Understanding the Negative Temperature Coefficient of Resistance in Semiconductors

The temperature coefficient of resistance (TCR) is a measure of how a material's electrical resistance changes with temperature. For semiconductors, this coefficient is typically negative, meaning their resistance decreases as temperature increases. This property is due to several key factors in the behavior of semiconductors at different temperatures.

Key Reasons for the Negative TCR in Semiconductors

Increased Carrier Concentration: In a semiconductor, the resistance TCR is primarily influenced by the concentration of charge carriers, which are electrons and holes. As the temperature rises, more electrons gain enough energy to jump from the valence band to the conduction band, increasing the number of free charge carriers. This increase in carrier concentration is the primary reason for the negative TCR in semiconductors.

Enhanced Conductivity: With more free charge carriers, the material's conductivity increases. Since resistance is inversely related to conductivity, a higher conductivity results in a lower resistance. Mathematically, the relationship can be expressed as: R ∝ 1/σ, where R is resistance and σ is conductivity. As the number of charge carriers increases, the resistance decreases, hence the negative TCR.

Temperature Dependence of Band Gap: The energy band gap of semiconductors typically decreases with increasing temperature. A smaller band gap means that electrons can more easily be excited into the conduction band, further increasing the number of free charge carriers.

Impact of Increased Carrier Concentration on Resistance

The increase in carrier concentration at higher temperatures leads to an increase in electrical conductivity, which directly impacts the overall resistance of the material. This relationship is well illustrated by the equation: R ∝ 1/σ. Since σ (conductivity) increases with temperature, R (resistance) decreases. The dominant factor here is the increase in free charge carriers, which enhances the material's ability to conduct electricity more effectively as the temperature rises.

Role of Scattering Mechanisms

Scattering mechanisms, such as phonon scattering, can also affect the resistance of semiconductors. However, at elevated temperatures, the increase in charge carrier concentration typically outweighs the effects of scattering. This is why, in semiconductors, the dominant factor contributing to the negative TCR is the increased number of charge carriers.

Applications of Negative TCR in Semiconductors

The negative TCR of semiconductors is an important property that allows their use in temperature sensing and control applications. Materials with a large negative TCR are particularly useful as they exhibit a greater sensitivity to temperature changes. For example, temperature-dependent resistors (thermistors) made from materials with large negative TCRs can be used to measure temperature accurately.

In summary, the negative temperature coefficient of resistance in semiconductors is primarily due to the increase in charge carrier concentration and conductivity with rising temperature. This characteristic is crucial for the design and application of semiconductor materials in various industries, including electronics, sensors, and integrated circuits.

Keywords: Temperature Coefficient of Resistance, Negative TCR, Semiconductor Materials