Electronic Devices and Circuits Formula Sheet

February 9, 2017 | Author: mumsn | Category: N/A
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Helpful for E.D.C subject preparation....

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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'
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