Solid State Electronic Devices, 7th Edition

p-n Junctions

Equilibrium: $$V_0=\frac{kT}{q}\text{ln}\frac{p_p}{p_n}=\frac{kT}{q}\text{ln}\frac{N_a}{n_i^2/N_d}=\frac{kT}{q}\text{ln}\frac{N_a{N}_d}{n_i^2}$$ (5–8)

$$\frac{p_p}{p_n}=\frac{n_n}{n_p}=e^{q{V}_0/kT}$$(5–10)

$$W={\left[\frac{2ϵ\left(V_0-V\right)}{q}\left(\frac{N_a+N_d}{N_a{N}_d}\right)\right]}^{1/2}$$(5–57)

One-sided abrupt p⁺ -n: $$x_{n0}=\frac{W{N}_a}{N_a+N_d}\simeq \text{}W$$ (5-23b)

$$V_0\text{}=\frac{q{N}_d{W}^2}{2ϵ}$$(5–29)

$$\Delta p_n=p\left(x_{n0}\right)-p_n=p_n\left(e^{qV/kT}-1\right)$$(5–29)

$$\text{δ}p\left(x_n\right)=\Delta p_n{e}^{-x_n/L_p}=p_n\left(e^{qV/kT}-1\right)e^{-x_n/L_p}$$(5–31b)

Ideal diode: $$I=qA\left(\frac{D_p}{L_p}{p}_n+\frac{D_n}{L_n}{n}_p\right)\left(e^{qV/kT}-1\right)=I_0\left(e^{qV/kT}-1\right)$$ (5–36)

Non-ideal: $$\begin{array}{l}I={I^{\prime }}_0(e^{qV/nkT}-1)\\ \left(n\text{ = 1 to 2}\right)\end{array}$$ (5–74)

With light: $$I_{\text{op}}=qA{g}_{\text{op}}\left(L_p+L_n+W\right)$$ (8–1)

Capacitance: $$C=\left|\frac{dQ}{dV}\right|$$ (5–55)

Junction depletion: $$C_j=ϵA{\left[\frac{q}{2ϵ(V_0-V)}\frac{N_d{N}_a}{N_d+N_a}\right]}^{1/2}=\frac{ϵA}{W}$$ (5–62)

Stored charge exp. hole dist.: $$Q_p=qA{\displaystyle {\int }_0^{\infty }\text{δ}p\left(x_n\right)d{x}_n}=qA\Delta p_n{\displaystyle {\int }_0^{\infty }{e}^{-x_n/L_p}d{x}_n}=qA{L}_p\Delta p_n$$ (5–39)

$$I_p\left(x_n=0\right)=\frac{Q_p}{{\tau }_p}=qA\frac{L_p}{{\tau }_p}\Delta p_n=qA\frac{D_p}{L_p}{p}_n\left(e^{qV/kT}-1\right)$$(5–40), (5–29)

$$G_s=\frac{dI}{dV}=\frac{qA{L}_p{p}_n}{{\tau }_p}\frac{d}{dV}\left(e^{qV/kT}\right)$$