纤锌矿GaN柱形量子点中类氢施主杂质态

Hydrogenic Donor Impurity States in a Cylindrical Wurtzite GaN Quantum Dot

在有效质量近似和变分原理的基础上,选取含两个变分参数的波函数,研究了纤锌矿结构的GaN/AlxGa1-xN单量子点中类氢施主杂质体系的结合能随量子点(QD)尺寸以及杂质在量子点中位置的变化,并与以前使用不同尝试波函数的计算结果进行了比较。结果表明:由我们选取的两变分参数波函数得到的结果与前人选取的两变分参数波函数得到的结果相比有所改进,而与选取一个变分参数波函数得到的结果一致。同时我们还计算了体系的维里定理值随量子点半径的变化情况,所得结果与前人工作结果一致,说明本文选取的两变分参数波函数能很好地描述柱形量子点中施主杂质态的运动。

Based on the framework of effective-mass approximation and variational approach,the binding energy of a hydrogenic donor impurity state is investigated theoretically as functions of the impurity position and the quantum dot size by employing a trial wavefunction with two variational parameter for a cylindrical wurtzite GaN/AlxGa1-xN quantum dot（QD） with finite potential barriers.The numerical results show that the donor binding energy of the hydrogenic impurity is highly dependent on the impurity position and QD size.When the built-in electric field is ignored or considered,the donor binding energy has a maximum value with moving the impurity position along the growth direction.The donor binding energy increases firstly,reachs a maximum value,then decreases with increasing the height and the radius of QDs.The strong built-in electric field induces an asymmetrical distribution of the donor binding energy with respect to the center of the QD.In particular,we find that the donor binding energy is insensitive to the dot height when the impurity is located near the top boundary（z0=L/2,z0=L/4）of the WZ GaN/AlxGa1-xN QD.And we compare the above results with previous calculation results using different trial wavefunction.The present results using two variational parameter wavefunction is better than the results given by previous two-parameter wavefunction.A good agreement between the present results using two variational parameter wavefunction and the results of the wavefunction with one variational parameter is found.Using the binding energy obtained from the present calculations,we further calculate the virial theorem number as a function of the quantum dot radius.Our present result coincides with the previous finding,so we may say that the present trial wavefunction with two variational parameter can describe better the internal motion of hydrogenic donor impurity state in the cylindrical wurtzite QD.