Intro Semicon

8/3/2019 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).

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