氢化杂质和厚度效应对高斯势量子点中二能级体系量子跃迁的影响

在计及氢化杂质和厚度效应下，分别选取抛物线型限定势阱和高斯函数型限定势阱描写盘型量子点中电子的横向限定势和纵向限定势，采用Lee-Low-Pines-Pekar变分法推导出量子点中电子的基态和第一激发态能量本征值和本征函数，以此为基础，构造了一个二能级结构，并基于二能级体系理论，讨论了电子在磁场作用下的量子跃迁.结果表明，高斯函数型限定势比抛物线型限定势更能精准反映量子点中真实的限定势；量子点的厚度对电子的跃迁概率的影响不凡；电声耦合强度、介电常数比、磁场的回旋频率、高斯函数型限定势阱的阱深和阱宽等对电子基态与第一激发态声子平均数、能量以及量子跃迁的影响显著.

Influence of Hydrogen-like impurity and thickness effect on quantum transition of a two-level system in an asymmetric Gaussian potential quantum dot

Considering hydrogen-like impurity and the thickness effect,the eigenvalues and eigenfunctions of the electron ground state and first exited state in a quantum dot (QD) are derived by using the Lee-Low-Pines-Pekar variational method with a parabolic confinement potential well (PCPW) and an asymmetric Gaussian functional confinement potential well (AGFCPW) serving as the transverse and longitudinal confinement potential,respectively.Based on the above two states,a two-level system is constructed.Then,the electron quantum transition affected by a magnetic field is discussed in terms of the two-level system theory.The numerical calculations indicate that the electron transition probability Q deceases with the range R₀ of the PCPW decreasing.With R₀ decreasing,the amplitude of the transition probability Q decreases greatly when R₀ is small (R₀ < 2.5r_p),but the decrease becomes small when R₀ is large (R₀ > 2.5r_p).The transition probability Q decreases with the dielectric constant ratio η increasing.For different values of the well width L of the AGFCPW,the change forms of the transition probability Q with the well width L are different:the transition probability Q decreases monotonically with the decreasing of the well width L when L is large (L > 1.3r_p), which is similar to the trend of the transition probability Q changing with the range R₀ of the PCPW,but the oscillation of the transition probability Q is small with the decreasing of the well width L when L is small (L < 1.3r_p).Whereas, both changes are consistent basically when the range of the confinement potential (the value of R₀ or L) is large since the AGFCPW can be approximated by the PCPW when z/L ? 1.For the electronic state and its change in the QD with a confinement potential,in any case,the results are rough without regard to the influence arising from the thickness of the QD.This shows that the AGFCPW is more accurate than the PCPW in reflecting the real confinement potential. This conclusion is in accordance with the experimental results.In addition,the transition probability Q decreases with increasing V₀.The amplitude of the transition probability Q decreasing with increasing the dielectric constant ratio η is enlarged with reducing the coupling strength α.This indicates that the phonon (the polarization of the medium) effect cannot be ignored when investigating the change of the electronic state in the QD.The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency ω_c.The external magnetic field is a kind of inducement causing the quantum transition of electronic state.The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency ω_c,and is affected dramatically by the coupling strength α:with increasing the coupling strength α,the oscillation period of Q increases,but the oscillation amplitude decreases.In a word,the transition probability of the electron is influenced significantly by some physical quantities,such as the coupling strength α,the dielectric constant ratio η,the resonant frequency of the magnetic field ω_c,the well depth V₀, and the well width L of AGFCPW.