Properties of Silicon

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, N_c T=300 K )

2.8x10¹⁹

cm^-3

Effective density of states
(valence, N_vT=300 K )
1.04x10¹⁹

cm^-3

Electron affinity
133.6

kJ / mol

Energy Gap E_g at 300 K

(Minimum Indirect Energy Gap at 300 K)

1.12

eV

Energy Gap E_g 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 (E_ΓL)
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 C_n
1.1·10^-30

cm⁶ / s

Auger recombination coefficient C_p
3·10^-31

cm⁶ / s

Temperature dependence of the energy gap:

E_g = 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
2628

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 Silicon Substrate

Dopant:

Arsenic
Boron
Phosphorus
Dopant Concentration:

(cm^-3)

Mobility:

[cm²/Vs]

Resistivity:

[W x cm]

Resistivity (ohm-cm) P Concentration N Concentration .

Concentration (cm-3) P Resistivity N Resistivity .

Accuracy of decimal places.

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:
V_hkl =d_hkl / t
where: d_hkl - etching deep, t - etching time

EXAMPLE: Silicon membrane

W = a₀ + 2^1/2 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.

Web Site Developed By: Lukasz Sikora

*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*

*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

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