CARRIER TRANSPORT PHENOMENA transport... · CARRIER TRANSPORT PHENOMENA Topics 2 Carrier Transport...
Transcript of CARRIER TRANSPORT PHENOMENA transport... · CARRIER TRANSPORT PHENOMENA Topics 2 Carrier Transport...
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CARRIER TRANSPORTPHENOMENA
Topics 2
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Carrier Transport Phenomenon
Carrier drift: mobility, conductivity and velocity saturation
Carrier Diffusion: diffusion current density, total current density
The Einstein relation
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Densities of charged particles are important to understand the electrical
properties of a semiconductor material and device.
Net flow of the electrons and holes in a semiconductor generate currents.The process by which these charged particles move is called transport.
Two basic transport mechanisms in a semiconductor crystal are:•Drift:- the movement of charge due to electric fields,•Diffusion:-the flow of charge due to density gradients.
Carrier transport determines the current-voltage characteristicsof semiconductor devices.
Carrier Transport Phenomenon
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2th
*B vm
2
1Tk
2
3holeorelectronofenergythermal.Av
The carriers undergo collision with vibrating atoms and charged dopant ions after travelling a distance resulting in scattering of the carriers.
nm10m1010x10sosec,10
vpathfreemean
collisionsbetweentimeaverage
813513
c
cth
c
Carrier Drift
sec/m10x3.2m
Tk3v,velocityThermal 5
*B
th
Electric field applied produces a force on electrons and holes, so that they are accelerated.This net movement of charge due to an electric field is called drift, which give rise to drift current.
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fielddrifttoduecarrierofvelocitynetAveragev,velocityDrift d
Carrier DriftOn application of an electric field, E, and a , = qE/m* acts on the carrier between collisions.
tm
q)t(v
p,n
t
v(t)
vd
p,n
p,n
p,n
p,n
dm
q
m
qv
,smallFor
.iscollisionbetweentimeAverage p,n
When the charged particle collides with anatom in the crystal, the particle loses most ofits energy. The particle will again begin toaccelerate and gain energy until it is againinvolved in a scattering process. Thiscontinues over and over again. Throughoutthis process, the particle will gain an averagedrift velocity which, for low electric fields, isdirectly proportional to the electric field.
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VelocitySaturation
p,n
p,n
p,n
dm
qv
,0For
E
v d
Drift velocity saturates at high fields
p
p
ppdp
n
nnndn
m
q,v,holesFor
m
q,v,electronsFor
Mobility:
mobilitym
q
p,n
p,n
p,n
vsat
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0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
1E+19 1E+21 1E+23 1E+25 1E+27
at/m3
m2/V
-se
c
µn
µp
Electron & hole mobilities:
• At low doping levels, the mobility is limited by collision with lattice, i.e., phonons
• At high doping levels, mobility is limited by scattering by dopant ions
• µn > µp for same doping level, since holes have higher effective mass than electrons.
For Silicon
Ge Si GaAs
μn,, m2/V-sec
(cm2/V-Sec)
0.39
(3900)
0.14
(1400)
0.85
(8500)
μp, m2/V-sec
(cm2/Vsec)
0.19
(1900)
0.047
(470)
0.04
(400)
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Drift Current :
ndndriftn qnqnvJdensitycurrentdriftElectron
)pn(qJJJ pndriftp
driftn
drift
Current due to drift of carriers in presence of an electric field then will be given by:
)pn(q1
tyconductiviwhereJ
pn
drift
pdpdriftp qpqpvJdensitycurrentdriftHole
driftnJ
driftpJ
vdn
Electron Drift Flow
vdp
Hole Drift Flow
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Resistivity of Silicon :
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Mobility of carriers is affected by scattering mechanisms.Scattering mechanism is of two types – phonon and impurity[A] Electrons move freely and unperturbed in a perfect periodic
potential in a solid.•But the thermal vibrations cause a disruption of the potentialfunction, resulting in an interaction between the electrons orholes and the vibrating lattice atoms.•This affect the velocity and mobility of the carriers which iscalled to as phonon scattering.[B]Impurity atoms are added to the semiconductor to control oralter its characteristics.•These impurities are ionized at room temperature so that acoulomb interaction exists between the electrons or holes andthe ionized impurities.•This coulomb interaction produces scattering or collisions andalso alters the velocity of the charge carrier:- impurity scattering.
Scattering Mechanisms:
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IPTpnIPT
111111
,
• Phonon scattering increases with temperaturep = collision time of carriers due to phonon scattering p 1/(phonon density x thermal velocity) 1/(T*T
1/2) T-3/2
• Impurity scattering increases with concentration of impurityatoms and defects.
• As temp. increases, carriers posses high thermal vel., so easily pass by the impuritiesI = coll. time of electron due to impurities and defects • Total Scattering effect =
Scattering Mechanisms:
pn
Tpn m
q,
,
)N(N
T
da
3/2
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Mobility vs. Temperature
Mobility is determined by• Lattice scattering (dominant
at high T)At small dopant conc., μ decreases with increasing T, Indicating the dominance of phonon scattering
• Impurity scattering (dominant at low T)
At very high dopant conc.,and low temperature, impurity Scattering dominate, so μ increases with increasing T
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Microelectronics I
Carrier diffusion
Diffusion; process whereby particles from a region of high concentration toward a region of low concentration.
dividerCarrier
Ele
ctr
on c
oncentr
ation,
n
Position x
Electron diffusion
current density
Electron flux
dx
dneDJ
dx
dnDeJ
ndifnx
ndifnx
=
−−=
|
| )(
Dn; electron diffusion coefficient
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Microelectronics I
Hole
centr
ation,
p
Hole diffusion
current density
Hole flux
dx
dpeDJ
dx
dpeDJ
pdifpx
pdifpx
−=
−=
|
|H
ole
centr
ation,
p
Position x
current density
Dp; hole diffusion coefficient
Diffusion coefficient; indicates how well carrier move as a result of density gradient.
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Carrier Diffusion
The left hand side particle is likely to move to the right and vice versa: Net flow (L R) per second= nL* v - nR* v
nDdx
dnDF
F
D: diffusion coefficient
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Number of particles change / second = Net number of leaving or entering particles:
nDnDt
n 2
F
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Total Current Flow Electron diffusion current:
Hole diffusion current:
Net electron current:
dx
dneDeFxJ nDn
dx
dpeDeFxJ ppDp
dx
dneDxExnexJ nnn
dx
dpeDxExpexJ ppp
Net electron current:
Net hole current:
xJxJxJ np Net current:
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