Theoretical analysis of lasing characteristics of stacked lnGaN quantum dot lasers from atomic scale

用偏振势依赖的sp3紧束缚方法分析了GaN势垒层中Ln&lt；0.2&gt；Ga_&lt；0.8&gt；N锥体量子点的电子结构。应变和原子位置的计算采用基丁势的价力场方法。对于直径为86.4A、高度为20.8A、小平面倾角为30度的QD，计算得到的最大压电场为1.64 mV/cm。由于量子受限斯塔克效应，能隙红移了0.100 eV。该场导致量子点中电子和空穴波函数的空间分离。可以完全屏蔽场的电子-空穴对的数量被估计为直径的函数。我们发现，直径为86.4A的量子点需要13个电子-空穴对才能完成全场屏蔽。在Damilano等人的实验中，对于直径为100A，高度=20A的分子束外延生长的量子点，测得其光致发光峰值能量E_&lt；PL&gt；为2.71 eV(室温)，与测量能量E_&lt；Pl&gt；=2.71eV，对于棱镜量子点，Eg=2.502 eV。

We have analyzed the electronic structures of ln_<0.2>Ga_<0.8>N pyramidal quantum dots (QDs) in a GaN barrier layer using a polarization-potential dependent sp^3 tight-binding method. A valence-force-field method using the Keating potential was used for the strain and atom-position calculations. For the QD with the diameter 86.4 A, height of 20.8 A, and facet inclination angle of 30 degree, the maximum piezoelectric field is calculated to be1.64 MV/cm. The energy gap shows a red shift of 0.100 eV due to the quantum-confined Stark effect. The field causes a spatial separation of the electron and hole wave functions in the QD. The number of electron-hole pairs, which can screen the field totally, is estimated as a function of the diameter. We find that 13 electron-hole pairs are required for the complete field screening for the QD with the diameter 86.4 A. In experiments by Damilano et al., the photoluminescence peak energy, E_<PL>, of 2.71 eV (at room temperature) was measured for the MBE-grown In_<0.2>Ga_<0.8>N QDs with the similar QD size ; diameter = 100 A, heitht = 20 A. Eg = 2.706 eV for the pyramidal QD is in better agreement with the measured energy, E_<PL> = 2.71 eV, than Eg = 2.502 eV for the prismatic QD.