Intrinsic Semiconductor Temperature Coefficient Explained

An intrinsic semiconductor is defined as a semiconductor material in its purest form, meaning it has not been doped with any impurity atoms to increase the number of charge carriers. Examples of intrinsic semiconductors include pure silicon (Si) and germanium (Ge). The electrical properties of these materials are inherently based on the number of charge carriers generated naturally within the material itself, primarily through thermal excitation.

Understanding Resistance and Temperature Coefficient

Electrical resistance ($R$) quantifies how much a material opposes the flow of electric current. The temperature coefficient of resistance, often denoted by $\alpha$, measures the fractional change in resistance per degree Celsius (or Kelvin) change in temperature. It can be mathematically expressed as: $$ \alpha = \frac{1}{R} \frac{dR}{dT} $$ Here, $R$ is the resistance at a given temperature, and $\frac{dR}{dT}$ represents how resistance changes with temperature.

• If $\alpha$ is positive, resistance increases as temperature increases.
• If $\alpha$ is negative, resistance decreases as temperature increases.
• If $\alpha$ is zero, resistance is independent of temperature.

How Temperature Affects Intrinsic Semiconductors

In intrinsic semiconductors, electrical conduction occurs due to the movement of both electrons (negatively charged) and holes (positively charged). These charge carriers are generated when atoms gain enough thermal energy to break free from their covalent bonds.

• Thermal Energy: As the temperature ($T$) of an intrinsic semiconductor rises, the atoms within the material vibrate more vigorously.
• Carrier Generation: This increased thermal energy breaks more covalent bonds, generating a greater number of electron-hole pairs. The intrinsic carrier concentration ($n_i$) increases significantly, often exponentially, with temperature.
• Conductivity Change: A higher concentration of charge carriers leads to increased electrical conductivity ($\sigma$).
• Resistance Change: Since conductivity and resistance are inversely related ($\sigma = \frac{1}{\rho} = \frac{L}{RA}$, where $\rho$ is resistivity), an increase in conductivity results in a decrease in electrical resistance ($R$).

Temperature Coefficient Analysis

The relationship described above shows that as the temperature of an intrinsic semiconductor increases, its resistance ($R$) decreases. This inverse relationship means that the temperature coefficient of resistance ($\alpha$) for intrinsic semiconductors is **negative**. This behavior contrasts sharply with that of metals. Metals typically have a positive temperature coefficient of resistance because their resistance is mainly due to collisions between the free electrons and the vibrating metal lattice. As temperature increases, lattice vibrations intensify, causing more frequent collisions and thus higher resistance.

Conclusion: Why the Coefficient is Negative

The primary reason intrinsic semiconductors exhibit a negative temperature coefficient is the significant increase in the number of charge carriers (electrons and holes) with rising temperature. This increase in carrier concentration dramatically enhances conductivity and reduces resistance, making the temperature coefficient negative.