Question

Ideally in a semiconductor, intrinsic energy energy level should be in the middle of the band gap. Estimate the position of the intrinsic energy level (Ei) for intrinsic Ge at 300K, assuming the effective mass values for electrons and holes are me = 0.041m0 and mp = 0.28m0 , respectively.

Answer 1

Answer:

The position of  intrinsic energy level (Ei) for intrinsic Ge at 300 K is at 0.024 eV above the middle band gap.

Explanation:

We know that

Fermi level of intrinsic semiconductor given as

$E_i=\dfrac{E_c+E_v}{2}-\dfrac{KT}{2}\ ln\left(\dfrac{m_e}{m_p}\right)^{3/2}$

KT = average thermal energy at 300 K = 0.026 eV

$\dfrac{E_c+E_v}{2}-E_i=\dfrac{KT}{2}\ ln\left(\dfrac{m_e}{m_p}\right)^{3/2}$

Now by putting the values

$\dfrac{E_c+E_v}{2}-E_i=\dfrac{KT}{2}\ ln\left(\dfrac{m_e}{m_p}\right)^{3/2}$

$\dfrac{E_c+E_v}{2}-E_i=\dfrac{0.026}{2}\ ln\left(\dfrac{0.041m_0}{0.28m_0}\right)^{3/2}$

$\dfrac{E_c+E_v}{2}-E_i=-0.024$

$E_i=\dfrac{E_c+E_v}{2}+0.024$

So the position of  intrinsic energy level (Ei) for intrinsic Ge at 300 K is at 0.024 eV above the middle band gap.