Advertisement Remove all ads

The Conductivity of an Intrinsic Semiconductor Depends on Temperature as σ = σ0e−δE/2kt, Where σ0 is a Constant. - Physics

Short Note

The conductivity of an intrinsic semiconductor depends on temperature as σ = σ0eΔE/2kT, where σ0 is a constant. Find the temperature at which the conductivity of an intrinsic germanium semiconductor will be double of its value at T = 300 K. Assume that the gap for germanium is 0.650 eV and remains constant as the temperature is increased.

(Use Planck constant h = 4.14 × 10-15 eV-s, Boltzmann constant k = 8·62 × 10-5 eV/K.)

Advertisement Remove all ads

Solution

Let the conductivity at temperature T1 be \[\sigma_1\]  and the conductivity at temperature T be \[\sigma_2\] .

Given: \[T_1    =   300  K\]

Band gap, E = 0.650 eV
Now,
According to the question,

\[\sigma =  \sigma_0 e -^\frac{\Delta E}{2KT}\]

\[\sigma_2    =   2 \sigma_1\]

\[\Rightarrow  \sigma_0  e^\frac{- \Delta E}{2kT}    =   2 \times  \sigma_0  e^\frac{- \Delta E}{2 \times k \times T_1} \] 

\[ \Rightarrow  \sigma_0  e^\frac{- \Delta E}{2kT}  =     2 \times  \sigma_0  e^\frac{- \Delta E}{2 \times k \times 300} \] 

\[ \Rightarrow  e^\frac{- 0 . 650}{2 \times 8 . 62 \times {10}^{- 5} \times T}    =   2 \times  e^\frac{- 0 . 650}{2 \times 8 . 62 \times {10}^{- 5} \times 300} \] 

\[ \Rightarrow  e^\frac{- 0 . 650}{2 \times 8 . 62 \times {10}^{- 5} \times T}    =   6 . 96561 \times  {10}^{- 6} \] 

On taking natural natural log on both sides, we get

\[\frac{- 0 . 650}{2 \times 8 . 62 \times {10}^{- 5} \times T}   =    - 11 . 874525\] 

\[ \Rightarrow \frac{1}{T}   =   \frac{11 . 874525 \times 2 \times 8 . 62 \times {10}^{- 5}}{0 . 65}\] 

\[ \Rightarrow T   =   317 . 51178   \approx   318\] K

Concept: Energy Bands in Conductors, Semiconductors and Insulators
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 23 Semiconductors and Semiconductor Devices
Q 14 | Page 419
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×