2009200920092009Optoelectronics and Optoelectronics and

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1616 675967591616--67596759Lecture 1Module descriptionIntroduction to solid state physics

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p y

Module description20 Credit points, Course work/ exam marks ratio: 40/ 60 %Lecturer: Dr. Alexei Nabok (room 9419, tel: x6905, a.nabok@shu.ac.uk)

Semester 1, Lectures (10 x 1 h), Tuesdays, 1800 - 1900 (EMB 3213), ( ), y , ( )Lecture 1. Module description. Introduction into solid state physics Lecture 2 Basics of semiconductors physicsLecture 3 Semiconductor devices (MS contact p n junction)Lecture 3. Semiconductor devices (MS contact, p-n junction)Lecture 4. Semiconductor devices (MOS structures, MOSFET, CMOS logic)L t 5 Sili l t h l ( id ti d i fil d itiLecture 5. Silicon planar technology (oxidation, doping, film deposition, and patterning)Lecture 6. Silicon planar technology (ICs fabrication)Lecture 7. ICs design (comparison of logic designs, hierarchy of design, ASICs, yield, cost calculation, IC testing)Lecture 8. Modern microelectronics, nanotechnology

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Lecture 9-10. Optoelectronics devices and systems (optoelectronic systems, light sources, light detectors, optoelectonic devices, memory)

Seminars (6 x 1 h, Tuesdays, 1700 - 1800, Furnival 9006

Seminar 1. Basic calculations in semiconductor physics

Seminar 2. MS contact and pn junction. Calculation of current.

Seminar 3 MOS structure and MOSFETSeminar 3. MOS structure and MOSFET

Seminar 4. Silicon planar technology, ICs fabrication

Seminar 5. ICs design, cost calculation

Seminar 6. Optoelectronic devices and systems

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Lab. works (4x 2h)

Lab. work 1-3. Semiconductor devices: CV characteristics of MOS structures, characteristics of MOSFET , characteristics of LED (electronics lab, Furnival , 9335)

Lab. work 4. Silicon planar technology (clean room, Owen 827)ab o S co p a a tec o ogy (c ea oo , O e 8 )

Assignment 1 (20% from total mark)Comprehensive reports on all four lab. works (including theory, results and analysis)Deadline of submission (Week 20, Tuesday, 8 Dec, 2009, 4pm)

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Recommended literature

S.O.Kasap, Electrical Engineering Materials and Devices, McGraw-Hill, 1997S.M Sze, Physics of semiconductor devices, John Wiley & Sons, 19811981B.G.Streetman, Solid State Electronic Devices, Prentice-Hall Inc, 1972F.J.Bailey, Introduction to Semiconductor Devices, George Allen & U i Ltd 1972Unwin Ltd, 1972 Kanaan Kano, Physical and Solid State Electronics, Addison-Wesley, 1972C R M Grovenor Microelectronic Materials in Graduated StudentC.R.M.Grovenor, Microelectronic Materials, in Graduated Student Series in Materials Science and Engineering, Ser.Edit. B.Cantor, IOP Publishing Ltd, 1989 M.J. Morant, Integrated Circuit Design and Technology, Chapman and Hall 1990and Hall,1990N.Weste, K. Eshaghian, Principles of CMOS VLSI design, Addison-Wesley, 1985Large Scale Integration, Ed. M.J.Howes, D.V.Morgan, John Wiley &

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g g , , g , ySons,1981D.Hodges, H.G.Jackson, Analysis and Design of Digital Integrated Circuits, McGraw-Hill, 1988

Introduction to solid state physicst oduct o to so d state p ys csElectrical conductivity. Classical theory of conductivity.Classification of solids regarding their conductivity:Classification of solids regarding their conductivity:

conductors (metals), semiconductors and insulators(dielectrics).

Electron in quantum boxElectrons in atom. Periodic system of elementsElectronic structure of solid stateElectronic structure of solid state

Conduction by electronsyElectric current density is the net amount of charge flowing across a unit area per unit timetA

qJΔ

Δ=

6

unit time tAΔ

Definition of conductivityn = N/V is the concentration of freel t ( 1028 3)

AEx² x

electrons ( n ≈ 1028 m-3)During time Δt electronsmove a distance of

Jx

vdx

move a distance of Δx = vdxΔt

and total charge crossing

N g g

the area A is Δq = enA Δx

N

v

Nvvvv

v ixi

xNxxxdx

∑=

++++=

...321

Thus current density in the x direction is:

Fig. 2.1: Drift of electrons in a conductor in the presence of an applied electric field Electrons drift with an average

NN

of an applied electric field. Electrons drift with an average velocity vdx in the x-direction.

dxdx

x envtA

tenAvtA

qJ =Δ

Δ=

ΔΔ

=

Electron drift velocity

(a)

u

xe

dx Emev τ

=

where τ is the time betweencollisions (or relaxation time)The drift mobility can be

Vibrating Cu+ ions

Ex The drift mobility can beintroduced as

dxeτμ =

Therefore

² x

V

edx m

μ

EEenJ d σμ ==

and conductivity can be definedas:

(b)Fig. 2.2: (a) A conduction electron in the electron gas moves about randomlyin a metal (with a mean speed u) being frequently and randomly scattered byby thermal vibrations of the atoms. In the absence of an applied field there isno net drift in any direction. (b): In the presence of an applied field, Ex,there is a net drift along the x direction This net drift along the force of the

dμ

as:there is a net drift along the x-direction. This net drift along the force of thefield is superimposed on the random motion of the electron. After manyscattering events the electron has been displaced by a net distance, Δx, fromits initial position toward the positive terminal

ne dμσ =

Conductivity: , Units: [σ]= (Ω⋅cm)-1,(Ω⋅m)-1 or S/cm S/m

ne dμσ =(Ω⋅m) or S/cm , S/m

Resistivity: , Units: [ρ] = Ω⋅cm , Ω⋅mσ

ρ 1=

Resistance: Units [Ω] Sheet resitance : Units [Ω/ ]

lw

ll ρ

C d ti it d i ti it l f diff t t i l

l AJd

wdl

AlR ρρ == w

rsρ

=w

Conductivity and resistivity values for different materialsConductivity (S/cm) Resistivity (Ω cm) Type of solid

107 10-2 10-7 102 cond ctors (metals)107 - 10 10 7 - 10 conductors (metals)10-8 - 10-14 108 - 1014 insulators (dielectrics)

1 - 10-8 1 - 108 semiconductors1 10 1 10 semiconductors∞ 0 superconductors

Free electron

Electron is an elementary negative charge. According to basic principles of quantum mechanics, electron is a

ti l d t th tiparticle and a wave at the same time.Free electron:

is wavenumber, λ - wavelength, π2=k

momentum can be defined as: , whereλ

=k

λhkp == h

is Plank’s constant,

is the energ of a free electron

seVsJh ⋅×=⋅×== −− 1534 10135.410626.62 hπ

kp )( 22 h is the energy of a free electron

There is no restriction on energy of a free electron. mk

mpE

2)(

2h

==

Electron in a quantum box The box must contain an integer number of

fV(x) l electron half-waves V(x)

V 0

Electron

V V 2λna =

Thus

n = 4

Energy levels in the wellψ4

ψ(x) ∝ sin(nπx/a) Probability density ∝ |ψ(x)|20 a x0

V = 0V = V =

,2na

=λank π

λπ

==2

where n = 1, 2, 3, …..is the quantum number

E3

E4

n = 3

n = 4

ψ3

n aλ

0E1

3

E2

n = 1

n = 2

ψ1

ψ2

E n e r g y o f e l e c t r o n

2

22222

22 an

mmkEn

hh π==

The energy of the electron in a quantum box is quantized, e.g.

x = 0 x = a0

0 a a0x

Fig. 3.15: Electron in a one-dimensional infinite PE well.has certain energy values

gThe energy of the electron is quantized. Possiblewavefunctions and the probability distributions for theelectron are shown.

Electrons in atompotential energyr

ZeV0

2

4πε−=V(r)

rEnergy of the electron in atom is quantized

0

224 )6.13( ZeVZmeE

rn=4

n=3

Actually, electrons in atom are characterized

22220

)6.3(8 n

eVnh

meE −=−=ε

n=2

y,by four quantum numbers:n – principal quantum numbercharacterises an electron shell K, L, M, N, in respect to n = 1 2 3

n=1+

l - orbital angular quantum number [ l = 0, 1, 2, … , (n-1) ]characterises sub-shells (s, p, d, f, …) of different spherical symmetry m orbital magnetic quantum number

respect to n = 1, 2, 3, ….

ml – orbital magnetic quantum number (projection of l on the external magnetic field axes)ms – spin (intrinsic magnetic quantum number), ms = ± 1/2(analog of the intrinsic rotation of electrons)(analog of the intrinsic rotation of electrons)Pauli Exclusion Principle: No two electrons within a given system (e.g. an atom) may have all four identical quantum numbers, n, l, ml and ms

Electron energy, En.

0E = KE

n = ∞Continuum of energy. Electron is free

0

2

Excited states3–1.51

4–0.85

5–0.546–0.38

n = ∞

–5

2–3.40

Ionization

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Ionizationenergy, EI

–10

–15

1–13.6 eV Ground state

n

n = 1

Fig. 3.23: The energy of the electron in the hydrogen atom(Z = 1).

Electron structure of atoms

L shell withtwo subshells y

z

x x

y

z

Nucleus

1sK

x

y

z

x

y

z

Y for a 2px orbitalY for a 1s orbital

2s2p

KL

y

z

y

z

Y for a 2py orbital Y for a 2pz orbital (ml = 0)(a)

1s22s22p2 or [He]2s22p2

zz

xx

|Y |2 for a 1s orbital |Y |2 for a 2px orbital

Fig. 1.1 : The shell model of the atom in which the electronsare confined to live within certain shells and in subshells

x

y

x

y

|Y |2 for a 2py orbital |Y |2 for a 2pz orbital (ml = 0)

(b)

F ig 3 22: (a) T he polar p lots of Yn l (θ φ) for 1s and 2pwithin shells.

Fig. 3 .22: (a) T he polar p lots of Yn ,l (θ ,φ) for 1s and 2pstates. (b) T he angular dependence of the probabilitydistribution which is proportional to |Yn,l (θ ,φ) |2.

Magnetic quantum numbers (ml, ms)zzBexternal Bexternal

LLz

θ

θ LLz

Spin UpSz (along Bz)

0

θ

l(l+1)cosθ = ml

y

x Orbiting electron

( )

+h/2

S3h2

ms = +1/2

(b)(a)

2

ml

l = 2

zBexternal S0

ms = –1/2–h/2

3h2

0

1L = h 2(2+1)

(c)Spin Down

–1

–2

(c)

Fig. 3.26:(a) The electron has an orbital angular momentum which has aFig. 3.28: Spin angular momentum exhibits space

i i I i d l i i d h hFig. 3.26:(a) The electron has an orbital angular momentum which has aquantized component, Lz, along an external magnetic field, Bexternal. (b) Theorbital angular momentum vector L rotates about the z-axis. Its componentLz is quantized and therefore the orientation of L, the angle θ, is alsoquantized. L traces out a cone. (c) According to quantum mechanics, onlycertain orientations (θ) for L are allowed as determined by l and ml .

quantization. Its magnitude along z is quantized so that theangle of S to the z-axis is also quantized.

The ladder of electron l l i t

Energy O

levels in atom

By filling these levels with 5f

6p

5g

N

electrons one by one and following the Pauli Exclusion Principle you

b ild i di t4

4d

4f

5s5p

5d6s

Mcan build periodic system of elements

3s3p

3d 4s4p

L

Electrons on outer shell (valence electrons) determine the chemical

ti f th l t1s n

1 2 3 4 5 6

2s2p

K

properties of the element1 2 3 4 5 6

Fig. 3.33: Energy of various one-electron states. The energydepends on both n and l

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p

C N O

sL

sK

F Ne

s

pL

sK

Fig. 3.36: Electronic configurations for C, N, O, F and Neatoms Notice that Hund's rule forces electrons to align theiratoms. Notice that Hund s rule forces electrons to align theirspins in C, N and O. The Ne atom has all the K and Lorbitals full.

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Bonding and types of lid

r = ro

solids

E = EA + ER, FA = Attractive force

FN = Net force

+Molecule

Separated atoms

EA due to attraction force , ER due to repulsion force

. .

Interatomic separation, r0

FR = Repulsive force

N

ro

A t t r a c t i o n

F o r c e

F = dE/drR

–

(a) Force vs r

R e p u l s i o n

ER = Repulsive PE

+

ro - bond length, EO - bond energyr0

ER Repulsive PE

E = Net PE

Eo

ro

E ( r )R e p u l s i o n

EA = Attractive PE

(b) Potential energy vs r

P o t e n t i a l E n e r g y ,

A t t r a c t i o n

Fi 1 2 ( ) F i t t i ti d (b)Fig. 1.2: (a) Force vs interatomic separation and (b)Potential energy vs interatomic separation

Covalent bonding

Electron shellH-atom H-atom

H H

Covalent bond

H

1s

Electron shell

1s

H

H H

H

L shell

K shell

C C

H

H H

H

covalentbonds

109.5°

(a)(b)

Covalent bond

H-H Molecule12

C

HH

1 2

12

Fig. 1.3: Formation of a covalent bond between two H atoms

H

H(c)

Fig 1 4: (a) Covalent bonding in methane CH4 involvesgleads to the H2 molecule. Electrons spend majority of theirtime between the two nuclei which results in a net attractionbetween the electrons and the two nuclei which is the originof the covalent bond.

Fig. 1.4: (a) Covalent bonding in methane, CH4, involvesfour hydrogen atoms sharing electrons with one carbonatom. Each covalent bond has two shared electrons. The fourbonds are identical and repel each other. (b) Schematicsketch of CH4 on paper. (c) In three dimensions, due to

Fig. 1.5: The diamond crystal is a covalently bonded network of carbon atoms. Each carbon atom is bonded

l l f i hb f i l hcovalently to four neighbors forming a regular three dimensional pattern of atoms which constitutes the diamond crystal.

Metallic Bondingeta c o d g

Free valenceelectrons forming

an electron gas

Positive metalion cores

Fig. 1.6: In metallic bonding the valence electrons from themetal atoms form a "cloud of electrons" which fills the spacebetween the metal ions and "glues" the ions together throughbetween the metal ions and glues the ions together throughthe coulombic attraction between the electron gas andpositive metal ions.

Ionic BondingCl

3p3s

Na3s

Cl–Na+ Na+ Na+Cl– Cl–

Cl–Na+ Na+ Na+Cl–Cl–

Cl–Na+ Na+ Na+Cl– Cl–

Closed K and L shellsClosed K and L shells

(a)

Cl

Cl–Na+ Na+ Na+Cl–Cl–

Cl–Na+ Na+ Na+Cl– Cl–

Cl–Na+ Na+ Na+Cl–Cl–

Cl–

3p3sNa+

FA FA

(a)

r

(b)

Cl–

Na+

r

(b)Fig. 1.8: (a) A schematic illustration of a cross sectionfrom solid NaCl NaCl solid is made of Cl– and Na+ ionsro

(c)

Fig. 1.7: The formation of an ionic bond between Na and Clatoms in NaCl. The attraction is due to coulombic forces.

from solid NaCl. NaCl solid is made of Cl and Na+ ionsarranged alternatingly so that the oppositely charged ions areclosest to each other and attract each other. There are alsorepulsive forces between the like-ions. In equilibrium the netforce acting on any ion is zero. (b) Solid NaCl.

Formation of a moleculeFollowing the Pauli exclusion principle the energy levels of electrons

HTwo hydrogen atoms

HrA e– rB e–

ψσ∗

E(a)

g p p gyin the molecules split up

rR =

Two hydrogen atomsapproaching each other.

ψ1s(rA)

A B

ψ1s(rB)

σ

Eσ∗(R)ψ1sE1s

E (a)Eσ(R)

0

SYSTEM2 H-Atoms2 Electrons1 Electron/Atom1 Orbital/Atom

BondingEnergy

r

ψσ = ψ1s(rA) + ψ1s(rB)Bonding Molecular Orbital

Eσ∗ (b)

ψσ

Eσ(a)

aR, InteratomicSeparation0 R =

a

r H -atom H -atomH2

σ

Eσ

² E = Bonding Energy

( )

E1s E1s

ψσ* = ψ1s(rA) – ψ1s(rB)Antibonding Molecular Orbital

Fig. 4.1: Formation of molecular orbitals, bonding andib di ( d ) h h

Fig. 4.3: Electron energy in the system comprising twohydrogen atoms. (a) Energy of ψσ and ψσ∗ vs. the

antibonding ( ψσ and ψσ∗ ) when two H atoms approacheach other. The two electrons pair their spins and occupy thebonding orbital ψσ.

interatomic separation, R. (b) Schematic diagram showingthe changes in the electron energy as two isolated H atoms,far left and far right, come to form a hydrogen molecule.

Eψa

A B C

ψb

E

Ec

b

c

ψc

ψc

E1sa

Eb

Ea ψa

ψb

SYSTEMIN ISOLATION

3 H-Atoms3 Electrons

3 Orbitals (1s)6 States (with spin)

SeparationR = R = a

6 States (with spin)

(b)(a)

Fig 4 7: (a) Three molecular orbitals from three ψ1s atomicFig. 4.7: (a) Three molecular orbitals from three ψ1s atomicorbitals overlapping in three different ways. (b) The energiesof the three molecular orbitals labeled as a, b and c in asystem with 3 H atoms.

Energy bands in solids

When bringing two or more atoms together to form a moleculeWhen bringing two or more atoms together to form a molecule, a cluster, or a solid state, energy levels of electrons split up

according to the Pauli exclusion principle.

Metals: Energy band diagram E

E

r ro

Semiconductors: Energy band diagram

Conductionband

EEE E

Valence

Band gap

band

rrro