Solid State Electronic Devices, 7th Edition

BJT-p-n-p

$$\begin{array}{c}{I}_{Ep}=qA\frac{D_p}{L_p}\left(\Delta p_E\text{ctnh}\frac{W_b}{L_p}-\Delta p_C\text{csch}\frac{W_b}{L_p}\right)\\ I_C=qA\frac{D_p}{L_p}\left(\Delta p_E\text{csch}\frac{W_b}{L_p}-\Delta p_C\text{ctnh}\frac{W_b}{L_p}\right)\end{array}$$(7–18)

$$\begin{array}{l}\Delta p_E=p_n\left(e^{q{V}_{EB}/kT}-1\right)\\ \Delta p_C=p_n\left(e^{q{V}_{CB}/kT}-1\right)\end{array}$$(7–8)

$$I_B=qA\frac{D_p}{L_p}\left[\left(\Delta p_E+\Delta p_C\right)\text{tanh}\frac{W_b}{2L_p}\right]$$(7–19)

$$B=\frac{I_C}{I_{Ep}}=\frac{\text{csch }{W}_b/L_p}{\text{ctnh }{W}_b/L_p}=\text{sech}\frac{W_b}{L_p}\simeq 1–\left(\frac{W_b^2}{2L_p^2}\right)$$(7–26)

(Base transport factor)

$$\gamma =\frac{I_{Ep}}{I_{En}+I_{Ep}}={\left[1+\frac{L_p^n{n}_u{\mu }_n^p}{L_n^p{p}_p{\mu }_p^n}\tanh \frac{W_b}{L_p^n}\right]}^{-1}\simeq {\left[1+\frac{W_b{n}_n{\mu }_n^p}{L_n^p{p}_p{\mu }_p^n}\right]}^{-1}$$(7–25)

(Emitter injection efficiency)

$$\frac{i_C}{i_E}=B\text{γ}\equiv \alpha$$(7–3)

(Common base gain)

$$\frac{i_C}{i_B}=\frac{B\text{γ}}{1-B\text{γ}}=\frac{\alpha }{1-\alpha }\equiv \text{β}$$(7–6)

(Common emitter gain)

$$\frac{i_C}{i_B}=\text{β}=\frac{{\tau }_p}{{\tau }_t}$$(7–7)

(For γ = 1)