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MOSFET MODELING FOR VLSI SIMULATION - Theory and Practice Episode 3

Tham khảo tài liệu 'mosfet modeling for vlsi simulation - theory and practice episode 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 56 2 Basic Semiconductor and pn Junction Theory Fig. 2.16 Behavior of a pn junction depletion capacitance Cj as a function of the voltage vd across the diode approximation is used instead see curve c in Figure 2.16 . In this case we define a parameter Fc 0 Fc 1 such that when the diode is forward bias and Vd Fcộbi the following equation for Cj is used Cj Ợ 0 1 Fc 1 m m . y- Vd 1 - Fc l m -Vbi Vd Fc l bi 2.75 that is obtained by matching slopes at Fcộbi. Thus Fc determines how depletion capacitance is calculated when the junction is forward biased. Normally Fc is taken as 0.5. The above approximation avoids infinite capacitance and though not accurate is acceptable for circuit design work. This is because under forward bias conditions diffusion capacitance as discussed below dominates. It should be pointed out that for circuit models ộbi and m become fitting parameters and are obtained by fitting Eq. 2.74 to experimental capacitance data as is discussed in detail in section 9.14.2. 2.7.2 Diffusion Capacitance The variation in the stored charge gdif associated with excess minority carrier injection in the bulk region under forward bias is modeled by another capacitance Cdf. The capacitance Cdf is called diffusion capacitance because the minority carriers move across the bulk region by diffusion. Since gdif is proportional to the current Id for an n p diode we can write 5 12 0dif - Vd C cm2 . 2.76 Ad 2.7 Diode Dynamic Behavior 57 For a short base diode Tp is replaced by Tt the transit time of the diode. For the case of a long base diode the transit time Tt is the excess minority carrier lifetime. Differentiating Eq. 2.76 gives c lf Qdif i Fd CA u I I dvd Adv VtJ F cm2 . 2.77 A more accurate derivation results in a Cdf half of that shown in Eq. 2.77 11 12 .26 Let us compare the magnitude of the two capacitances at a forward bias of say 0.3V assume we have a n p diode with Na 1015cm-3 and Nd 10 9 cm3 then Eq. 2.44 gives ộbi 0.814 V. For a forward bias of 0.3 V Eq. 2.50