Explain the concept of the Fermi energy level in semiconductors and its relationship to the probability of electron occupation in energy states. Discuss how the position of the Fermi level influences the electrical properties of doped and intrinsic semiconductors.
The Fermi energy level, often referred to simply as the Fermi level (E_f), is a critical concept in solid-state physics that plays a fundamental role in determining the electronic properties of materials, including semiconductors.
In intrinsic semiconductors,
$$f\left(E\right)=\;\frac1{\left(1+e^{\left({\displaystyle\frac{\left(E-E_f\right)}{k_BT}}\right)}\right)}$$
As the temperature increases,
Now, let’s discuss how the position of the Fermi level influences the electrical properties of doped and intrinsic semiconductors:
Intrinsic Semiconductors:
As mentioned earlier, in intrinsic semiconductors,
Doped Semiconductors:
Doping is the intentional introduction of impurity atoms into the semiconductor lattice to alter its electrical properties.
In conclusion,