常用物理常数

物理常数

\[q = 1.602176634\times 10^{-19}C\\ m_0 = 9.1093837015\times 10^{-31} kg\\ eV = 1.602176634\times 10^{-19}J\\ h = 6.62607015\times 10^{-34} J\cdot s \\ \hbar =\frac{h}{2\pi}= 1.054571817\times 10^{-34} J\cdot s \\ k_0 = 1.380649\times 10^{-23} J/K \\ \epsilon_0 = 8.854187817\times 10^{-12} F/m \]

半导体常用

\(T=300K\) 时, \(k_0T=0.025852 eV\).

带边有效状态密度

\[N_c = 2(\frac{m_nk_0T}{2\pi\hbar^2})^{3/2}\\ N_v = 2(\frac{m_pk_0T}{2\pi\hbar^2})^{3/2} \]

载流子浓度乘积

\[n_0p_0 = N_cN_v \mathbf{exp}(-\frac{E_g}{k_0T}) \]

300K时的硅的状态密度有效质量为 \(m_{dn}=1.18m_0,m_{dp}=0.81m_0\). (刘恩科, 半导体物理学 P67).

\[N_c = 2(\frac{m_nk_0T}{2\pi\hbar^2})^{3/2} = 3.2166\times 10^{19} cm^{-3}\\ N_v = 2(\frac{m_pk_0T}{2\pi\hbar^2})^{3/2} = 1.8294\times 10^{19} cm^{-3} \]

计算可得硅的本征载流子浓度为:

\[n_i = 9.4899\times 10^{9} cm^{-3} \]

准费米能级

参考文献

[1] Wikipedia
[2] 百度百科
[3] https://doi.org/10.1016/0038-1101(82)90143-5
[4] https://nanohub.org/groups/ece656_f13/File:notes_on_FD_integral3rdEd.pdf

附件

点击查看代码

q=1.602176634e-19;%C
m_0 = 9.1093837015e-31;%kg
k = 1.380649e-23;%J/K
hbar = 1.054571817e-34;%J.s
m_n = 1.18*m_0;
m_p = 0.81*m_0;

N_c = 2*(m_n*k*300/(2*pi*hbar^2))^(3/2)
N_v = 2*(m_p*k*300/(2*pi*hbar^2))^(3/2)

Eg = 1.12;
kT = 0.025852;
ni = (N_c*N_v)^(1/2)*exp(-Eg/(2*kT))