Intro Semicon
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Transcript of Intro Semicon
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Introduction to Semiconductors
Ohm Law: V=R I
R= L / A
: electrical resistivity (property of the material)
Material Resistivity
insulator > 105 cm
semiconductor 10-3 105 cm
conductor < 10-3 cm
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Semiconductor band structure
Electrons in an isolated atom occupy discrete
energy levels.
Energy levels of short-distance interacting atomsdegenerate into bands.
Energy
Forbidden gap
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Relationship between conductivity
and band-structure Conductivity depends on the availability of
unoccupied states in the most external occupied
energy band: conductors: external band is partially occupied;
insulators and Semiconductors: external band is fully
occupied at 0 K (valence band).
Insulators and semiconductors differ in terms of
gap amplitude (0.5 eV 1.5 eV for S.C.).
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Relationship between conductivity
and band-structure Insulators' gap is larger than 5 eV
Larger gap amplitude leads to a lower probability
of transition from the valence to the conductionband.
Interband transitions are thermally activated.
S.C. EG
Silicon 1.12 eV
Germanium 0.66 eV
Gallium-Arsenide 1.42 eV
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Intrinsic carrier concentration
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Holes in Semiconductors
Electrons in an intrinsic semiconductor usually
belong to the valence band.
Transition of an electron from valence toconduction band is mainly induced by thermal
energy or by light.
Such a transition leaves an hole in valence band. Holes feature a positive electric charge and an
equivalent conduction mass.
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Mono-Crystalline Silicon
Silicon belongs to the fourth group: four valence
electrons available to form covalent bonds.
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Doping of Mono-Crystalline Silicon
Doping: substitution of silicon atoms with atoms of theIII (lack of an electron ---> hole) or of the V group
(electron in excess in conduction band).
Donors: elements of the V group; ND
Acceptors: elements of the III group; NA
1014 < NA/D
< 1021 cm-3
At T=300 K almost all doping atoms are activated(ionized)
in case of N-type doping: n=ND
=ND
+
in case of P-type doping: p=NA=NA-
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Doped semiconductors
at equilibrium: np=ni
2
charge neutrality: p+ND
-n-NA
=0
N-Doped semiconductor (ND
>NA
):
P-Doped semiconductor (NA>ND):
Doping compensation
n=NDNANDNA
24ni2
2N
DN
Ap=
ni
2
NDNA
p=NANDNAND
24ni2
2NAND n=
ni
2
NAND
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Mathematical model of transport and
electrostatics
Drift-diffusion Equations J
n= q
nnE + qD
ngrad(n)
Jp
= qp
pE - qDp
grad(p)
E = -grad
n/p conductivity: qnn / q
pp
Poisson Equation :
2=
q
pnN
DN
A
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Resistivity vs. doping concentration
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Drift velocity vs. Electric Field
vD
= E
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Mobility vs. doping concentration
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Mobility vs. Temperature
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The Junction-Diode
n
p
p
n
B ASiO
2Al
A
B
Al
A
B
Cross-section of pn-junction in an IC process
One-dimensional
representation diode symbol
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The junction diode
The Junction Diode
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The Junction-Diodehole diffusion
electron diffusion
p n
hole drift
electron drift
ChargeDensity
Distance
x+
-
Electrical
xField
x
PotentialV
W2-W1
0
(a) Current flow.
(b) Charge density.
(c) Electric field.
(d) Electrostatic
potential.
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Giunzione polarizzata
Polarizzazione diretta --> abbassamento della
barriera; diffusione dei portatori verso la regione
in cui questi sono minoritari.
Polarizzazione inversa --> incremento della
barriera; incremento del campo elettrico nella
regione svuotata. Bassa corrente a causa della
ridotta concentrazione di portatori di carica.
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Current Equation
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Forward Bias
x
pn0
np0
-W1 W20
pn
(W2)
n-regionp-region
Lp
diffusion
Excess of minority carriers diffusing across the junction
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Reverse Bias
x
pn0
np0
-W1 W20
n-regionp-region
diffusion
Depletion --> increase of the fixed depletion charge
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Diode's Models
VD
ID= IS(eVD/T 1)
+
VD
+
+
VDon
ID
(a) Ideal diode model (b) First-order diode model
Temperature dependence: VDon = VDon(300 K) + TC (T 300 K)
For Silicon Junction Diodes at T ~ 300 K: TC
= -2mV/ K
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Reverse Breakdown
25.0 15.0 5.0 5.0
VD(V)
0.1
ID(A)
0.1
0
0
Usually requires large reverse bias (up to several hundreds of Volts) in
conventional diodes.
Zener Diodes: intentionally designed in order to obtain low breakdown
voltage (good voltage generator).
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The PN junction as a solar cell
Photo-generated carriers surviving recombination and separated by the junction
field contribute a negative current -IL that (approximately) superimposes to the
conventional I-V characteristic.
M.A. Green, Solar Cells, Univ. South Wales.
S
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PN junction solar cell
M.A. Green, Solar Cells, Univ. South Wales.
S
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Conversion Efficiency
Efficiency requires:
large open-circuit voltage VOC
Low saturation current IS (dark I-V charact.)
Large short-circuit current ISC
Low IS --> low recombination rates
Large ISC --> small band-gap (downside: energywasted into heat generation).