Semiconductor HEMT Mobility Vs Temperature Calculator
Fit actual HEMT mobility-temperature power exponent from observations instead of existing fixed phonon/impurity power defaults, query only observed range.
Description
Temperature-dependent mobility can be summarized by a fitted power law on a measured HEMT branch.
Temperature-dependent mobility can be summarized by a fitted power law on a measured HEMT branch.1
Its exponent is inferred from the supplied observations rather than fixed by a universal scattering model.
When to use Semiconductor HEMT Mobility Vs Temperature Calculator
Use this tool when you need to calculate the stated measurement summary or conditional model from matched observations. Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
How to use Semiconductor HEMT Mobility Vs Temperature Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter observedHemtTemperaturesKelvin, observedHemtMobilities, queryTemperatureKelvin, following the field table and calculation rules below, then run the tool.
- Read fittedTemperatureExponent, modeledHemtMobility, fitRSquared. Use the output table and calculation rules below to interpret units, signs, crossings, and flags.
- Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedHemtTemperaturesKelvin | Observed HEMT temperatures kelvin | list of number | Required |
| observedHemtMobilities | Observed HEMT mobilities | list of number | Required |
| queryTemperatureKelvin | Query temperature kelvin | number | Required |
Use at least two strictly increasing positive Kelvin temperatures and aligned positive mobilities. Fit ln(mobility) against ln(temperature) with an intercept. Require a positive query within the observed temperature range, evaluate exp(intercept)×query^exponent, and report log-domain R².
The regression helper accepts 2–10000 aligned finite pairs with nonzero predictor variance. It fits ordinary least squares with a free intercept using shifted coordinates; samples need not be sorted unless this tool additionally requires it. R² is clamped to [0,1] and is one for constant responses. Transformed fits use the stated log or reciprocal predictor/response basis; R² is a fit summary rather than a confidence interval.
ln(μ)=a+p×ln(T); μquery=exp(a)×Tquery^p Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| fittedTemperatureExponent | Fitted temperature exponent | number |
| modeledHemtMobility | Modeled HEMT mobility | number |
| fitRSquared | Fit r squared | number |
{
"input": {
"observedHemtTemperaturesKelvin": [
100,
200
],
"observedHemtMobilities": [
4,
1
],
"queryTemperatureKelvin": 150
},
"output": {
"fittedTemperatureExponent": -2.000000000000002,
"modeledHemtMobility": 1.7777777777777755,
"fitRSquared": 1
}
}Limitations and assumptions
Measurements, branch identification, units, and model applicability must be independently established. Results do not supply universal material constants, a complete physical model, or operating-condition approval.
Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Arrays must be dense, with no missing cells. Numeric lists allow at most 10000 entries, subject to smaller tool-specific bounds above.
Alternative or Complementary methods
For a related task, use Semiconductor Ge Quantum Well Hole Mobility Calculator: Hall hole sheet density and sheet resistance can define an extracted Ge quantum-well mobility. Interpreting that value requires independently resolving Hall factors and multiple carrier bands. For a complementary step, use Semiconductor Dopant Solubility Limit Calculator: Equilibrium dopant solubility is measured under a particular material and assay context. An observed temperature calibration supports interpolation while leaving activation and diffusion as separate quantities.
References
Similar or alternative tools
- Semiconductor Ge Quantum Well Hole Mobility Calculator
Hall hole sheet density and sheet resistance can define an extracted Ge quantum-well mobility. Interpreting that value requires independently resolving Hall factors and multiple carrier bands.
- Semiconductor Dopant Solubility Limit Calculator
Equilibrium dopant solubility is measured under a particular material and assay context. An observed temperature calibration supports interpolation while leaving activation and diffusion as separate quantities.