Library / Electrical / ELE-43
Electrical
Thermal voltage
Voltage that sets the scale of semiconductor junction behaviour at absolute temperature T: about 25.85 mV at 300 K.
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- VT [mV]
The thermal voltage VT = kBT/q is the natural voltage scale of a semiconductor junction, with kB = 1.381 × 10−23 J/K, q = 1.602 × 10−19 C and T in kelvin. It is about 25.9 mV at 300 K and rises by 86 µV for every kelvin. It sets how fast diode and transistor currents rise with voltage, and also appears in thermal-noise and ion-transport calculations.
Voltage that sets the scale of semiconductor junction behaviour at absolute temperature T: about 25.85 mV at 300 K. It appears in the diode and transistor equations.
Calculator
- Rate of change with temperature, kB/q86.17 µV/K
- Voltage rise for ten times the current in an ideal diode, VT ln 1059.53 mV
- Thermal voltage at 25 °C (298.15 K)25.69 mV
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 300 K the thermal voltage is 25.85 mV. An ideal diode needs 59.5 mV more to pass ten times the current, close to the 60 mV per decade that is quoted.
- At 25 °C it is 25.7 mV and at 100 °C it is 32.2 mV: a diode’s voltage–current curve stretches as the temperature rises, which is why a transistor’s gain and bias drift with temperature.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mV) | Local step | Change in result |
|---|---|---|---|---|---|---|
| T Absolute temperature | 200 to 500 K | 17.23 | 43.09 | 25.85 | +10% | +10 % |
Sweep of Absolute temperature
| Absolute temperature (K) | Thermal voltage (mV) |
|---|---|
| 200 | 17.23 |
| 237.5 | 20.47 |
| 275 | 23.7 |
| 312.5 | 26.93 |
| 350 | 30.16 |
| 387.5 | 33.39 |
| 425 | 36.62 |
| 462.5 | 39.86 |
| 500 | 43.09 |
Sweep one variable
Variables and how each one contributes
Thermal voltage
What the equation gives you. Everything else feeds it.
Absolute temperature
The absolute temperature, in kelvin. Raises the thermal voltage in direct proportion. Raising it by 10 K (to 310 K) moves the result by +3.33 %, from 25.85 to 26.71 mV.
Worked example with the values above
- Constants: kB/q = 1.380649×10−23 / 1.602177×10−19 = 8.617×10−5 V/K.
- Multiply by the temperature: 8.617×10−5 × 300 K.
- VT = 25.85 mV.
Assumptions and limits
- Absolute temperature in kelvin and the standard values of kB and q.
- A junction in thermal equilibrium at a single temperature.
Common mistakes
- Using degrees Celsius for T.
- Remembering it as 26 mV regardless of temperature, which is only right near room temperature.
Statistics and uncertainty
The thermal voltage is exact for a given temperature; the uncertainty is in the temperature, and the junction temperature may be well above the ambient value due to self-heating.
Where it is used
- The scale factor in diode, bipolar-transistor and thermistor characteristics.
- Estimating the thermal-noise voltage scale and ion transport voltages.
Maths you need
- Boltzmann constant: links temperature to energy
- Elementary charge: the charge of an electron