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:
\[n_i = 9.4899\times 10^{9} cm^{-3}
\]
参考文献
[1] Wikipedia
[2] 百度百科
附件
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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))