carrier transport
TRANSCRIPT
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 11
Carrier transport phenomenaCarrier transport phenomena
(i) Drift(i) Drift(ii) Diffusion(ii) Diffusion
Two kinds of charges exist in semiconductors: (i) electronsTwo kinds of charges exist in semiconductors: (i) electronsand (ii) holesand (ii) holes
Drift Current Density:Drift Current Density:
(i) Electron drift current:(i) Electron drift current:
(i) Hole drift current:(i) Hole drift current:
EnenevJ ndndriftn ==)(
EpepevJ pdpdriftp ==)(
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 22
Total drift current:Total drift current:
)()( driftpdriftndrift JJJ +=
EpeEneJ pndrift +=
EpneJ pndrift )( +=
EJdrift =
)( pn pne +=
)(
11
pn pne +
==
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 33
Diffusion current density:Diffusion current density:
(I) Diffusion hole current density:(I) Diffusion hole current density:
(ii) Diffusion electron density(ii) Diffusion electron density
Total diffusion current density:Total diffusion current density:
dx
dpeDJ pdiffusionp =)(
dx
dneDJ ndiffusionn =)(
dx
dpeD
dx
dneDJ pndiffusion =
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 44
Total current density:Total current density:
Epnedx
dpeD
dx
dneD
JJJ
pnpn
diffusiondrift
)( ++=
+=
Epnepn
)( + Epne pn )( +
Induced electric field:Induced electric field:
Consider a semiconductor which is nonConsider a semiconductor which is non--uniformalyuniformaly doped withdoped with
donor impurity atoms. The donor concentration decreases as xdonor impurity atoms. The donor concentration decreases as x
increases. There will be diffusion of electrons from higherincreases. There will be diffusion of electrons from higherconcentration region to the lower concentration region i.e.concentration region to the lower concentration region i.e.
electrons will flow in positive xelectrons will flow in positive x--direction.direction.
The flow of electrons leaves behind a positively charged donorThe flow of electrons leaves behind a positively charged donor
ions.ions.
This separation of positive and negative charge induces anThis separation of positive and negative charge induces an
electric field, which opposes the diffusion process.electric field, which opposes the diffusion process.
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 55
)(xNd
dx
xdN
xNe
kTE d
d
x
)(
)(
1
=
If is the concentration of donor atoms at a particIf is the concentration of donor atoms at a particularular
value of x , then the value of this electric field is given by:value of x , then the value of this electric field is given by:
In general, we can consider for nIn general, we can consider for n--type semiconductortype semiconductor
)()( xNxnorNn dd =
Einstein relation:Einstein relation:
For a non uniformly doped semiconductor in thermalFor a non uniformly doped semiconductor in thermal
equillibriumequillibrium, electron current and hole current should be zero., electron current and hole current should be zero.
0=+=dxdneDEenJ nxnn
)()( xNxn d=usingusing
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 66
2v
And substituting the value of EAnd substituting the value of Exx
e
kTD
n
n=
0==dx
dpeDEepJ pxpp
ekTD
p
p=
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 77
Hall Effect:Hall Effect:
2v
LL
WW
dd
xx
zz yy
BBzz
ee--hh++
EEHHVVHH
IIxxVVxx
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 88
Hall effect is usedHall effect is used
-- to determine that the given semiconductor is nto determine that the given semiconductor is n--type or ptype or p--type.type.
-- measure majority carrier concentration and majority carriermeasure majority carrier concentration and majority carrier
mobility.mobility.
2v
ZxH BqvqE =
The induced electric field in yThe induced electric field in y--direction is known as Hall Field.direction is known as Hall Field.
wEV HH =
wBvV zxH =
Drift velocity of holes:Drift velocity of holes:
)()( wdep
I
Aep
I
ep
Jv xxxdx ===
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 99
2v
z
x
z
x
H Bepd
I
wBepwd
I
V ==
edV
BIp
H
Zx=
Drift velocity of electrons:Drift velocity of electrons:
)()( wden
I
Aen
I
en
Jv xxx
dx
===
zx
zx
H Bend
IwB
enwd
IV ==
edV
BIn
H
Zx=
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 1010
2v
xpx
x Epe
A
IJ ==
L
Vpe
wd
IJ xp
xx ==
wdepV
LI
x
xp =
wdenV
LI
x
x
n=
Similarly for nSimilarly for n--type:type:
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 1212
2v
The Doping of Semiconductors (Extrinsic Semiconductors)
The addition of a small percentage of foreign atoms in the regularcrystallattice of silicon or germanium produces dramatic changes in theirelectrical properties, producing n-type and p-type semiconductors.
Pentavalent impurities:
Impurity atoms with 5 valence electrons produce n-type semiconductorsby contributing extra electrons.
Trivalent impurities:Impurity atoms with 3 valence electrons produce p-type semiconductorsby producing a "hole" or electron deficiency.
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 1313
2v
p- and n- type semiconductors
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 1515
2v
p-type semiconductor
The addition of trivalent impurities such as boron, aluminum or gallium to an
intrinsic semiconductor creates deficiencies of valence electrons,called"holes".The addition of acceptor impurities contributes hole levels low in thesemiconductor band gap so that electrons can be easily excited from the
valence band into these levels, leaving mobile holes in the valence band.This shifts the effective Fermi level to a point about halfway between theacceptor levels and the valence band.
Electrons can be elevated from the valence band to the holes in the band gapwith the energy provided by an applied voltage. Since electrons can beexchanged between the holes, the holes are said to be mobile. The holes aresaid to be the "majority carriers" for current flow in a p-type semiconductor.
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 1717
2v
0=+=dxdneDEenJ nnn
When the external voltage is zero, the total electron and hole current
will be separately zero.
n
dnDEdx
n
n
=
=
n
p
n
p
n
nn
n
x
x n
dnDEdx
=n
p
n
nn
n
V
V n
dnDdV
2
1
p
n
p
n
n
nB
n
n
e
kT
n
nDVVVV lnln12 ====
=
kT
eVnn Bpn exp
=
kT
eVpp Bnp exp
Similarly, we may prove
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 2020
If V=-V2 at x=-xn, then
xxeNxeN
V ndd
+=
2
2DCx
xeNV d ++=
2
2
At x=0, V=0 it gives D=0, hence
22
222
2ndndnd xeNxeNxeNV
=+=
0=dx
dV
ndxeNC=At x=xn, it gives
)(2
22)(
22
22
12
ndpa
pandB
xNxNe
xeNxeNVVVV
+=
+===
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 2121
From the charge neutrality, we may say that
the space charge in n-region = space charge in p-region
ndpa xeNxeN =
d
pa
n N
xN
x =
+=
2
2
2 d
pa
dpaBN
xNNxN
eV
2
1
1
2
+
=
d
aa
B
p
N
NeN
V
x
Similarly
a
ndp
N
xNx =
+=
2
2
2 a
ndandB
N
xNNxN
eV
2
1
1
2
+
=
a
dd
Bn
N
NeN
Vx
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 2222
The total width of the depletion layer isnp xxx +=
2
1
2
1
1
2
1
2
+
+
+
=
a
dd
B
d
aa
B
N
NeN
V
N
NeN
Vx
2
1
)(2
+=
da
daB
NeN
NNVx
2
1
BVx
Hence the width of the depletion layer is proportional to theBV
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 2323
P-n junction diode characteristics
Forward BiasReverse Bias
Various p-n junction diodes:
Zener DiodeZener Breakdown
Avalanche Breakdown
Varactor diode (Reverse biased p-n diode)
Tunnel Diode (very highly doped forward biased p-n junction)
Photo diode (reversed biased p-n diode & exposed to radiation)
Light Emitting Diode (recombination of holes and
electrons in forward bias)
Solar Cell (basically high efficiency photo diodes)
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Dr.Dr. VinodVinod PatidarPatidar
Solid State Physics for B. Tech (CSE/IT)Solid State Physics for B. Tech (CSE/IT)
Sir Padampat Singhania University, Udaipur 2424
2v