Calculator Inputs
Use the grid below for responsive inputs. Large screens show three columns, smaller screens show two, and phones show one.
Formula Used
For an abrupt p-n junction under the depletion approximation, the built-in potential is:
Vbi = VT ln[(NAND) / ni2]
The thermal voltage is:
VT = kT / q
The total depletion width is:
W = √[(2εs/q)(1/NA + 1/ND)(Vbi − Va)]
The side partitions are:
xn = W NA / (NA + ND) and xp = W ND / (NA + ND)
This page converts doping values from cm-3 to m-3 before evaluating SI-unit equations. Width outputs are shown in micrometers for easier device interpretation.
How to Use This Calculator
- Choose whether the sweep varies acceptor doping, donor doping, or both equally.
- Enter fixed junction values for the non-swept side.
- Set the sweep start, sweep end, and number of logarithmic points.
- Provide material permittivity, temperature, intrinsic concentration, and applied voltage.
- Press Calculate and Plot to show the summary, table preview, and logarithmic graph above the form.
- Use the CSV button for the full dataset or the PDF button for a report-style summary.
Example Data Table
This example uses the default values shown in the form before any submission.
| # | Sweep Doping (cm-3) | NA (cm-3) | ND (cm-3) | Vbi (V) | W (µm) | xn (µm) | xp (µm) |
|---|---|---|---|---|---|---|---|
| 1 | 1.000e+14 | 1.000e+14 | 1.000e+16 | 0.5953 | 2.7883 | 0.0276 | 2.7607 |
| 2 | 1.259e+14 | 1.259e+14 | 1.000e+16 | 0.6012 | 2.5007 | 0.0311 | 2.4696 |
| 3 | 1.585e+14 | 1.585e+14 | 1.000e+16 | 0.6072 | 2.2433 | 0.0350 | 2.2083 |
| 4 | 1.995e+14 | 1.995e+14 | 1.000e+16 | 0.6131 | 2.0132 | 0.0394 | 1.9738 |
| 5 | 2.512e+14 | 2.512e+14 | 1.000e+16 | 0.6191 | 1.8075 | 0.0443 | 1.7632 |
| 6 | 3.162e+14 | 3.162e+14 | 1.000e+16 | 0.6250 | 1.6238 | 0.0498 | 1.5740 |
Frequently Asked Questions
1) What does this calculator plot?
It plots total depletion width against a logarithmic doping sweep. It also tracks n-side and p-side partitions. This helps you inspect how junction width changes as one side or both sides become more heavily doped.
2) Why does depletion width shrink at higher doping?
Higher doping increases charge density near the junction. The required space-charge region becomes narrower to balance the same electric field relationship. That is why heavily doped junctions usually show smaller depletion widths than lightly doped junctions.
3) What is the difference between total width and side widths?
Total width is the full depletion span across both sides. The n-side width extends into the donor region. The p-side width extends into the acceptor region. Their sum equals the plotted total depletion width.
4) Why is the graph logarithmic on the horizontal axis?
Doping values often cover several decades, from around 1014 to 1019 cm-3. A logarithmic axis keeps low and high concentrations visible together and makes trend comparisons much easier.
5) How does applied voltage affect the result?
Reverse bias increases the effective potential across the junction and usually widens depletion. Forward bias reduces that potential and narrows depletion. When the entered forward bias exceeds the built-in value, the simplified model collapses width toward zero.
6) Which material values should I enter?
Use the relative permittivity and intrinsic concentration that match your semiconductor and temperature. The default numbers fit silicon near room temperature, but other materials may need very different values for realistic junction behavior.
7) Are the equations valid for every junction?
No. The calculator assumes an abrupt junction and the depletion approximation. It does not model graded profiles, tunneling, degeneracy, strong high-field corrections, or full semiconductor transport effects.
8) What should I use the CSV and PDF downloads for?
Use CSV when you need the complete sweep for further analysis in spreadsheets or scripts. Use PDF when you want a compact report containing the summary metrics, chart image, and table preview for documentation.