Silicon (Si)
- Practical Electron Microscopy and Database -
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Page2393 lists the properties of single-crystalline, polycrystalline, and amorphous silicon (Si) materials.

Table 2019a. Bond density (x1015/cm2) of various Si crystal planes.

Plane

In-plane
Surface
Total
(110)
0.96
0.96
1.92
(522)
0.35
1.06
1.41
(100)
0.00
1.36
1.36
(111)
0.00
0.78
0.78

                                                           * The direction of the closest Si atoms in the {111} planes is along <110>.

Table 2019b. Relationship between resistivity (Ωcm) and dopant concentration (cm-3 ) for crystalline Si at 23 °C.

Doping concentration
Phosphorus, n-type
Boron, p-type
1012
3.8 x 103
1.3 x 104
1013
4.0 x 102
1.3 x 103
1014
4.3 x 101
1.30 x 102
1015
4.5
1.4 x 101
1016
0.52
1.5
1017
8.5 x 10-2
0.2
1018
2.3 x 10-2
4.5 x 10-2
1019
5.5 x 10-3
8.5 x 10-3
1020

7.8 x 10-4

1.2 x 10-3
1021
1.2 x 10-4
1.3 x 10-4

Table 2019c. Surface energies (J/m2) of low-index Si surfaces. The types of reconstructions are indicated. (1x1) relaxed denotes an unreconstructed cleavage surface.

Solid
(100)
(110)
(111)
(522)

Si

1.41     c(4 × 4)

1.7     (1 × 1) relaxed

1.36    7 × 7
Si
2.13     at 77 K
1.51     at 77 K
1.23    at 77 K
1.56

Table 2019d. Other properties of crystalline Si surfaces.

(100)
(110)
(111)
Atomic density (1014/cm2)
6.78
9.59
15.66
Lattice spacing/constant (Å)
5.43
3.84
3.13

Figure 2019a shows the absorption coefficient of silicon (Si) at 300 K. Note that the band gap of Si is about 1100 nm.

Absorption coefficient of silicon at 300 K

Figure 2019a. Absorption coefficient of silicon at 300 K.

Crystalline Si has the space group of Fd-3m (see in Table 2019a) and the space group for GaAs and InP is F-43m. Both these space groups are simple face-centred cubic (fcc) lattices.

Table 2019e. Etchants used in semiconductor manufacturing.

Film
Etchant
SiO2(Silicon oxide)
Dilute hydrofluoric acid (DHF)
Buffered HF (BHF)
Polysilicon
Alkaline hydroxide + organic
Si3N4(silicon nitride)-selective to SiO2
Boiling phosphoric acid (H3PO4)
Si3N4/SiO2 (non-selective)
Hydrofluoric acid + organic

Table 2019f. Etching selectivity of Si3N4:SiO2:Si in various solutions.

Etching selectivity of Si3N4:SiO2:Si
BHF
1:200:0
40% HF
1:≥110:0.1
H3PO4
10:1:0.3
CF4-4% O2 plasma
3:2.5:17

Table 2019g lists silicon wafers used in different technologies, and Table 2019h lists the chemical reactions used in CVD for Si film growth.

Table 2019g. Silicon wafers used in different device technologies.

Period
Wafer diameter Wafer thickness (μm)
(inch) (mm)  
  1 25  
  2 51 275
1970-1975
3 76 375
1975-1980 4 100 450-500
1980-1985 4.9?or 5 125 or 130 525-625
1985-1990 ~6 (5.9) 150 675
1990-1995 ~8 (7.9) 200 725
1995-present ~12 (11.8) 300 770

 

~18 (17.7) 450 925

Table 2019h. Chemical reactions used in CVD for Si film growth.

Chemical reactions used in CVD for Si film growth

As listed in Table 2019i, substances with large bonding energies usually have high melting temperatures.

Table 2019i. Bonding energies and melting temperatures of covalent substances.

Bonding type

Substance
Bonding energy
Melting point (°C)
kJ/mol kcal/mol eV/Atom, Ion, or Molecule
Covalent
Typical value 200-1000      
Si 450 108 4.7 1410
Diamond C 713 170 7.4 >3550

Table 2019j. Comparison of properties between single, polycrystalline, and amorphous Si.

Single-crystal
Poly-crystal
Amorphous Si
Basics

 

 

 

 

Atomic properties
Atomic number
14
Electron Shells
1s22s22p63s23p2
Radius of Si atom
1.18 Å
Structure
Cubic, diamond
Densest planes of Si atoms
{111} planes
Common Ions
Si4+, Si4-
Atomic density
(atoms/cm3)
4.96 x 1022

Bond angle of adjacent atoms

109 °
Deviation of bond angles
±10° of ideal crystalline Si bond angle
Deviation of bond lengths
±2% of ideal crystalline Si bond length
Density at 300K (g/cm3)
2.329
Atomic weight
28.09 g/g-mol
Lattice spacing (a0 ) at 300K
0.54311 nm
Number of atoms in 1 cm3
4.995 x 1022
Distance between two neighboring atoms
2.35 Å
Atoms per unit cell
8
Space Group
Effective masses of heavy holes (mhh/m0)
0.49    
Effective masses of light holes (mlh/m0)
0.16    
Defect density
    10-15 cm-1 for a-Si:H-10 at.%
Effective masses of (100) electrons in longitudinal direction (ml/m0)
0.98    
Effective masses of (100) electrons in transverse direction (mt/m0)
0.19    

Radiative recombination coefficient (cm3s−1)

1.1 × 10−14
Mechanical properties

Piezoresistive coefficient

n-Si: p11 = -102
p-Si: p44 = +138
Gauge factor of 90
Gauge factor of 30 - 50

Fracture strength (GPa)

6

0.8 to 2.84 (undoped)
Residual stress
None
Depending on structure; compressive
Poisson ratio
0.262 maximum for (111)
0.23
Young's modulus (N/m2)
1.90 x 1011 for (111) 1.61 x 1011  
Elastic constant (dyn cm-2)
C11=16.6 ×10−11 at 300 K; C12=6.4 ×10−11 at 300 K; C44=7.96 ×10−11 at 300 K
Thermal properties
Thermal conductivity (W/cm-°C)

1.5-1.57

Smaller for poly-Si films with fine grains and much greater with large grains

Thermal expansion (/°C)

2.3

2-2.7

Specific heat (cal/g-°C)

0.169
Boiling point
2480 °C
Melting temperature
1412 °C
Melt heat (Qm, J-g-1)
337
Critical temperature
4920 °C

Vapor pressure (Pa)

1 at 1,650 °C; 10-6 at 900 °C

Vaporization temperature (Tv, °C)
2355
Vaporization heat (Qv, J-g-1)
1446
Critical pressure (atm)
1450
Coefficient of thermal expansion (CTE) (°C-1)
(2.6 - 4.68) x 10-6 for average between 15-1000 °C; 4.2 x 10-6 at 25 °C; zero at -157 °C; negative at liquid air temperature
Thermal diffusion coefficient (cm2/s)
0.9
Entropy at 298 °K
4.5 cal/mol/°K

Diffusion length

300 nm for a-Si:H-10 at.%
Hole diffusion length
1 µm for a-Si:H-10 at.%
Optical properties
Refractive index
3.42 - 3.44
4.05 at 500 nm; 4.1 at 600 nm; 3.93 after deposition at T < 580 °C; 3.51 after deposition at T > 600 °C
Cathodoluminescence (minimum voltage for excitation)
2400
1600

Photoluminescence peak

1.25 eV for a-Si:H(F)-10 at.% at 77 K
Color
Dark, steel gray for single crystal; Black, six-sided plates for graphitoidal Si;
Transparent or light orange for small crystal (similar to c-Si film);
Dark brown
Absorption coefficient
(cm-1)
5.82 x 106 at 3.5 eV

Pre-exponent conductivity factor (Ω-1-cm-1)

>103 for a-Si:H(F)-10 at.%
Energy gap/Optical band gap Eg (eV)
1.12 at 300 K; 1.17 at 0 K (Minimum indirect Eg)
1.6 at 210 °C; 2.0 at 350 °C;
1.55 for a-Si; 1.68 for a-Si:H,F; 1.7 - 1.8 for a-Si:H-10 at.% at 300 K
Indirect bandgap (Eg,ind, eV)
1.12    
Direct bandgap (Eg, dir, eV)
3.2    
Variation of optical band gap with temperature
(eV-K-1)
2x - 4x 10-4

ESR spin density (cm-3)

1015 for a-Si:H(F)-10 at.%
Spin–orbit splitting (eV)
0.044    
Infra-red spectra
    2000/640 cm-1 for a-Si:H(F)-10 at.%
Raman spectra
Silicon    

Optical phonon energy (meV)

64
Electrical properties

Conduction band tail slope (meV)

25 for a-Si:H(F)-10 at.%; 30 for a-Si

Valence band tail slope (meV)

40 for a-Si:H(F)-10 at.%; 50 for a-Si

Activation energy (ΔE)

≤0.05 for n-type a-Si:H ~1% addition of PH3 to gas phase; ≤0.05 for p-type a-Si:H ~1% addition of B2H6 to gas phase
0.8 - 0.9 for a-Si:H(F)-10 at.%; 0.2 for n-type a-Si:H ~1% addition of PH3 to gas phase; 0.3 for p-type a-Si:H ~1% addition of B2H6 to gas phase
Urbach energy E0 (meV)
46 for a-Si:H; 48 for a-Si:H,F
Electron affinity
4.05 eV

Density of states
in band gap (cm-3)

1 x 1019 for a-Si; 1 x 1016 for a-Si:H
Energy gap at Γ (eV)
3.5    

Density of states at the minimum (cm-3eV-1)

>1015 – 1017 for a-Si:H(F)-10 at.%
Fermi level density of states g (EF) (cm-3eV-1)
1015 for a-Si:H; 1015 for a-Si:H,F
Effective density of states at the conduction band edge (Nc, cm-3eV-1)
2.8 x 1019 at 300 K
1021 for a-Si:H(F)-10 at.%
Effective density of states at the valence band edge (Nv, cm-3eV-1)
1.04 x 1019at 300 K

Extended state mobility: electron (cm2s-1V-1)

>10 for a-Si:H(F)-10 at.%
Extended state mobility: hole (cm2s-1V-1)
~1 for a-Si:H(F)-10 at.%
Hole drift mobility µh
(cm2V-1s-1)
450-600
10-20 for a-Si:H; 10-2 for a-Si:H(F)-10 at.%
Electron drift mobility µe
(cm2V-1s-1)
≤1500
20 - 40
1 for a-Si:H-10 at.%
Intrinsic carrier concentration ni
1.0 x 1010 cm-3
Minority carrier lifetime
2.5 x 10-3 s
8 x 10-11 for grain size 0.2 µm; 7 x 10-6 for grain size 4,000 µm
Intrinsic Debye length
24 µm
Dielectric Constant at 300 K
11.9
Temperature resistivity coefficient (TCR, °C-1)

p-type: 0.0017
Nonlinear; e.g. 0.0012; between negative and positive depending on doping level

Dark conductivity
-1-cm-1)

≥1 for n-type a-Si:H: ~1% addition of PH3 to gas phase; ≥1 for p-type a-Si:H: ~1% addition of B2H6 to gas phase
10-10 for a-Si:H(F)-10 at.% at 300 K; 10-2 for n-type a-Si:H: ~1% addition of PH3 to gas phase; 10-3 for p-type a-Si:H: ~1% addition of B2H6 to gas phase
Electrical resistivity (Ω-cm)
Depending on doping level at room temperature; 2 x 103 at -190°C; (2.3 - 3.2) x 105 at 22 °C; 15 at 300 °C; 0.4 at 500 °C
Strong function of the grain structure of the film; always higher than that of Si single crystals; 4 x 105 for doping level <1015 cm-3;
1011 for undoped a-Si:H-10 at.% at 300 K; 102 for n+ a-Si:H-10 at.% at 300 K; 103 for p+ a-Si:H-10 at.% at 300 K
Breakdown field
3 x 105 V/cm
Electron diffusion constant
34.6 cm2s-1
Hole diffusion constant
12.3 cm2s-1

Table 2019k lists the angles (2θB) between the direct beam 000 and diffracted beams as well as the lattice spacings for Si at accelerating voltages of 200, 300 and 400 kV. The angles can be computed with the DM scripts in the table.

Table 2019k. Reflection angles for silicon (Si, a = 5.431195(9) Å).

hkl
Reflection angles (1° = 17.45 mrad)
Lattice spacing (nm) Forbidden reflections
200 kV 300 kV 400 kV λ = 1.5405929 Å and T = 295.6 K
111
8.01 mrad 6.28 mrad 5.23 mrad 28.441° 0.3135  
200
          Presents in [110] orientation due to double diffraction
220
13.07 mrad 10.26 mrad 8.54 mrad 47.300° 0.1920  
311
15.33 mrad 12.03 mrad 10.02 mrad 56.120° 0.1637  
222
16.00 mrad       0.1568 Forbidden
400
18.49 mrad 14.51 mrad 12.08 mrad 69.126° 0.1358  
331
20.67 mrad 15.81 mrad 13.16 mrad 76.372° 0.1246  
422
22.65 mrad 17.77 mrad 14.80 mrad 88.025° 0.1108  
511/333
24.02 mrad 18.85 mrad 15.69 mrad 94.947° 0.1045  
440
      106.701°    
531
      114.084°    
620
      127.534°    
533
      136.880°    
622
30.66 mrad 24.07 mrad 20.03 mrad   0.0819 Forbidden
444
      158.603°    
hkl
          h, k, l are mixed odd and even; or, all even and h + k + l ≠ 4n (Or defined by h + k + l = 4n + 2)

The valence band electrons normally originate from the electrons in the incomplete outer shell of atoms, for instance, the valence band is formed for silicon (Si) crystals as shown in Figure 2019b. An isolated Si atom contains 14 electrons, which occupy 1s, 2s, 2p, 3s and 3p orbital in pairs. When atoms are far away from each other, the electrons in the out shell do not interact. As the distance between atoms is reduced to d1, there is an overlap of electron wavefunctions across adjacent atoms. This leads to a splitting of the energy levels consistent with Pauli exclusion principle, and forming energy bands. This splitting leads to 2N states in the 3s band and 6N states in the 3p band, where N is the number of Si atoms in the crystal. A further reduction of the lattice spacing causes the 3s and 3p energy bands to merge into a single band having 8N available states, and then split again into two bands containing 4N states each. At the temperature of zero Kelvin, the lower band is completely filled with electrons and named as the valence band. The upper band is empty and named as the conduction band. Note that in crystal Si (with lattice spacing d0), the core level electrons do not start yet to interact.

Detailed illustration of electronic structure of silicon as a function of distance between atoms

Figure 2019b. Detailed illustration of electronic structure of silicon as a function of distance between atoms. The left red circle is a zoom-in of the right red circle.

 

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