采用基于密度泛函理论的第一性原理方法(DMOL3程序)， 在广义梯度近似(GGA)下, 计算了硅纳米晶（Si75H76）在B和P掺杂和乙基（—CH2CH3）、 异丙基（—CH(CH3)2）表面改性等情形下态密度、 结合能及能隙的变化。 结果表明： 掺杂对体系的禁带宽度（约3.12 eV）几乎没有影响， 但会引入带隙态； 三配位的B掺杂， 在禁带中靠近导带约0.8 eV位置引入带隙态， 三配位的P掺杂在禁带中靠近价带0.2 eV位置引入带隙态； 四配位的B掺杂， 在禁带中靠近价带约0.4 eV位置引入带隙态， 四配位的P掺杂在禁带中靠近导带约1.1 eV位置引入带隙态； 且同等掺杂四配位时体系能量要低于三配位； 适当的乙基或异丙基表面覆盖可以降低体系的总能量， 且表面覆盖程度越高体系能量越低， 但在表面嫁接有机基团过多将导致过高位阻， 计算时系统不能收敛。

Using the first-principles method based on density functional theory, at the generalized gradient approximation (GGA), the state density, the change of binding energy and the energy gap of the silicon nanocrystals (Si75H76) with the circumstances of boron (B)-doped , phosphorus (P)-doped and the surface modification with ethyl (CH2CH3), isopropyl (—CH(CH3)2) have been calculated. The results showed that the B or P-doped have little impact on the energy gap value (3.12 eV) of silicon nanocrystals (SiNcs), except that some energy levels will be introduced in the forbidden band. The energy level caused by three-coordinated B-doped SiNcs is Ec-0.8 eV, while it is Ev+0.2 eV for the three-coordinated P-doped. However, the energy level position is Ev+0.4 eV for the four-coordinated B-doped SiNcs, and Ec-1.1 eV for the four-coordinated P-doped. Total energy of the system with the four-coordinated doped is lower than that with the three-coordinated doped in the other same conditions. The total energy of SiNcs system lessen when the surface is modified with appropriate ethyl or isopropyl. The total energy decreases with the surface coverage of organo-functional group increasing. But, the calculation can’t converge because of too high resistance when the SiNcs surface are grafted with too many organic groups.