Scattering in abrupt heterostructures using a position dependent mass Hamiltonian

Abstract

Transmission probabilities of the scattering problem with a position dependent mass are studied. After sketching the basis of the theory, within the context of the Schrödinger equation for spatially varying effective mass, the simplest problem, namely, tranmission through a square well potential with a position dependent mass barrier is studied and its novel properties are obtained. The solutions presented here may be adventageous in the design of semiconductor devices.

The propagator for step potential and mass using path decomposition method

“…Other choices of ( ) have been investigated in the literature by different authors and their influences on the potential shape have been computed in [1,2,5] and [4].…”

“…The effective masses could have a spatially variation depending on the microstructure of the medium. Systems with position dependent mass are studied in several works during the last years [1][2][3][4][5] and [6]. A general method was outlined in [1] for obtaining exact solutions of Schrödinger equations with a position dependent effective mass and the results were compared with other approaches [7,8] and [9].…”

“…It was also concluded that distinct effective mass Hamiltonians proposed in the literature have identical spectra. Considering scattering in abrupt heterostructures and us- * E-mail: lyazidchetouani@gmail.com ing a position dependent mass Hamiltonian with a square well potential in [2], the authors had chosen the framework of the Schrödinger equation approach. However, in [3] the Green's function equation was used to study the problem of systems with position dependent masses.…”

Osciladores quânticos com massa dependente da posição

“…Sistemas onde a massa depende da posição são importantes não apenas do ponto de vista teórico, mas também do ponto de vista prático, pois podem ser utilizados para descrever heteroestruturas abruptas ou suaves [1], no estudo das propriedades eletrônicas de semicondutores [2], de cristais homogêneos [3], de pontos [4] e líquidos quânticos [5]. Em 2015, Macedo e Guedes [6] resolveram a equação de Schrödinger e calcularam a Informação de Fisher e a e Entropia de Shannon para três diferentes osciladores com massa dependente da posição (OMDP).…”

“…A segunda distribuiçãoé análoga as que são utilizadas no estudo de estados eletrônicos confinados em estruturas do tipo Al y Ga 1−y As [8]. Já a terceira distribuição pode ser utilizada na análise das estruturas GaAs/Al x Ga 1−x As [1] Recentemente, na Ref. [9], estudamos classicamente um OMDP cuja distribuição de massa era dada por m (x) = m 0 (x 2 + λ 2 ) , queé muito parecida com a distribuição de massa (iii) considerada por Macedo e Guedes [6].…”