tidy3d.CaugheyThomasMobility

class CaugheyThomasMobility

Bases: Tidy3dBaseModel

The Caughey-Thomas temperature-dependent carrier mobility model.

Parameters:

• attrs (dict = {}) – Dictionary storing arbitrary metadata for a Tidy3D object. This dictionary can be freely used by the user for storing data without affecting the operation of Tidy3D as it is not used internally. Note that, unlike regular Tidy3D fields, attrs are mutable. For example, the following is allowed for setting an attr obj.attrs['foo'] = bar. Also note that Tidy3D` will raise a TypeError if attrs contain objects that can not be serialized. One can check if attrs are serializable by calling obj.json().

• mu_n_min (PositiveFloat) – Minimum electron mobility at reference temperature (300K) in cm^2/V-s.

• mu_n (PositiveFloat) – Reference electron mobility at reference temperature (300K) in cm^2/V-s

• mu_p_min (PositiveFloat) – Minimum hole mobility at reference temperature (300K) in cm^2/V-s.

• mu_p (PositiveFloat) – Reference hole mobility at reference temperature (300K) in cm^2/V-s

• exp_t_mu (float) – exp_d_n : PositiveFloat Exponent for doping dependence of electron mobility at reference temperature (300K).

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

• ref_N (PositiveFloat) – Reference doping at reference temperature (300K) in #/cm^3.

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

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

• exp_t_d_exp (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

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

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_n_min, mu_p_min	Minimum low-field mobility for \(n\) and \(p\)
\(\mu_{max}\)	mu_n, mu_p	Maximum low-field mobility for \(n\) and \(p\)
\(\alpha_1\)	exp_t_mu_min	Exponent for temperature dependence of the minimum mobility coefficient
\(\alpha_2\)	exp_t_mu	Exponent for temperature dependence of the maximum mobility coefficient
\(\alpha_{n,p}\)	exp_d_p, exp_d_n	Exponent for doping dependence of hole mobility.
\(\alpha_4\)	exp_t_d_exp	Exponent for the temperature dependence of the exponent \(\alpha_n\) and \(\alpha_p\)
\(N_{ref}\)	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
>>> default_Si = td.CaugheyThomasMobility(
...   mu_n_min=52.2,
...   mu_n=1471.0,
...   mu_p_min=44.9,
...   mu_p=470.5,
...   exp_t_mu=-2.33,
...   exp_d_n=0.68,
...   exp_d_p=0.719,
...   ref_N=2.23e17,
...   exp_t_mu_min=-0.57,
...   exp_t_d=2.4,
...   exp_t_d_exp=-0.146,
... )

Warning

There are some current limitations of this model:

• High electric field effects not yet supported.

Attributes

attrs

Methods

Inherited Common Usage

mu_n_min

mu_n

mu_p_min

mu_p

exp_t_mu

exp_d_n

exp_d_p

ref_N

exp_t_mu_min

exp_t_d

exp_t_d_exp

__hash__()

Hash method.