Mechanism of drift and diffusion

1. Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
8/14/2020 1Arpan Deyasi, RCCIIT
Topic: Drift and Diffusion

2. Carrier transport
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Fext
External force may be electric field
Movement will be called Drift
Approximation: electron’s don’t interact with each other

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Carrier transport
Movement in absence of external force, called Diffusion
Movement is due to concentration gradient

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Calculation of Drift Velocity
*avg sc d
q
v v
m
ξτ=− =
Electric field
2
*d sc
nq
J nqv
m
ξτ=− =

5. 8/14/2020 5Arpan Deyasi, RCCIIT
Calculation of Drift Velocity
J σξ=
2
* sc
nq
J
m
τ ξ=
2
* sc
nq
m
σ τ=

6. 8/14/2020 6Arpan Deyasi, RCCIIT
dv µξ= −
Calculation of Drift Velocity
*d sc
q
v
m
τ ξ= −
* sc
q
m
µ τ=

7. 8/14/2020 7Arpan Deyasi, RCCIIT
Calculation of Drift Velocity
2
* *
. .sc sc
nq q
n q
m m
σ τ τ= =
* sc
q
m
µ τ=
. .n qσ µ=

8. 8/14/2020 8Arpan Deyasi, RCCIIT
Calculation of Drift Velocity
Considering both electrons and holes
. . . .n pn q p qσ µ µ= +
. ( )n pJ n q µ µ ξ= +

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Scattering mechanisms
I. phonon/lattice scattering
II. ionized impurity scattering
3/ 2
L Tµ −
∝ 3/ 2
I Tµ ∝
1I INµ ∝

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Scattering mechanisms
T
μ
μI μL
1 1 1
L Iµ µ µ
= +
Matthiessen’s rule

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Diffusion
l
nL nR
Flux
~
( , ) .
2
L R
sc
n n
z t lφ
τ
=
~ .L R
dn
n n l
dz
= −

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Diffusion
2
( , ) [ ( , )]
2 sc
l d
z t n z t
dz
φ
τ
= −
( , ) [ ( , )]n
d
z t D n z t
dz
φ = −

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Diffusion
for p-type
( , ) [ ( , )]p
d
z t D p z t
dz
φ = −
net diffusion flux
[ ( , )] [ ( , )]diff n p
d d
J D n z t D p z t
dz dz
=− −

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Diffusion
net diffusion current
[ ( , )] [ ( , )]diff n p
d d
J qD n z t qD p z t
dz dz
−

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Einstein’s Relation
Assume: non-uniformly doped semiconductor
both diffusion and drift transport
mechanisms are present
EC
EV
EFI
EF
Electric potential
1
( )F FIE E
q
φ= −

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Einstein’s Relation
z
d
E
dz
φ
= −
Electric field
1
z FI
d
E E
q dz
=

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Einstein’s Relation
Assume: quasi-neutrality condition
i.e., electron concentration becomes equal
to donor concentration
0 exp ( )F FI
i D
E E
n n N z
kT
− 
≈ 
 
( )
( ) ln D
F FI
i
N z
E E kT
n
 
− =  
 

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Einstein’s Relation
[ ( )]
( )
FI D
D
d kT d
E N z
dz N z dz
− =
1 1
. [ ( )]
( )
z FI D
D
d kT d
E E N z
q dz q N z dz
= = −

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Einstein’s Relation
Under thermal equilibrium
. . 0n n z n
dn
J q n E qD
dz
µ= + =
. ( ). ( ) 0D n z n D
d
q N z E qD N z
dz
µ + =

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Einstein’s Relation
1
. ( ). . ( ( ))
( )
( ) 0
D n D
D
n D
kT d
q N z N z
q N z dz
d
qD N z
dz
µ−
+ =
n
n
D kT
qµ
=