Chapter 1

• Van der Waals-London force : there exists a weak type of attraction ( secondary bonds ) between all atoms and molecules due to a net electrostatic attraction between the ‘e’ distribu[r]

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General Information for KEE220

Instructor: Prof Tae Geun Kim, 213 Engineering Building

Recommended: Solid-State Physics

1 Solid-State Electronic Devices, by Streetman

2 Teaching Materials, by T G Kim

Grading: Midterm 30%, Final 30%, Quiz 20%, Task 10% Attitude 10%

- Task: Selected problems will be given to solve at the end of each chapter

KEE220 Websites: http://asl.korea.ac.kr

T.A : Dong Ju Chae, 3290-3664, chaedju@korea.ac.kr

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What to learn ?

Through the course, we learn about fundamental physics for electrical/ electronic materials and devices, semiconductors, integrated circuits & processes, and materials characterizations The course will be

developed to the subject "semiconductor engineering" open every first semester of the 3rd grade

Chapter 1 Elementary materials science concepts Chapter 2 Electrical and thermal conduction in solids Chapter 3 Elementary quantum physics

Chapter 4 Modern theory of solids

Chapter 5 Semiconductors

Chapter 6 Semiconductor devices Chapter 7 Dielectric materials and insulation Chapter 8 Magnetic properties and superconductivity Chapter 9 Optical properties of materials

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1 9.1-9 Ch 1 Atomic Structure, Bonding and Types of Solid p.1-25

2 10 16 Ch.1 Kinetic Molecular Theory, Thermally p

26-2 10-16

3 17-21 Ch.1 Crystalline State, Crystalline Defects, Single

Crystal, Amorphous Semiconductors

p 99

50-Ch.1 Problem solving

4 24-28 1(28일)stQuiz Ch.2.Electrical and Thermal Conduction in Solids,

Drude Model

p 140

113-5 29- Ch.2 Matthiessen's Rule Mixture Rules & Electrical p

6 8-13 Ch.2 Skin Effect, Hall Effect, Thermal Conductivity 190p

176-7 14–20 Ch.2 Interconnection, Electro-migration 220p

8 21 26 중간고사

8 21-26 (21일)사

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Ch 3 Photons Electrons as a Wave Infinite p 221

9 27-31 Ch.3 Photons, Electrons as a Wave, Infinite

Potential Well

p 235

221-10 11.1-7 Ch.3 Heisenberg's Uncertainty, Tunneling

Phenomenon Potential Box Hydrogen Atom

p 252

236-Phenomenon, Potential Box, Hydrogen Atom 252

11 8-15 Ch.3 Helium Atom & Periodic Table, Lasers

Ch.4 Band Theory of Solids, Semiconductors

p 268

12 16.23 2(23일)ndQuiz Ch.4 Electron Effective Mass, Energy Bands,

Statistics

p 328

340-15 10-16 Ch.4 Band Theory of Metals

p 361

353-Ch.4 Problem Solving Review of Semester and Discussions of Related

16 11-19 기말고사 Review of Semester and Discussions of Related

This time table may be subject to change depending on the situation.

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Chapter 1.

Elementary Materials Elementary Materials Science Concepts

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Ch1.1 Atomic Structure and Atomic Number

Ch1.2 Atomic Mass and Mole

Ch1.3 Bonding and Types of Solids

Ch1.4 Kinetic Molecular Theory

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Ch1.1 Atomic Structure and Atomic Number

To understand the atom’s general behavior one should involve QM; however in

• To understand the atom s general behavior, one should involve QM; however, in

• Nucleus: positively charged protons and electrically neutral neutrons

- strong nucleus force: neutrons + protons

• Atomic number (Z): the number of proton in the nucleus

• Electrons: assumed to be orbiting the nucleus at very large distances

Figure 1.1 The shell model of the carbon atom,

in which the electrons are confined to certain shells and subshells within shells

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Ch1.1 Atomic Structure and Atomic Number

and orbital angular momentum quantum number ( )

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Ch1.1 Atomic Structure and Atomic Number

Useful terminologies

• valence electron: the outermost electron, determining the valency of the atom

Useful terminologies

to interact with outer electrons on neighboring atoms

• ionization energy: the smallest energy required to remove a single electron from

a neutral atom and thereby create a positive ion (cation) and an isolated electron

• electron affinity: the energy that is needed, or released, when we add an electron

• Virial theorem:

E = KE + PE , KE = - PE

2

1 Ex) Assume that E of the ‘e’ in H is -13.6eV; It takes 13.6eV to ionize the H atom

KE = average kinetic energy

PE = average potential energy

2

The average PE of the ‘e’ due to its Coulombic interaction with the + nucleus is -27.4eV by Virial theorem Its average KE turns out to be 13.6eV

E = average total or overall energy

g

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Ch1.2 Atomic Mass and Mole

atomic mass number (A): the total number of protons and neutrons

• atomic mass number (A): the total number of protons and neutrons

• isotopes: the same number of protons, a different number of neutrons

• atomic mass unit (amu) u: equal to 1 of the mass of a neutral carbon atom which

• atomic mass unit (amu) u: equal to of the mass of a neutral carbon atom which

• atomic weight (Mat ): the average atomic mass of all the naturally occurring isotopes

Convert the composition of a substance from weight to atomic percentage or vice

• Convert the composition of a substance from weight- to atomic- percentage or vice versa (assuming the substance consists of A, B)

A A

A

M w

A , w B = weight fractions of A and B (mat Eng.)

n A n B = atomic or molar fractions of A and B (chem)

B B

A A

A

M w

n

/

/ + n B = 1 n A n A , n B = atomic or molar fractions of A and B (chem)

M A , M B = atomic masses of A and B

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1 3 1 Molecules and General Bonding Principles

• The general principle of molecule formation: a bond between the two atoms

1.3.1 Molecules and General Bonding Principles

E required to separate the two atoms

- Net force : FN = FA + FR

dr dE

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1 3 2 Covalently Bonded Solids : Diamond

• covalent bond: the sharing of valence electrons to complete the subshells of each atom and thereby reducing the overall potential E of the combination.each atom and thereby reducing the overall potential E of the combination

between two H atoms, leading to the

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1 3 2 Covalently Bonded Solids : Diamond

• coordination number (CN): the number of nearest neighbors for a given atom

The diamond crystal is a covalently bonded network of carbon atoms.Each carbon atom is bonded

forming a regular three-dimensional

pattern of atoms that constitutes the diamond crystal

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• Properties :

nuclei, the covalent bond E is the highest for all bond type

→ lead to very high y g melting temperaturesg p , very , y hard solids ex) diamond)

- insoluble in nearly all solvents

- poor electrical conductivity because ‘e’ is not free in a crystal

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1 3 4 Metallic Bonding : Copper

• Metal atoms have only a few valence electrons; easily lost from individual atoms and become collectively shared by all the ions when many metal atoms are

brought together to form a solid (delocalized and form an electron gas or cloud)

• ions are packed as closely as possible by the gluing effect of the electrons

good thermal conductivity

In metallic bonding, the valence electrons from the metal atoms form a

electrons from the metal atoms form a

“cloud of electrons” which fills the metal ions and “glues” the ions together

through Coulmbic attraction between thethrough Coulmbic attraction between the electron gas and the positive metal ions

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1 3 4 Ionically Bonded Solids : (NaCl)

• frequently found in materials that normally have a metal and a nonmetal as the constituent elements (i.e., NaCl, LiF, MgO, CsCl, ZnS)

• ionization energy : the energy needed to remove the electron from the atom

• cohesive energy : the energy required to take solid apart into individual atoms

(i.e., NaCl Æ Na, Cl)

f transfer

Coulombic force balanced

look like Ne w/+, Ar

w/-Fig 1.8 the formation of an ionic bond between

Na and Cl atoms in NaCl.

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1.3.3 Ionically Bonded Solids : Salt

• Properties :Properties :

- strong, brittle materials with high melting temperatures compared to metals

- most become soluble inmost become soluble in polar liquidspolar liquids such as watersuch as water

→ lower thermal conductivity

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1 3 5 Secondary Bonding

• Van der Waals-London force : there exists a weak type of attraction (secondary bonds) between all atoms and molecules due to a net electrostatic attraction between the ‘e’ distribution of one atom and the positive nucleus of the other

• In many molecules the concentrations of +/- charges do not coincide shown in

(a) A permanently polarized molecule

is called an electric dipole moment (b) Dipoles can attract or repel each other depending on their relative

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1 3 5 Secondary Bonding

between neutral atoms and nonpolar molecules

The center of mass of the ‘e’

in the closed shells, when

averaged over time, coincides

with the location of the +

with the location of the

nucleus

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Ch1 4 Ki ti M l l Th f G

Ch1.4 Kinetic Molecular Theory of Gases

1 4 1 Mean Kinetic Energy and Temperature

pressure of gas, heat capacity of metals, average speed of ‘e’, noise in resistors

1.4.1 Mean Kinetic Energy and Temperature

• Let’s consider a collection of gas molecules in a container & apply classical

• The change in the momentum of the molecule following its collision with the wall

is Δp = 2mv x

mv mv

p

2

2 Δ

( m = the mass of the molecule) F exerted by the molecule on face A is

a v

a t

= Δ

=

( △t = the time to traverse twice the length of the box)

) (

2

2 1 3

3

2 v x v x v xN

a a

V

v Nm P

3

2

2 2

2 v x v y v z 3v x

( )

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• the gas equation

by theory vs by experiment

V

v Nm P

v m N

PV =

RT N

N PV

A

)(

m

2

32

• When heat is added to a gas, its internal E and its temperature both increase

- if we consider 1 mole of gas then the heat capacity Æif we consider 1 mole of gas, then the heat capacity Æ molar heat capacitymolar heat capacity (C )(Cm)

m N

2

3)2

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• Maxwell’s principle of equipartition of energy is a useful theorem, which assigns

an average of 1KT/2 to each independent energy term in the expression for total E

1 Total E for a monatomic molecule

2 2

2

12

1

z y

2 2

2

12

1

z z y

y z

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3 A atom in a solid

11

1

2

12

1

z K y

K x

K mv

mv mv

From Kinetic E of vibration + potential E of the spring in all directions

(a) The ball-and-spring model of solids , in which the springs represent the interatomic bonds p g p Each ball (atom) is linked to its neighbors by springs Atomic vibrations in a solid involve three dimensions

(b) An atom vibrating about its equilibrium position The atom stretches and

compresses its springs to its neighbors and has both kinetic and potential energy

has both kinetic and potential energy.

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1 4 2 Thermal Expansion:

• Since the amplitude of atomic vibrations increases with temperature

→ all materials expand as the temperature increases

KE PE

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Ch1.5 Molecular Velocity and Energy Distribution

• From the kinetic theory we can determineFrom the kinetic theory, we can determine the root mean square velocitythe root mean square velocity of theof the

Stern-type experiment (see p 37)

Maxwell-Boltzmann distribution of molecular speeds in nitrogen gas at two temperatures The ordinate is dN/(Ndv)

temperatures The ordinate is dN/(Ndv), the fractional number of molecules per unit speed interval in (s/km)

• Maxwell-Boltzmann distribution function : describe the statistics of particle velocities

dN = nvdv

) 2

exp(

) 2

( 4

2 2

2 / 3

kT

mv v

kT

m N

π π

p

in thermal equilibrium

( nv=velocity density function, N=the total number of molecules, m=molecular mass )

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Ch1.5 Molecular Velocity and Energy Distribution

What is the E distribution of molecules in a gas?

dv n dE

nE = v

• These are the atoms with velocities in the range v to v+dv, Æ

)

1(

2 / 1

kT

E E

kT kT

Energy distribution of gas molecules at two different temperatures.

The number of molecules that have energies greater than E Ais the shaded area This area depends strongly on the temperature as

N

N = the total number of molecules in the system

exp( E A /kT).

y

C = a constant that relates to the specific system(see Fig 1.23)

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Ch1.6 Heat, Thermal Fluctuations, and Noise

• thermal equilibriumq : the condition where no net transfer of energy is made from one gy

• However, if ½(MV2) > 3kT/2, E will be transferred from solid atoms to gas molecule until both are equilibrated in temperature

until both are equilibrated in temperature

of the random motions and collisions of the atoms and molecules

SOLID

GAS

M V

m v

Gas Atom

Solid in equilibrium in air During collisions between the gas and solid atoms, kinetic energy is exchanged.

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• On example is observed in fluctuations of a mass attached to a spring, due to

If the mass m compresses the spring

by △x, then at time t, the energy

On example is observed in fluctuations of a mass attached to a spring, due to random bombardment by air molecules

1)

2

Over a long period, the average value of

PE will be the same as KE, and by Maxwell equipartition of E theorem

equipartition of E theorem,

and finally the rms value of

kT x

K

2

1)

(2

and finally the rms value of the fluctuations of the mass

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• To understand the origin of electrical noiseg , let’s consider the thermal fluctuations ,

in the instantaneous local electron concentration in a conductor

- the mean energy stored on C due to thermal fluctuations

1

kT t

v C t

E

2

1)

(2

1)

C

kT t

v( )2 =

should be related to R

Noise voltage

Fig 1.26 Random motion of conduction electrons

in a conductor, resulting in electrical noise.

Fig 1.27 charging and discharging of a capacitor by a conductor, due to random thermal motions of the conduction electrons

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Ch1.7 Thermally Activated Processes (TAP)

1 7 1 Arrhenius Rate Equation

• Many physical and chemical processes strongly depend on T and follow an

Arrhenius behavior, in which the rate of change is proportional to

• One example of TAP diffusion of impurity atoms in a solid

• One example of TAP – diffusion of impurity atoms in a solid

- the rate of jump of the impurity – diffusion – from A to B depends on :

1 vibrational frequency (v 0 ) : the number of times the atom tries to go over the

potential barrier

kT

2 the probability that the atom has sufficient energy to overcome the PE barrier

Probability (E>E A ) = Number of impurities with E>EA

Total number of impurities

)

exp(

kT

E A

N

dE n

A

= ∫∞

p

the frequency of jump from void to voidϑ

ϑ = (Frequency of attempt along AB) (Probability of E>E A )

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