Solid State Electronic Devices, 7th Edition

Semiconductor Physics

Electron momentum: $$\text{p}\text{}\text{=}\text{m*v}\text{}\text{=}\text{}\hslash K=\frac{h}{\lambda }$$

Planck: $$E=hv=\hslash \omega$$

Kinetic: $$E=\frac{1}{2}m*{\text{v}}^2=\frac{1}{2}\frac{{\text{p}}^2}{m^{*}}=\frac{{\hslash }^2}{2m*}{k}^2$$ (3–4)

Effective mass: $$m*=\frac{{\hslash }^2}{d^{2}E\text{/}d{k}^2}$$ (3–3)

Total electron energy$$=P.E.+K.E.=E_c+E\left(k\right)$$

Fermi-Dirac e^– distribution: $$f\left(E\right)=\frac{1}{1+e^{\left(E-E_F\right)\text{/}kT}}\cong e^{\left(E_F-E\right)/kT}\text{for}E\gg E_F$$ (3–10)

Equilibrium:$$n_0={\displaystyle {\int }_{E_c}^{\infty }f\left(E\right)N\left(E\right)dE=Nf_c\left(E_c\right)}=N_c{e}^{-\left(E_c-E_F\right)\text{/}kT}$$ (3–15)

$$N_c=2{\left(\frac{2\pi m_n^{*}kT}{h^2}\right)}^{3\text{/2}}$$(3–16a)

$$N_v=2{\left(\frac{2\pi m_p^{*}kT}{h^2}\right)}^{3\text{/}2}$$(3–20)

$$p_0=N_v\left[1-f\left(E_v\right)\right]=N_v{e}^{-\left(E_F-E_v\right)\text{/}kT}$$(3–19)

$$n_i=N_c{e}^{-\left(E_c-E_i\right)\text{/}kT},p_i=N_v{e}^{-\left(E_i-E_v\right)\text{/}kT}$$(3–21)

$$n_i=\sqrt{N_c{N}_v}{e}^{-E_g\text{/}2kT}=2{\left(\frac{2\pi kT}{h^2}\right)}^{3\text{/}2}{\left(m_n^{*}{m}_p^{*}\right)}^{3/4}{e}^{-E_g\text{/2}kT}$$(3–23), (3–26)

Equilibrium: $$\begin{array}{c}{n}_0=n_i{e}^{\left(E_F-E_i\right)\text{/}kT}\\ p_0=n_i{e}^{\left(E_i-E_F\right)\text{/}kT}\end{array}$$(3–25)

$$n_0{p}_0=n_i^2$$ (3–24)

Steady state: $$\begin{array}{l}n=N_c{e}^{-\left(E_c-\text{}\text{}{F}_n\right)/kT}=n_i{e}^{\left(F_n-E_i\right)/kT}\hfill \\ p=N_v{e}^{-\left(E_p-\text{}\text{}{F}_v\right)/kT}=n_i{e}^{\left(E_i-F_p\right)/kT}\hfill \end{array}$$ (4–15)

$$nP=n_i^2{e}^{(F_{}}$$