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Silicon crystal grown by the Czochralski method

Figure 111Silicon crystal grown by the Czochralski method. This large single-crystal ingot provides 300 mm

(12-in.) diameter wafers when sliced using a saw. The ingot is about 1.5 m long (excluding the

tapered regions), and weighs about 275 kg. (Photograph courtesy of MEMC Electronics Intl.)

1

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Physics and Modeling ofMicroelectronic Devices

MEL G 631

Dr. RAMESHA C K - IC

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Course plan

Text Book:Muller R. S and Kamins T. I., Device Electronics for Integrated circuits,

John Wiley, 3rd ed., 2003.

Reference Books:

(i) Sze S. M., Physics of Semiconductor Devices, 2nd Ed., Wiley Eastern, 1981.

(ii) Tyagi M. S., Introduction to Semiconductor Materials and Devices, John

Wiley & Sons, 1991.

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Course plan

Lecture

Number

Learning Objectives Topics to be Covered References (C

hap/Sec)

(Text Book)

1-2 Fundamental of semiconductors; Band and

Bond Models

Semiconductor Materials 1.1

3-5 Concepts of Holes, Mobility Drift, Diffusion

, etc.

Free Carriers and Hall Ef

fect Measurements

1.2 & 1.3

6 Meaning of Equilibrium in Electronic Syste

m

Metal-Semiconductor Co

ntact.

3.1

7-8 Ideal M-S Contact Without & With Bias and

Variation of Charge, Potential, Field, etc.

M-S Junctions 3.2

9 Schottky Contacts M-S Contact 3.3 & 3.4

10 & Effects Surface Effects 3.5

11-13 Effects of Impurity Distribution and Types o

f p-n junction and their properties.

pn junction 4.1 & 4.2

14 Effect of Bias and Junction Breakdown. pn junction under bias 4.3 & 4.415-16 JFET, its working and analysis JFET 4.5

17-19 Continuity Equation, Generation & Recombi

nation, Localized States

Currents in pn junction 5.1 & 5.2

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Lecture

Number

Learning Objectives Topics to be Covered References (C

hap/Sec)

(Text Book)

20-21 Ideal- Diode Analysis and Validity of Appro

ximations in the same.

Current-Voltage Characte

ristics of pn junction.

5.3

22-23 Transistor action, Various bias conditions an

d use in IC.

Bipolar transistor 6.1

24-26 npn transistor under active bias, its function,

parameters

Transistor under active bi

as

6.2

27 Transistor switching and different regions of

operation

Transistor switching 6.3

28-30 MOS structure, energy band diagrams in equilibrium and under various bias conditions

MOS system 8.1 & 8.2

31-32 Equilibrium and non-equilibrium analysis in

MOS electronics

MOS Electronics 8.3

33 Capacitance of MOS system and its variatio

n

MOS Capacitance 8.4

34 Effect of oxide and interface charges on M

OS system

Oxide charges in MOS 8.5

35 Basic MOSFET Behavior MOSFET-Physical Effect

s

9.1

36-37 Improved models for short channel MOSFE

Ts

Short channel MOSFET 9.2

38 Various parameters of MOSFET MOSFET 9.3 & 9.4

39-40 High Field Effects in MOSFETs MOSFET-Physical Effect

s

10.1 to 10.4

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ECNo.

EvaluationComponent

Duration Weightage (%)

Date Time Nature ofComponent

1. Test I 1 hour 20% 16-09-2011

(12 noon1pm)

Closed Book

2. Test II 1 hour 20% 21-10-2011

(12 noon1pm)

Open Book

3. Assignments/

Presentations

20% To be announced

in the class

4. Comprehensi

ve Examinati

on

3 hrs. 40% 05-12-2011 (FN) Closed Book

/ Open Book

4. Evaluation Scheme:

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Importance Semiconductor Devices

These devices enhance Performance

Reliability

Cost effectivenes

of

Energy Systems Information Systems

Generate, distribute and store, process and

regulate energy communicate information

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Energy Bands and Charge

carriers in Semiconductors

- Specific mechanisms by which current flows in a solid

- Dependence of the conductivity of a semiconductor on the temperature and

impurity concentration

- Discrete energy levels within atoms

- Large gaps in the energy scale where no energy states are available

- Basic difference between electron in an isolated atom and one in an atom ina solid

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Bonding Forces in Solids

Ionic bonding

Metallic bonding

Covalent bonding

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Ionic bonding: NaCl (Alkali halides)

Each Na atom is surrounded by 6 Cl atoms, and vice

versa.

Na (Z=11) has [Ne]3s1 and Cl (Z=17) has [Ne]3s23p5

electronic structure.

Each Na atom gives up its outer3s electron to a Cl atom

so that the crystal is made of ions with the electronic

structures of the inert atoms Ne orAr :

Thus, NaCl is called a good insulator.

Bonding Forces in Solids

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Figure 31Different types of chemical bonding in solids: (a) an example of ionic

bonding in NaCl; (b) covalent bonding in the Si crystal, veiwed along a

direction (see also Figs. 18 and 19).

Ionic Bonding (NaCl) & Covalent Bonding (Si)

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Metallic bonding

A metal atom has the outer electronic shell which

is partially filled, usually no more than 3

electrons.

The alkali metals such as Na have only one electron

in the outer orbit that is loosely bound and easily

given up in ion formation.

This fact accounts for not only the great chemical

activity of the alkali metals but also their high

electrical conductivity.

Bonding Forces in Solids

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Covalent bonding

In diamond lattice semiconductors ( Si, Ge, and C), eachatom is surrounded by 4 nearest neighbors, each with four

electrons in the outer orbit.

Each atom shares its valence electrons with its four

neighbors.

The bonding forces arises from a quantum mechanical

interaction between the shared electrons. Each electron

pair constitutes a covalent bond.

In the sharing process it is no longer relevant to ask which

electron belongs to a particular atom, in other words, both

electrons belong to the bond.

Bonding Forces in Solids

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Figure 31Different types of chemical bonding in solids: (a) an example of ionic

bonding in NaCl; (b) covalent bonding in the Si crystal, veiwed along a

direction (see also Figs. 18 and 19).

Ionic Bonding (NaCl) & Covalent Bonding (Si)

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Energy Band

What will happen when several isolated atoms are brought

together to form a solid ? The forces of attraction and repulsion

between atoms will find a balance at the proper interatomic spacing

for the crystal. In this process, important changes occur in electron

energy level configurations, thus resulting in the varied electricalproperties of solids.[(ex) For Si atoms, the outermost shell (or

valence shell), n = 3, where two 3s and 3p electrons interact each

other to form the four hybridized sp3 electrons when the atoms

are brought close together].

Si1S2 2S2 2P6 3S2 3P2

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Energy Band in a Silicon Solid

As many atoms are brought together, the split energylevels form continuous bands of energies.

- An isolated Si atom has an electronic structure in ground state :

1s22s22p63s23p2

- Noted that each atom has available two 1s states, two 2s states, six

2p states, two 3s states, six 3p states, and higher states .

- ForNatoms, there will be available 2N 1s states, 2N 2s states, 6N2p states, 2N 3s states, 6N 3p states.

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Energy Band in a Silicon Solid

As the interatomic spacing decreases, these energy levels split into

bands, beginning with the outer shell (n = 3). As the 3s and 3p

bands grow, they merge into a single band composed of a mixture

of energy levels. This band of 3s-3p levels contains 8N

available states.

As the distance between atoms approaches the equilibrium

interatomic spacing of Si, this band splits into two bands separated

by an energy gap, Eg. The upper band (conduction band) contains

4N states and the lower band (valence band) contains 4N states.

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Figure 3

3Energy levels in Si as a function of inter-atomic spacing. The core levels (n = 1, 2) in Si

are completely filled with electrons. At the actual atomic spacing of the crystal, the

2N electrons in the 3s sub-shell and the 2N electrons in the 3p sub-shell undergo

sp3hybridization, and all end up in the lower 4N states (valence band), while the

higher lying 4N states (conduction band) are empty, separated by a bandgap.

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Energy Bands and Charge Carriers in Semiconductors

Metals, Semiconductors, and Insulators in Energy Band Structure

For electrons to experience an acceleration in an applied

electric field, they must be able to move into new energy

states.

This implies that there must be empty states (allowed energy

states which are not already occupied by electrons) available to

the electrons.

For example, if relatively few electrons reside in an otherwise

empty band, ample unoccupied states are available into which

the electrons can move.

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Energy Bands and Charge Carriers in Semiconductors

Metals, Semiconductors, and Insulators in Energy Band Structure

On the other hand, the Si band structure is such that at 0K, the

valence band is completely filled with electrons and the

conduction band is empty.

Thus, there can be no charge transport within the valence band

because no empty states are available into which electrons can

move.

Also, there are no electrons in the conduction band so that no

charge transport can take place there either. This is why a pure Si

has a high resistivity typical of insulators.

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Figure 34

Typical band structures at 0 K.

Typical Energy Bands (Insulator, Semiconductor, Metal)

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Direct and Indirect Semiconductors

When a single electron is assumed to travel through a perfectly periodic lattice,

the wave function of the electron is assumed to be in the form of a plane wavemoving in thex-direction with propagation constant (or wave vector) k.

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(a) Direct Semiconductor (GaAs) : an electron in the conduction band can fall

to an empty state in the valence band, giving off the energy difference (Eg)

as a photon of light. Thus, this semiconductor material is used for lightemitters and lasers.

(b) Indirect Semiconductor (Si) : an electron in the conduction band minimum

in Si can not fall directly to the valence band maximum. Instead, it mustundergo a momentum change as well as changing its energy. The

indirect transition involves a change in k, and the energy is generally

given up as heat to the lattice rather than as an emitted photon.

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Energy Bands Variation vs. Composition (x)

Figure 36Variation of direct and indirect conduction bands in AIGaAs as a function of composition: (a) the ( E,k)

diagram for GaAs, showing three minima in the conduction band; (b) AIAs band diagram; (c) positions ofthe three conduction band minima in AIx Ga1- x As as x varies over the range of compositions from

GaAs ( x = 0) to AIAs ( x = 1). The smallest band gap, Eg (shown in color), follows the direct band tox = 0.38, and then follows the indirect X band.

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Charge Carriers in Semiconductors

Consideration of Current Conductions :

- Metals : Metal atoms are imbedded in a sea of free electrons, and these electrons canmove as a group under the influence of an electric field.

- Semiconductors : Since the semiconductors has a filled valence band and an empty

conduction band at 0K, the increase of electrons in conduction band by thermal

excitations across the band gap must be considered as the temp. is raised. In addition, after

electrons are excited to the conduction band, the empty states left in the valence band can

contribute to the conduction process. Also, the introduction of impurities is considered to

have an important effect on the energy band structure and on the availability of charge

carriers.

Electrons & Holes : As the temp. is raised from 0K, some electrons in theV.B. receive enough thermal energy to be excited across the band gap to theC.B., and this results in a semiconductor with some electrons in an otherwise

empty C.B. and some unoccupied states (called holes) in an otherwise filled

V.B.

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Figure 37Electron-hole pairs in a semiconductor.

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Electron-Hole Pair (EHP)

EHP = A pair of conduction band electron and valence band hole created by the excitation of a

valence band electron to the conduction band.

- Equilibrium number of EHPs in pure Si at RT = 1010 EHP/cm3

- Si atom density = 5 x 1022 atoms/cm3

Very few electrons are free to move about via the many available empty states

In the filled valence band, all available energy states are occupied. For every electron

moving with a given velocity, there is an equal and opposite electron motion elsewherein the band. If we apply an electric field, the net current is zero because for every electronj

moving with velocity vj, there is a corresponding electronj with velocity -vj.

With N electrons/cm3 in the band, the current density J :

N

i

iVqJ 0)(

N

i

jji qVVqVqJ )()(

(filled band),

(j-th electron missing)

If we create a hole by removing thej-th electron, the net current J in V.B. will be,