$E=eV$

$v=\sqrt{\displaystyle\frac{2eV}{m}}$

$j_z=AT^2(1-\gamma)e^{-\phi/kT}$

$\rho_e(T)=\rho_u\left(\displaystyle\frac{T}{T_u}\right)^u$

$T=\left(\displaystyle\frac{\rho_uI_e^2}{2\epsilon\pi^2\sigma r_f^3T_u^u}\right)^{1/(4-u)}$

$A=\displaystyle\frac{4\pi m_ek^2e}{h^3}$

$j_{max}=-\displaystyle\frac{4\epsilon_0}{9}\sqrt{\displaystyle\frac{2e}{m_e}}\displaystyle\frac{V^{3/2}}{d^2}$

$I_f^2\rho_e(T)\displaystyle\frac{l_f}{\pi r_f^2}=2\pi r_fl_f\epsilon\sigma(T^4-T_0^4)$


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