Consider the following statements:

The intrinsic carrier concentration of a semiconductor

1. Depends on doping

2. Increase exponentially with a decrease of the bandgap of the semi-conductor.

3. Increase non-linearly with an increase of temperature

4. Increases linearly with increase of temperature

Which of the above statements are correct?

Intrinsic carrier concentration depends on various factors defined by an expression

\(n_i^2 = {N_C}{N_V}{e^{ - \frac{{{E_g}}}{{KT}}}}\)

where K = Boltzmann constant

N_C = Effective density of states in the conduction band.

N_V = Effective density of states in the valence band

T = Temperature, E_g = Bandgap energy

The above equation increases exponentially with the decrease of the bandgap of the semiconductor and increases non-linearly with an increase of temperature.