Abstract
We compute the hole states in the GaAs free-standing nanowires, and in the GaAs/(Al,Ga)As core-shell nanowires of type I-s, which are grown along the [100] direction. The hole states are extracted from the 4-band Luttinger-Kohn Hamiltonian, which explicitly takes into account mixing between the light and heavy holes. The axial aproximation is adopted, which allowed classification of states according to the total angular monentum (fz when expressed in units of the Planck constant). The envelope functions are expanded in Bessel functions of the first kind. The dispersion relations of the subbands E(kz) obtained by the devised method do not resemble parabolas, which is otherwise a feature of the dispersion relations of the conduction subbands. Furthermore, the energy levels of holes whose total orbital momentum is fz=1/2 are shown to cross for a free-standing wire. The low energy fz=1/2 states are found to anticross, but these anticrossings turn into crossings when the ratio of the inner and outer radius of the core-shell wire takes a certain value. The influence of the geometric parameters on the dispersion relations is considered for both free standing and core-shell nanowires.
Highlights
The hole subbands in the core-shell nanowires with 5 nm inner and 15 nm outer radius
C.E. Pryor, Band structure of core–shell semiconductor nanowires, Phys
Summary
U ovom radu se posmatraju šupljinska stanja u GaAs slobodnostojećim nanožicama i GaAs/(Al,Ga)As jezgro–omotač nanožicama tipa I-s, narastanih u pravcu [100]. Tehnike koje se koriste za realizaciju nanožica su brojne, pa će ovde biti navedene osnovne i najčešće korišćene. Nanožice se mogu dobiti korišćenjem planarnih tehnologija, dobro poznatih u mikroelektronici, kao što su litografija i nagrizanje [8]. Koji se ugrađuje preferentno aksijalno, može se dobiti aksijalni heterospoj i aksijalna superrešetka (dole levo na slici 1). Ako se ugradnja materijala vrši preferentno radijalno, dobijaju se nanožice jezgro–omotač (core–shell), koje su prikazane dole desno na slici 1 [12]. Šematski prikaz rasta nanožica i nanožičanih heterostruktura pomoću VLS metode: materijal se nanosi preferentno aksijalno u prisustvu katalizatora (gore), ali promena materijala pri aksijalnom nanošenju, dovodi do aksijalnih heterostruktura, kao što su heterospoj (levo dole), dok ako se materijal nanosi preferentno radijalno, formira se nanožica jezgro– –omotač, koja može imati više slojeva u omotaču (desno dole). U provodnoj zoni zavisnost energija od longitudinalnog talasnog vektora je parabolična, pa provodna zona neće biti posmatrana
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