module2-1 semi annrfic.eecs.berkeley.edu/105/pdf/module2-1_semi_ann.pdfEE 105Fall 2016 Prof. A. M....
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Department of EECS University of California, Berkeley Drift Currents University of California, Berkeley
Transcript of module2-1 semi annrfic.eecs.berkeley.edu/105/pdf/module2-1_semi_ann.pdfEE 105Fall 2016 Prof. A. M....
Department of EECS University of California, Berkeley
Drift Currents
University of California, Berkeley
EE 105 Fall 2016 Prof. A. M. Niknejad
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Thermal Equilibrium
University of California, Berkeley
Rapid, random motion of holes and electrons at “thermal velocity” vth = 107 cm/s with collisions every τc = 10-13 s.
Apply an electric field E and charge carriers accelerate … for τc seconds
zero E field
vth
positive E
vth
a c
(hole case)
x
kTvm thn 212*
21 =
cthv tl =
cm1010/cm10 6137 -- =´= ssl
EE 105 Fall 2016 Prof. A. M. Niknejad
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Drift Velocity and Mobility
University of California, Berkeley
Ev pdr µ=
Emq
mqE
mFav
p
cc
pc
p
ecdr ÷
÷ø
öççè
æ=÷
÷ø
öççè
æ=÷
÷ø
öççè
æ=×=
tttt
For electrons:
Emq
mqE
mFav
p
cc
pc
p
ecdr ÷
÷ø
öççè
æ-=÷
÷ø
öççè
æ -=÷
÷ø
öççè
æ=×=
tttt
For holes:
Ev ndr µ-=
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Mobility vs. Doping in Silicon at 300 oK
University of California, Berkeley
Typical values: 1000=nµ 400=pµ
Department of EECS University of California, Berkeley
Diffusion Currents
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Diffusionl Diffusion occurs when there exists a concentration
gradientl In the figure below, imagine that we fill the left
chamber with a gas at temperate Tl If we suddenly remove the divider, what happens?l The gas will fill the entire volume of the new
chamber. How does this occur?
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EE 105 Fall 2016 Prof. A. M. Niknejad
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Diffusion (cont)l The net motion of gas molecules to the right
chamber was due to the concentration gradientl If each particle moves on average left or right then
eventually half will be in the right chamberl If the molecules were charged (or electrons), then
there would be a net current flowl The diffusion current flows from high
concentration to low concentration:
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EE 105 Fall 2016 Prof. A. M. Niknejad
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Diffusion Equationsl Assume that the mean free path is λl Find flux of carriers crossing x=0 plane
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)(ln)0(n
)( l-n
0l- l
thvn )(21 lthvn )(
21 l-
( ))()(21 ll nnvF th --=
÷÷ø
öççè
æúûù
êëé +-úû
ùêëé -=
dxdnn
dxdnnvF th ll )0()0(
21
dxdnvF thl-=
dxdnqvqFJ thl=-=
EE 105 Fall 2016 Prof. A. M. Niknejad
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Einstein Relationl The thermal velocity is given by kT
University of California, Berkeley
kTvm thn 212*
21 =
cthv tl =Mean Free Time
dxdn
qkTq
dxdnqvJ nth ÷÷
ø
öççè
æ== µl
nn qkTD µ÷÷
ø
öççè
æ=
**2
n
c
n
ccthth m
qqkT
mkTvv tttl ===
EE 105 Fall 2016 Prof. A. M. Niknejad
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Total Current and Boundary Conditions
l When both drift and diffusion are present, the total current is given by the sum:
l In resistors, the carrier is approximately uniform and the second term is nearly zero
l For currents flowing uniformly through an interface (no charge accumulation), the field is discontinous
University of California, Berkeley
dxdnqDnEqJJJ nndiffdrift +=+= µ
21 JJ =
2211 EE ss =
1
2
2
1
ss
=EE
)( 11 sJ
)( 22 sJ
EE 105 Fall 2016 Prof. A. M. Niknejad
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Referencel Edward Purcell, Electricity and Magnetism,
Berkeley Physics Course Volume 2 (2nd Edition), pages 133-142.
EECS
