lecture 4
DESCRIPTION
Lecture 4. OUTLINE Semiconductor Fundamentals (cont’d) Properties of carriers in semiconductors Carrier drift Scattering mechanisms Drift current Conductivity and resistivity Reading : Pierret 3.1; Hu 1.5, 2.1-2.2. Mobile Charge Carriers in Semiconductors. - PowerPoint PPT PresentationTRANSCRIPT
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Lecture 4
OUTLINE• Semiconductor Fundamentals (cont’d)
– Properties of carriers in semiconductors– Carrier drift
• Scattering mechanisms• Drift current
– Conductivity and resistivity
Reading: Pierret 3.1; Hu 1.5, 2.1-2.2
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Mobile Charge Carriers in Semiconductors
• Three primary types of carrier action occur inside a semiconductor:
– Drift: charged particle motion under the influence of an electric field.
– Diffusion: particle motion due to concentration gradient or temperature gradient.
– Recombination-generation (R-G)
Lecture 4, Slide 2EE130/230A Fall 2013
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Electrons as Moving Particles
F = (-q)E = moa F = (-q)E = mn*a
where mn* is the conductivity effective mass
In vacuum In semiconductor
Lecture 4, Slide 3EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 2.9
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Conductivity Effective Mass, m*Under the influence of an electric field (E-field), an electron or a hole is accelerated:
electrons
holes
acceleration qE–mn---------=
*nm
qa
*pm
qa
Lecture 4, Slide 4
Si Ge GaAsmn*/mo 0.26 0.12 0.068
mp*/mo 0.39 0.30 0.50
mo = 9.110-31 kg
Electron and hole conductivity effective masses
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How to Measure the Effective Mass
Cyclotron Resonance Technique:
Centripetal force = Lorentzian force
• fcr is the Cyclotron resonance frequency, which is independent of v and r.
• Electrons strongly absorb microwaves of that frequency.
By measuring fcr , mn can be found.
qvBr
vmn 2
nm
qBrv
ncr m
qB
r
vf
22
C.Hu, Modern Semiconductor Devices for Integrated Circuits, Fig. 1-15
Lecture 4, Slide 5EE130/230A Fall 2013
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Carrier Scattering• Mobile electrons and atoms in the Si lattice are always in
random thermal motion.– Electrons make frequent collisions with the vibrating atoms
“lattice scattering” or “phonon scattering” – increases with increasing T
• Other scattering mechanisms:– deflection by ionized impurity atoms– deflection due to Coulombic force between carriers
“carrier-carrier scattering” – only significant at high carrier concentrations
• The net current in any direction is zero, if no E-field is applied.
123
45
electron
Lecture 4, Slide 6EE130/230A Fall 2013
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Thermal Velocity, vth
Average electron kinetic energy 2*
2
1
2
3thnvmkT
cm/s103.2m/s103.2
kg101.926.0
J/eV)106.1(eV026.033
75
31
19
*
nth m
kTv
Lecture 4, Slide 7EE130/230A Fall 2013
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Carrier Drift• When an electric field (e.g. due to an externally applied voltage)
exists within a semiconductor, mobile charge-carriers will be accelerated by the electrostatic force:
12
3
45
electron
EElectrons drift in the direction opposite to the E-field net current
Because of scattering, electrons in a semiconductor do not undergo constant acceleration. However, they can be viewed as quasi-classical particles moving at a constant average drift velocity vdn
Lecture 4, Slide 8EE130/230A Fall 2013
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Carrier Drift (Band Model)
Ec
Ev
Lecture 4, Slide 9EE130/230A Fall 2013
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Electron Momentum• With every collision, the electron loses momentum
• Between collisions, the electron gains momentum–qEmn
mn ≡ average time between electron scattering events
dnnvm*
Lecture 4, Slide 10
Conservation of momentum |mn*vdn | = | qEmn|
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Carrier Mobility, |vdn| = qEmn / mn* ≡ nE
n [qmn / mn*] is the electron mobility
p [qmp / mp*] is the hole mobility
Similarly, for holes: |vdp|= qEmp / mp* pE
Lecture 4, Slide 11
Si Ge GaAs InAsn (cm2/Vs) 1400 3900 8500 30,000
p (cm2/Vs) 470 1900 400 500
Electron and hole mobilities for intrinsic semiconductors @ 300K
For electrons:
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Example: Drift Velocity Calculationa) Find the hole drift velocity in an intrinsic Si sample for E = 103 V/cm.
b) What is the average hole scattering time?
vdp = pE
q
m
m
q ppmp
p
mpp
*
*
Lecture 4, Slide 12
Solution:
a)
b)
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Mean Free Path• Average distance traveled between collisions
mpthvl
Lecture 4, Slide 13EE130/230A Fall 2013
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Mechanisms of Carrier ScatteringDominant scattering mechanisms:
1. Phonon scattering (lattice scattering)2. Impurity (dopant) ion scattering
2/32/1
1
velocityermalcarrier thdensityphonon
1
TTTphononphonon
Phonon scattering limited mobility decreases with increasing T:
= q / m Tvth
Lecture 4, Slide 14EE130/230A Fall 2013
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Impurity Ion Scattering
DADA
thimpurity NN
T
NN
v
2/33
There is less change in the electron’s direction if the electron travels by the ion at a higher speed.
Lecture 4, Slide 15
Ion scattering limited mobility increases with increasing T:
EE130/230A Fall 2013
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Matthiessen's Rule
Probability that a carrier will be scattered by any mechanism
within a time period dt is
impurityphononimpurityphonon 111
111
i i
dt
i
dt
Lecture 4, Slide 16
• The probability that a carrier will be scattered by mechanism i
within a time period dt is
i ≡ mean time between scattering events due to mechanism i
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Mobility Dependence on DopingCarrier mobilities in Si at 300K
Lecture 4, Slide 17EE130/230A Fall 2013
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Mobility Dependence on Temperature
impurityphonon 111
Lecture 4, Slide 18EE130/230A Fall 2013
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Velocity Saturation• At high electric field, carrier drift velocity saturates:
The saturation velocity, vsat , is the maximum drift velocity
Lecture 4, Slide 19
Siin holesfor cm/s 106
Siin sonfor electr cm/s 1086
6
satv
J. Bean, in High-Speed Semiconductor Devices, S.M. Sze (ed.), 1990
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Hole Drift Current Density, Jp,drift
vdp t A = volume from which all holes cross plane in time t
p vdp t A = number of holes crossing plane in time t
q p vdp t A = hole charge crossing plane in time t
q p vdp A = hole charge crossing plane per unit time = hole current
Hole drift current per unit area Jp,drift = q p vdpLecture 4, Slide 20EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 3.3
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Conductivity and Resistivity
Lecture 4, Slide 21
)( npdrift qnqpJ
)( ,, ndriftnpdriftp qnJqpJ
npdriftndriftpdrift qnqpJJJ ,,
• In a semiconductor, both electrons and holes conduct current:
np qnqp • The conductivity of a semiconductor is– Unit: mho/cm
1
• The resistivity of a semiconductor is– Unit: ohm-cm
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Resistivity Dependence on Doping
Lecture 4, Slide 22
For n-type material:
nqn 1
For p-type material:
pqp 1
Note: This plot (for Si) does not apply to compensated material (doped with both acceptors and donors).
EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 3.8
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Electrical Resistance
where is the resistivity
Resistance Wt
L
I
VR [Unit: ohms]
V+ _
L
tW
I
uniformly doped semiconductor
Lecture 4, Slide 23EE130/230A Fall 2013
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Example: Resistivity CalculationWhat is the resistivity of a Si sample doped with 1016/cm3 Boron?
Answer:
cm 4.1)450)(10)(106.1(
11
11619
ppn qpqpqn
Lecture 4, Slide 24EE130/230A Fall 2013
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Example: Compensated Doping
cm 93.0)750)(109)(106.1(
11
11619
npn qnqpqn
Consider the same Si sample doped with 1016/cm3 Boron, and additionally doped with 1017/cm3 Arsenic. What is its resistivity?Answer:
Lecture 4, Slide 25EE130/230A Fall 2013
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Example: T Dependence of
Consider a Si sample doped with 1017 As atoms/cm3. How will its resistivity change when T is increased from 300K to 400K?
93.1400
770
Lecture 4, Slide 26
Answer: The temperature dependent factor in (and therefore ) is n.
From the mobility vs. temperature curve for 1017 cm-3, we find that n decreases from 770 at 300K to 400 at 400K.
Thus, increases by
EE130/230A Fall 2013
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Summary• Electrons and holes can be considered as quasi-classical
particles with effective mass m*
• In the presence of an electric field E, carriers move with average drift velocity vd = E , is the carrier mobility– Mobility decreases w/ increasing total concentration of ionized dopants – Mobility is dependent on temperature
• decreases w/ increasing T if lattice scattering is dominant• decreases w/ decreasing T if impurity scattering is dominant
• The conductivity () hence the resistivity () of a semiconductor is dependent on its mobile charge carrier concentrations and mobilities
Lecture 4, Slide 27
np qnqp 1
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