The electron concentration in a silicon sample doped with

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The electron concentration in a silicon sample doped with 10¹⁵ cm^{– 3} P atoms, will vary, in the temperature range of 4·2 – 1000 K, as follows—

1. It will be 10⁵ cm^{– 3} over the whole range
2. It will be 10¹⁵ cm^{– 3} up to a temperature T at which intrinsic concentration is 10¹⁵ cm^{– 3} and then it will increase exponentially
3. It will first increase exponentially up to a temperature T then remain constant at 10¹⁵ cm^{– 3} over the remaining range
4. It will first increase exponentially upto a temperature T₁ then remain constant at 10¹⁵ cm^–3 upto a temperature T_{2_{and then increase exponentially}}

Correct Option: D

The electron concentration in a silicon sample doped with 10¹⁵ cm^–3 atoms will first increases exponentially upto a temperature T₁ then remain constant at 10¹⁵ cm^–3 upto a temperature T_{2_{and then increases exponentially. Since, as the temperature is raised, the donar electrons are donated to the conduction band and at temperature T₁ all the donar atoms are ionized. This temperature range is called the ionization region in which electron concentration increases exponentially.
When every available extrinsic electron has been transferred to the conduction band, the conduction band electron concentration n₀ is virtually constant with temperature until the concentration of extrinsic carriers n_i becomes comparable to the extrinsic concentration N_d.
Finally at higher temperature, ni is much greater than Nd and the intrinsic carriers dominate. The electron concentration increases exponentially again now as}}

n_i² = AT ³e	-E_g
	KT

The above concept can be better understood by the figure shown below—