Question

A Si sample is doped with 10¹⁷ Arsenic atoms/cm³. Displacement of E_F relative to E_i is ______
1. Positive, 0.589 eV
2. Negative, 0.589 eV
3. Positive, 0.407 eV
4. Negative, 0.407 eV

Answer 1

Correct Answer - Option 3 : Positive, 0.407 eV

Concept:

Displacement of fermilevel with respect to intrinsic termi level is given by-

\({{\rm{E}}_{\rm{F}}} - {{\rm{E}}_{\rm{i}}} = {{\rm{K}}_{\rm{T}}}{\rm{In}}\left( {\frac{{{{\rm{N}}_{\rm{D}}}}}{{{{\rm{N}}_{\rm{i}}}}}} \right){\rm{\;or\;KT\;In}}\left( {\frac{{{{\rm{N}}_{\rm{A}}}}}{{{{\rm{n}}_{\rm{i}}}}}} \right)\)

Where N_D = donor type doping concentration

N_A = Acceptor type doping concentration

n_i = intrinsic carrier concentration

Calculation:

Given N₀ = 10¹⁷ / cm³ (Arsenic - Pentavalent- donor type)

n_i = 1.5 × 10¹⁰ / cm³

displacement of E_F relative to \({{\rm{E}}_{\rm{i}}} = {{\rm{K}}_{\rm{T}}}{\rm{In}}\left( {\frac{{{{\rm{N}}_{\rm{D}}}}}{{{{\rm{n}}_{\rm{i}}}}}} \right)\)

\({{\rm{E}}_{\rm{F}}} - {{\rm{E}}_{\rm{i}}} = .0258{\rm{In}}\left( {\frac{{{{10}^{17}}}}{{1.5\; \times \;100}}} \right)\)

E_F – E_i = .407 ev

In donor type impurity E_F shifts up with respect to intrinsic fermi level so it will be positive.