中文摘要：

采用基于密度泛函理论的第一性原理平面波赝势法计算了稀土元素Ce，Pr掺杂GaN的晶格参数、能带、电子态密度和光学性质，使用LSDA＋U的方法处理具有强关联作用的稀土4f态，并分析比较计算结果．计算表明：掺入Ce和Pr后的体系相比未掺杂的GaN晶格常数增大，带隙变窄，并分别在禁带中和价带顶附近引入了局域的杂质能级，该能级主要由Ce和Pr的4f电子提供；掺杂后都发生了磁有序化并产生磁矩；最后定性分析了掺杂前后介电函数和光吸收系数的变化，掺Ce的体系在介电函数和吸收系数的低能区出现了峰值，该峰的出现和禁带中的杂质能级到导带底的跃迁有关，而掺Pr的体系由于带隙变窄使介电峰和吸收边发生红移．

英文摘要：

Using the pseudopotential plane-wave method within the density functional theory as implemented in the Vienna ab-initio simu- lation package, we investigate the crystal parameters, electronic structures and optical properties of rare earth Ce and Pr doped GaN. The local spin density approximation with Hubbard-U corrections method is used to treat the correlation effect of strongly localized rare-earth 4f electron states. The results show that the crystal parameters increase after doping Ce and Pr in GaN. The Ce impurity introduces defect level in the gap while for Pr the level lies near the valence band maximum, and the defect levels are contributed by Ce and Pr 4f electron states. In addition, the dopings of Ce and Pr give rise to spin polarization and magnetic-order. For GaN：Ce, there appear two new peaks, one is in the low energy region of imaginary dielectric function and the other is in the low energy region of absorption coefficient. These new peaks are probably related to the defect level in the gap. For GaN：Pr, red shifts of the dielectric peak and absorption edge duo to bandgap narrowing are observed.