Applicability of the {bold k}{center_dot}{bold p} method to the electronic structure of quantum dots
- National Renewable Energy Laboratory, Golden, Colorado 80401 (United States)
The {bold k}{center_dot}{bold p} method has become the {open_quotes}standard model{close_quotes} for describing the electronic structure of nanometer-size quantum dots. In this paper we perform parallel {bold k}{center_dot}{bold p} (6{times}6 and 8{times}8) and direct-diagonalization pseudopotential studies on spherical quantum dots of an ionic material{emdash}CdSe, and a covalent material{emdash}InP. By using an equivalent input in both approaches, i.e., starting from a given atomic pseudopotential and deriving from it the Luttinger parameters in {bold k}{center_dot}{bold p} calculation, we investigate the effect of the different underlying wave-function representations used in {bold k}{center_dot}{bold p} and in the more exact pseudopotential direct diagonalization. We find that (i) the 6{times}6{bold k}{center_dot}{bold p} envelope function has a distinct (odd or even) parity, while atomistic wave function is parity-mixed. The 6{times}6{bold k}{center_dot}{bold p} approach produces an incorrect order of the highest valence states for both InP and CdSe dots: the p-like level is above the s-like level. (ii) It fails to reveal that the second conduction state in small InP dots is folded from the L point in the Brillouin zone. Instead, all states in {bold k}{center_dot}{bold p} are described as {Gamma}-like. (iii) The {bold k}{center_dot}{bold p} overestimates the confinement energies of both valence states and conduction states. A wave-function projection analysis shows that the principal reasons for these {bold k}{center_dot}{bold p} errors in dots are (a) use of restricted basis set, and (b) incorrect {ital bulk} dispersion relation. Error (a) can be reduced only by increasing the number of basis functions. Error (b) can be reduced by altering the {bold k}{center_dot}{bold p} implementation so as to bend upwards the second lowest bulk band, and to couple the conduction band into the s-like dot valence state. Our direct diagonalization approach provides an accurate and practical replacement to the standard model in that it is rather general, and can be performed simply on a standard workstation. {copyright} {ital 1998} {ital The American Physical Society}
- OSTI ID:
- 600990
- Journal Information:
- Physical Review, B: Condensed Matter, Vol. 57, Issue 16; Other Information: PBD: Apr 1998
- Country of Publication:
- United States
- Language:
- English
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