University of California, Irvine

EECS 170A

Ch.8.1 PN Junction Diode HW#6
J=q*exp((qVa)/(kT))-1)*(((ni
2Dn)/(N
aLn))+((ni
2Dp)/(NdLp)))
J=Js(exp(Va/(kT))-1)
J=Jp(xn)+Jn(-xp)
Jp(xn)=((qDppn0)/Lp)*(exp(Va/(kT))-1
)=qpn (Dp/?p0) [at edge]√
Jn(-xp)=((qDnnp0)/Ln)*(exp(Va/(kT))-
1)=qnp (Dn/?n0) [at edge]√
Jp(x)=((qDppn0)/Lp)*(exp(Va/(kT))-1)
*exp((xn-x)/Lp) [If x≥nn]
Jn(x)=((qDnnp0)/Ln)*(exp(Va/(kT))-1)
*exp((xp+x)/Ln) [If x≤-xp]
Js=(qni
2)((1/Na (Dn/?n0))+(1/Nd
√ √
(Dp/?p0)))[A/cm2]
Js=J?p+J?n=((qDppn0)/Lp)+((qDnnp0)/Ln)
I=Is*exp(Va/Vt)
Is=Js*A[A] Js=Is/A
nn0=Nd pp0=Na
npo=ni
2/(pp0=Na)[cm-3]
pno=ni
2/(nn0=Nd)[cm-3]
np=npo*exp(Va/(kT))
pn=pno*exp(Va/(kT))
?np=np-np0 ?pn=pn-pn0
?pn(x)=pn(x)-p0=pn0(exp(Va/(kT))-1)*
exp((xn-x)/Lp) [If x≥nn]
?np(x)=np(x)-np0=np0(exp(Va/(kT))-1)
*exp((xp-x)/Ln) [If x≤-xp]
np0=(nn0=Nd)*exp((-Vbi)/(kT))
ni
2/(NdNa)=exp((-Vbi)/(kT))
Ch.7 PN Junction HW#5
?==V [Not Vbi]
Vbi=(kT=Vt)*ln((NaNd)/ni
2)=|?Fn|+|?Fp|
VB=(?s?0)Ecrit
2/(2qNB)[NBis lw dopd pnjunc sd]
|?F|=Efi-Ef
e?Fn=e?Fp=Efi-Ef
?Fn=-kT*ln(Nd/ni)
?Fp=kT*ln(Na/ni)
?=(Ef-Efi)/q
?(x)=((qNa)/(2?s?0))*(x-xp)2 [-xp≤x≤0]
xn= ((2?s?0VbiNa)/(qNd(Na+Nd)))[cm]√
xp= ((2?s?0VbiNd)/(qNa(Na+Nd)))[cm]√
W=xn+xp=xn(1+(Nd/Na))= √
((2?s?0(
Vbi+VR)(Na+Nd))/(qNaNd))
[Ans:~?m][
Vbi+VR or
Vbi-Va or
Vbi]
Carrier Density scale by
exp((qVa)/(kT)) when Va changes
Naxp=Ndxn
E(x)=-((qNd)/(?s?0))(xn-x)
Emax[V/cm]=-(qNdxn)/(?s?0)=-(qNaxp)/(?s?
0)=-(2(Vbi+VR))/W=- √
((2q(Vbi+VR)NaNd)/(?s?0(Na+Nd)))
[Ans:~5E4] C=C’*A
C’= ((q?NaNd)/(2(Vbi+VR)(Na+Nd)))√
np=ni
2((Efn-Efp)/(kT))
Ch.6 Non Eq Excess Carrier HW#4
n=n0+?n=ni*exp((Efn-Efi)/(kT))
p=p0+?p=ni*exp((Efi-Efp)/(kT))
Rn
’=Rp
’=Δn(t)/?n0 [p-type,Low In]
Rn
’=Rp
’=Δn(t)/?p0 [n-type,Low In]
Rno=?R*ni
2 ?R=1/(Nd*?p)=1/(Na*?n)
D’=(DnDp(n+p))/(Dnn+Dpp)
?’=(?n?p(p-n))/(?nn+?pp)
ptype@lowin & Dn~Dp->D’=Dn & ?’=?n
ntype@lowin & Dn~Dp->D’=Dp & ?’=?p
Ln= (Dn?n0)√ Lp= (Dp?p0)√
E(x)=-kT(1/Nd(x))(dNd(x)/dx)
Infinte&Homog. p-type semi.
?n(x)=?n(0)exp(-x/Ln) [x≥0]
?n(x)=?n(0)exp(x/Ln) [x≤0]
?n(t)=?p(t)=?p(0)exp(-t/?n0)
?n(t)=g’?n0(1-exp(-t/?n0))
dΔp/dt=-Δp?p(dE/dx)-?pE(dΔp/dx)+D
p(d2Δp/dx2)+GL-Δp/?p for p
Ca1 SS, no cg, no drf(Eext)
0=Dn(d2Δn/dx2)-Δn/?n ->
Δn(x)=A*exp(-x/L)+B*exp(x/L)
Ca2 no drf(Eext), no diff(cgrad)
dΔn/dt=GL-Δn/?n ->
Δn(t)=g*?n(1-exp(-t/?n))+Δn(0)exp
(-t/?n)
Ca3 SS, no cg, no drf(Eext), no ?
0=Dn(d2Δn/dx2) ->