EEE 537 L10 Electronic 3

EEE 537 L10 Electronic 3 - Band Structure Engineering by...

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Band Structure Engineering by Heterostructuring: Quantum Wells A a GaAs 65 . 5 = A a AlAs 66 . 5 = Mismatch parameter % 2 . 0 < EEE537_Fall 2010 C.Z. Ning ASU ECEE AlAs GaAs AlAs / / As Ga Al As Ga Al As Ga Al x x y y x x 1 1 1 / / x y < Could be more general: Bandgap can be “engineered” through x and y variations, or through well thickness ! 1
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Band Edge Discontinuity and Offset Bandgap difference Δ E g =E g A -E g B Band Edge iscontinuity Ratio v c E E Δ + Δ = E 2 Vacuum level A χ B EEE537_Fall 2010 C.Z. Ning ASU ECEE 35% 65% ~ 40% 60% ΔE ΔE v c = Discontinuity Ratio for GaAs and GaAlAs. E g A E g B E c E v E 1 We have two wells to solve! Bandgap can be “engineered” through well thickness variation! 2
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Schrödinger Equation and Boundary Condition (z) ψ E (z) ψ V(z) z (z) 2m z n z * B A, 2 = + ] [ 2 2 d d h A A B (z) L 1 L 1 ) , ψ( z y y ik y x x ik x z y x ψ = = e e k r EEE537_Fall 2010 C.Z. Ning ASU ECEE n E (z) : Potential profile : Energy level (confinement energy) Boundary conditions (conservation of particle current): z ψ m 1 and ψ z * z d d continuous ) ( * , z m B A : Effective masses 3
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Region II 0 2 2 = (z) E z (z) 2m [ z n * 2 d d h = 0 (z) Region I and III Region II V c n =3 EEE537_Fall 2010 C.Z. Ning ASU ECEE A = (z) ψ z 0 Region I and III W z n B W z n A π cos sin + 2 * 2 ) ( 2 W n m E A n h = n =1, 2, 3, . to width squared! 4
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This note was uploaded on 01/02/2012 for the course ECE 537 taught by Professor Czning during the Fall '10 term at ASU.

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EEE 537 L10 Electronic 3 - Band Structure Engineering by...

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