Carrier mobility, diffusion coefficient and diffusion length calculator (silicon)
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KEY POINTS
In lightly doped silicon at room temperature this model gives an electron mobility of about 1,340 and a hole mobility of about 460 cm²/V·s; impurity scattering lowers mobility at high doping and lattice scattering lowers it at high temperature. The diffusion coefficient is D = μkT/q (about 35 cm²/s for electrons at room temperature) and the diffusion length is L = √(Dτ). Above 10⁴ V/cm, drift velocity saturates near 10⁷ cm/s.
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Bulk silicon mobility from the Arora model (1982). In a MOSFET inversion layer, surface scattering and the vertical field reduce mobility to one-half to one-third of this value (effective mobility). At high concentrations (10¹⁹ cm⁻³ and above), minority carrier mobility also differs from the majority carrier value.
Impurity concentration and mobility (by temperature)
Electric field and drift velocity (velocity saturation)
Temperature and mobility (concentration 1.00×10¹⁶ cm⁻³)
| Temperature | Electrons (cm²/Vs) | Holes (cm²/Vs) | Diffusion coefficient D (cm²/s) |
|---|---|---|---|
| 200 K (-73 °C) | 2723 | 995 | 46.9 |
| 250 K (-23 °C) | 1762 | 634 | 38 |
| 300 K (27 °C) | 1218 | 437 | 31.5 |
| 350 K (77 °C) | 888 | 321 | 26.8 |
| 400 K (127 °C) | 676 | 246 | 23.3 |
| 450 K (177 °C) | 531 | 196 | 20.6 |
| 500 K (227 °C) | 430 | 161 | 18.5 |
Two kinds of scattering that limit mobility
Mobility measures how fast carriers move under an electric field and is proportional to the average time between scattering events. At low doping, scattering by lattice vibrations dominates, and mobility falls roughly as T^−2.3 as temperature rises. At high doping, scattering by ionized impurities adds to it; above 10¹⁸ cm⁻³, electron mobility drops to about one-fifth of its low-doping value.
Mobility is the proportionality constant at low fields. Above about 10⁴ V/cm, drift velocity in silicon levels off near 10⁷ cm/s (velocity saturation). The channel field of short-channel MOSFETs falls in this range, so drive current depends more on saturation velocity than on mobility, which limits the benefit of raising mobility with strained silicon or SiGe and Ge channels.
FAQ
What is the Einstein relation?
D = μkT/q links the diffusion coefficient to mobility. At room temperature kT/q is about 25.9 mV, so D is μ multiplied by about 0.026 V.
Why is inversion layer mobility lower?
In a MOSFET channel, surface roughness scattering and the vertical field reduce mobility to roughly one-half to one-third of the bulk value.
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Last updated: October 23, 2026