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Device Physics

박 기 찬

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Contents

- Energy Band

- Carrier Action

- p-n Junction

- Metal-Semiconductor Contact

- Metal-Insulator-Semiconductor Capacitor

- MOSFET

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Energy Band

- Atomic bonding and energy band

- Fermi level and carrier concentration

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Atomic Bonding and Energy Band

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Periodic Table of Elements

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Electronic Energy Levels in Si Atom

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sp3 Hybridized Atomic Orbitals

Tetrahedron

s orbital px orbital py orbital pz orbital

sp3 hybrid orbital

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Crystal Structures

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Energy Band Split

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Insulator, Semiconductor, Metal

Insulator Semiconductor Metal

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Electron Energy in Solid

Insulator, Semiconductor Metal

EVAC

EC

EF

EV

work functionionizationpotential

Eg

electron affinity work function

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Energy Band and Bond Model

T = 0 K T > 0 K

For an intrinsic

silicon,

n = p = ni = 1010 cm-3

@ 300 K

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Concept of Hole

The movement of a valence electron into the “empty state” is equivalent to the

movement of the positively charged “empty state” itself.

This is equivalent to a positive charge (“hole”) moving in the valence band.

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Temp. Dependence of Bandgap

Energy bandgap decreases as temperature rises.

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N-Type Doping

A substitutional phosphorous atom (donor)

with five valence electrons replaces a silicon

atom and a negatively charged electron is

donated to the lattice in the conduction band.

T = 0 K

T > 0 K

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P-Type Doping

A boron atom (acceptor) with three valence

electrons substitutes for a silicon atom and an

additional electron is accepted to form four

covalent bonds around the boron leading to

the creation of positively charged hole in the

T = 0 K

T > 0 Kvalence band.

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Donor vs. Acceptor

Donor Acceptor

Filled with Electron 0 6̶

Empty + 0

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Impurity Levels

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Fermi Level and Carrier Concentration

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Fermi Level

F(E) gives the probability that an available energy state at E is occupied by an

electron at absolute temperature T.

k is Boltzmann’s constant ( k = 8.6210-5 eV/K = 1.3810-23 J/K ).

EF is called the Fermi level.

For an energy state at E equal to the Fermi level EF, the occupation probability

is 1/2.

Electrons in solids obey Fermi-Dirac statistics.

The distribution of electrons over a range of allowed energy levels at thermal

equilibrium is governed by the equation,

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Fermi-Dirac Distribution

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Carrier Concentration

Number of electrons in the conduction band is given by the total number of states

multiplied by the occupancy , integrated over the conduction band.

> 3 ,

so Boltzmann statistics apply.

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Distribution of Electrons and Holes

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Distribution of Electrons and HolesN-type semiconductor P-type semiconductor

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Fermi Level Position vs. Doping

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Carrier Concentration

Number of electrons in the conduction band is determined by the position of

with respect to .

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Mass Action Law

2inpn for nondegenerate semiconductor

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Intrinsic Carrier Concentration

,

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Temperature Dependence of ni

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Donor and Acceptor Level

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Carrier Conc. vs. Temperature

for nondegenerate semiconductorDD NNnRT ,@

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Fermi Level Position vs. Temp.

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Carrier Action

- Drift and diffusion

- Recombination and generation

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Drift and Diffusion

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Drift of Carriers

Typical random behavior of a hole in a semiconductor (a) without an electric field

and (b) with an electric field.

Vth = 107 cm/s @ 300K

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Drift Velocity

Drift velocity of an electron with an applied electric field.

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Mobility

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Temperature Effect on Mobility

RT@

Mobility decreases

as temperature

rises.

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Impurity Effect on Mobility

RT@

RT@

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Drift Currents

Electrons and hole flow in opposite directions when under the influence

of an electric field at different velocities.

The drift currents associated with the electrons and holes are in the same

direction.

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Resistivity

EqpΕqn

qpvqnv

JJJ

pn

dpdn

pn

conductivity

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Resistivity vs. Dopant Concentration

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Velocity Saturation in High E-field

At low electric fields, .

The mobility is independent of the

electric field.

When the fields are sufficiently large,

however, nonlinearities in mobility and,

in some cases, saturation of drift

velocity are observed.

→ saturation velocity @ RT:

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Band Bending

(a) Carrier kinetic energies

(b) Electron potential energy

P.E. of charge Q = QV

(c) Electrostatic potential (Voltage)

q

EP

Q

EPV

....

!!!1

1..

dx

dE

qdx

dV

EEqq

EPV

C

refC

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Diffusion of Carriers

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Diffusion of Carriers

The flow or flux of carriers proportional to the concentration gradient (Fick’s law).

is call the diffusion coefficient.

This flux of carriers constitutes a diffusion current,

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Total Current in Semiconductor

Einstein relation

The total conduction current is given by the sum of electron and hole currents.

Each carrier current is composed of both drift and diffusion currents.

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Einstein Relation

These two equations give the relationship

and similarly for p-type semiconductor,

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Constancy of Fermi Level

E1/2 = EF

E3/4

E1/4

In Equilibrium, there are no external influences such as electric field and temperature gradient. Accordingly electrons are evenly distributed and do not move macroscopically. Their distribution is determined by their energy and described by

This indicates that the Fermi level is constant in equilibrium.

kTEE

EfFexp1

1)(

Wheat does “evenly distributed” mean?In thermal equilibrium, what is even in a system?→ Temperature!!Regarding the distribution of electrons, “evenly distributed” means that the probability of electron occupation for every state at the same energy level is constant.

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Diffusion Length

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Recombination and Generation

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Carrier Recombination-Generation

Electrons and holes are generated or recombine in pairs.

In equilibrium, the generation and recombination rates are same.

Recombination Generation

Band-to-band

Shockley-Read-Hall(via

traps)

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Photoluminescence

Optical absorption of a photon with hν1 > Eg : (a) An EHP is created during photon

absorption; (b) the excited electron gives up energy to the lattice by scattering

events; (c) the electron is trapped by the impurity level Et and remains trapped until

it can be thermally reexcited to the conduction band (d); finally direct recombination

occurs giving off a photon (hν2) of approximately the band gap energy.

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Optical Absorption

lt

x

eII

eIxI

xIdx

xdI

0

0)(

)()(

Optical absorption experiment

Dependence of optical absorption

coefficient α for a semiconductor

on the wavelength of incident light

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SRH Recombination-Generation

Shockley-Read-Hall statistics

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Impact Ionization

When the electric field in a semiconductor is increased

above a certain value, the carriers gain enough

energy to excite electron–hole pairs.

Ionization rate a is defined as the number of electron–

hole pairs generated by a carrier per unit

distance traveled.

Multiplication of electrons and

holes from impact ionization, due to

electrons (αn) in this example (αp = 0).

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Ionization Rate

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p-n Junction

- Space charge region

- Ideal current equation

- Actual I-V characteristic

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Space Charge Region

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Electric Field vs. Charge

Gauss’ law,

Integral form,

Integration over the surface of the cylinder,

If can be

neglected (h << S or 1-D case),

ED

QsdE

E1n E2n

h

S

QsdESEE

surfacelcylindrica

nn 1122

hS

QEE nn 1122

surfacelcylindrica

sdE

hS

QEE nn 1122

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Space Charge Region

Movement of electrons an holes when

forming the junction

Space charge or depletion region

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Abrupt p-n Junction

qND

-qNA

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Built-In Potential

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E-field in SCR

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Potential Energy in SCR

The built-in potential is

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Depletion Width

qND

-qNA

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p-n Junction under Equilibrium

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p-n Junction with Bias

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Depletion Layer Capacitance

)(2 V

Nq

WdV

dQC

bi

S

D

SDD

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Ideal Current Equation

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Current Flow under Equilibrium

Electron Drift Flow

Electron DiffusionFlow

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Current Flow with Forward BiasElectron Diffusion Flow

Electron Drift Flow

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Current Flow with Reverse BiasElectron Drift

Electron Diffusion Flow negligible due to large energy barrier

Flow

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Ideal I-V Characteristics

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Carrier Concentration with Bias

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Quasi-Fermi Level

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Derivation of Current Equation

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Ideal Current Equation

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Carrier Distribution & Current

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Actual I-V Characteristic

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Reverse Breakdown

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Avalanche Breakdown

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Breakdown Voltage vs. Doping

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Edge Effect on Breakdown

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Tunneling

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Zener Breakdown

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Generation Current

The current due to generation in SCR

The total reverse current

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Recombination Current

The current due to recombination in SCR

The total forward current

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I-V Characteristic of p-n Junction

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Metal-Semiconductor Contact

- Potential barrier at MS contact

- I-V characteristic of MS contact

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Potential Barrier at MS Contact

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Metal vs. n-type Si : Schottky

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Metal vs. n-type Si : Ohmic

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Metal vs. p-type Si : Schottky

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Metal vs. p-type Si : Ohmic

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Metal Work Function in Vacuum

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Schottky Barrier with Bias

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Equations for Depletion Region

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Analysis with Interface States

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Density of Interface States

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Image-Force Lowering

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Barrier Lowering by Image Charge

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Barrier Lowering vs. E-field

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I-V Characteristic of MS Contact

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Current Transport

JTE converges to very small

value under reverse bias.

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Schottky Diode in Forward Bias

The built-in voltage of the

Schottky barrier diode, V(SB), is

about ½ as large as the built-in

voltage of the p-n junction diode,

V(pn).

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Schottky Contact in Reverse Bias

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Tunneling Current

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Ratio of FE and TE Current

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Ohmic Contact by Tunneling

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RC vs. Doping

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RC vs. Doping