Calculation of the Change in the Madelung Energy of Doped ZnO

Jing Wen ； Chun-Ying Zuo ； Cheng Zhong

《Chinese Journal of Physics》 48卷6期 (2010/12) Pp. 844-854

並列摘要

One of the main mechanisms leading to doping difficulty is the low dopant solubility in realizing p-type ZnO. The calculation of the impurity formation energy is widely accepted for investigating doping methods. Actually the calculation of the change in the Madelung energy of doped ZnO can also be taken as a guide for investigating the doping methods and impurity solubility, due to its larger proportion of ionic bond to the chemical bond. But we found that more than one value can be obtained during the calculation because a conditionally convergent series must be considered. Firstly, a symmetry rule is introduced especially in this paper to calculate the Madelung constant by considering the NaCl-type, CsCl-type, and ZnO-type crystal lattices. The advantage of this method is that the series can converge quickly using the symmetry rule without changing the form of the series. Then we calculate the difference in the Madelung energy between pure ZnO and ZnO doped by C and C-Ga, respectively, with the help of the method mentioned above. The results show that the C-Ca co-doping method is better than the C doping method from the stability point of view, which can effectively enhance the C impurity solubility. The method can be used to calculate this type of conditionally convergent series, whereby the arbitrary results which can come from different arrangements of the terms during the calculation can be avoided.