Course Outline

Solid State Electronics (EE Solid State Electronics (EE 6201)6201)

Course Outline

By Dr. Yaseer A. DurraniUET, Taxila

Course outline Crystal Properties & Growth of

Semiconductors

Atoms & Electrons

Energy Bands & Charge Carrier in Semiconductors

Junctions

Field-Effect Transistors

2

Field-Effect Transistors

Bipolar Junction Transistors

Optoelectronic Devices

Integrated Circuits

Books Course Book

Solid State Electronic Devices, Ben G. Streetman, Sanjay K. Banerjee, 6th

Ed. Prentice Hall, Upper Saddle, NJ 07458, 2000ISBN # 013149726-X

Reference Books– Fundamental of Semiconductor Devices, Betty L. Anderson, Richard L. Anderson, Mc-

Graw Hill

– Introduction to Solid State Physics, Charles Kittel, Wiley Pub. (6th Ed.)

– Semiconductor Device Fundamentals, Robert Pierret, Addison-Wesley, 1996, ISBN

#0201543931

3

#0201543931

– Solid State Electronic Devices, D.K. Bhattacharya, R. Sharma

– Solid-State Physics for Electronics, Andre Moliton

Grading policy Assignments 08%

Quizzes 12%

Mid 30%

Final 50%

4

Crystal Properties & Growth of

Solid State Electronics (EE Solid State Electronics (EE 62016201))

Crystal Properties & Growth of Semiconductors

By Dr. Yaseer A. DurraniUET, Taxila

Crystallography Basic Knowledge of Elementary Crystallography is Essential for Solid

State Physicists!!!

Crystallography is the branch of science that deals with geometricdescription of crystals & their internal arrangements. It is the science ofcrystals & math used to describe them

Crystal’s symmetry has a profound influence on many of its properties

Crystal structure should be specified completely, concisely & Crystal structure should be specified completely, concisely &unambiguously

Structures are classified into different types according to the symmetriesthey possess

In this course, we only consider solids with “simple” structures

6

States of Matter Matter: has mass, occupies space

Mass: has weight, resistance to acceleration

Solids: has volume, shape

Liquids: has volume, no fixed shape, Flows

Gases: No volume, no shape. Takes volume & shape of its container

Plasma: No volume, no shape. Composed of electrically charged particles, plasmas are electrically conductive, produce magnetic fields & electric currents, & respond strongly to electromagnetic forcescurrents, & respond strongly to electromagnetic forces

7

Solids Particles (ions, atoms, molecules) are packed closely together. Forces

between particles are strong enough so that particles cannot move freely but can only vibrate. As a result, a solid has a stable, definite shape, & definite volume. Solids can only change their shape by force, as when broken or cut

Solids can be transformed into liquids by melting, & liquids can be transformed into solids by freezing. Solids can also change directly into gases through the process of sublimationgases through the process of sublimation

Solids can be classified under criteria based on: atomic arrangements,electrical properties, thermal properties, chemical bonds etc.

– Using electrical criterion: Conductors, Insulators, Semiconductors

– Using atomic arrangements: Crystalline, Amorphous, Polycrystalline

Long term atomic arrangement determines the crystal type. Properties such aselectrical, mechanical & optical are intimately tied to crystal type

8

Types of Solids

CsCl ZnS CaF2

Ionic Crystals or Solids

– Lattice points occupied by cations and anions

– Held together by electrostatic attraction

– Hard, brittle, high melting point

– Poor conductor of heat and electricity

Molecular Crystals or Solids

– Lattice points occupied by molecules

– Held together by intermolecular forces

– Soft, low melting point

9

– Soft, low melting point

– Poor conductor of heat and electricity

Network or Covalent Crystals or Solids

– Lattice points occupied by atoms

– Held together by covalent bonds

– Hard, high melting point

– Poor conductor of heat and electricity

Metallic Crystals or Solids

– Lattice points occupied by metal atoms

– Held together by metallic bond

– Soft to hard, low to high melting point

– Good conductor of heat and electricity

diamond graphite

Solids

10

Resistivity vs Temperature(a) Linear rise in resistivity with increasing temperature at all but

very low temperatures(b) Curve flattens & approaches a nonzero resistance as T → 0(c) Resistivity increases dramatically as T → 0

Materials

11

Solid-State Electronic Materials Solid electronic materials based on their conducting properties fall into

three categories:

– Insulators Resistivity (ρ) > 105 Ω-cm

– Semiconductors 10-3 < ρ < 105 Ω-cm

– Conductors ρ < 10-3 Ω-cm

Elemental semiconductors are formed from a single type of atom, typically Silicon

Compound semiconductors are formed from combinations of column III and V elements or columns II and VIand V elements or columns II and VI

Germanium was used in many early devices

Silicon quickly replaced Germanium due to its higher bandgap energy, lower cost, and is easily oxidized to form silicon-dioxide insulating layers

12

Solid-State Electronic Devices Deals with circuits or devices built entirely from solid materials, in which

electrons, or other charge carriers, are confined entirely within solid material

Deals with circuit or devices involving theory of flow of electrons confinedwithin solid material. This includes devices like Diodes, Transistors etc.

Solid-state can include Crystalline, Polycrystalline, Amorphous solids refers to:

– Electrical conductors, insulators, semiconductors (building material is mostoften crystalline semiconductor)

Common solid-state devices include: Integrated circuit (IC), light-emitting diode(LED), liquid-crystal display (LCD)(LED), liquid-crystal display (LCD)

In solid-state component, current is confined to solid elements & compoundsengineered specifically to switch & amplify it

– Current flow can be understood in two forms: as negatively chargedelectrons, and as positively charged electron deficiencies called holes

13

Semiconductor is a solid material that has electrical conductivity in betweenconductor & insulator

Semiconductor is very similar to insulators. Two categories of solids differprimarily in that insulators have larger energy band gaps that electrons mustacquire to be free to move from atom to atom

In Semiconductor production, doping is the process of intentionally introducingimpurities into extremely pure (referred as intrinsic) semiconductor in order tochange its electrical properties

– Number of dopant atoms needed to create a difference in ability of asemiconductor to conduct is very small

Semiconductor

semiconductor to conduct is very small

– Small number of dopant atoms are added (order of 1 every 100,000,000atoms) then doping is said to be low, or light

– More dopant atoms are added (order of 1 in 10,000) then doping is said tobe heavy, or high. This is often shown as n+ for n-type dopant or p+ for p-type doping

B C N

Al Si P S

Zn Ga Ge As Se

Cd In Sb Te14

Semiconductor Materials

Si SiC AlP ZnS

Ge SiGe AlAs ZnSe

AlSb ZnTe

Several semiconductors used in electronic & optoelectronic functions

Used in transistors, rectifiers, ICsInfrared & nuclear radiation detectors

Used earlier days of developments in transistors/diodes, & currentlyInfrared & nuclear radiation detectors

Fluorescent materialsTelevision screens

15

AlSb ZnTe

GaN CdSe

GaP CdTe

GaAs

GaSb

InP

InAs

InSb

detectors

Used in LEDs

Light detectors

Significance of Semiconductors Computers, palm pilots, laptops: Silicon (Si) MOSFETs, ICs, CMOS Cell phones, pagers: Si ICs, GaAs FETs, BJTs CD players: AlGaAs, InGaP laser diodes, Si photodiodes TV remotes, mobile terminals: Light emitting diodes Satellite dishes: InGaAs MMICs Fiber networks: InGaAsP laser diodes, pin photodiodes Traffic signals, car: GaN LEDs (green, blue) Taillights: InGaAsP LEDs (red, amber)

16

Why Silicon dominates? Abundant, cheap, wider band gap, wide operation temperature

SiO2 is very stable, strong dielectric & it is easy to grow on thermal process

Atomic number: 14, Atomic mass/weight: 28.0855

Silicon group: IV elements (C, Ge)

Crystal structure: diamond cubic

Silicon forms: fcc structure with lattice spacing: 5.430710 A (0.5430710 nm)

Band gap energy: 300 K 1.12eV

Density of solid: 2.33 gm/cm3

Each Si atom has 4 nearest neighbors

Magnetic ordering: diamagnetic

Electric resistivity : (20 °C) 103]Ω·m

Thermal conductivity: (300 K) 149 W·m−1·K−1

Thermal expansion: (25 °C) 2.6 µm·m−1·K−1

Speed of sound: (thin rod) (20 °C) 8433 m/s

Young’s modulous: 185 Gpa Shear moduluos : 52 Gpa

Bulk modulous: 100 GPa

Melting point: 1414ºC, Boiling point: 2900ºC

Molar Volume: 12.06 cm3

17

How many Silicon atoms/cm-3?1

1s 2s 2p 3s 3p 3d

1 H 1 1s1

2 He 2 1s2

3 Li 2 1 1s2 2s1

4 Be 2 2 1s2 2s2

5 B 2 2 1 1s2 2s2 2p1

6 C 2 2 2 1s2 2s2 2p2

7 N 2 2 3 1s2 2s2 2p3

8 O 2 2 4 1s2 2s2 2p4

9 F 2 2 5 1s2 2s2 2p5

10 Ne 2 2 6 1s2 2s2 2p6

11 Na 2 2 6 1 1s2 2s2 2p6 3s1

12 Mg 2 2 6 2 1s2 2s2 2p6 3s2

13 Al 2 2 6 2 1 1s2 2s2 2p6 3s2 3p1

Z Name Notation

2 3

# of Electrons 14 electrons occupying the 1st 3 energy levels: 1s,

2s, 2p orbitals filled by 10 electrons 3s, 3p orbitals

filled by 4 electrons

To minimize the overall energy, the 3s and 3p orbitals

hybridize to form 4 tetrahedral 3sp orbitals

Each has one electron and is capable of forming

a bond with a neighboring atom

How many Silicon atoms/cm-3?

Number of atoms in a unit cell:

– 4 atoms completely inside cell

– Each of 8 atoms on corners are shared among cells count as 1 atom inside cell

– Each of 6 atoms on faces are shared among 2 cells count as 3 atoms inside cell

• Total number inside the cell=4+1+3=8

Cell volume:(0.543 nm)3 =1.6 x 10-22 cm3

Density of silicon atoms=(8 atoms)/(cell volume)=5x1022 atoms/cm3

18

13 Al 2 2 6 2 1

14 Si 2 2 6 2 2 1s2 2s2 2p6 3s2 3p2

15 P 2 2 6 2 3 1s2 2s2 2p6 3s2 3p3

16 S 2 2 6 2 4 1s2 2s2 2p6 3s2 3p4

17 Cl 2 2 6 2 5 1s2 2s2 2p6 3s2 3p5

18 Ar 2 2 6 2 6 1s2 2s2 2p6 3s2 3p6

Crystalline Solids In crystalline solids, the particles (atoms, molecules, or ions) are

packed in a regularly ordered, repeating pattern

To understand the distinction b/w solid material types, we must firstunderstand the concept of order. Order can be described as therepetition of identical structures or identical placement of atoms

For example, an atom has six nearby atoms, each 5 A° away, arranged in apattern:

If one where to pick any other atom in material & find same arrangement, thenmaterial would be described as having order. This order can be Short RangeOrder (SRO) or Long Range Order (LRO)

SRO is typically on the order of 100 inter atom distances or less, while longrange is over distance greater than 1000 inter atom distances, with atransitional region in between

19

Crystalline Solids Different crystal structures & same substance can have more than one structure

– Iron has body-centred cubic structure at temperatures below 912 °C, & face-centred cubic structure b/w 912-1394°C

– Ice has 15 known crystal structures at various temperatures & pressures

Perfect Crystal: is an idealization that does not exist in nature. In some ways,even a crystal surface is an imperfection, because periodicity is interrupted there

– Each atom undergoes thermal vibrations around their equilibrium positionsfor temperatures T > 0K. These can also be viewed as “imperfections”

Real Crystals: always have foreign atoms (impurities), missing atoms(vacancies), & atoms in b/w lattice sites (interstitials) where they should not be.Each of these spoils the perfect crystal structure

20

Crystalline Solids:

– Single/mono crystals have a periodic atomic structure across its wholevolume in 3-D long range

– Any good quality semiconductor have periodic arrangements of atoms in 3-D

– Atoms have both SRO & LRO

Amorphous Solids:

– Continuous random network structure of atoms

– Amorphous Si do not have any ordering at all

– Atoms may have some local order, SRO, no LRO

Structure of Solids

21

– E.g. Polymers, cotton candy, common window glass, ceramic

Polycrystalline Solids

– An aggregate of a large number of small crystals or grains in which structureis regular, but crystals or grains are arranged in a random fashion

– Semiconductors deposited on non-lattice matched substrate have only shortrange ordering of atoms

Grains

Single crystalline materials properties vary with direction, i.e. anisotropic

Polycrystalline materials may or may not vary with direction

– If polycrystal grains are randomly oriented, properties will not vary withdirection i.e. isotropic

– If polycrystal grains are textured, properties will vary with direction i.e.anisotropic

Single Vs Polycrystals

22

Crystal structure is called Lattice or Lattice structure Lattice is an infinite array of points in space in which each point has

identical surroundings to all others. The points are arranged exactly in aperiodic manner

Lattice must be described in terms of 3-D coordinates related totranslation directions. Lattice points, Miller indices, Lattice planes (andthe “d-spacings” between them) are conventions that facilitatedescription of lattice

Although it is an imaginary construct, lattice is used to describe thestructure of real materials

Lattice Structure

Although it is an imaginary construct, lattice is used to describe thestructure of real materials

23

Crystal Structure Crystal structure consists of: lattice type, lattice parameters, motif

– Lattice type: Location of lattice points within unit cell

– Lattice parameters: Size & shape of unit cell

– Motif/basis: List of atoms associated with each lattice point, along with their fractional coordinates relative to lattice point. Since each lattice point is, by definition, identical, if we add the motif to each lattice point, we will generate the entire structure:

Simplest structural unit for a given solid is called the basis

Crystal Structure = Lattice + BasisCrystal Structure = Lattice + Basis

24

motif

Atoms do not necessarily lie at lattice points!!

Crystal Lattice In crystallography, only geometrical properties of crystal are of interest,

therefore one replaces each atom by a geometrical point located at the equilibrium position of that atom

Crystalline structures are characterized by a repeating pattern in 3-D. Periodic nature of structure can be represented using a lattice

– Infinite array of points in space

– Each point has identical surroundings to all others

– Arrays are arranged in a periodic manner

25

r=3a+2b

Lattice Vectors Lattice vector is a vector joining any two lattice points

Any lattice vector can be written as a linear combination of unit cellvectors a,b,c:

– t = Ua+Vb+Wc or t = [UVW]

– Negative values are not prefixed with a minus sign. Instead a bar is placed above the number to denote that the value is negative:

– t = −Ua+Vb−W c

26

a

b

t=Ua+Vb

a

b

t

t=2a+1b

tt

a

b

t=3a+2b

Unit Cell Simplest repeating unit in a crystal is called a unit cell

Simplest portion of structure which is repeated & shows its full symmetry

– Opposite faces of a unit cell are parallel

– Edge of unit cell connects equivalent points

– Not unique. There can be several unit cells of a crystal

– Each unit cell is defined in terms of lattice points

– Lattice point not necessarily at an atomic site

– For each crystal structure, a conventional unit cell, is chosen to make the – For each crystal structure, a conventional unit cell, is chosen to make the lattice as symmetric as possible. However, conventional unit cell is not always the primitive unit cell

– By repeated duplication, a unit cell should reproduce the whole crystal

27Unit Cell

latticepoint

Unit cells in 3-D

At lattice points:

Atoms, Molecules, Ions

Unit Cell Types Primitive unit cells

– Contains single lattice point/cell, which is made up from lattice points at each of the corners

– Smallest area in 2-D, smallest volume in 3-D

– Primitive unit cell whose symmetry matches the lattice symmetry is called Wigner-Seitz cell

Non-primitive unit cells

– Contain additional lattice points, either on a face of unit cell or within unit cell

– Integral multiples of the area of primitive cell

28

Wigner-Seitz cell(a) 2-D space lattice(b) BCC space lattice(c) FCC space lattice

1

2

3

4

1,2,3=Primitive translation vector4=Non Primitive translation vectors

Lattices Geometry Unit cell: smallest repetitive volume which contains the complete

lattice pattern of a crystal

Length of unit cell along x,y,z direction are defined as a,b,c. Angles b/w crystallographic axes are defined by:

– α = angle between b & c

– β = angle between a & c

– γ = angle between a & b

– a, b, c, α, β, γ are collectively know as lattice parameters

29a, b, and c are the lattice constant

Crystal System Set of rotation & reflection symmetries

which leave a lattice point fixed

Lattice systems are grouping ofcrystal structures according to axialsystem used to describe their lattice

Each lattice system consists of a setof 3-axes in particular geometricalarrangement

– Cubic (Isometric), Hexagonal, Tetragonal, Rhombohedral (Trigonal), Orthorhombic, Monoclinic & Triclinic

30

Cubic Crystal Lattice Large number of semiconductors are cubic Primitive(P) unit cell with one lattice point per unit cell

Face-centred(F) unit cell with additional lattice points at centre of each face & four lattice points per unit cell

Body-centred(I) unit cell with a lattice point in middle of unit cell & two lattice points per unit cell

Other cell types are C-face-centred & rhombohedral unit cell

All unit vectors identifying the traditional unit cell have same size

Crystal structure is completely defined by single number. This number is the Crystal structure is completely defined by single number. This number is the lattice constant, a

8-corners

31

Cubic Crystal Lattice

BCCFCCSC

32

BCCNew atom is at:

a/2+b/2+c/2

FCCNew atoms are at:

(a/2+b/2),(b/2+c/2),(a/2+c/2), (a+b/2+c/2),(a/2+b+c/2),(a/2+b/2+c)

SCa,b,c are basis

vectors along edges

Diamond LatticeFCC & then add 4-additional internal atoms at locations

a/4+b/4+c/4 away from each of atoms

Basic FCC Cell Merged FCC Cells

Crystalline Structure

Basic FCC Cell Merged FCC Cells

Omit atoms outside Cell

Bonding of Atoms

33

8 atoms at each corner, 6 atoms

on each face, 4 atoms entirely

inside the cell

Crystalline Structure

inside the cell

34Wurtzite Rocksalt

Cubic Crystal Structures

Crystal Structure

Bravais or Space Lattice

Example Number of atoms/unit

cell

Nearest Neighbour Distance

Simple Cubic

Simple Cubic

P 1 a

B.C.C. B.C.C. Na, W 2 √3 a/2

F.C.C. F.C.C. Al, Au 4 √2 a/2 Diamond

Cubic F.C.C. Si, Ge 8 √3 a/4

H.C.P. Hexagonal Mg 7 a

35

Zinc Blende F.C.C. GaAs 4A+4B √3 a/4(A-B)

√2 a/2(A-A,B-B)

Wurtzite Hexagonal CdS 7A+7B

Rock Salt F.C.C. NaCl 4A+4B a/2(A-B)

√2 a/2(A-A,B-B)

Crystal Lattices

2-D Crystals

36

(a) Square (d) hexagonal (b) Rectangular (e) oblique (c) centered rectangular

3-D Crystals

Miller indices Miller indices describes the directions & planes in a crystal To find miller indices of plane:

1. Find the intercepts of plane in each of 3-axes in terms of lattice constants2. Take reciprocals of these numbers3. Converts them to the smallest 3-intergers having the same ratio, by

multiplying with appropriate integers Notations: (hkl) -> plane; [hkl]-> denotes a crystal direction

Notation Interpretation

( h k l ) crystal plane

h: inverse x-intercept of plane

k: inverse y-intercept of plane

l: inverse z-intercept of plane

Direction Plane

[100]

[111][011]

(100)

h k l equivalent planes

[ h k l ] crystal direction

< h k l > equivalent directions

l: inverse z-intercept of plane

(Intercept values are in multiples of the lattice constant;

h, k and l are reduced to 3 integers having the same ratio.)

37

Crystallographic Planes & Si Wafers Silicon wafers are usually cut along a 100 plane with a flat or notch to

orient the wafer during IC fabrication:

38

Planes with Negative Indicesz

y

x

(100)

plane

(010)

plane

(001) plane Planes (100), (010), (001), (100), (010), (001) are

equivalent planes. Denoted by 1 0 0

Atomic density and arrangement as well as electrical,optical, physical properties are also equivalent

x

39

Example

40

Example Plane has intercepts at 2a, 4b and 1c along three crystal axes

– Take the reciprocal: (1/2, ¼, 1)

– Multiplying by 4: (2,1,4) plane

– Exception: if the intercept is a fraction of lattice constant a, in this case we do not reduce it to the lowest set of integers

z

(214)

41

c

x

a

b

y

(214)

Example (100),(110),(111) surfaces considered above are the so-called low index

surfaces of cubic crystal system ("low" refers to Miller indices being small numbers - 0 or 1 in this case)

Surface(110)

Intercepts : a , a , ∞Fractional intercepts :1,1,∞Miller Indices : (110)

Surface (111)

Intercepts : a , a , a

Fractional intercepts :1,1,1

Miller Indices : (111)

Surface (210)

Intercepts : ½ a , a , ∞Fractional intercepts : ½ ,1,∞Miller Indices : (210)

42

Crystal Directions

43

]100[],010[],001[],001[],010[],100[ 100 >⇒<

z

y

x

Examples

z

x y z

[1] Draw a vector and take components 0 -a 2a

x y z

[1] Draw a vector and take components 0 2a 2a

[2] Reduce to simplest integers 0 1 1

[3] Enclose the number in square brackets [0 1 1]

y

x

[2] Reduce to simplest integers 0 -1 2

[3] Enclose the number in square brackets [ ]210

z

y

x

1

2

31: [100]

2: [010]

3: [001]

Equivalent directions due to crystal symmetry:

44

.

Example The intercepts of a crystal plane with the axis defined by a set of unit vectors

are at 2a, -3b and 4c. Find the corresponding Miller indices of this and all other crystal planes parallel to this plane?

The Miller indices are obtained in the following three steps:

1. Identify the intersections with the axis, namely 2, -3 and 42. Calculate the inverse of each of those intercepts, resulting in 1/2, -1/3 and 1/43. Find the smallest integers proportional to the inverse of the intercepts.

Multiplying each fraction with the product of each of the intercepts (24=2x3x 4) does result in integers, but not always the smallest integers

( )346

does result in integers, but not always the smallest integers4. These are obtained in this case by multiplying each fraction by 125. Resulting Miller indices is6. Negative index indicated by a bar on top

45

z

y

x

z=∞

y=∞

x=a

x y z

[1] Determine intercept of plane with each axis a ∞ ∞

[2] Invert the intercept values 1/a 1/∞ 1/∞

[3] Convert to the smallest integers 1 0 0

[4] Enclose the number in round brackets (1 0 0)

Examples

z

x y z

[1] Determine intercept of plane with each axis 2a 2a 2a

y

x

[1] Determine intercept of plane with each axis 2a 2a 2a

[2] Invert the intercept values 1/2a 1/2a 1/2a

[3] Convert to the smallest integers 1 1 1

[4] Enclose the number in round brackets (1 1 1)

x y z

[1] Determine intercept of plane with each axis a -a a

[2] Invert the intercept values 1/a -1/a 1/a

[3] Convert to the smallest integers 1 -1 -1

[4] Enclose the number in round brackets

z

y

x( )11146

Diamond Lattice Basic crystal structure of many important semiconductors is fcc lattice

with basis of 2-atoms, giving rise to diamond structure, characteristic ofSi, Ge, C in diamond form

Many compound semiconductors, atom are arranged in basic diamondstructure but are different on alternating sites. This is called zinc-blendestructure and typical of III-V compounds GaAs, InP, GaP, GaN, etc.have crystal structure that is similar to diamond

Each atom still has four covalent bonds, but these are bonds to atoms of other type

Important for optoelectronics & high-speed ICs Important for optoelectronics & high-speed ICs

Diamond lattice of Si & Ge

Unit cell of diamond lattice constructed by placing ¼,1/4,1/4 from each atom in fcc 47

Zinc-blend Crystal Structure III-V compounds has the ability to vary mixture of elements on each of two

interpenetrating fcc sublattices of sinc-blende crystal Ternary compound (AlGaAs):

– It is possible to vary composition of ternary alloy by choosing fraction of Al or Ga atoms on column III sublattice

– AlxGa1-xAs contains a fraction of x of Al atoms and 1-x of Ga atoms– Al0.3Ga0.7 has 30% Al & 70% Ga on column III sites, with interpenetrating

column V sublattice occpied entirely by As atoms It is extremely useful to grow ternary alloy crystal

48

Crystalline SiO2

Materials & Packing Crystalline materials:

– Atoms pack in periodic, 3-D arrays

– Typical of: Metals, Many Ceramics, Some Polymers

NonCrystalline materials:

– Atoms have no periodic packing

– Occurs for: Complex structures, Rapid Cooling

Si

Oxygen

Noncrystalline SiO2

Non dense, random packing Dense, ordered packing

Dense, ordered packed structures tend to have lower energies

49

Metallic Crystal Structures Atoms are packed into lattice in different arrangements

Distance b/w neighboring determined by balance b/w forces that attract them together and other forces for particular solids

Tend to be densely packed

– Typically, only one element is present, so all atomic radii are same

– Metallic bonding is not directional

– Nearest neighbor distances tend to be small in order to lower bond energy

– Electron cloud shields cores from each other

How can we stack metal atoms to minimize empty space?

vs.vs.

Now stack these 2-D layers to make 3-D structures

How can we stack metal atoms to minimize empty space?

– 2-dimensions

50

Cubic Cells

51

Atomic Packing Factor (APF) Atomic packing factor (APF) or packing fraction is the fraction of volume in a

crystal structure that is occupied by atoms

It is dimensionless & always less than unity

For practical purposes, APF of crystal structure is determined by assumingthat atoms are rigid spheres

Radius of spheres is maximal value such that atoms do not overlap

52

Cubic Cells Distance b/w neighboring determined by balance b/w forces

Assuming 1- atom/lattice point in primitive cubic lattice with cube side length a

53

Shared by 8 unit cells

Shared by 2 unit cells

Cubic Cells

54

1 atom/unit cell

(8 x 1/8 = 1)

2 atoms/unit cell

(8 x 1/8 + 1 = 2)

4 atoms/unit cell

(8 x 1/8 + 6 x 1/2 = 4)

Example What fraction of SC Lattice can be filled by atoms?

– Assume atoms are perfect hard sphere & touching their nearest neighbour, called “Hard Pack approximation”

– Each sides of SC have length a, thus the volume of cube is a3

a

R=0.5a

55

Atom at originSC Lattice

close-packed directions

R=0.5a

contains 8 x 1/8 =

1 atom/unit cell

Atoms touch each other along cube diagonals

– All atoms are identical; center atom is shaded differently only for ease of viewing

– ex: Cr, W, Fe (α), Tantalum, Molybdenum

Atomic Packing Factor (APF):BCC

Coordination # = 8

2 atoms/unit cell: 1 center + 8 corners x 1/8

aR

a

a2

a3

= 0.68

56

2

a

Face Centered Cubic Structure: (FCC) Atoms touch each other along face diagonals

– All atoms are identical; the face-centered atom is shaded differently only for ease of viewing

– ex: Al, Cu, Au, Pb, Ni, Pt, Ag

a

57

Hexagonal Close-Packed Crystal Structure For Hexagonal Close-Packed (HCP) structure the derivation is similar. The unit

cell is a hexagonal prism containing six atoms. Let a be the side length of its base and c be its height. Then:

58

n = number of atoms/unit cell

A = atomic weight

VC = Volume of unit cell = a3 for cubic

NA = Avogadro’s number= 6.022 x 1023 atoms/mol

Density= ρ =VC NA

n Aρ =CellUnitofVolumeTotal

CellUnitinAtomsofMass

Structure of Crystalline Solids

Ex: Cr (BCC)

A = 52.00 g/mol

a = 4R/ 3 = 0.2887 nm

52.002 g/molatoms/unit cell

aR

A = 52.00 g/mol

R = 0.125 nm

n = 2 atoms/unit cell

ρtheoretical

ρactual

ρ = a3

52.002

6.022 x 1023

= 7.18 g/cm3

= 7.19 g/cm3

atom/mol

volume/unit cell

atoms/unit cell

59

Examples

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Which one has most packing ?

For that reason, FCC is also referred to as cubic closed packed (CCP)

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Growth of Semiconductors

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Si Starting material Silicon prepared by the reaction of high-purity silica with wood,

charcoal, & coal, in electric arc furnace using carbon electrodes at more than 1900, carbon reduces silica to silicon– SiO2 + C → Si + CO2

– SiO2 + 2C → Si + 2CO (~1800ºC)

Form of metallurgical grade Si (MGS)– Si has impurities like Al, Fe & heavy metal at 100s to 1000s parts/million

MGS is further refined with electronic-grade Si (EGS): Levels of impurities arereduced to parts pet billion or ppb 5x1013 cm-3

– Si +3HClSiHCl3 + H2– Si +3HClSiHCl3 + H2

– 2SiHCl3+2H22Si+6HCl

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Growth of Single-Crystal Ingots Growth process of purifying silicon: It converts high purity but still

polysilicon EGS to single crystal Si ingots or boules

– Heating to produce 95% ~ 98% pure polycrystalline Si

Czochralski (CZ) Growth: Main stream growth technology for large diameter wafer

Float Zone (FZ) Growth: For small & medium diameter wafer less contaminations than CZ method

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Seed Crystal A seed crystal is a small piece of single crystal/polycrystal material from

which a large crystal of same material typically is to be grown. The large crystal can be grown by dipping the seed into a supersaturated solution, into molten material that is then cooled, or by growth on the seed face by passing vapor of the material to be grown over it

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Czochralski Si Growth To grow single-crystal material, it is necessary to have a seed which can

provide a template for growth To melt EGS in a quartz-lined graphite crucible by resistively heating it

to melting point of Si (1412ºC) Seed crystal is lowered into molten material and then is raised slowly,

allowing the crystal to grows to provide a slight stirring of melt and to average out any temperature variations that would cause inhomogenoussolidification of compound semiconductors

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•Growth Control:•Pulling Speed•Rotation Speed

•Final Control:•Pulling Speed•Rotation Speed

•Critical Control:•Seed Crystal•First Pull•Pulling Speed•Rotation Speed

Czochralski Si Growth A cylindrical ingot of high purity monocrystalline semiconductor, such

as Si or Ge, is formed by pulling a seed crystal from a 'melt‘

Donor impurity atoms, such as boron or phosphorus in case of Si, canbe added to molten intrinsic material in precise amounts in order todope the crystal, thus changing it into n-type or p-type extrinsicsemiconductor

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Start with polysilicon rod inside chamber either in vacuum or an inert gas RF heating coil melts ≈2 cm zone in rod RF coil moves through the rod, moving the molten silicon region with it This melting purifies the silicon rod Oxygen can be diffused into silicon – called Diffusion Oxygenated Float Zone

(DOFZ) (done at the wafer level)

Float Zone Si Growth

Single crystal silicon

Poly silicon

RF Heating coil

Float Zone Growth

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Liquid-Encapsulated Czochralski GaAs Growth To prevent volatile elements (e.g. As) from vaporizing, it requires to

add a dense & viscous molten layer (B2O3) over the melt. Such process is called liquid-encapsulated Czochralski growth technique

To prevent the decomposition of GaAs under molten condition, a high pressure is used over the GaAs melt

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Crystalline Wafer Wafers are formed of highly pure (99.9999999% purity) nearly defect-

free single crystalline material

Ingot is sliced with a wafer saw (wire saw) & polished to form wafers

Size of wafers for photovoltaics is 100–200mm square & thickness is 200–300 µm

Electronics use wafer sizes from 100–300mm diameter

From Ignot to Wafer

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From Ignot to Wafer•Shaping•Grinding•Sawing or Slicing•Edge Rounding•Lapping•Etching•Polishing•Cleaning•Inspection•Packaging•Shipping

Doping Intentional addition of impurities or dopants to the crystal to change its

electronic properties (varying conductivity of semiconductors)

Doping of 1014 to 1017 atom/cm3

Typically hydrides of atoms are used as the source of dopants e.g. PH3, AsH3 or B2H6 for controlled doping

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Doping during growth of substrate Purpose: To change the electronic properties of the molten Electronic-grade Si

(EGS), we add international impurities or dopants to Si melt

Method: Dopant atoms usually have one (or in some cases more) electrons deficient or excess compared to atoms of semiconductor. Excess electrons can contribute to conduction and dope the material n-type. In case of electron deficiency, “holes” are formed and they can also take part in conduction, through not as efficiently as electrons (holes are more sluggish)

Distribution Coefficient (kd): Ratio of concentration of impurity in solid Cs to the concentration in liquid CL at equilibriumCs to the concentration in liquid CL at equilibrium

– Kd=Cs/CL

– Dependence of kd:

• Material properties

• Impurities

• Temperature of solid-liquid interface

• Growth rate

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Example

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Epitaxial Growth Growth of a thin crystal layer on a wafer of a compatible crystal

Purpose: To achieve desired electrical, mechanical, or thermalproperties of thin film material grown. Epitaxial crystal layer usuallymaintains the crystal structure & orientation of substrate

Methods:

– Chemical Vapor Deposition (CVD)

– Molecular Beam Epitaxy (MBE)

– Liquid-Phase Expitaxy (LPE)– Liquid-Phase Expitaxy (LPE)

Advantage over bulk (wafer) growth techniques: Epitaxial technique canmake possible controlled growth of very thin films, with well controllabledoping & composition that are essential for modern day electronicdevices. Some devices such as quantum mechanical ones, would notthe possible without epitaxial growth

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Epitaxial Growth with Lattice match Homo-epitaxy: Expitaxial layer grown is same as substrate (Same

substrate & film)

– Main advantage is to control thickness & doping of epitaxial layer

– E.g. Si on Si, GaAs GaAs

Hetero-epitaxy: Expitaxial layer grown is different (and has different lattice constant, which depends on composition) from substrate Different substrate & film)– Advantage is tunability of bandgap difference of adjacent layers (apart

from thickness and doping) which is a bid deal in device designs from thickness and doping) which is a bid deal in device designs – e.g. Si on Sapphire

Some examples of lattice matched hetero-epitaxy:

– AlxGa1-xAs on GaAs

– In0.53Ga0.47As on InP

– In0.5Ga0.5P on GaAs

– InxGa1-xAsyP1-y on InP or GaAs

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Epitaxial Growth with Lattice match Lattice structure and lattice constant must match for two materials e.g.

GaAs and AlAs both have zincblende structure

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1.43 eV

0.36 eV

5.65 6.06

In0.53Ga0.47As

Types of Epitaxy Liquid phase epitaxy

– III-V epitaxial layer GaAs

– Grow crystals from liquid solution below their melting point

– Low temperature eliminates many problems of impurity

– Refreeze of laser melted silicon

Molecular beam epitaxy

– Crystalline layer grows in vacuum

– Substrate is held in high vacuum in the range 10-10 torr– Substrate is held in high vacuum in the range 10-10 torr

– Components along with dopants, are heated in separate

– cylindrical cells.

– Collimated beams of these escape into the vacuum and are

– directed into the surface of a substrate

– Sample held at relatively low temperature (600oC for GaAs)

– Conventional temperature range is 400o C to 800oC

– Growth rates are in the range of 0.01 to 0.3 µm/min

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Types of Epitaxy Vapor phase epitaxy

– It is performed by chemical vapor deposition (CVD)

– Provides excellent control of thickness, doping and crystallinity

– High temperature (800º C – 1100ºC)

– Crystallization from vapor phase

– Better purity and crystal perfection

– Offers great flexibility in the actual fabrication of devices

– Epitaxial layers are generally grown on Si substrates by controlled – Epitaxial layers are generally grown on Si substrates by controlled deposition of Si atoms onto the surface from a chemical vapor containing Si e.g. SiCl4 + 2H2 Si + 4HCl (for deposition as well as for etching)

– Four Si sources used for growing epitaxial Si: Silicon tetrachloride (SiCl4), Dichlorosilane (SiH2Cl2), Trichlorosilane (SiHCl3), Silane(SiH4)

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Chemical Vapor Deposition (CVD) Basics: Expitaxial Growth that is achieved by crystallization from vapor

phase of the reactants

Example: Growth of Si thin film on Si substrate, growth of SiC layers on SiC substrate

SiCl4 + 2H2 Si + 4HCl

79Generic CVD machine

Metalorganic Chemical Vapour Decomposition (MOCVD)

Basics:The expitaxial layer is formed by the reaction between hydride speciessuch as NH3, AsH3, and metalorganic species such as Tri-methyl Ga(TMG), Tri-methyl Indium (TMI), Tri-methyl Aluminum (TMA) etc. Note all the reactants arein the vapor phase, hence this technique is a subset of the CVD technique.

Example: Expitaxial growth of compound semiconductors such as GaAs, GaP,GaN

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Molecular Beam Epitaxy (MBE) Substrate is held in a high vacuum while molecular or atomic beams of constituents

impinge upon its surface

In growth of AlGaAs layers on GaAs substrates, Al, Ga, & As components along with

dopants are heated in separate cylindrical cells

Collimated beams in vacuum are directed onto the surface of substrate & strike the

surface closely controlled and growth of very high quality crystals results

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