Constants

Physical Constants

elementary charge

\(e\) or \(q\)

\(1.602\times10^{-19}\) C

Speed of light

\(c\)

\(2.998\times10^{8}\) m/s

Boltzmann constant

\(k\)

\(8.617\times10^{-5}\) eV⋅K-1

\(1.381\times10^{-23}\) J⋅K-1

electric permittivity (vacuum)

\(\varepsilon_0\)

\(8.854\times10^{-12}\) F⋅m-1

\(1/\mu_0c^2\)

magnetic permeability (vacuum)

\(\mu_0\)

\(1.256\times10^{-6}\) N⋅A-2

Avogadro constant

\(N_A\)

\(6.022\times10^{23}\) mol-1

Planck constant

\(h\)

\(6.626\times10^{-34}\) J⋅s

\(4.136\times10^{-15}\) eV⋅s

Relative Permittivities

\[\kappa = \varepsilon = \varepsilon_r \varepsilon_0\]

Material

\(\varepsilon_r\)

Vacuum

1

Air

1.000589

PTFE

2.1

Polystyrene

2.4-2.7

Silicon dioxide

3.9

Silicon nitride

7-8

Silicon

11.68

GaAs

12.4

Material Band Gaps

\[E = \frac{hc}{\lambda}\]

Group

Material

Type

Band gap (eV) at 302K

IV

Silicon

Indirect

1.14

IV

Germanium

Indirect

0.67

III-V

GaAs

Direct

1.43

EM Radiation Ranges

Name

eV

nm

THz

UV-B

4.43 - 3.94

280 - 315

1070 - 952

UV-A

3.94 - 3.26

315 - 280

952 - 789

Violet

3.26 - 2.85

380 - 435

780 - 689

Blue

2.85 - 2.48

435 - 500

689 - 600

Cyan

2.48 - 2.38

500 - 520

600 - 577

Green

2.38 - 2.19

520 - 565

577 - 531

Yellow

2.19 - 2.10

565 - 590

531 - 508

Orange

2.10 - 1.98

590 - 625

508 - 480

Red

1.98 - 1.59

625 - 780

480 - 384

NIR-A

1.58 - 0.886

780 - 1400

384 - 214

NIR-B

0.886 - 0.413

1400 - 3000

214 - 100

MIR

0.413 - 0.0248

3e3 - 50e3

100 - 6.0

FIR

0.0248 - 0.0012

50e3 - 1e6

6.0 - 0.3

Thermal Voltage

\[V_T = \frac{kT}{q}\]

T (K)

T (\(^oC\))

\(V_T\)

218.15

-55

18.80mV

233.15

-40

20.09mV

273.15

0

23.54mV

298.15

25

25.69mV

300.15

27

25.86mV

343.15

70

29.57mV

358.15

85

30.86mV

398.15

125

34.31mV