Electron States and Light Absorption in Strongly Oblate and Strongly Prolate Ellipsoidal Quantum Dots in Presence of Electrical and Magnetic Fields

Abstract

In framework of the adiabatic approximation the energy states of electron as well as direct light absorption are investigated in strongly oblate and strongly prolate ellipsoidal quantum dots (QDs) at presence of electric and magnetic fields. Analytical expressions for particle energy spectrum are obtained. The dependence of energy levels’ configuration on QD geometrical parameters and field intensities is analytically obtained. The energy levels of electrons are shown to be equidistant both for strongly oblate and prolate QDs. The effect of the external fields on direct light absorption of a QD was investigated. The dependence of the absorption edge on geometrical parameters of QDs and intensities of the electric and magnetic fields is obtained. Selection rules are obtained at presence as well as absence of external electric and magnetic fields. In particular, it is shown that the presence of the electric field cancels the quantum numbers selection rules at the field direction, whereas in radial direction the selection rules are preserved. Perspectives of practical applications for device manufacturing based on ellipsoidal quantum dots are outlined.

Analytical and numerical calculations of spectral and optical characteristics of spheroidal quantum dots

“…Then in the effective mass approximation of the k · p-theory the Schrödinger equation for the slow-varying envelope wave functionΨ(r e ,r h ) of an electron (e) and a hole (h) in a uniform magnetic field H with the vector-potential A = H ×r and electric field F in oblate and prolate QDs reads as [8]:…”

“…The models with nonzero values of these parameters were announced in [8,25]. Throughout the paper we make use of the reduced atomic units [2,5]:…”

“…To ensure the prescribed accuracy of calculation of the lower part of the spectrum discussed below with eight significant digits we used j max = 16 basis functions in the expansion (8) and the discrete approximation of the desired solution by Lagrange finite elements of the fourth order with respect to the grid pitch Ω p hs (x s ) = [x s;min ; x s;k = x s;k−1 + h s ; x s;max ]. The details of the corresponding computational scheme are given in [24].…”

“…In general case for the calculation f ν,ν (u) by formula (48), (51), or (52) we used the eigenvalues In the regime of strong dimensional quantization the frequencies of the interband transitions (h → e) in GaAS between the levels n o = 1, n ρo = 0, m = 0 for OSQD or n p = 1, n zp = 0, m = 0 for PSQD at the fixed valuesã = 2.5a e andc = 0.5a e for OSQD orã = 0.5a e andc = 2.5a e for PSQD, are equal to ∆ω to the IR spectral region [7,8], taking the band gap value (2π ) −1Ẽ g = 346 THz into account. In Fig.…”

“…Electronic, kinetic, optical and other properties of QDs have been investigated experimentally and theoretically in many papers [4][5][6][7][8][9][10][11][12][13]. Particularly, the optical absorption characteristics of QDs have been shown to be strongly correlated with their geometry, on one hand, and with their physical-chemical properties, on the other hand.…”