3.4.3 Source Side Potential and Charge Calculation

The core model calculation at the source side is shown below:

qdep=qdepnVtm(3.271) qdep = \dfrac{qdep}{nVtm} \qquad (3.271)

vch=0.0+ΔVt,QM(3.272) vch = 0.0 + \Delta V_{t,QM} \qquad (3.272)

Here 0.0 refers to the quasi-fermi potential at the source side

If BULKMOD≠0 BULKMOD \ne 0 then,

T1=hypsmooth(2.0⋅ϕB+vch−ves,1.0)(3.273) T1 = hypsmooth(2.0 \cdot \phi_B + vch - ves, 1.0) \qquad (3.273)

T3=−(K1_t2.0⋅nVtm)⋅(T1−2.0⋅ϕB)(3.274) T3 = - \Big( \dfrac{K1\_t}{2.0 \cdot nVtm} \Big) \cdot \Big( \sqrt{T1} - \sqrt{2.0 \cdot \phi_B} \Big) \qquad (3.274)

T0=−qdep−T3+vth_fixed_factor_sub+QMFACTOR⋅(−qdep)2/3(3.275) T0 = -qdep - T3 + vth\_fixed\_factor\_sub + QMFACTOR \cdot (-qdep)^{2/3} \qquad (3.275)

T1=−qdep−T3+vth_fixed_factor_SI(3.276) T1 = -qdep - T3 + vth\_fixed\_factor\_SI \qquad (3.276)

For the terms vth fixed factor sub and vth fixed factor SI, please see the Verilog-A source code file (bsim- cmg body.include)

If BULKMOD=0 BULKMOD = 0 then

T0=−qdep−T3+vth_fixed_factor_sub+QMFACTOR⋅(−qdep)2/3(3.277) T0 = -qdep - T3 + vth\_fixed\_factor\_sub + QMFACTOR \cdot (-qdep)^{2/3} \qquad (3.277)

T1=−qdep+vth_fixed_factor_SI(3.278) T1 = -qdep + vth\_fixed\_factor\_SI \qquad (3.278)

T2=vgsbeff−vchnVtm(3.279) T2 = \dfrac{vgsbeff - vch}{nVtm} \qquad (3.279)

F0=−T2+T1(3.280) F0 = -T2 + T1 \qquad (3.280)

T3=0.5⋅(T2−T0)(3.281) T3 = 0.5 \cdot (T2 - T0) \qquad (3.281)

qm=exp(T3)(3.282) qm = exp(T3) \qquad (3.282)

If qm>10−7 qm > 10^{-7} then

T7=ln(1+qm)(3.283) T7 = ln (1 + qm) \qquad (3.283)

qm=2.0⋅(1.0−1.0+T7⋅T7)(3.284) qm = 2.0 \cdot (1.0 - \sqrt{1.0 + T7 \cdot T7} ) \qquad (3.284)

T8=(qm⋅alpha_UFCM+qdep)⋅rc(3.285) T8 = (qm \cdot alpha\_UFCM + qdep) \cdot rc \qquad (3.285)

T4=T8exp(T8)−T8−1.0(3.286) T4 = \dfrac{T8}{exp(T8) - T8 - 1.0} \qquad (3.286)

T5=T8⋅T4(3.287) T5 = T8 \cdot T4 \qquad (3.287)

e0=F0−qm+ln(−qm)+ln(T5)+QMFACTOR⋅[−(qm+qdep)]2/3(3.288) e0 = F0 - qm + ln (-qm) + ln (T5) + QMFACTOR \cdot \Big[ -(qm + qdep) \Big]^{2/3} \qquad (3.288)

e1=−1+1qm+(2T8−T4−1)⋅rc−23⋅QMFACTOR⋅[−(qm+qdep)]−1/3(3.289) e1 = -1 + \dfrac{1}{qm} + \Big( \dfrac{2}{T8 - T4 -1} \Big) \cdot rc - \dfrac{2}{3} \cdot QMFACTOR \cdot \Big[ -(qm + qdep) \Big]^{-1/3} \qquad (3.289)

e2=−1qm⋅qm−29⋅QMFACTOR⋅[−(qm+qdep)]−4/3(3.290) e2 = \dfrac{-1}{qm \cdot qm} - \dfrac{2}{9} \cdot QMFACTOR \cdot \Big[ -(qm + qdep) \Big]^{-4/3} \qquad (3.290)

qm=qm−(e0e1)⋅(1.0+e2⋅e22.0⋅e1⋅e1)(3.291) qm = qm - \Big( \dfrac{e0}{e1} \Big) \cdot \Big( 1.0 + \dfrac{e2 \cdot e2}{2.0 \cdot e1 \cdot e1} \Big) \qquad (3.291)

T8=(qm⋅alpha_UFCM+qdep)⋅rc(3.292) T8 = (qm \cdot alpha\_UFCM + qdep) \cdot rc \qquad (3.292)

T4=T8exp(T8)−T8−1.0(3.293) T4 = \dfrac{T8}{exp(T8) - T8 - 1.0} \qquad (3.293)

T5=T8⋅T4(3.294) T5 = T8 \cdot T4 \qquad (3.294)

e0=F0−qm+ln(−qm)+ln(T5)+QMFACTOR⋅[−(qm+qdep)]2/3(3.295) e0 = F0 - qm + ln (-qm) + ln (T5) + QMFACTOR \cdot \Big[ -(qm + qdep) \Big]^{2/3} \qquad (3.295)

e1=−1+1qm+(2T8−T4−1)⋅rc−23⋅QMFACTOR⋅[−(qm+qdep)]−1/3(3.296) e1 = -1 + \dfrac{1}{qm} + \Big( \dfrac{2}{T8 - T4 -1} \Big) \cdot rc - \dfrac{2}{3} \cdot QMFACTOR \cdot \Big[ -(qm + qdep) \Big]^{-1/3} \qquad (3.296)

e2=−1qm⋅qm−29⋅QMFACTOR⋅[−(qm+qdep)]−4/3(3.297) e2 = \dfrac{-1}{qm \cdot qm} - \dfrac{2}{9} \cdot QMFACTOR \cdot \Big[ -(qm + qdep) \Big]^{-4/3} \qquad (3.297)

qm=qm−(e0e1)⋅(1.0+e2⋅e22.0⋅e1⋅e1)(3.298) qm = qm - \Big( \dfrac{e0}{e1} \Big) \cdot \Big( 1.0 + \dfrac{e2 \cdot e2}{2.0 \cdot e1 \cdot e1} \Big) \qquad (3.298)

If qm≤10−7 qm \le 10^{-7} then

qm=−qm⋅qm(3.299) qm = - qm \cdot qm \qquad (3.299)

qis=−qm⋅nVtm(3.300) q_{is} = -qm \cdot nVtm \qquad (3.300)

ψs=Vgsfbeff−qis(3.301) \psi_s = V_{gsfbeff} - q_{is} \qquad (3.301)

Eeffs=10−8⋅(qbs+η⋅qisϵratio⋅EOT)(3.302) E_{effs} = 10^{-8} \cdot \Big( \dfrac{q_{bs} + \eta \cdot q_{is}}{\epsilon_{ratio} \cdot EOT} \Big) \qquad (3.302)

results matching ""

    No results matching ""