Semiconductor Electronics – JEE Main PhysicsPractice Questions & PYQs

The contrasting temperature dependency of resistance in metals versus semiconductors stems fundamentally from how temperature impacts their respective charge carrier populations. In metallic conductors, the density of free charge carriers remains effectively stable as temperature rises, so the increase in resistance is driven primarily by more frequent collisions between electrons and positive kernels. Conversely, in semiconductors, increasing the temperature provides sufficient energy to liberate bounded electrons, which leads to a significant increase in the number of available charge carriers and causes a net decrease in resistance.

The temperature dependence of electrical resistance is determined by the distinct electronic structure of the material, which dictates how charge carriers respond to cooling. For a metal like copper, lowering the temperature to 80 K minimizes the thermal vibrations of lattice atoms, which reduces scattering and causes the resistance to decrease. Conversely, for a semiconductor like germanium, cooling the material to 80 K reduces the thermal excitation of electrons into the conduction band, leaving fewer charge carriers available to move current and causing the resistance to rise.

Energy band theory categorizes materials based on the gap between valence and conduction bands, where the width of this forbidden energy zone fundamentally determines electrical conductivity. In metallic materials, these bands overlap or lack a gap, and in semiconductors, the gap is narrow enough to allow electron transition, whereas insulators possess a significantly wide forbidden region. This immense energy barrier is why the energy band gap reaches its maximum value in insulators.

The specific resistance or resistivity is determined by the relationship $\rho = \frac{m}{n e^2 \tau}$, where $n$ represents the number of charge carriers per unit volume and $\tau$ denotes the average relaxation time. In metallic conductors, rising temperature increases atomic vibrations, which causes a reduction in $\tau$ that is much more significant than the slight increase in $n$, leading to a net increase in resistivity. Conversely, in semiconductors, an increase in temperature generates a massive surge in the number of free charge carriers $n$, and because this growth in carrier density is far more dominant than the simultaneous decrease in $\tau$, the overall specific resistance drops.

Semiconductors rely on thermal energy to promote electrons from the valence band to the conduction band, which enables electrical current to flow. At absolute zero, the complete lack of thermal agitation means there is no energy available to break the covalent bonds holding the electrons in place. Consequently, all electrons remain trapped in the valence band, leaving the conduction band entirely empty and devoid of the mobile charge carriers required for conductivity. This complete absence of free electrons and holes renders pure silicon an insulator.

A transistor functions by moving charge through its structure, where the primary job of the emitter is to inject a massive quantity of majority charge carriers into the base so they can pass to the collector. Because the magnitude of current flow is dictated by this injection process, the emitter is intentionally manufactured with the highest doping concentration of all the transistor regions.