Table of contents
Solid-state physics..................................................................................................................................2
P-N junction diode..................................................................................................................................3
Bipolar transistor....................................................................................................................................5
MOS capacitors.......................................................................................................................................8
MOSFET..................................................................................................................................................9
General concepts
Holes move to in direction of E-field
E-field go from holes to electrons
NMOS hence p body/substrate
ϵ Q'
C '= =
d V
, Solid-state physics
Conductivity σ =e μ n n+ e μ p p [S /cm] with μ carrier mobility
Drift current J drf =σE Due to E-field
dn , p
Diffusion current J diff n , p=± e D n , p Due to conc. difference
dx
Total current: J n , p=J drf +J diff
D n , p kT
Einstein relationship = D n , p elec/hole diffusion const.
μn, p e
Doping: N-type: higher Fermi level (more electrons) P-type: lower fermi level (more holes)
Donor Acceptor
−( Ec −E f ) E F −EF
Dopant concentration: n o=N c exp
[ kB T ]
= ni exp [
kT
i
]
−( Ef −Ev ) E −E F
po =N v exp
[ k BT ] =ni exp Fi[
kT ]
2
Mass action law: ni =n0 p 0
−E g
Material characteristic:
2
ni =N c N v exp ( ) kT
2
∂ δp ( x ) ∂ δp ( x ) ' δp ( x ) ∂ δp ( x )
Ambipolar transport Dp 2
−μ p E +g − = N-
∂x ∂x τ p0 ∂t
type
∂2 δn ( x ) ∂ δn ( x ) ' δn ( x ) ∂ δn ( x )
Low-level Dn 2
+ μn E +g − = P-
∂x ∂x τn0 ∂t
type
Injection Diffusion E field Gen Recom concentration
Boundary conditions: δp and dδp ( x )/dx are continuous
Recombination: R ( t )=α r n p ( t ) p p ( t )=α r ( nn 0+ δn )( p n 0+ δp )
Diffusion length: LB =√ Dτ
EF ,n −EFi E Fi−E Fp
Quasi-fermi energy level: n0 + δn=ni exp ( kT ) p0 +δp= p i exp ( kT )
Solid-state physics..................................................................................................................................2
P-N junction diode..................................................................................................................................3
Bipolar transistor....................................................................................................................................5
MOS capacitors.......................................................................................................................................8
MOSFET..................................................................................................................................................9
General concepts
Holes move to in direction of E-field
E-field go from holes to electrons
NMOS hence p body/substrate
ϵ Q'
C '= =
d V
, Solid-state physics
Conductivity σ =e μ n n+ e μ p p [S /cm] with μ carrier mobility
Drift current J drf =σE Due to E-field
dn , p
Diffusion current J diff n , p=± e D n , p Due to conc. difference
dx
Total current: J n , p=J drf +J diff
D n , p kT
Einstein relationship = D n , p elec/hole diffusion const.
μn, p e
Doping: N-type: higher Fermi level (more electrons) P-type: lower fermi level (more holes)
Donor Acceptor
−( Ec −E f ) E F −EF
Dopant concentration: n o=N c exp
[ kB T ]
= ni exp [
kT
i
]
−( Ef −Ev ) E −E F
po =N v exp
[ k BT ] =ni exp Fi[
kT ]
2
Mass action law: ni =n0 p 0
−E g
Material characteristic:
2
ni =N c N v exp ( ) kT
2
∂ δp ( x ) ∂ δp ( x ) ' δp ( x ) ∂ δp ( x )
Ambipolar transport Dp 2
−μ p E +g − = N-
∂x ∂x τ p0 ∂t
type
∂2 δn ( x ) ∂ δn ( x ) ' δn ( x ) ∂ δn ( x )
Low-level Dn 2
+ μn E +g − = P-
∂x ∂x τn0 ∂t
type
Injection Diffusion E field Gen Recom concentration
Boundary conditions: δp and dδp ( x )/dx are continuous
Recombination: R ( t )=α r n p ( t ) p p ( t )=α r ( nn 0+ δn )( p n 0+ δp )
Diffusion length: LB =√ Dτ
EF ,n −EFi E Fi−E Fp
Quasi-fermi energy level: n0 + δn=ni exp ( kT ) p0 +δp= p i exp ( kT )
