For a simple cubic structure with lattice parameter a, the energy dispersion in the tight-binding (TB) approximation is obtained by E(k) = Eo – a – 2y [cos(ka) + cos(kya) + cos(k,a)] , where a and y are overlap integrals of the TB approximation. ) Expand the energy E(k) near the bottom of the band (i.e., near the I point, |k| = k = 0) where ka «1 to the second order in k. You may define for simplicity Er = Eo – a – 6y, and effective () -1 Ə² E electron mass m = h? Ək² Use Er and m in the energy relation. %3D Expand E(k) near the first Brillouin zone boundary at the W point (k = ky = kz = -) in %3D terms of dk = |8k|. Sk « 1, where kį - Ski, and i = x, y, z. Give the result using Er and %3D а m defined above.
For a simple cubic structure with lattice parameter a, the energy dispersion in the tight-binding (TB) approximation is obtained by E(k) = Eo – a – 2y [cos(ka) + cos(kya) + cos(k,a)] , where a and y are overlap integrals of the TB approximation. ) Expand the energy E(k) near the bottom of the band (i.e., near the I point, |k| = k = 0) where ka «1 to the second order in k. You may define for simplicity Er = Eo – a – 6y, and effective () -1 Ə² E electron mass m = h? Ək² Use Er and m in the energy relation. %3D Expand E(k) near the first Brillouin zone boundary at the W point (k = ky = kz = -) in %3D terms of dk = |8k|. Sk « 1, where kį - Ski, and i = x, y, z. Give the result using Er and %3D а m defined above.
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![For a simple cubic structure with lattice parameter a, the energy dispersion in the tight-binding
(TB) approximation is obtained by
E(k) = Eo – a – 27 [cos(ka) + cos(kya) + cos(k,a)] ,
where a and y are overlap integrals of the TB approximation.
) Expand the energy E(k) near the bottom of the band (i.e., near the I point, |k| = k = 0) where
= Eo – a – 6y, and effective
ka < 1 to the second order in k. You may define for simplicity Er
2² E`
-1
()
electron mass m = h
Use Er and m, in the energy relation.
) Expand E(k) near the first Brillouin zone boundary at the W point (k = ky = kz = ")
in
%3D
terms of dk = |8k]. Sk « 1, where k; =
- Ski, and i = x, y, z. Give the result using Er and
a
m defined above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d1fc48-d7b2-428e-9847-83620ea7fe5b%2F892d6dfc-1c92-44f3-ad8b-94ee52bebefe%2Fz7582c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For a simple cubic structure with lattice parameter a, the energy dispersion in the tight-binding
(TB) approximation is obtained by
E(k) = Eo – a – 27 [cos(ka) + cos(kya) + cos(k,a)] ,
where a and y are overlap integrals of the TB approximation.
) Expand the energy E(k) near the bottom of the band (i.e., near the I point, |k| = k = 0) where
= Eo – a – 6y, and effective
ka < 1 to the second order in k. You may define for simplicity Er
2² E`
-1
()
electron mass m = h
Use Er and m, in the energy relation.
) Expand E(k) near the first Brillouin zone boundary at the W point (k = ky = kz = ")
in
%3D
terms of dk = |8k]. Sk « 1, where k; =
- Ski, and i = x, y, z. Give the result using Er and
a
m defined above.
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