ELEC 321

Introduction to SemiconductorMaterials and Devices

INTRODUCTION

• The Information Age requires faster, more accurate and less expensive information as the main foundation of new technologies.

• Solid State Electronic and Optoelectronic Devices are designed to receive, process and transmit information, and are the main building blocks to construct the Information Highway.

• Advances could not have been accomplished without semiconductorspresent in all electronic and optoelectronic devices

• The purpose of this course is to provide a good understanding ofphysical properties of semiconductor materials and microelectronic devices which is essential for future electrical engineers

Conductivities in Materials

• Superconductors• Conductors• Semiconductors• Insulators

Why Semiconductors?

• Semiconductors are used in Design and Structures of almost all Solid State Electronics and Optoelectronics Devices.

• These are possible by controlling the electron behavior in solids.

Application of Semiconductors

• Electronic Devices/equipments• Optoelectronic Devices/equipments• MEMS• Nanodevices• NEMS

Classification of Devices

• Combination of Electrics and Mechanics form Micro/Nano-Electro-Mechanical Systems (MEMS/NEMS)

• Combination of Optics, Electrics and Mechanics form Micro/Nano-Opto-Electro-Mechanical Systems (MOEMS/NOEMS)

Optical Electronics

Mechanical

MEMS

MOEMS

Micro/ Nanotechnology

1/4/2005 ECE, Concordia 7

10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Scale (meters)

Atom DNA

NEMS

Nano manipulation

NanotubeFET

TR on ICBacteria

Human hair

Ant’s eye segment

MEMS

Electronic Devices• Electronics components: logic gates, adders, counters,

multiplexers• Passive: resistors, capacitors, • Active: amplifiers, transistors, diode,• Circuit boards • Analog circuits• Digital circuits• Integrated devices: Microprocessors, Digital signal

processor (DSP), Field programmable gate array (FPGA)• Electronic equipments: Computers. TV, calculators,

Microelectronic ComponentsDiodes

Transistors

Capacitors

Memories

Amplifiers

Switches

Analog & Digital IC

Microelectronics

Schematic illustration of the the structure of a double heterojunction stripecontact laser diode

Oxide insulator

Stripe electrode

SubstrateElectrode

Active region where J > Jth.(Emission region)

p-GaAs (Contacting layer)

n-GaAs (Substrate)

p-GaAs (Active layer)

Currentpaths

L

W

Cleaved reflecting surfaceEllipticallaserbeam

p-AlxGa1-xAs (Confining layer)

n-AlxGa1-xAs (Confining layer) 12 3

Cleaved reflecting surface

Substrate

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Optical Sources; Laser, LED

Switches

Photodiodes

Photodetectors

Solar Cells

Optoelectronic Devices

MEMS

MEMS

Hinged positionable mirror

Surface Micromachining

Integrated MEMS Technology

•Sensors + Actuators + Decision/Control units, all on one chip.

Anisotropic Wet Etching

Wet Etching (cont..)

Isotropic Etching• All Directions are etched at the

same rate

Anisotropic Etching• Different directions are etched at

different etch rates• Different structures can be

fabricated

• Anisotropic etching of silicon is one of the key technologies for the fabrication of MEMS/microsystems.

• 3D geometric shapes limited by flat surfaces are formed in the bulk of silicon. Examples: cavities, grooves, and channels.

MEMS heater showing an active free standing membrane released by anisotropic etching.

ConnectionsMembrane

Heater

Cavity

fiber optic

clip SiN

cavity

Fiber optics alignment in grooves of silicon

Better control of the technique is necessary to achieve more complex structures.

Nano Devices

The mentioned textured silicon was electrochemically etched using the same anodization conditions as sampl#7 (I=85mA, t=30min (all conditions are kept constant)).

Silicon nano-rods were fabricated on the tip of the pyramidal porous silicon structure with diameter of 200nm and length of 800nm.

Figure 22-a: Cross section of pyramidal PS fabricated on Si surface of high-concentration hillocks-sample#10.

Figure 22-b: Cross section of one pyramid from sample#10. This image is representing a silicon nano-rod.

This structure is of potential for photovoltaic applications. The nano-rods with sharp tips can be also used as AFM probes. 21

Semiconductor NanoparticlesSemiconductor NanowiresQuantum Dots

• They have potential applications in a number of areas:

• Healthcare and Life Science• Information and Communication Technologies,

Energy applications, solar cells.• Fine Chemicals.• Sensors (chemical, biological, mechanical,…)

Type of Semiconductors

• Simple Semiconductors• Compound Semiconductors• Direct Band gap• Indirect Band gap

Some Properties of Some Important Semiconductors

Compound Eg Gap(eV) Transition λ(nm) BandgapDiamond 5.4 230 indirectZnS 3.75 331 direct

ZnO 3.3 376 indirect

TiO2 3 413 indirect

CdS 2.5 496 direct

CdSe 1.8 689 direct

CdTe 1.55 800 direct

GaAs 1.5 827 direct

InP 1.4 886 direct

Si 1.2 1033 indirect

AgCl 0.32 3875 indirect

PbS 0.3 4133 direct

AgI 0.28 4429 direct

PbTe 0.25 4960 indirect

Required Knowledge and Background

• In order to understand the behaviour of electrons in solid state materials and how to control them, we need to study the materials structures, and the physics that describe the states of electrons in semiconductors. For this we will go through,

• An introduction to Crystal Structures• An introduction to Quantum Mechanics• A touch of Statistical Physics• Electrons in Solid State Materials• Carrier Transport in Semiconductors• Semiconductors in Equilibrium/Non-Equilibrium States• Basis Structure of pn Junctions (which is the foundation of

almost all electronic and optoelectronic devices).

Silicon Production

• Produced silicon at this stage is 98% pure and is called Metallurgical Grade Silicon (MGS).

• For electronic purposes very high pure silicon - Electronic Grade Silicon (EGS) is needed.

• To obtain EGS from MGS the following reactions are used:

)()()()()( 180016002 gasCOgasSiOliquidSisolidSiOsolidSiC C ++⎯⎯⎯⎯ →⎯+ °−

heatHgasSiHClgasHClsolidSi C ++⎯⎯ →⎯+ °23

300 )()(3)(

)(6)(2)(2)(2 23 gasHClsolidSigasHgasSiHCl +→+

The above process is called chemical vapour deposition (CVD) and the produced Si is polycrystalline and 99.999% pure.

Silicon Wafer

• Type– n-type (e.g.,As,P, Bi

doping)– P-type (B, Ga, In doping)

• Orientation

– {100}, {111},…

Crystals

• An IDEAL CRYSTAL is constructed by infinite repetition of identical structure units in space.

• A LATTICE represents a set of points in space that form a periodic structure, where each point sees the same environment. A building block of atoms called the BASIS is then attached to each lattice point yielding the crystal structure.

LATTICE + BASIS = CRYSTAL STRUCTURE• Identical structure units that have small volume are called UNIT CELL• The smallest unit cell is called PRIMITIVE CELL and the cell that is

most convenient to study crystal structures is called CONVENTIONAL UNIT CELL.

• Unit cells contain all the structural and physical properties of the crystal and ARE NOT unique entities.

Example of two-dimensional unit cell structure:

A D

CB

a

b

In the 2D lattice above, the unit cell is represented as ABCD and any point in the lattice can be represented using the basis vectors a and b:

R = pa + qb, p, q are integers

For a 3D lattice there are three basis vectors so that:

R = pa + qb + sc, p, q, s are integers

Cubic P Cubic I Cubic F

Tetragonal P Tetragonal I

Orthorhombic P

Orthorhombic C

Orthorhombic I Orthorhombic F

Monoclinic P Monoclinic C Triclinic

Trigonal R Trigonal and Hexagonal R

a

c

b

γ

β

α

Common Planes

• {100} Plane• {110} Plane• {111} Plane

a

aa – Lattice ConstantFor Silicon

a = 5.34 Ao

Two Interpenetrating Face-Centered Cubic LatticesSilicon – Diamond Structure

Principles of Quantum Mechanics

The principle of Energy Quanta:• Experiments which showed inconsistency between

experimental results and classical theories.– Thermal Radiation– Hydrogen Atoms– Photoelectric Effect

Principles of Quantum Physics– Planck’s postulate in 1900 that

radiation from a heated sample is emitted in discrete units of energy, called quanta.

– Einstein in 1905 interpreted the photoelectric results by suggesting that the energy in a light wave is also contained in discrete packets. The particle-like packet of energy is called photon.

(Planck’s Constant)

sJhhE .10625.6 34−×== ν

Wave-Particle Duality Principle:

• Photoelectric Effect• Compton Effect• Diffraction pattern by electrons

Since waves behave as particles, then particles should be expected toshow wave-like properties.

• De Broglie hypothesized that the wavelength of a particle can beexpressed as

• The momentum of a photon is then: p = h/λ

ph

=λλ = de Broglie wavelength

p = momentum of the particle

The Uncertainty Principle (Heisenberg)

• It is impossible to simultaneously describe with absolute accuracy the position (energy) and momentum (instant of time) of a particle.

• ħ is very small so this principle only applies to very small particles

Quantum Mechanics does not predict a deterministic course of events, but rather the probabilities of various alternative possible events.

sJhxp .10054.12

34−×==≥ΔΔπ

hh

• Postulate I: (in one-dimensional system)– There exists a state function Ψ(x;t) which contains all the measurable

information about each particle of a physical system. Ψ(x;t) is also called wave function.

• Postulate II:– Every dynamical variable has a corresponding operator. This operator is

operated on the state function to obtain measurable information about the system.

– In a one-dimensional system:

Dynamical Variable Quantum Mechanic OperatorPosition x XX ≡ˆ

Momentum px XJPx ∂

∂≡hˆ

Total Energy E tJE

∂∂

−≡hˆ

Potential Energy V(x) )()(ˆ xVxV ≡

• Postulate III:– The state function Ψ(x;t) and its space derivative ∂Ψ/∂x must be

continuous finite and single-valued for all values of x.– The state function must be normalized i.e.

– Ψ* is the complex conjugate of Ψ. Obviously Ψ Ψ* is a positive and real number and is equal to /Ψ/².

– Assume a single particle-like electron; then Ψ Ψ* is interpreted as the statistical probability that the particle is found in a distance element dx at any instant of time. Thus Ψ Ψ* represents the probability density.

1=ΨΨ∫∞

∞−

∗dx

For a three dimensional system Ψ Ψ* dτ represents the probability density. dτ is an element of volume about the point where Ψ and Ψ* are determined.

• The average value ⟨Q⟩ of any variable corresponding to the state function Ψ is given by expectation value:

• ⟨Q⟩ is the expected value of many observations.

• Once the state function corresponding to any particle was found, it was possible to calculate the average position, energy and momentum of the particle within the limit of the uncertainty principle.

∫∞

∞−

∗ ΨΨ= τdQQ ˆ

Principles of QM

• Schrodinger Wave Equation• Physical meaning and its application• Some examples: infinite potential well,

potential step function, potential barrier…• Tunneling Effect

Quantum Well

2

222

2manEn

h π=

222

4

2)4( n

qmE

o

on

hπε

−=

0/2/3

0100

11 arqa

−⎟⎟⎠

⎞⎜⎜⎝

⎛=

πψ

One Electron Atom

Energy band structure in solids

1s

2s

2p

1s

2s

2p

1s

2s

2p

1s

2s

2p

1s

The potential wells due to the interactions between 2 atoms (in one molecule). Some

electrons are shared between the atoms. Due to the interactions between electrons-

electrons, nucleons-nucleons, and electrons-nucleons, the energy levels split, creating 1s,

2s, 2p,… doublets.

The potential experienced by an electron due to the coulombinteractions around an atom. 1s, 2s, 2p,… are the energy

levels that the electron can occupy.

Larger molecules, larger splitting.

In Solid with n≈ 1023 atoms, the sublevels are extremely close to each other. They coalesce and form an energy band. 1s, 2s, 2p… energy bands.

Periodical Potential

r

r

Non-Periodical Potential

r

r

)(rV

2)(rΨ

)(rV

2)(rΨ

jkrerur ⋅=Ψ )()(

The Kronig-Penney Model

The Concepts of:

1) Effective Mass

*2

2

2

11mdk

Ed=

h

2) Negative Mass

3) Positive charge

4) Holes

Atomic Bonding in Semiconductors

Concept of positive charges in solids (holes)

EEhm

Eg

EEhmEg

vp

v

cn

c

−=

−=

3

2/3*

3

2/3*

)2(4)(

)2(4)(

π

π

Density of State.

Electrons Distribution.

⎟⎠⎞

⎜⎝⎛ −

+=

kTEE

EfF

F

exp1

1)(

Fermi-Dirac Distribution:

E EF

0

1/2

1.0

T = 0

T = T1

T = T2 > T1

The Fermi probability function versus energy for differential temperatures.

nn

⎥⎦⎤

⎢⎣⎡ −−

=kT

EENp vFv

)(exp0

⎥⎦⎤

⎢⎣⎡ −−

=kT

EENn Fccc

)(exp)()()( EfEgEN F=

)()()( EfEgEN F=

I Intrinsic Semiconductors:A pair of an electron and a hole (EHP) is generated due to the thermal excitation.

Conduction electron+4

Si+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

Eg

Ec

Ev

Ef

Valance hole

Electron and hole pairs (EHP) are generated due to the thermal excitation. no is the electron density (number of electrons / cm3), po is the hole density (number of holes / cm3) . for intrinsic materials no = po = ni . For silicon ni = 1.5 x 1010 and for GaAsni = 106 .

Extrinsic Semiconductors:

+5As

+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

Eg

Ec

Ev

Ef

Ed

Conduction electron

N - Type

+3Al

+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

+4Si

Eg

Ec

Ev

Ef

Valence hole

Ea

In Extrinsic Materials, electrons and holes are generated by doping materials with impurities. n is the electron density and p will be hole density in the crystals. For n>p (crystals have electron-majority, hole-minority) the crystal is called n-type. For p>n ( crystals have hole-majority and electron-minority) the crystal is called p-type.

P - Type

⎥⎦⎤

⎢⎣⎡ −−

=kT

EEnp FiFi

)(exp0 ⎥⎦⎤

⎢⎣⎡ −

=kT

EEnn FiFi

)(exp0

Concept of donors, acceptors

Carrier Transport:

Current in Semiconductors: (Drift, Diffusion, Carriers Recommendation, Carriers Generation)

Drift Current:

EpnqJ pndrf )( μμ +=

Diffusion current:

dxdpqDJ

dxdnqDJ

ppdif

nndif

−=

=

)()(dxdpD

dxdnDqEpnqJ pnpntotal −++= μμ

Under Equilibrium Condition J(total) = 0.

qkTDD

p

p

n

n ==μμ

Einstein Relation

kT/q at room temperature = 0.0259 V

ponopn

tntnRRτδ

τδ )()(

===

tnng

xEn

xnE

xnD

tppg

xEp

xpE

xpD

nnnn

pppp

∂∂

=−+∂∂

+∂∂

+∂∂

∂∂

=−+∂∂

+∂∂

−∂∂

τμ

τμ

)(

)(

2

2

2

2

Continuity Equations

Surface Effects

pn Junction, diode structure

pn junction under biased conditions