Slide vật liệu nano và màng mỏng technical review materials

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2. Technical Review – Materials

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Crystal structure
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Basics
A crystal is a repeating array
= lattice + unit cell
Lattice: pattern of repetition; point with
identical surroundings for periodic stacking
Unit cell: what is repeated; the simplest choice
for a representative structural unit
Lattice constant: length of unit cell edges (a, b,

c) and angles between crystallographic axes
(α, β, γ)

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Example

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Simple square
Simple rectangle
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Point lattices for 2-D crystal

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7 crystal systems

There are only
seven unique unit
cell shapes to fill 3D space

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14 Bravais lattices

There are only 14
ways to arrange
lattice points in 3-D
space

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Indices of crystals
Point
xyz or (x,y,z) along a,b and c axis
e.g. 100, 111, ½½½, (1,0,0)
‰ Direction
<hkl> family of directions
[hkl] individual direction
Use the smallest integer positions
<111> = [111], [111], [ ], [ ], [ ], [

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‰ Plane
{hkl} family of planes: integer representing inverse
of axial intercept
(hkl) individual plane: Miller indices expressed by
the inverse of axial intercept
(hklm) for hexagonal system: Miller-Bravais
indices

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Cubic system
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Angle between [hkl] and [mnp]
cos θ =
(hm + kn + lp)
√(h2+k2+l2) √(m2+n2+p2)

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(hkl) ⊥ [hkl]
dhkl = a / √(h2+k2+l2)

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Diamond (Si, Ge, C)

Zincblende (GaAs, GaP)

Interpenetrating FCC (1/4a offset)

Sublattice of Ga and As

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Point defects: 0-D
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Substitutional
Interstitial
Schottky:Vacancy by missing atom
Frenkel : Interstitial lattice Si + Vacancy

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Nd = A exp (-Ea/kT)
Nd : Conc. of point defect
Ea : Activation energy, A : const.
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from Sze, “VLSI Technology”
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Linear defects: 1-D
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Dislocation: extra half plane of atoms

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Twin boundary: highly
symmetrical 2-d

discontinuity in the lattice
Grain boundary:
mismatched region of two
adjacent grains of different
orientations

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Planar defects: 2-D

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Volume defects: 3-D
Precipitates of dopants or impurities
- Precipitates are undesirable : active sites
for dislocation generation from volume
mismatch between precipitates and lattice
‰ Void

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{111}
‰ Highest planar density
‰ Crystal grows most easily
‰ Oxidize faster than {100}
<111>
‰ Highest tensile strength
Preferred applications
<100> MOS, MEMS
<111> Bipolar circuit

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Properties and crystal structure

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Crystal growth
CZ(Czochralski) method
- 80-90 % of Si crystal production
- Solidification of silicon from a liquid phase at
an interface
- Mass transport + temperature gradient
‰ FZ(Float Zone) method

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CZ Si crystal growth
Sand(SiO2) to MGS(metallurgical grade
silicon)
SiC + SiO2 -> Si(l) + SiO2(g) + CO(g)
@ 2000oC
‰ MGS to Trichlorosilane
Si + 3HCl(g) -> SiHCl3(g) + H2(g) + heat
@300oC
‰ Trichlorosilane to polysilicon
2SiHCl3(g) + 2H2(g) -> 2Si + 6HCl(g)
‰ CZ > Tm, 1415oC

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CZ steps
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A cylindrical crystal rod (d = 4-8”) is pulled
vertically from the melt in a heated crucible.
The crystal rod and the crucible are usually rotated
in opposite directions.
Solid crystals are afterwards cut to form thin
semiconductor wafers from which, e.g., integrated
circuits, are produced.

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CZ theory
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‰ Macroscopic model from heat transfer condition

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L dm/dt + kl (dT/dX1)A1 = ks (dT/dX2)A2

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L: latent heat of fusion
dm/dt: mass solidification rate
T: temperature
kl, ks: thermal conductivities of solid and liquid
dT/dX1, dT/dX2 : thermal gradient at points 1 and 2
A1, A2 : Areas of the isotherm at point 1 and 2
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Under the zero thermal gradient in melt, dT/dX1 = 0
Maximum pull rate: Vmax = (ks/Ld) (dT/dX)
where, d: density of solid silicon

from Sze, “VLSI Technology”

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k seg = Cs/Cl <1
Cs , Cl :
equil. conc. of impurity in

the solid and liquid near
the interface

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‰ Segregation coeff.

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Requirement
- impurity segregation
- uniform distribution

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