Chapter 1 The Crystal Structure of Solidsocw.nctu.edu.tw/course/physics/semiconductor... · Chapter...

W.K. Chen Electrophysics, NCTU 1

Chapter 1 The Crystal Structure of Solids


Outline

Semiconductor materialType of solidsSpace latticesAtomic bondingImperfections & impurities in solidsGrowth of semiconductor materials


Elemental semiconductors: (C, Si, Ge)- composed of single species of atoms

Compound semiconductors: (binary, ternary, quarternary)III-V, II-VI, IV-IV

1.1 Semiconductor Materials


1.2 Types of SolidsAmorphous: degree of order only within a few atomic or molecular dimensionsPolycrystalline: degree of order over many atomic or molecular dimensions.- The ordered regions vary in size and orientation with respect to one

another- The single crystal regions are called grainsSingle crystal: regular geometric periodicity throughout the entire volume of material


1.3 Space lattices- The periodic arrangement of atoms in the crystal is called

lattice

cbaV rrr⋅×= )( volumecellunit cnbnanT

rrrr321 ++=

latticeLattice pointUnit cellPrimitive cell


Lattice: the periodic arrangement of atoms in crystalLattice point: a dot used to present a particular atomic arrayUnit cell: a small volume of the crystal that can be used to reproduce the entire crystalA unit cell is not a unique entity Unit cell A, B, C and D all can be used to construct the entire lattice by appropriate translation

Lattice point


csbqapr rrrr++=

Every equivalent lattice point in primitive cell for 3-dim crystal can be found using the vector

Primitive cell: the smallest unit cell



1.3.2 Basic crystal structure in semiconductors

α=β=90o, γ≠=90oa=b≠cHexagonal (六方晶系)α=β=γ=90oa=b=cCubic (立方晶系)

α=β=γ=90oa=b≠cTetragonal (四方晶系)α=β=γ=90oa≠b≠cOrthorhombic (正交晶系)

γα

β

ba

accb

rr

rr

rr

,:

,:,:

γ

βα

∠

∠∠

a, b are primitive vectors lie on the base plane


1.3.2 Basic crystal structureThree basic (cubic) crystal structuresSimple cubic (sc): - has an atom located at each cornerBody-centered cubic (bcc): - has an additional atom at the center of cubic Face-centered cubic (fcc):

- has additional atoms on each center of face plane

Simple cubic Body-centered cubic Face-centered cubic


The Fourteen Bravais LatticesThe ways in which we can specify the lattice points in space and keep translational symmetry is limited. In 1848, Auguste Bravais demonstrated that there are in fact only fourteen possible point lattices and no more. For his efforts, the term Bravais lattice is often used in place of point lattice. 3D models of the possible lattices can be found here.

a=b≠c α =β =90° γ=120°P1Hexagonal

a=b=c α=β =γ


1.3.3 Crystal plane & Miller indicesHow to describe the crystal plane?

The crystal plane intercepts x,y and z axes at pa, qb and sc

Assume g is the plane vector, which is perpendicular to any vector on the plane

csapbqap rrlrrr

lr

−=−= 21 let

] [

vector plane

lkhclbkahg =++= rrrr

21 and lrr

lrr

⊥⊥⇒ gg

1 bqaprr

lr

−=

csap rrlr

−=2 gr


)111()()(

0

0)()( 0

0

0)()( 0

22

11

⇒

==⇒

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

=⇒=−⇒

=−⋅++⇒=⋅⇒⊥

=⇒=−⇒

=−⋅++⇒=⋅⇒⊥

⇒

s

q

ph

sph

qph h k

sp

hllshp

csapclbkahggqp

hkkqhp

bqapclbkahgg

l

rrrrrlrr

lrr

rrrrrlrr

lrr

)111()( indicesMiller s

q

p

h k =l

1 bqaprr

lr

−=

csap rrlr

−=2

For any plane that parallel to each other, they bear the same miller indices

The integers are referred as the Miller indices.We will refer to a general plane as (h k l) planeAnd the associated plane vector g is denoted by [hkl]

plane)( vector][ lh k lkh ⊥

(h k l) plane[h k l] vector


Example 1.2 Miller indices

)632()11

21

31()(

1 and 2,3 plane of Intercepts

==⇒

===

hkl

sqp


Lattice Planes: Miller indeces

)111)s

q

p

h k (( index Miller =l

plane)001()( and ,1

=∞=∞==

lh k sqp

plane)101()( and 1,1

=∞===

lh k sqp

plane)111()( 1 and 1,1

====

lh k sqp


Example 1.3 surface density

21428

11

atoms/cm 1066.52)105(

2

)2)((atoms 2plane (110)at density Surface

×=×

=

=

−

aa

oAa

1 5=

bcc structure

12 a 1a


1.3.4 Diamond structure

Diamond structure is basically consisted of body-centered cubics with four of the corner atoms missingEach atom in the tetrahedral structure ( 四方體) has four nearest neighbors and it is this structure which is the basic building block of diamond lattice

Diamond structure is the most common structure in elemental semiconductors, such as Si, Ge

Tetrahedral structure a=b≠c α=β=γ=90o



Zincblende (sphalerite) structureFor GaAs, each Ga atom has four nearest As neighbors and each Ga has four nearest As atoms

Zincblende structure differs from diamond structure only in that there are two different types of atoms in the lattice


Zincblende Lattice(閃鋅結構)

4)21(6)

41(4

4

=×+×=

=

As

Gacell unit per

1

2

4

3

1

26

5

4

3

corner Face center


1.4 Atomic bonding

Ionic bond:Covalent bond:Metallic bondVan der Waals bond

The interaction of atoms in crystal is determined largely by the outmost, i.e., valence electrons of an atom


Covalent bond:electrons being shared between bond atoms so that the valence energy shell of each atom is fully occupied (8 eletrons) by electrons (II-VI, III-V, IV-IV)


Metallic bondingsuch as solid sodium (Na). Solid sodium has a body-centered cubic structure, each sodium has one valence electron, so each atoms has eight nearest neighbors with each atom sharing many valence electronsVan der Waals bondInteraction between dipoles(most in gaseous form, solid form exhibits a relatively melting temperature

Body-centered cubic

HF

HFHF


1.5 Imperfections & impurities in solids

Native defects (Imperfections)vacancyinterstitialline dislocationanti-siteImpuritiessubstitutional impurityinterstitial impurity

Perfect crystal for most of time is less useful,In a real crystal, the lattice is not perfect, but contains imperfections or defects. Such imperfections tend to alter the electrical properties of a material, in some cases, electrical parameters can be dominated by these defects or impurities


Native defects (Imperfections)vacancy:

missing of atom at a particular lattice siteinterstitial

atoms located between lattice sites


Native defects (Imperfections)Frenkel defect

vacancy-interstitial defectline dislocation

entire row of atoms is missing from its normal lattice sites


Impuritiessubstitutional impurityinterstitial impurityanti-site

Anti-site


Point defect- The point defects involve single atoms or single-atom locations. That is one atom is missing or misplaced in the crystal lattice

vacancyinterstitialsubstitialanti-site


1.6 Growth of semiconductor materials

Ingot growthEpitaxial growth


Silicon Crystal Pulling Apparatus


Liquid Encapsulated Czochralski (LEC)

Encapsulation by thin (8-17 mm) molten B2O3 layerHigh inert gas pressure (up to 100 bar) to suppress volatility of group V50 mm round-shaped GaAs, 200-400 cm-2


1Semiconductor Thin Film Deposition

Liquid Phase Epitaxy (LPE)Metalorganic Chemical Vapor Deposition(MOCVD)Molecular Beam Epitaxy (MBE)Chemical Beam Epitaxy (CBE, MOMBE)

Trichloride Vapor Phase Epitaxy (ClVPE)Hydride Vapor Phase Epitaxy (HVPE)

3Å→300μm


Liquid Phase Epitaxy


Metal-Organic Chemical Vapor Deposition


MOCVD Growth Mechanism

III族V族


Molecular Beam Epitaxy


Chemical Beam Epitaxy


Trichloride Vapor Phase Epitaxy

Hot wall reactorEtch & growPure AsCl3 and PCl3 attainableLow-background doping epilayerLow costNot possible to grow AlGaAs(TAlAs=1100oC>>TGaAs=750oC)Difficult in composition control ( use both group III & V clorides)Poor reproducibilty

Ga(l)+HCl →GaCl+1/2H24AsCl3+6H2→As4+12HCl

4GaCl+As4+2H2→4GaAs+4HCl


Hydride Vapor Phase Epitaxy

Etch & growthIndept. Control of III & V speciesMulti-wafer featureAll GaInAsP alloyHighly toxicComplicated reactionMemory effectPoor hydride purityUse corrosive HCl gasDifficult to grow Al and Sbcompound Ga(l)+HCl →GaCl+1/2H2

AsH3→1/2As2+3/2H22GaCl+1/2As4 → 2GaAs+2HCl

hydride


Figure 2. Schematic diagram of MBE machine.


n Deflection (RHEED) measurement system. Electrons are scattered more when a new mono-layer of atoms are being form. The intensity of the RHEED signal oscillates a


W.K. Chen Electrophysics, NCTU 441 GaAsHCl:H 2 O 2 :H 2 O (1:4:80)

1-10 Most III-Vs Br:CH 3 OH (1:100)

0.5 InGaAsH 2 SO 4 :H 2 O 2 :H 2 0 (1:8:80)

0.1 GaAsH 2 O 2 :NH 4 OH:H 2 O (0.7:2:100)

2-5 Most III-V compounds HBr:CH 3 COOH:K 2 Cr 2 O 7 (1:1:1)

0.5 GaAsH 2 O:NH 4 OH:H 2 O 2 (20:2:1)

6 GaAsH 3 PO 4 :H 2 O 2 :H2O (3:4:3)

0.75 InPH 3 PO 4 :HCl (3:1)

6.6 InPH 3 PO 4 :HCl (1:3)

4.8 InPH 3 PO 4 :HCl (1:2)

2.5 InPH 3 PO 4 :HCl (1:1)

0.09 InPHCl:H 2 O (1:2)

0.7 InPHCl:H 2 O (1:1)

8 InPHCl:H 2 0 (2:1)

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