Thermal Voltage: Formula, Definition & Value at 300 K

Thermal voltage is an important parameter in semiconductor physics that represents the ratio of thermal energy to the electric charge of a carrier. It is denoted by $V_T$ and depends on the absolute temperature of the semiconductor.

At a temperature of 300 K (approximately 27°C), the thermal voltage is about 25.85 mV. It is widely used to analyze the current-voltage characteristics of diodes, bipolar junction transistors (BJTs), and other semiconductor devices.

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What Is Thermal Voltage?

Thermal voltage $V_T$ is the voltage equivalent of the thermal energy available to charge carriers, such as electrons and holes, in a semiconductor. It describes the relationship between the thermal energy of a carrier and its electric charge.

Thermal voltage is not an independently generated voltage source across a semiconductor junction. Instead, it is a temperature-dependent quantity used in semiconductor equations to describe carrier behavior.

As the temperature increases, the thermal energy of charge carriers also increases, causing the thermal voltage to rise. This relationship is important when studying semiconductor devices such as PN junction diodes, BJTs, MOSFETs, and IGBTs.

Thermal Voltage Formula

The thermal voltage is calculated using the following formula:

V_T=\frac{kT}{q}

Where:

$V_T$ = Thermal voltage in volts (V)
$K$ = Boltzmann constant, $1.380649\times10^{-23}\text{ J/K}$
$T$ = Absolute temperature in kelvin (K)
$q$ = Magnitude of the electronic charge, $1.602176634\times10^{-19}\text{ C}$

The formula shows that thermal voltage is directly proportional to absolute temperature. Therefore, its value increases linearly as the temperature rises.

Thermal Voltage at Room Temperature (300 K)

At room temperature, the absolute temperature is commonly approximated as 300 K. Substituting this value into the thermal voltage equation gives:

V_T=\frac{kT}{q}

V_T=\frac{1.380649\times10^{-23}\times300}{1.602176634\times10^{-19}}

V_T=0.025852\text{ V}

Converting volts into millivolts:

V_T\approx25.85\text{ mV}

Thus, the thermal voltage at 300 K is approximately 25.85 mV. In many electronic circuit calculations, it is rounded to 26 mV for convenience.

Thermal Voltage in a Diode

Thermal voltage is an essential parameter in the diode current equation, also known as the Shockley diode equation. It describes how the current through an ideal PN junction diode changes with the applied voltage.

The diode equation is:

{I=I_S\left(e^{\frac{V_D}{nV_T}}-1\right)}

Where:

$I$ = Diode current
$I_S$ = Reverse saturation current
$V_D$ =Voltage applied across the diode
$n$ = Ideality factor of diode
$V_T$ = Thermal voltage

In this equation, thermal voltage appears in the exponential term. It helps determine how strongly the diode current responds to a change in the applied voltage.

At a constant diode voltage, a change in temperature can affect the current through changes in thermal voltage and other temperature-dependent parameters, particularly the reverse saturation current.

Solved Example: Calculate Thermal Voltage at Different Temperatures

Problem: Calculate the thermal voltage of a semiconductor at 50°C and 60°C. Compare the results.

Case 1: Thermal voltage at 50°C

First, convert the temperature into kelvin:

T=50+273.15=323.15\text{ K}

Using the formula:

V_T=\frac{kT}{q}

V_T=\frac{1.380649\times10^{-23}\times323.15} {1.602176634\times10^{-19}}

V_T\approx27.85\text{ mV}

Case 2: Thermal voltage at 60°C

Convert the temperature into kelvin:

T=60+273.15=333.15\text{ K}

Substitute the value into the formula:

V_T=\frac{kT}{q}

V_T=\frac{1.380649\times10^{-23}\times333.15} {1.602176634\times10^{-19}}

V_T\approx28.71\text{ mV}

Result: The thermal voltage increases from approximately 27.85 mV at 50°C to 28.71 mV at 60°C. This confirms that thermal voltage increases with absolute temperature.

Importance of Thermal Voltage in Semiconductors

Thermal voltage is used in several areas of semiconductor analysis and electronic circuit design.

Diode current calculation: It helps determine the exponential relationship between the applied voltage and diode current.
BJT analysis: It is used to calculate the thermal voltage-dependent transconductance of a bipolar junction transistor.
Temperature analysis: It helps engineers evaluate how temperature affects semiconductor device characteristics.
Circuit simulation: It is an important parameter in mathematical models of semiconductor components.
Analog circuit design: It is used in the analysis of biasing circuits, differential amplifiers, and other transistor-based circuits.

Advantages of Understanding Thermal Voltage

Understanding thermal voltage helps engineers analyze semiconductor behavior under different operating temperatures. It simplifies calculations involving diode current, transistor transconductance, and temperature-dependent circuit performance.

It is particularly useful in designing temperature-sensitive circuits, precision analog electronics, and semiconductor models where temperature variations must be considered.

Conclusion

Thermal voltage $V_T$ is the voltage equivalent of the thermal energy per unit charge in a semiconductor. It is calculated using the formula $V_T=kT/q$ , where the value depends directly on absolute temperature.

At 300 K, thermal voltage is approximately 25.85 mV. This parameter is fundamental to the analysis of PN junction diodes, BJTs, and other semiconductor devices because it appears in equations describing their electrical behavior.

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Thermal Voltage: Definition, Formula, and Value at 300 K