器件设计中费密积分的精确近似计算  

Accurate Approximate Calculation of Fermi Integral for Device Design

作　　者：孟晖 王建峰[2] 

机构地区：[1]河北神舟卫星通信有限公司,石家庄050200 [2]中国电子科技集团公司第十三研究所,石家庄050051

出　　处：《半导体技术》2009年第8期755-758,共4页Semiconductor Technology

摘　　要：用MATLAB软件中的自适应洛巴托求积公式精确计算了费密积分,精确值比被广泛采用的G.J.Mc-DO和E.C.Stoner计算值多一位有效数字,根据精确值求出了费密积分的近似、易用的多项式回归方程,相关系数R2=1,相对误差εr*<0.4%;最后以GaAs掺Si(300K)为例,应用费密积分值计算出掺杂浓度与费密能级关系,与玻耳兹曼分布作了比较。结果表明,两种分布情况下,当Nd<1.0×1017cm-3时,费密能级基本重合;当Nd>1.0×1017cm-3时,两者费密能级差别逐渐增大,采用费密分布更符合实际情况。结果还表明,GaAs开始发生简并时掺杂浓度差别较大。费密分布时Nd≥1.21171×1018cm-3;玻耳兹曼分布时Nd≥1.54321×1018cm-3。The Fermi integral was accurately calculated with adaptive Lobatto quadrature in MATLAB, a significant digit was enhanced than G.J.Mc-DO and E.C.Stoner value. According to the accurate value, some polynomial regression equations were obtained, the correlation coefficient R^2 = 1, relative error εr^＊ 〈 0.4%. An example Si-doped GaAs （T= 300 K） was given, the doping concentration and Fermi level was calculated by Fermi integral accurate value and Bohzmann distribution, the results show that when Nd 〈 1.0 × 10^17 cm^-3, the Fermi level values of them are basically similar, while when Nd 〉 1.0 × 10^17 cm^-3, the difference between them becomes large gradually, the Fermi level is more fit. It also shows that the difference of doping concentration is great at the beginning of GaAs degenerating. When it is at Fermi level distribution, Nd ≥ 1.211 71 × 10^18 cm^-3, while at Boltzmann distribution, Nd ≥ 1.543 21× 10^18 cm^-3.

关 键 词：MATLAB 费密积分 近似表达式 费密分布 玻耳兹曼分布 掺杂浓度 费密能级 

分 类 号：TP319[自动化与计算机技术—计算机软件与理论]