Semiconductor Junction Depth Gaussian Calculator
Evaluate explicit Gaussian profile/background crossing with caller independently established surface concentration/diffusivity/time; not diffusion-length-only, processing instructions or actual dopant activation.
Description
A Gaussian dopant profile crosses a uniform background at a model-defined depth.
A Gaussian dopant profile crosses a uniform background at a model-defined depth.1
The supplied surface concentration, diffusivity, and elapsed time specify that conditional profile.
When to use Semiconductor Junction Depth Gaussian 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 Junction Depth Gaussian Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter callerSurfaceDopantPerM3, callerBackgroundDopantPerM3, callerDiffusivityM2Second, callerElapsedSeconds, following the field table and calculation rules below, then run the tool.
- Read modeledGaussianJunctionDepthM. 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 |
|---|---|---|---|
| callerSurfaceDopantPerM3 | Caller surface dopant per m3 | number | Required |
| callerBackgroundDopantPerM3 | Caller background dopant per m3 | number | Required |
| callerDiffusivityM2Second | Caller diffusivity m2 second | number | Required |
| callerElapsedSeconds | Caller elapsed seconds | number | Required |
Require all four inputs positive and surface concentration strictly above background. Evaluate the positive square-root expression with the natural logarithm of their concentration ratio.
depth=2sqrt(D×t×ln(Nsurface/Nbackground)) Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| modeledGaussianJunctionDepthM | Modeled gaussian junction depth m | number |
{
"input": {
"callerSurfaceDopantPerM3": 1e+24,
"callerBackgroundDopantPerM3": 1e+22,
"callerDiffusivityM2Second": 1e-16,
"callerElapsedSeconds": 100
},
"output": {
"modeledGaussianJunctionDepthM": 4.2919320525786947e-7
}
}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.
Alternative or Complementary methods
For a related task, use Semiconductor Junction Depth Erfc Calculator: An independently verified erfc-like depth profile can be compared with a supplied background concentration. Interpolating measured crossings avoids assuming an unmeasured analytic profile or diffusivity. For a complementary step, use Semiconductor Oxidation Enhanced Diffusion Calculator: Oxidation-related diffusion changes can be compared with an independently matched unoxidized baseline. Keeping both ratios and signed differences distinguishes enhancement from suppression in the supplied measurements.
References
Similar or alternative tools
- Semiconductor Junction Depth Erfc Calculator
An independently verified erfc-like depth profile can be compared with a supplied background concentration. Interpolating measured crossings avoids assuming an unmeasured analytic profile or diffusivity.
- Semiconductor Oxidation Enhanced Diffusion Calculator
Oxidation-related diffusion changes can be compared with an independently matched unoxidized baseline. Keeping both ratios and signed differences distinguishes enhancement from suppression in the supplied measurements.