electronics week 2

8/12/2019 Electronics Week 2

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2.0 Semiconductor materials

2.1 Elemental and compound semiconductors

---Periodic Table of some elements---

II III IV V VIB C (6) N O

Mg Al Si (14) P S

Zn Ga Ge (32) As Se

Cd In Sn Sb Te

Electron configuration of elemental semiconductors

1. C (diamond): (1s)2/(2s)2(2p)2,

inner orbital / outer orbital2. Si: (1s)2(2s)2(2p)6/(3s)2(3p)2

3. Ge: (1s)2(2s)2(2p)6/(3s)2(3p)6(3d)10/(4s)2(4p)2

Commom character of semiconductor

----outer orbital, (ns)2

(ns)2

------

Atomic number = Number of electrons


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Metal

Semi-

condu

ctor

Electronic

configuration of the

respective elements

Semi-

condu

ctor

Electron Energy of Na

Pauli Exclusion

principle (two

electrons of opposite

spin can occupy each

energy level)


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For optical devices like LED, LD, compound semiconductors

are very useful.

A. Elemental semiconductors CdiamondSi, Ge, Te,SnB. Compound Semi. III-V GaAs, GaPGaN, InSb, InAs, InP, AlP

II-VI ZnS, ZnSe, ZnO, CdS, CdSe, CdTe,

IV-IV SiGe, SiC, (V-VI Bi2Te3)C. Calcogen/Spinelmagnetic Semi.) CdCr2Se4, CdCrS4

D. Rare-earth,magnetic Semi.) EuO, EuS, EuSe

E. Amorphous Semi. Ge, Te, Se, GeTe, As2Te

F. Organic Semi. TCNQ

Compound Semiconductor (Man-made materials)Equivalent electron number (outer orbital) =4

Ga: (1s)2

(2s)2

(2p)6

/(3s)2

(3p)6

(3d)10

/(4s)2

(4p)1

As: (1s)2(2s)2(2p)6/(3s)2(3p)6(3d)10/(4s)2(4p)3


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2.2 Covalent bond and diamond structure

Covalent bond simplest case---Hydrogen molecule, H2,There are only three elements which form a crystal with a covalentbonddiamondCsilicon(Si)germanium(Ge)Covalent bond--one 3s orbital and three 3p (px, py, pz) orbital consist

of a new sp3

hybrid orbital

Electron distribution of sp3hybrid orbital

Tetrahedron structure


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Diamond structure


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Crystal structure of GaAs and GaN

Zinc-blend structure Wurzite structure


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Classification of Material structure

(a) Amorphous---no ordered atomic arrangement

(b) Polycrystallineshort range atomic order usually in small crystallinegrains (10Afew m)

(c) crystallinelong range, ordered, atomic arrangement, repeating unit

cell

All important semiconductor devices are based on crystalline materials (Siespecially) because of ---?


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Silicon ingot and wafer


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2.3 Electron Energy in the crystal

(The difference in the electrical characteristics among Metal,

Semiconductor and Insulator can be explained with the

Problems:

How does the electron energy change from atom to crystal?

New concept of energy band (Quantum theory of soild )


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2.3.1 Energy band by a qualitative model

---in case of electron Energy of Na crystal (Metal)

Energy level of outer electron (3s level)

sprits into N (number of Na atoms) levelswith very narrow distance-----called

Energy Band

While, energy levels of inner electron (2p,

2s and 1s) does not sprit and N levelsoverrapp.

Electron energy of Na atom

To form a crystal

Electron energy of Na crystal

Electronenergy

Electronen

ergy

Atom distance


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2.3.2 Energy band model (general model)

periodic potential

Vacuum level

Allowed

energy band

E, Electron Energy

K, wave number

Calculate the electron energy in the

crystal under periodic condition using

Schrodinger equation

Inside crystal

Outside

crystal

Forbidded

energy

band

A large number of energy levels = Number of atoms

Energy level

of innerorbit


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2.3.4 Band diagram of (a) metal, (b) semiconductor, and (c)

insulator.

Valence band

(completely full)Valence band

(almost full)

Valence band

Completely full)

Conduction bandCompletely empty)Conduction band(almost empty)Conduction band(half full)

Hole

Electron

EG: Energy Gap

Filled

band


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2.3.5 Energy band of Si and GaAs

Indirect semiconductor Direct semiconductor

Energy Band structure of Si Energy Band structure of GaAs

ElectronEnerg

y[eV]

ElectronEnergy[

eV]


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2.3.6 Electron effective mass, mn

Evs. krelation (E: electron energy, k:wave number)

-------parabolic--------- E=(k)2/2mn

Where1

=1

2(2

2)

called electron effective mass (the second derivative of E with respect to k)

For GaAs narrow conduction band, mn = 0.07m0, (m0:electron rest mass)

whereas for Si with a wider conduction band, mn = 0.19m0.

** Electron effective mass depends on crystal direction If we introduce the electron effective mass, electrons in the crystal under

electric field behave like as a single particle with effective mass.

(2.12)

(2.13)

(2.14)


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2.4 Extrinsic Semiconductors, n-type and p-type

Donor concentration :Nd[cm-3]

Electron concentration: n

Intrinsic carrier concentration: ni

n=Nd

p=ni2/Nd

(2.23)

(2.24)

Excess electron

submitted from

phosphorus atom

Positively ionized

phosphorus

atom

Conductionband

Valence

band

2.4.1 Donors


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2.4.2 acceptors

Acceptor concentration: Na[cm-3]

Hole concentration: p

p=Na

n=ni2/Na

(at room temperatures)

(2.25)

(2.26)

Negatively

ionized

boron atom

Breaking Si-Si bond, an

electron is emitted and it is

captured by boron atom,

completing covalent bond

An

missing

electron

leaves a

hole

hole


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2.4.3 intrinsic carrier concentration i

Ge: 2.40x1013cm -3at 300K

Si: 1.45x1010cm -3at 300K

GaAs: 1.79x106cm -3at 300K

Constancy of p product

p=ni2

ni={NcNv}1/2exp(-EG/2kT)

GaAs

Si

1.451010

1.79106

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

150

0100

0500 200 100 27 0 -50

T()

1000/T(K-1)

0.5106

107

108

10910

10

1011

1012

1013

1014

1015

1016

1017

10181019

ni

(cm-3)

(2.21)

(2.22)


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2.4.4 Temperature dependence of electron concentration

At high temperatures, for n-type semiconductors,

neutrality: n=p + Nd

np product constancy: np=ni2

Absolute Temperature [K]

At low temperatures

(


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Electric Field, Ex

In no electric field, free electrons and holes move through the crystal dueto random thermal motion ------ Thermal velocity : vth=10

7

cm/s

When the electric field, Exis applied, carriers move very slowly as compared

with thermal velocity. This situation seems to drift. Its velocity is called drift

velocity.

2.5 Carrier Transport in the electric field2.5.1 mobility

No Electric Field

Electron


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Electroncan be regarded as particle using effective mass. Ex: Electric field in x direction,

Vx: velocity of electron, mn: effective mass of electron

mn =qEx.

Then, vx=vxo (vxo: initial velocity of electron at t=0)

Above equation indicates the increase of electron velocity with time. However,real situation in the movement of many electrons differs. Electrons arescattered and collide with host atoms (Si) or other electrons. Average timebetween collision is called average relaxation time .

dt

dvx

n

x

m

tqE

This average velocity called drift velocity vd .

The proportional factor n is called mobility.

vd=n Ex, where n=nm

q

(2.30)

(2.31)

(2.32) (2.33) (2.34)


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Si GaAs


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2.5.2 Drift Current, Conductivity, and Ohms law

Electron drift curent Jnx=qnvx=qnnEx

Hole drift current Jpx=qpvx=qppEx

Total drift current J= Jnx +Jpx ,

=q(nn+ pp) Ex ,

where conductivity =q(nn+ pp)

Then, J= Ex, called Ohms law

In n-type semiconductor, n>>p, then =qnn

In p-type semiconductor, p>>n, then =qpp

Resistivity =1/

(2.35)

(2.36)

(2.37)

(2.38)

(2.39)

(2.40)

(2.41)

(2.42)


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2.5.3 Diffusion current----important in pn junction---

Flux F is proportional to the concentration gradient (dc/dx).

This is called Ficksfirst law.

F=D D: diffusion coefficient

c: concentration, x: distance

In semiconductor, diffusion current is generated due to the non-uniform distribution of carrier concentration .

Electron diffusion currentJdn=(q) (Dn )=q Dn

Hole diffusion currentJdp=(q) (Dp ) =q Dpdx

dn

dx

dn

dx

dpdx

dp

dx

dc(2.43)

(2.44)

(2.45)


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Total current

Electron current

Hole current

Total current J =Jn+Jp

Relationship between Mobility (Drift) and Diffusivity (Diffusion)

Einsteins Relation

(2.46)

(2.47)

(2.48)

(2.49)


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2.7 Carrier generation and recombination

In thermal equilibrium, electron-hole pairs are always generated and

recombine. In net, carrier concentrations are maintained at certain values

at temperatures.Consider that light is irradiated on a p-type semiconductor substrate

uniformly. We investigate the generation and recombination of the

minority carrier (here, electron) concentration.

During the irradiation of light, excess electron-hole pairs are generated.

GL: generation rate of electron-hole pairs: time constant for excess carrier to return to the thermal equilibrium

Time variation of electron concentration (minority carrier) in p-type

semiconductor is given by

At steady state(t


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If light is off (GL=0) at t=0, electron concentration returns to the thermal

concentration n0with time constant .

time

light

semiconductor

X: distance

(2.53)


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Summary of semiconductor materials--1


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Summary of semiconductor materials--2

electronics week 2

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