Physical Models

A range of physical models are available to be used in the simulation. The physical models implemented in the simulator are fully configurable. To edit or view the physical models properties:

1. From the main menu, select Model -> Model Selection.

Parameters

General

Name	Description	Unit
Refmat	Reference Material. The baseline material used to define reference energy levels in simulations.	-
Temp	Temperature. Ambient temperature for the simulation	Kelvin

Mobility

Low Field Mobility

Users can set low field mobility as constant, lattice, impurity, or carrier-carrier:

• Constant Model: Mobility is fixed to the value specified in the properties command.
• Lattice Model: Accounts for mobility reduction due to increased lattice collisions at higher temperatures.
• Impurity Model: Considers mobility reduction due to additional collisions caused by impurities.
• Carrier-Carrier Model: Similar to the impurity model but also accounts for carrier concentration effects, which are crucial at high injection levels.

Note: If the high-field model is selected, the low-field mobility model will feed into it. Otherwise, the selected mobility model will be used in the simulation.

Name	Description	Unit
Const_Mob	Reference Material. The baseline material used to define reference energy levels in simulations.	-
Temp	Temperature. Ambient temperature for the simulation.	Kelvin

High Field Mobility

Users can set high field mobility as none, e_field or j_field. The e_field or j_field models are used to select the high-field mobility model, which can be based on either the electric field magnitude or the magnitude of the field in the direction of the current.

High Field Calculation

Users can set as edge or element. Used to determine how the high field mobility field is calculated. This will either use the values along an element edge or calculate the field based on the whole element.

Surface Mobility

Users can set as yes or no. Used to select surface mobility along oxide semiconductor interfaces. This model only affects those edges that actually lie along the interface.

Name	Description	Unit
Surf_Mob	Used to select surface mobility along oxide semiconductor interfaces. Options: [On, Off]	-

Recombination

SRH (Shockley Read Hall)

Name	Description	Unit
SRH_rec	Selects the Shockley Read Hall recombination model. Options: [On, Off]	-

Auger

Name	Description	Unit
Auger_rec	Selects the Auger recombination model. Options: [On, Off]	-

Direct

Name	Description	Unit
Dir_rec	Selects the direct band-to-band recombination model. Options: [On, Off]	-

Impact Ionisation

There are two models for available impact ionisation, Chynoweth and Okuto-Crowell.

Users can set these option to Off, II_edge, II_elem, OC_edge, OC_elem but only one can be selected at any time.

Name	Description	Unit
II_elem	Selects the Chynoweth impact-ionisation model using full elemental discretisation. Options: [On, Off]	-
II_edge	Selects the Chynoweth impact-ionisation model based on edge discretisation. Options: [On, Off]	-
OC_elem	Selects the Okuto–Crowell impact-ionisation model using full elemental discretisation. Options: [On, Off]	-
OC_edge	Selects the Okuto–Crowell impact-ionisation model based on edge discretisation. Options: [On, Off]	-

Chynoweth Impact Ionisation Model

The electron ($\alpha$) and hole ($\beta$) ionisation coefficients are given by:

$$\alpha,\;\beta(F) \;=\; A \,\exp\!\left( -\frac{B}{F} \right)$$

where:

Symbol	Description	Units	Property (holes)	Property (electrons)
$A$	Ionisation coefficient prefactor	cm⁻¹	K_aval_alpha_p	K_aval_alpha_n
$B$	Field scaling parameter	V/cm	K_aval_beta_p	K_aval_beta_n
$F$	Electric field	V/cm	–	–

Okuto–Crowell Impact Ionisation Model [1]

The electron ($\alpha$) and hole ($\beta$) ionisation coefficients are given by:

$$\alpha,\;\beta(F, T) \;=\; a \cdot \bigl(1 + c \,(T - 300)\bigr)\cdot F^{\,n} \cdot \exp\!\left[ - \left( \frac{b \cdot \bigl(1 + d\,(T - 300)\bigr)}{F} \right)^{m} \right]$$

where:

Symbol	Description	Units	Property (holes)	Property (electrons)
$a$	Pre-exponential factor	cm⁻¹	OC_a_p	OC_a_n
$b$	Field scaling parameter	V/cm	OC_b_p	OC_b_n
$c$	Temperature coefficient (prefactor)	1/K	OC_c_p	OC_c_n
$d$	Temperature coefficient (field scaling)	1/K	OC_d_p	OC_d_n
$m$	Exponent in exponential term	–	OC_m_p	OC_m_n
$n$	Field-power exponent	–	OC_n_p	OC_n_n
$F$	Electric field	V/cm	–	–
$T$	Lattice temperature	K	–	–

References

[1] Y. Okuto and C. R. Crowell, "Ionization coefficients in semiconductors: A nonlocalized property," Phys. Rev. B, vol. 10, no 10, pp. 4284–4296, 1974, doi:10.1103/PhysRevB.10.4284.