Threshold voltage is an important parameter in the field of electrical engineering, particularly in the design and operation of field-effect transistors (FETs). It refers to the minimum voltage required to establish a conducting channel between the source and drain terminals of a FET.

The threshold voltage is primarily determined by the characteristics of the gate oxide layer and the doping concentrations in the transistor structure. However, temperature also has an impact on the threshold voltage.

Here is a detailed explanation of why the threshold voltage decreases on increasing temperature:

1. Introduction to threshold voltage:
The threshold voltage is the voltage level at which a FET starts to conduct current between the source and drain terminals. Below the threshold voltage, the FET is in the off state, and above the threshold voltage, it is in the on state.

2. The effect of temperature on the threshold voltage:
a) Temperature dependence of the mobility: The mobility of charge carriers (electrons or holes) in the channel region of a FET decreases with increasing temperature. As a result, the conductivity of the channel decreases, requiring a higher voltage to establish a conducting channel. This leads to an increase in the threshold voltage.

b) Temperature dependence of the threshold voltage equation: The threshold voltage of a FET can be expressed using an equation that includes a term for the temperature. This equation takes into account the temperature dependence of various parameters such as the doping concentrations and the bandgap of the semiconductor material. In general, this equation shows that the threshold voltage decreases with increasing temperature.

c) Impact of temperature on the gate oxide layer: The gate oxide layer in a FET is typically made of silicon dioxide (SiO2). The electrical properties of SiO2, such as its dielectric constant, can change with temperature. This can affect the capacitive coupling between the gate electrode and the channel, and consequently, the threshold voltage.

3. Conclusion:
In summary, the threshold voltage of a FET decreases on increasing temperature due to the temperature dependence of the mobility of charge carriers, the threshold voltage equation, and the properties of the gate oxide layer. It is essential to consider the temperature effects when designing and operating FET-based circuits to ensure reliable performance.