Properties of silicon and silicon wafers

Silicon material properties Silicon wafer properties
1. Crystal properties 1. Properties
2. Band structure properties 2. Typical Sizes of Semiconductor Wafers
3. Thermal properties 3. Wafer Flats
4. Electrical properties 4. Cleaving

- Resistivity & Mobility Calculator

5. Silicon etching
5. Mechanical properties

 

Silicon properties

 

1.Crystal properties

PROPERTY

VALUE

UNITS
Structure

Cubic

  

Space Group

Fd3m

  

Atomic weight

28.0855

  

Lattice spacing (a0 ) at 300K

0.54311

nm

Density at 300K

2.3290

g/cm3
Nearest Neighbour Distance at 300K 0.235 nm

Number of atoms in 1 cm3

4.995 · 1022

  

Isotopes

28 (92.23%)

29 ( 4.67%)

30 ( 3.10%)

  
Electron Shells

1s22s22p63s23p2

 
Common Ions Si 4 +, Si 4 -  
Critical Pressure 1450 atm
Critical Temperature 4920 °C
 

 

2.Band structure properties

PROPERTY

VALUE

UNITS
Dielectric Constant at 300 K

11.9

  

Effective density of states
(conduction, Nc T=300 K )

2.8x1019

cm-3
Effective density of states
(valence, Nv T=300 K )

1.04x1019

cm-3
Electron affinity

133.6

kJ / mol

Energy Gap Eg at 300 K

(Minimum Indirect Energy Gap at 300 K)

1.12

eV

Energy Gap Eg at ca. 0 K

(Minimum Indirect Energy Gap at 0K)

1.17 (at 0 K)

eV
Minimum Direct Energy Gap at 300 K

3.4

eV
Energy separation (EΓL)

4.2

eV
Intrinsic Debye length

24

um
Intrinsic carrier concentration

1·1010

cm-3
Intrinsic resistivity

3.2·105

Ω·cm
Auger recombination coefficient Cn

1.1·10-30

cm6 / s
Auger recombination coefficient Cp

3·10-31

cm6 / s

Temperature dependence of the energy gap:

Eg = 1.17 - 4.73·10-4·T2/(T+636) (eV)

where: T is temperature in degrees K.

 

3.Thermal properties

PROPERTY

VALUE

UNITS

Melting point

1414

1687

°C

K
Boiling point

3538

K

Specific heat

0.7

J / (g  x °C)

Thermal conductivity [300K]

148

W / (m x K)

Thermal diffusivity

0.8

cm2/s

Thermal expansion, linear

2.6·10-6

°C -1

Debye temperature

640

K
Temperature dependence of band gap  -2.3e-4  eV/K
Heat of:

fusion / vaporization / atomization

  

39.6 / 383.3 / 452

  

kJ /  mol

 

 

4. Electrical properties

PROPERTY

VALUE

UNITS

Breakdown field

≈ 3·105

V/cm
Index of refraction

 3.42

  

Mobility electrons

≈ 1400

cm2 / (V x s)

Mobility holes

≈ 450

cm2 / (V x s)

Diffusion coefficient electrons

≈ 36

cm2/s

Diffusion coefficient holes

≈ 12

cm2/s

Electron thermal velocity

2.3·105

m/s
Electronegativity 1.8 Pauling`s

Hole thermal velocity

1.65·105

m/s

Optical phonon energy

0.063

eV
Density of surface atoms (100) 6.78

(110) 9.59

(111) 7.83

 1014/cm2

1014/cm2

1014/cm2

Work function (intrinsic)  4.15 eV
Ionization Energies for Various Dopants

Donors

Sb 0.039

P 0.045

As 0.054

Acceptors

B 0.045

Al 0.067

Ga 0.072

In 0.16 

  

eV

eV

eV

 

eV

eV

eV

eV

 

 

Resistivity & Mobility Calculator for Semiconductor Silicon
Dopant:
Arsenic (As)
Boron (B)
Phosphorus (P)
Antimony (Sb) 		Type:

 Dopant Density:

(a/cm3)

(a/cm3)

 Concentration:

ppma

ppma

 Resistivity:

Ohmcm

Ohmcm

 Mobility:

cm2/Vs

cm2/Vs
Please note:
  • To calculate Resistivity, choose Dopant and enter/modify Dopant Density in either one of two Dopant Density fields;
    the Calculator will compute Type, Resistivity and Mobility in corresponding columns.
  • To calculate Dopant Density, choose Dopant and enter/modify Resistivity.
  • Concentration and Mobility are always computed; they cannot be entered/modified. Likewise type is a consequence of the Dopant chosen.
  • Two rows of fields are provided to help display low and high Dopant Density limits and corresponding Resistivities.


5. Mechanical properties

PROPERTY VALUE UNITS
Bulk modulus of elasticity 9.8·1011 dyn/cm2
Density 2.329 g/cm3
Hardness 7 on the Mohs scale
Surface microhardness (using Knoop's pyramid test) 1150 kg/mm2
Elastic constants C11 = 16.60·1011
C12 = 6.40·1011
C44 = 7.96·1011		 dyn/cm2
dyn/cm2
dyn/cm2
Young's Modulus (E) [100]
[110]
[111]		 129.5
168.0
186.5		 GPa
GPa
GPa
Shear Modulus 64.1 GPa
Poisson's Ratio 0.22 to 0.28 -

 

 

Silicon wafers properties

Silicon, Si - the most common semiconductor, single crystal Si can be processed into wafers up to 300 mm in diameter. Wafers are thin (thickness depends on wafer diameter, but is typically less than 1 mm), circular slice of single-crystal semiconductor material cut from the ingot of single crystal semiconductor.

All lattice planes and lattice directions are described by a mathematical description known as a Miller Index. In the cubic lattice system, the direction [hkl] defines a vector direction normal to surface of a particular plane or facet.

A crystal can always be divided into a fundamental shape with a characteristic shape, volume, and contents.

As a crystal is periodic, there exist families of equivalent directions and planes. Notation allows for distinction between a specific direction or plane and families of such.

Miller convention:

  • Use the [ ] notation to identify a specific direction,
  • Use the < > notation to identify a family of equivalent directions,
  • Use the ( ) notation to identify a specific plane,
  • Use the { } notation to identify a family of equivalent planes.

Planes configurations for (100) and (110) wafers: 

 

Angles Between Planes

ANGLE

100

110

010

001

101

100

0.00

45.0

90.0

90.0

45.0

011

90.0

60.0

45.0

45.0

60.0

111

54.7

35.3

54.7

54.7

35.3

211

35.2

30.0

65.9

65.9

30.0

311

25.2

31.4

72.4

72.4

31.4

511

15.8

35.2

78.9

78.9

35.2

711

11.4

37.6

81.9

81.9

37.6

 

Stereographic projection of silicon crystal:

 

  • Bow - Concavity, curvature, or deformation of the wafer centerline independent of any thickness variation present. 

 

  • Orientation- the growth plane of the crystalline silicon. Orientations are described using Miller Indices such as (100), (111), (110), etc. Different growth planes and orientations have different arrangements of the atoms or lattice as viewed from a particular angle.

 

  • TTV - total thickness variation - Absolute difference in thickness between the thickest and thinnest parts of wafer.

TTV = A - B  

 

  • GTIR - Global Total Indicated Reading - Maximum peak to valley deviation of a wafer from a given reference plane.

GTIR = A + B  

 

  • Haze Free  -  A silicon wafer having the best possible surface finish and micro-roughness on the order of less than 10A.

 

  • Prime Grade - The highest grade of a silicon wafer. SEMI indicates the bulk, surface, and physical properties required to label silicon wafers as "Prime Wafers".

 

  • Reclaim Grade - A lower quality wafer that has been used in manufacturing and then reclaimed , etched or polished, and then used a second time in manufacturing.

 

  • Test Grade - A virgin silicon wafer of lower quality than Prime, and used primarily for testing processes. SEMI indicates the bulk, surface, and physical properties required to label silicon wafers as "Test Wafers".

 

  • Warp - Deviation from a plane of a slice or wafer centerline containing both concave and convex regions.

 

  • Thickness - The normal distance through a slice or wafer in a direction normal to the surface at a given point.

 

  • Resistivity - The resistance that a unit volume of a material offers to the passage of electricity, the electric current being perpendicular to two parallel faces. More generally, the volume resistivity is the ratio of the potential gradient parallel with the current in the material to the current density.

 

  •  Slice Orientation - The crystallographic orientation of the surface of a wafer. The primary and most common slice orientations are (100), (111) and (110).

 

  • Conductivity Type

An n-type (negative-type) extrinsic silicon semiconductor is a semiconducting material that was produced by doping silicon with an n-type element of Group V A, such as P, As, or Sb. Consequently, electrons are the majority charge carriers of the material.

A p-type (positive-type) extrinsic silicon semiconductor is a semiconducting material that was produced by doping silicon with an p-type element of group III A, such as B, Al, or Ga. Since the dopants are acceptor atoms, holes are the majority charge carriers of the material.

Measurement of wafer characteristics - dark field and bright field detection

 

1. Typical Sizes of Semicoductor Wafers 

(The Diameter of a wafer is measured through its center and not through any flats):

1 inch or 25mm

2 inch or 50mm

3 inch or 75mm

4 inch or 100mm

5 inch or 125mm

6 inch or 150mm

8 inch or 200mm

12 inch or 300mm

 

 

2. Wafer Flats - orientation for automatic equipment and indicate type and orientation of crystal.

Primary flat – The flat of longest length located in the circumference of the wafer. The primary flat has a specific crystal orientation relative to the wafer surface; major flat.

Secondary flat – Indicates the crystal orientation and doping of the wafer.

 

3. Cleaving

Cleaves will run according to the crystal orientations.

If the crystal orientation of the Si is <100> cleave at 90 deg. angles.

If the crystal orientation of the Si is <111> cleave at 60 deg. angles.

 

5. Silicon etching

In general, there are two classes of etching processes:

  • Wet etching where the material is dissolved when immersed in a chemical solution
  • Dry etching where the material is sputtered or dissolved using reactive ions

Wet etching

Wet etching is a blanket name that covers the removal of material by immersing the wafer in a liquid bath of the chemical etchant. Wet etchants fall into two broad categories; isotropic etchants and anisotropic etchants.

Silicon, exhibit anisotropic etching in certain chemicals. Anisotropic etching in contrast to isotropic etching means different etch rates in different directions in the material. The classic example of this is the <111> crystal plane sidewalls that appear when etching a hole in a <100> silicon wafer in a chemical such as potassium hydroxide (KOH). The result is a pyramid shaped hole instead of a hole with rounded sidewalls with a isotropic etchant. 

 

Plane hkl etching speed:

Vhkl =dhkl / t

where:  dhkl - etching deep, t - etching time

 

EXAMPLE: Silicon membrane

W = a0 + 21/2 x (d-m) - 2u

where: u = (V111 x t)/sinQ,  Q = 54.74°

 

 

Dry etching

The most common form of dry etching is reactive ion etching (RIE). Ions are accelerated towards the material to be etched, and the etching reaction is enhanced in the direction of travel of the ion. RIE is an anisotropic etching technique. RIE is not limited by the crystal planes in the silicon.

 

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