behave as for Γ25+ . Then yz + | p y |yz − = 0, using C2x and yz + | p y |ε2l− = 0, using C2y but yz + | p y |x y − = 0. Thus, M = H1 + H2 . 3 N Parameter Finally, we study N : N = 2 m 20 lνα ∼ Γ2− + yz| px |lνα lνα| p y |yz + yz| p y |lνα lνα| px |yz E Γ25+ − El − − − Γ12 + Γ15 + Γ25 .
2 2 The D matrix is then ⎛ ⎞ ∗ ∗ D11 D21 −D23 ⎜ D21 D11 D23 ⎟ 0 ⎜ ⎟ ⎜ −D23 D ∗ D33 ⎟ 23 ⎜ ⎟. 8. For WZ, we have  L 1 − M1 = N 1 . 8 Six-band Chuang–Chang Hamiltonian in u basis ⎛ |u |u 2 |u 3 |u 4 |u 5 |u 6 ⎞ 1 ⎜ ⎟ ⎜ F 0 0 0 ⎟ −K ∗ −H ∗ ⎜ ⎟ ⎜ ⎟ ⎜ −K ⎟ G H 0 0 Δ ⎜ ⎟ ⎜ ⎟ ⎜ H∗ λ 0 Δ 0 ⎟ HCC (k) = ⎜ −H ⎟, ⎜ ⎟ ⎜ 0 ⎟ 0 0 F −K H ⎜ ⎟ ⎜ ⎟ ∗ ∗⎟ ⎜ 0 0 Δ −K G −H ⎜ ⎟ ⎝ ⎠ 0 Δ 0 H ∗ −H λ where F = Δ1 + Δ2 + λ + θ, G = Δ1 − Δ2 + λ + θ, λ = L 2 k z2 + M3 (k x2 + k 2y ), θ = (M2 − L 2 )k z2 + ( K = L 1 + M1 − M3 )(k x2 + k 2y ), 2 N1 (k x + ik y )2 , 2 N2 H = √ (k x + ik y )k z , 2 √ Δ = 2Δ3 .
5) δmn δ j j + B 1 m0 j j i i pml pln + pml pln . 7) with AL = BL = CL = 2 2m 0 2 2m 0 + + m 20 l p1l pl1 , E Γ25+ − El y 2 m 20 y 2 2m 20 l x p1lx pl1 , E Γ25+ − El 2 l y y x p1lx pl2 + p1l pl2 . 2 Dresselhaus–Kip–Kittel Model 21 BL = M + CL = N . 9) Terms of higher order, for example, k 4 , have been considered by some authors  but will not be discussed in this book as they are not commonly used in the literature. 2 Eigenvalues The DKK Hamiltonian cannot be diagonalized analytically throughout the first Brillouin zone (FBZ).
The k p Method: Electronic Properties of Semiconductors by Lok C. Lew Yan Voon