Bipolar Junction Transistor:
æ qV ö ù
qD p é
1
J pE = E E 0 êexp ç BE ÷ -1ú
è kT ø û tanh(x E / LE )
LE ë
and
ìé
ü
æ qV ö ù
ïï êexp ç BE ÷ -1ú
ïï
è kT ø û
qDB nB0 ë
1
J nE =
+
í
ý
LB ï tanh(x B / LB )
sinh(xB / LB ) ï
ïî
ïþ
and J E = J nE + J pE
Simplified BJT model:
qni2 DnB   qVBE  
J nE =
exp
 −1
N BWB   kT  
and
qni2 D pE   qVBE  
J pE =
exp
 −1
N EWE   kT  
So,
J E = J nE + J pE
J pC =
J C = J nE
æ qVBC ö ù
qDC pC 0 é
qD p
÷ -1ú » - C C 0
êexp ç
è kT ø û
LC ë
LC
and
J B = J PE
ìé
ü
æ qV ö ù
ïï êexp ç BE ÷ -1ú
ïï
è kT ø û
qD n
1
ë
J nC = B B0 í
+
ý
LB ï sinh(x B / LB )
tanh(xB / LB ) ï
ïî
ïþ
and JC = J nC + J pC » J nC
Find Base current from J B + JC + J E = 0
Related to MOS Capacitor:
(𝐸𝐹𝑖 − 𝐸𝐹 ) for p-substrate:
where 𝜙𝑠 is the surface potential
Depletion Width
Maximum Depletion width is
Threshold Voltage:
VTN =
'
QSD
(max)
Cox
'
QSS
+ f ms + 2f fp
Cox
′
Where, 𝑄𝑆𝐷
= 𝑞 𝑁𝑎 𝑥or
𝑑𝑡 is the maximum depletion charge.
Q' (max)
SD
′
VTN oxide,
=
𝑄𝑆𝑆
is the charge in the
Cox
- VFB + 2f fp
𝜀
𝐶𝑜𝑥 = 𝑡𝑜𝑥 , (𝑡𝑜𝑥 is oxide thickness); and
𝑜𝑥
𝜙𝑚𝑠 is the metal-semiconductor work function difference.
a) accumulation
C'(acc) = Cox =
eox
t ox
b) Depletion
1
1
1
= ' + '
'
Cdep Cox CSD
c) Inversion
C'(inv) = Cox =
eox
t ox
Also
eox
'
CFlat
Band =
1/ 2
t ox +
eox æ KT es ö
ç
÷
es è q qN a ø
MOSFETs:
𝑉𝐷,𝑠𝑎𝑡 = 𝑉𝐺𝑆 − 𝑉𝑡ℎ
Triode (Linear, or Ohmic) regime:
𝑉𝐺𝑆 ≥ 𝑉𝑡ℎ and 𝑉𝐷𝑆 ≤ 𝑉𝐷,𝑠𝑎𝑡
Saturation region;
𝑉𝐺𝑆 ≥ 𝑉𝑡ℎ and 𝑉𝐷𝑆 ≥ 𝑉𝐷,𝑠𝑎𝑡
𝜕𝐼
Transconductance is: 𝑔 𝑚 ≜ 𝜕𝑉 𝐷 = 2𝐾𝑛 [𝑉𝐺𝑆 − 𝑉𝑡ℎ ]
𝐺𝑆