Semiconductor Dirac Fermi Velocity Calculator
Extract actual linear Dirac branch group velocity (1/ℏ) dE/dk in explicit SI conventions, not isotropic Fermi-energy velocity or branch crossing identification.
Description
A band-energy slope with respect to wavevector gives a signed group-velocity scale under a matched linear-branch convention.
A band-energy slope with respect to wavevector gives a signed group-velocity scale under a matched linear-branch convention.1
Using joules, inverse metres, and the supplied reduced Planck constant keeps the SI conversion explicit.
When to use Semiconductor Dirac Fermi Velocity 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 Dirac Fermi Velocity Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter observedDiracWavevectorsPerM, observedDiracBranchEnergiesJ, callerHbarJs, following the field table and calculation rules below, then run the tool.
- Read signedFittedDiracVelocityMSecond, diracSlopeFitRSquared. 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 |
|---|---|---|---|
| observedDiracWavevectorsPerM | Observed dirac wavevectors per m | list of number | Required |
| observedDiracBranchEnergiesJ | Observed dirac branch energies j | list of number | Required |
| callerHbarJs | Caller hbar js | number | Required |
Require positive hbar and fit aligned energy-versus-wavevector samples with a free intercept. Divide fitted slope by hbar and return R². Signed velocities and unsorted distinct predictor samples are accepted.
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.
E=a+b×k; velocity=b/ℏ Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| signedFittedDiracVelocityMSecond | Signed fitted dirac velocity m second | number |
| diracSlopeFitRSquared | Dirac slope fit r squared | number |
{
"input": {
"observedDiracWavevectorsPerM": [
0,
1,
2
],
"observedDiracBranchEnergiesJ": [
1,
3,
5
],
"callerHbarJs": 2
},
"output": {
"signedFittedDiracVelocityMSecond": 1,
"diracSlopeFitRSquared": 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 Dirac Point Energy Calculator: Two independently selected linear spectral branches can define a fitted crossing point. Their intersection is a model result and does not establish a protected Dirac node. For a complementary step, use Semiconductor Activation Energy Level Calculator: An Arrhenius branch expresses the natural logarithm of an activated rate against reciprocal temperature. Fitting observations estimates a signed activation-energy parameter and log prefactor under that model.
References
Similar or alternative tools
- Semiconductor Dirac Point Energy Calculator
Two independently selected linear spectral branches can define a fitted crossing point. Their intersection is a model result and does not establish a protected Dirac node.
- Semiconductor Activation Energy Level Calculator
An Arrhenius branch expresses the natural logarithm of an activated rate against reciprocal temperature. Fitting observations estimates a signed activation-energy parameter and log prefactor under that model.