6.012 Electronic Devices and Circuits Formula Sheet for Final Exam, Fall 2003 Parameter Values: q = 1.6x10 19 Coul 14 F/cm, o = 8.854 x10 Si
10
12
F/cm,
Periodic Table: r,Si
= 11.7,
3.5 x10
SiO 2
n i [
[email protected] ] 10 cm kT /q 0.025 V ; (kT /q) ln10 1 m = 1x10 4 cm 10
13
r,SiO 2
F/cm
3
0.06 V
Drift/Diffusion: sx = ±
Conductivity :
= q( e n + h p) ∂C Fm = Dm m ∂x Dm kT = q m
Einstein relation :
IV C Si Ge Sn
V N
P
As Sb
Electrostatics:
Drift velocity :
Diffusion flux :
III B Al Ga In
= 3.9
m
Ex
dE(x) = (x) dx d ( x) = E (x) dx d 2 ( x) = (x) dx 2
E (x) =
1
( x) = (x) =
( x)dx E (x)dx
1
(x)dxdx
The Five Basic Equations:
Electron concentration : Hole concentraton : Electron current density : Hole current density : Poisson's equation :
∂n ( x, t ) 1 ∂J e ( x, t) = gL (x, t) ∂t q ∂x ∂p( x, t) 1 ∂Jh (x,t) + = gL ( x, t) ∂t q ∂x
[n( x,t) ⋅ p( x,t)
n i2 ] r(T)
[n(x,t) ⋅ p(x,t)
n i2 ] r(T)
∂n(x, t) ∂x ∂p(x, t) J h (x, t) = q h p( x, t)E (x,t) qDh ∂x ∂E (x, t) q = [ p(x, t) n(x, t) + N d+ (x) N a (x)] ∂x
J e (x, t) = q e n( x, t)E (x,t) + qDe
Uniform doping, full ionization, TE
n - type, N d >> N a no
Nd
Na ≡ ND,
po = n i2 n o ,
n
=
n o = n i2 po ,
p
=
kT N D ln q ni
p - type, N a >> N d po
Na
Nd ≡ NA ,
kT N A ln q ni
Uniform optical excitation, uniform doping n = n o + n'
p = po + p'
Low level injection, n',p'
