tidy3d.CaugheyThomasMobility

class CaugheyThomasMobility

Bases: Tidy3dBaseModel

The Caughey-Thomas temperature-dependent carrier mobility model.

Parameters:

• mu_min (PositiveFloat) – [units = cm^2/V-s]. Minimum electron mobility \(\mu_{\text{min}}\) at reference temperature (300K).

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

• exp_2 (float)

• exp_N (PositiveFloat) – Exponent for doping dependence of mobility at reference temperature (300K).

• ref_N (PositiveFloat) – [units = 1/cm^3]. Reference doping at reference temperature (300K).

• exp_1 (float) – Exponent of thermal dependence of minimum mobility.

• exp_3 (float) – Exponent of thermal dependence of reference doping.

• exp_4 (float) – Exponent of thermal dependence of the doping exponent effect.

Notes

The general form of the Caughey-Thomas mobility model [1] is of the form:

\[\mu_0 = \frac{\mu_{max} - \mu_{min}}{1 + \left(N/N_{ref}\right)^z} + \mu_{min}\]

where \(\mu_0\) represents the low-field mobility and \(N\) is the total doping (acceptors + donors). \(\mu_{max}\), \(\mu_{min}\), \(z\), and \(N_{ref}\) are temperature dependent, the dependence being of the form

\[\phi = \phi_{ref} \left( \frac{T}{T_{ref}}\right)^\alpha\]

and \(T_{ref}\) is taken to be 300K.

The complete form (with temperature effects) for the low-field mobility can be written as

\[\mu_0 = \frac{\mu_{max}(\frac{T}{T_{ref}})^{\alpha_2} - \mu_{min}(\frac{T}{T_{ref}})^{\alpha_1}}{1 + \left(N/N_{ref}(\frac{T}{T_{ref}})^{\alpha_3}\right)^{\alpha_N(\frac{T}{T_{ref}})^{\alpha_4}}} + \mu_{min}(\frac{T}{T_{ref}})^{\alpha_1}\]

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

Symbol	Parameter Name	Description
\(\mu_{min}\)	mu_min	Minimum low-field mobility for \(n\) and \(p\)
\(\mu_{max}\)	mu	Maximum low-field mobility for \(n\) and \(p\)
\(\alpha_1\)	exp_1	Exponent for temperature dependence of the minimum mobility coefficient
\(\alpha_2\)	exp_2	Exponent for temperature dependence of the maximum mobility coefficient
\(\alpha_N\)	exp_N	Exponent for doping dependence.
\(\alpha_3\)	exp_3	Exponent for the temperature dependence of the reference doping
\(\alpha_4\)	exp_4	Exponent for the temperature dependence of the exponent \(\alpha_N\)
\(N_{ref}\)	ref_N,	Reference doping parameter

[1]

M. Caughey and R.E. Thomas. Carrier mobilities in silicon empirically related to doping and field. Proceedings of the IEEE, 55(12):2192–2193, December 1967

Example

>>> import tidy3d as td
>>> mobility_Si_n = td.CaugheyThomasMobility(
...   mu_min=52.2,
...   mu=1471.0,
...   ref_N=9.68e16,
...   exp_N=0.68,
...   exp_1=-0.57,
...   exp_2=-2.33,
...   exp_3=2.4,
...   exp_4=-0.146,
... )
>>> mobility_Si_p = td.CaugheyThomasMobility(
...   mu_min=44.9,
...   mu=470.5,
...   ref_N=2.23e17,
...   exp_N=0.719,
...   exp_1=-0.57,
...   exp_2=-2.33,
...   exp_3=2.4,
...   exp_4=-0.146,
... )

Warning

There are some current limitations of this model:

• High electric field effects not yet supported.

Attributes

mu_min
mu
exp_2
exp_N
ref_N
exp_1
exp_3
exp_4

mu_min

mu

exp_2

exp_N

ref_N

exp_1

exp_3

exp_4