Transmission of conduction electrons through a symmetric pair of delta-barriers or delta-wells embedded in a semiconductor or a metal
- Department of Solid State Physics, Faculty of Mathematics and Physics, Comenius University, 84215 Bratislava (Slovakia)
The transmission coefficient {ital T}({ital k}{sub 0}) is calculated for conduction electrons incident with a wave vector {ital k}{sub 0} upon a double barrier (double well) formed of two equal delta-barriers (of two equal delta-wells) embedded in a one-dimensional (1-D) semiconductor or in a 1-D metal. The stationary Schr{umlt o}dinger{endash}Wannier equation {ital E}({minus}{ital i}{partial_derivative}/{partial_derivative}{ital x}){psi}+{ital V}({ital x}){psi}=E{psi} is solved for {ital V}({ital x})={gamma}[{delta}({ital x}+{ital a}/2)+{delta}({ital x}{minus}{ital a}/2)] (with real and time-independent parameters {gamma}, {ital a}) and E={ital E}({ital k}{sub 0}){gt}0. (The interband transitions are neglected.) The operator {ital E}({minus}{ital i}{partial_derivative}/{partial_derivative}{ital x}) corresponds to a given (possibly nonquadratic) dispersion function {ital E}({ital k}) of the conduction electrons [{ital E}(0)=0]. It is shown that {ital T}({ital k}{sub 0}) is an oscillating function reaching the maximum value [{ital T}({ital k}{sub 0}){r_arrow}1] on an infinite set {l_brace}{ital K}{sup ({ital j})}{r_brace} of values of {ital k}{sub 0}. The shape of {ital T}({ital k}{sub 0}) depends on the shape of the dispersion function {ital E}({ital k}) in a simple way: {ital T}({ital k}{sub 0})={ital T}{sub par}{bold (}{ital mv}({ital k}{sub 0})/{h_bar}{bold )} where {ital T}{sub par}({ital k}{sub 0}) means the transmission coefficient in the special case when the dispersion function is quadratic, {ital E}{sub par}({ital k})={h_bar}{sup 2}{ital k}{sup 2}/2{ital m}, and {ital v}({ital k})=(1/{h_bar}){partial_derivative}{ital E}({ital k})/{partial_derivative}{ital k} is the group velocity due to {ital E}({ital k}). [Here {ital E}({ital k}) is taken as an increasing function.] {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 402309
- Journal Information:
- Journal of Mathematical Physics, Vol. 37, Issue 12; Other Information: PBD: Dec 1996
- Country of Publication:
- United States
- Language:
- English
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