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Electronic structure and optical properties of quantum-confined lead salt nanowires

机译：量子限制的铅盐纳米线的电子结构和光学性质

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In the framework of four-band envelope-function formalism, developed earlier for spherical semiconductor nanocrystals, we study the electronic structure and optical properties of quantum-confined lead salt (PbSe and PbS) nanowires (NWs) with a strong coupling between the conduction and the valence bands. We derive spatial quantization equations, and calculate numerically energy levels of spatially quantized states of a transverse electron motion in the plane perpendicular to the NW axis, and electronic subbands developed due to a free longitudinal motion along the NW axis. Using explicit expressions for eigenfunctions of the electronic states, we also derive analytical expressions for matrix elements of optical transitions and study selection rules for interband absorption. Next we study a two-particle problem with a conventional long-range Coulomb interaction and an interparticle coupling via medium polarization. We derive analytical expressions for an effective direct Coulomb coupling and an effective coupling via medium polarization averaging corresponding coupling energies over the fast transverse motion of charge carriers and then compute numerically the effective couplings for the lowest-energy electron-hole pair in a PbSe NW of the radius R=5 nm in vacuum. The obtained results show that due to a large magnitude of the high-frequency dielectric permittivity of PbSe material, and hence, a high dielectric NW/vacuum contrast, the effective coupling via medium polarization significantly exceeds the effective direct Coulomb coupling at all interparticle separations along the NW axis. Furthermore, the strong coupling via medium polarization results in a bound state of the longitudinal motion of the lowest-energy electron-hole pair (a longitudinal exciton) while fast transverse motions of charge carriers remain independent of each other. For a PbSe NW of the radius R=5 nm, the binding energy of the longitudinal exciton is found to be about 77.9 meV that is approximately two times smaller than the energy of spatial quantization of the lowest-energy electronic states. Thus, the strong interparticle coupling via medium polarization in quantum-confined lead salt NWs significantly modifies the single-particle electronic spectrum and could result in essential modifications such Coulomb phenomena as impact ionization, Auger recombination, and carrier multiplication.
机译：在早期为球形半导体纳米晶体开发的四波段包络函数形式主义的框架下，我们研究了量子受限的铅盐（PbSe和PbS）纳米线（NWs）的电子结构和光学性质，该纳米线具有导电性和导电性之间的强耦合。价带。我们导出空间量化方程，并在垂直于NW轴的平面中计算横向电子运动的空间量化状态的能级，并计算由于沿NW轴的自由纵向运动而产生的电子子带。使用显式的电子态本征函数表达式，我们还可以得出光学跃迁矩阵元素的解析表达式，并研究带间吸收的选择规则。接下来，我们研究具有常规远程库仑相互作用和经由介质极化的粒子间耦合的两粒子问题。我们推导了有效的直接库仑耦合和通过介质极化的有效耦合的解析表达式，平均了电荷载流子快速横向运动上的相应耦合能，然后通过数值计算了PbSe NW中最低能量的电子-空穴对的有效耦合。真空中半径R = 5 nm。所得结果表明，由于PbSe材料的高频介电常数很大，因此，NW /真空介电常数高，通过介质极化产生的有效耦合大大超过沿所有粒子间距离的有效库仑直接耦合。 NW轴。此外，经由介质极化的强耦合导致最低能量的电子-空穴对的纵向运动（纵向激子）处于束缚状态，而电荷载流子的快速横向运动保持彼此独立。对于半径为R = 5 nm的PbSe NW，发现纵向激子的结合能约为77.9 meV，大约是最低能级电子态的空间量化能的两倍。因此，量子受限的铅盐纳米线中经由介质极化的强粒子间耦合显着地修饰了单粒子电子光谱，并可能导致本质上的修饰，例如碰撞电离，俄歇重组和载流子繁殖等库仑现象。

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