[반도체공학] 6.4. Special Considerations

2020. 6. 16. 07:19

728x90

4. Special Considerations

1. Charge-Control Approach

long-base 다이오드 : $J_P(\infty)=0$ $J_{P} (\infty) = 0$
- n-region hole charge $Q_P=qA\int_0^\infty \Delta p_n(x,t)dx$
- $\frac{dQ_p}{dt}=i_{diff}(0)-\frac{Q_P}{\tau_p}$
- 전하의 변화율 = 초기 diffusion - recombination으로 사라지는 전하량
steady state에서 $I_{diff}=\frac{Q_P}{\tau_P}=\frac{qAL_Pn_i^2}{\tau_PN_D}[e^{V_A/V_T}-1]$ $I_{d i f f} = \frac{Q _{P}}{τ _{P}} = \frac{q A L _{P} n _{i}^{2}}{τ _{P} N _{D}} [e^{V_{A} / V_{T}} - 1]$
$=\frac{qAD_Pn_i^2}{L_PN_D}[e^{V_A/V_T}-1](\because L_P^2=D_P\tau_P)$ $= \frac{q A D _{P} n _{i}^{2}}{L _{P} N _{D}} [e^{V_{A} / V_{T}} - 1] (∵ L_{P}^{2} = D_{P} τ_{P})$
- short-base 다이오드 : $\frac{dQ_p}{dt}=A[i_{diff}(0)-i_{diff}(x_c)]-\frac{Q_P}{\tau_p}$
- long-base 대비 흐르는 전류양이 늘어남

낮은 농도로 도핑된 영역이 minority carrier diffusion length보다 짧은 다이오드
- $\Delta p_n(x_c)=0$
- $\Delta p_n(0)=p_{n0}[e^{qV_A/kT}-1]\simeq\frac{n_i^2}{N_D}[e^{qV_A/kT}-1]$
- $\Delta p_n(x)=A_1exp[-x/L_P]+A_2exp[x/L_P]$
- By boundary condition,
  $\Delta p_n(x_c)=p_{n0}[e^{V_A/V_T}-1]\frac{sinh[x_c-x/L_P]}{sinh[x_c/L_P]}$
- narrow base( $x_c<<L_P$ )일 때는 recombination 발생이 없음 : $\frac{\Delta p_n}{\tau_P}$
$I_{Diff}=AJ_P(0)=I_0[e^{V_A/V_T}-1]$ $I_{D i f f} = A J_{P} (0) = I_{0} [e^{V_{A} / V_{T}} - 1]$
- $I_0=\frac{qAD_Pp_{n0}}{L_P}p_{n0}\frac{cosh(x_c/L_P)}{sinh(x_c/L_P)}$

728x90