Tool · Silicon modulators

Plasma Dispersion Calculator

Free-carrier index and absorption change in silicon from the Soref and Bennett relations at 1310 and 1550 nm and the Nedeljkovic fits at 1550 and 2000 nm: Δn and Δα for any electron and hole density, the phase shift and loss of a phase shifter of given length and mode overlap, the length for π and what it costs in decibels, and the loss of doped waveguides. Background: plasma dispersion effect, free-carrier absorption, and Mach-Zehnder modulator.

Carriers and wavelength

Wavelength

Relation

Electron density ΔN (cm⁻³)

Hole density ΔP (cm⁻³)

excess carriers from injection or depletion, or the dopant density of a doped waveguide; below 10¹⁴ the contribution is taken as zero

Mode overlap Γ

fraction of the mode power inside the region whose carrier density changes; 1 for a uniformly filled core, 0.1 to 0.4 for the depleted slice of a pn junction

Phase-shifter length L (µm)

Presets

The relations are empirical fits to the absorption spectra of doped silicon with a Kramers-Kronig transform for the index, so they apply to dopants as well as to injected or depleted carriers. Densities are spatially uniform in the modulated region; a real junction has a profile, which the overlap factor stands in for.

Readouts

Dopant density	n-type loss	p-type loss

Index change versus carrier density

electronsholes

Absorption change versus carrier density

electronsholes

Loss of a π phase shifter versus carrier density

electrons onlyholes onlyequal electrons and holes

Checked against

These checks run in your browser on every load. The relations are evaluated at the densities the sources quote and compared with the published coefficients times the density, the two 1550 nm relations are compared with each other, and the unit conversions are checked against hand-computed values.

Check	Expected	Computed