Semiconductor Junction Depth Erfc Calculator
Extract background crossings from actual independently verified monotone erfc-like depth measurements by piecewise linear interpolation, no assumed Gaussian fit or fabricated erfc solver.
Description
An independently verified erfc-like depth profile can be compared with a supplied background concentration.
An independently verified erfc-like depth profile can be compared with a supplied background concentration.1
Interpolating measured crossings avoids assuming an unmeasured analytic profile or diffusivity.
When to use Semiconductor Junction Depth Erfc Calculator
Use this tool when you need to locate all observed criterion crossings on a matched measurement branch. Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
How to use Semiconductor Junction Depth Erfc Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter observedErfcDepthsM, callerMeasuredErfcConcentrations, callerBackgroundConcentration, following the field table and calculation rules below, then run the tool.
- Read measuredErfcBackgroundCrossingDepthsM. 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 |
|---|---|---|---|
| observedErfcDepthsM | Observed erfc depths m | list of number | Required |
| callerMeasuredErfcConcentrations | Caller measured erfc concentrations | list of number | Required |
| callerBackgroundConcentration | Caller background concentration | number | Required |
Require nonnegative depths, concentrations, and background, with concentrations nonincreasing in sample order. Apply the crossing algorithm below; flat sections are allowed and exact background plateaus return their sampled positions.
The crossing helper requires at least two nonempty aligned response and coordinate lists, with coordinates strictly increasing. Record exact sample hits at the chosen level and linearly interpolate each adjacent strict sign change around that level. Preserve sample order and remove adjacent duplicate coordinates. No crossing returns an empty list; an exact-level plateau returns all its sampled coordinates. Additional domain restrictions above remain in force.
crossing=x_i+(x_(i+1)−x_i)×(level−y_i)/(y_(i+1)−y_i) for strict sign changes Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| measuredErfcBackgroundCrossingDepthsM | Measured erfc background crossing depths m | list of number |
{
"input": {
"observedErfcDepthsM": [
0,
1,
2
],
"callerMeasuredErfcConcentrations": [
100,
60,
20
],
"callerBackgroundConcentration": 40
},
"output": {
"measuredErfcBackgroundCrossingDepthsM": [
1.5
]
}
}Limitations and assumptions
The criterion and branch are independently supplied. Multiple crossings, exact-level plateaus, and absent crossings do not establish one unique physical rating or transition, and the tool does not select an experimental procedure.
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 Junction Depth Gaussian Calculator: A Gaussian dopant profile crosses a uniform background at a model-defined depth. The supplied surface concentration, diffusivity, and elapsed time specify that conditional profile. For a complementary step, use Semiconductor Halo Doping Concentration Calculator: Dopant density should pool observed counts over represented volume rather than average unequal voxels. Explicit evidence flags separate known halo measurements from unavailable measurements.
References
Similar or alternative tools
- Semiconductor Junction Depth Gaussian Calculator
A Gaussian dopant profile crosses a uniform background at a model-defined depth. The supplied surface concentration, diffusivity, and elapsed time specify that conditional profile.
- Semiconductor Halo Doping Concentration Calculator
Dopant density should pool observed counts over represented volume rather than average unequal voxels. Explicit evidence flags separate known halo measurements from unavailable measurements.