Question

The Debye length L_D is a characteristic length for semiconductor and is defined as

1. \(L_D = \sqrt{\frac{ϵ_s KT}{qN}}\)

2. \(L_D = \sqrt{\frac{ϵ_s KT}{q^2N}}\)

3. \(L_D = \sqrt{\frac{2ϵ_s KT}{q^2N}}\)

4. \(L_D = \sqrt{\frac{ϵ_s KT}{2qN}}\)

where. K is Boltzmann constant, T is temperature in Kelvin, q is unit electronic charge. N is impurity concentration of the substrate in per m³, ϵ_s is dielectric permittivity of silicon.

1. 1
2. 2
3. 3
4. 4

Answer 1

Correct Answer - Option 2 : 2

Debye length: It is named after Peter Debye and is a measure of the charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists.

A Debyesphere is a volume whose radius is debye length.

Debye length in a semiconductor:

The Debye length has become increasingly significant in the modeling of solid-state devices, as improvement in lithographic technologies has enabled small geometries.

The Debye length in the semiconductor is given by:

\({L_D} = \sqrt {\begin{array}{*{20}{c}} {\frac{{{K_B}T}}{{{q^2}{N_{dop}}}}}\\ \; \end{array}} \)

ϵ = is dielectric constant

K_B = Boltzmann’s constant

T = absolute temperature (K)

q = elementary change

N_dop = Net density of dopants (either donor or acceptor)

Option 2 correct