tidy3d.MasettiMobility

class MasettiMobility

Bases: Tidy3dBaseModel

The Masetti doping-dependent low-field carrier mobility model.

Parameters:

• mu_max (PositiveFloat) – [units = cm^2/V-s]. High-mobility plateau at reference temperature (300K).

• mu_0 (PositiveFloat) – [units = cm^2/V-s]. Mid-doping mobility floor at reference temperature (300K).

• mu_1 (NonNegativeFloat) – [units = cm^2/V-s]. High-doping clustering mobility amplitude.

• Cr (PositiveFloat) – [units = 1/cm^3]. First transition doping concentration.

• Cs (PositiveFloat) – [units = 1/cm^3]. Clustering-onset doping concentration.

• alpha (PositiveFloat) – First denominator doping exponent.

• beta (PositiveFloat) – Clustering denominator doping exponent.

• exp_max (float) – Temperature exponent for the high-mobility plateau.

• exp_0 (float) – Temperature exponent for the mid-doping mobility floor.

Notes

The Masetti mobility model [1] is

\[\mu(N,T) = \mu_0\left(\frac{T}{T_{ref}}\right)^{\gamma_0} + \frac{ \mu_{max}\left(\frac{T}{T_{ref}}\right)^{\gamma_{max}} - \mu_0\left(\frac{T}{T_{ref}}\right)^{\gamma_0}} {1 + \left(N/C_r\right)^{\alpha}} - \frac{\mu_1}{1 + \left(C_s/N\right)^{\beta}}\]

where \(N\) is the total ionized doping concentration (acceptors + donors) and \(T_{ref}\) is 300 K. The final subtractive term captures the high-doping clustering behavior absent from the Caughey-Thomas model.

This model is supported only by the accelerated charge solver. It must be used for both electron and hole mobility within a semiconductor medium.

The following table maps the symbols used in the equations above with the names used in the code:

Symbol	Parameter Name	Description
\(\mu_{max}\)	mu_max	High-mobility plateau at 300 K.
\(\mu_0\)	mu_0	Mid-doping floor at 300 K.
\(\mu_1\)	mu_1	High-doping clustering amplitude.
\(C_r\)	Cr	First transition doping concentration.
\(C_s\)	Cs	Clustering-onset doping concentration.
\(\alpha\)	alpha	First denominator exponent.
\(\beta\)	beta	Clustering denominator exponent.
\(\gamma_{max}\)	exp_max	Temperature exponent for mu_max.
\(\gamma_0\)	exp_0	Temperature exponent for mu_0.

[1]

G. Masetti, M. Severi, and S. Solmi. Modeling of carrier mobility against carrier concentration in arsenic-, phosphorus-, and boron-doped silicon. IEEE Transactions on Electron Devices, 30(7), 1983.

Example

>>> import tidy3d as td
>>> mobility_Si_n = td.MasettiMobility(
...   mu_max=1417.0,
...   mu_0=52.2,
...   mu_1=43.4,
...   Cr=9.68e16,
...   Cs=3.43e20,
...   alpha=0.68,
...   beta=2.0,
...   exp_max=-2.5,
...   exp_0=-0.57,
... )
>>> mobility_Si_p = td.MasettiMobility(
...   mu_max=470.5,
...   mu_0=44.9,
...   mu_1=29.0,
...   Cr=2.23e17,
...   Cs=6.10e20,
...   alpha=0.719,
...   beta=2.0,
...   exp_max=-2.2,
...   exp_0=-0.57,
... )

Attributes

mu_max
mu_0
mu_1
Cr
Cs
alpha
beta
exp_max
exp_0

mu_max

mu_0

mu_1

Cr

Cs

alpha

beta

exp_max

exp_0