The N-Channel MOSFET and P-Channel MOSFET blocks model an n-channel or p-channel field-effect transistor with a metal-oxide-semiconductor (MOSFET) structure based on surface potential equations.
The block also includes the ability to model thermal effects.
Model based on surface potential equations
The model based on surface potential equations takes into account the following effects:
A fully nonlinear capacitance model (including nonlinear Miller capacitance).
Charge conservation.
Carrier velocity saturation and channel length modulation.
Integrated diode.
Inverse recovery in the embedded diode model.
Influence of temperature on physical parameters.
Dynamic self-heating for the thermal effects modelling option (modelling the effect of self-heating on the electrical characteristics of the device).
This model is a simplified version of the standard PSP model [1], incorporating only some of it in order to find a balance between accuracy and complexity of the model. For more details on the physical assumptions of the phenomena included in this model, see [2].
The following are the surface potential equations for an n-channel MOSFET. The equations for a p-channel MOSFET are derived similarly, but the charges and currents are multiplied by -1.
The model is based on the Poisson equation:
where
- electrostatic potential;
- electron charge;
- concentration of acceptors in the substrate;
- dielectric constant of the semiconductor material (e.g. silicon);
- the difference between the intrinsic Fermi level and the Fermi level of bulk silicon;
- the quasipotential Fermi potential of the surface layer with respect to the bulk layer;
- temperature potential;
- Boltzmann constant;
- temperature.
The Poisson equation is used to derive the surface potential equation:
where
- is the applied gate-substrate voltage;
- is the stress of the flat zone;
- surface potential;
- substrate coefficient:
- specific surface capacitance.
The block uses an explicit approximation of the surface potential equation to avoid the need to numerically solve this implicit equation.
Once the surface potential is known, the drain current is determined as follows
where
- is the width of the device;
- channel length;
- mobility in weak fields;
- velocity saturation;
- surface potential difference between the drain and the source;
and - inversion charge densities at the source and the drain, respectively;
- average inversion charge density along the channel;
- mobility reduction factor. For more information, see the description of the Surface roughness scattering factor parameters;
- channel length modulation:
where
- is the modulation coefficient of the channel length;
- drain-substrate voltage;
- drain-substrate voltage cut to the maximum value corresponding to velocity saturation or cut-off (whichever comes first);
- channel length modulation voltage.
The unit calculates inversion charge densities directly from the surface potential.
The block also calculates nonlinear capacitances from the surface potential. The source and drain charge contributions are assigned using a bias-dependent Ward-Dutton charge separation scheme as described in [3]. These charges are calculated explicitly, so the charges are conserved in this model. Capacitive currents are calculated by taking the time derivatives of the corresponding charges. In practice, the charges within the modelling are normalised to the oxide capacitance and calculated in volts.
The gain of the MOSFET is determined as follows:
The threshold voltage for a shorted source-substrate junction is approximately determined as follows:
where is the surface potential at strong inversion.
In general, the three- and four-channel models consist of an intrinsic MOSFET defined by the surface potential formula, an integrated diode, series resistors, and fixed junction capacitances as shown in the schematic for an n-channel MOSFET.
Modelling an integrated diode
The block simulates an integrated diode with an exponential volt-ampere characteristic (VAC).
The junction capacitance and diffusion capacitance are calculated as:
where
- is the current through the diode;
- is the reverse saturation current;
- drain-substrate voltage;
- ideality factor;
- temperature potential;
- diode junction capacitance;
- junction capacitance at zero bias;
- voltage of the integrated diode;
- diffusion capacitance of the diode;
- transit time.
Modelling of temperature dependence
By default, temperature dependence is not considered and the device is modelled at the temperature for which the parameters are set. To take temperature dependence into account during simulation, set the Parameterization parameters to Model temperature dependence.
The surface potential equation model accounts for the effect of temperature on capacitive characteristics and also simulates the temperature dependence of the static behaviour of the transistor during the simulation.
The Measurement temperature parameter defines the temperature , at which some parameters of the device are set. Parameters in Temperature Dependence section set the simulation temperature and temperature dependence coefficients for other device parameters.
Thermal port
The unit has an optional thermal port hidden by default. To use the H thermal port, select the Enable thermal port checkbox.
Use the thermal port to simulate the effects of generated heat and unit temperature.
MOSFET gain . This parameter primarily determines the linear area on the characteristic -.
Units
A/V^2
Default value
18.0 A/V^2
Program usage name
reference_gain
Evaluatable
Yes
#Flatband voltage —
flat zone voltage
V | uV | mV | kV | MV
Details
Flat zone voltage determines the gate offset that must be applied to achieve a flat zone state on the silicon surface. You can use this parameter to arbitrarily shift the threshold voltage due to differences in the output of the materials, as well as due to trapped charges at the interface or oxide. However, in practice, it is usually recommended to first change the threshold voltage using the Body factor and Surface potential at strong inversion parameters, and use this parameter only for fine tuning.
Value in the drain current equation. Use this parameter in cases where good compliance with the linear mode results in too much saturation current. Increasing the value of this parameter leads to a decrease in the saturation current. For high-voltage devices, it often happens that good compliance with the linear mode leads to too low saturation current. In this case, the gain and ohmic resistance of the drain should be increased.
Ratio , which is the multiplier of the logarithmic term in the equation for . This parameter describes the beginning of the channel length modulation. For the characteristics of a device that exhibits positive saturation conductivity, increase the parameter value to match this behavior. The default value is 0, which means the channel length modulation is disabled.
Default value
0.0
Program usage name
modulation_factor
Evaluatable
Yes
#Channel-length modulation voltage —
channel length modulation voltage
V | uV | mV | kV | MV
Details
Voltage in the equation for . This parameter controls the drain voltage at which channel length modulation begins to operate.
The power of reducing mobility. Mobility is equal to , where — mobility in weak fields without the influence of surface scattering. Coefficient of reduction of mobility defined as , where — the scattering coefficient of surface roughness, and is the voltage that corresponds to the effective vertical component of the electric field strength in the channel . For high vertical electric fields, the electron mobility is approximately proportional to .
Units
1/V | 1/MV | 1/kV | 1/mV
Default value
0.0 1/V
Program usage name
reference_surface_roughness_factor
Evaluatable
Yes
#Linear-to-saturation transition coefficient —
linear region-saturation transition coefficient
Details
This coefficient characterizes the smooth transition of the MOSFET characteristic from the linear region to saturation, especially if speed saturation is enabled. This parameter can usually be left at the default value, but you can use it to fine-tune the bending characteristic. -. The expected range of values for this parameter is from 2 before 8.
Default value
8.0
Program usage name
linear_to_saturation_transition_coefficient
Evaluatable
Yes
#Measurement temperature —
Measurement temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Details
Temperature , at which the block parameters are measured. If the value of the Device simulation temperature parameter differs from this value, the device parameters will be determined according to the simulation temperature and the reference temperature.
The source resistance of the transistor, that is, the series resistance associated with the source contact. The value must be greater than or equal to 0.
The drain resistance of the transistor, that is, the series resistance associated with the drain contact. The value must be greater than or equal to 0.
Fixed linear capacity associated with the gate-drain junction.
Units
F | pF | nF | uF | mF
Default value
14.0 pF
Program usage name
C_gd_overlap
Evaluatable
Yes
Body Diode
#Reverse saturation current —
reverse saturation current
A | pA | nA | uA | mA | kA | MA
Details
Current in the equations for the built-in diode.
Set this parameter to a non-zero value to simulate the passage of current through the built-in diode, for applications where the MOSFET current changes sign during simulation, for example, when the MOSFET drives an inductive load.
For applications where the MOSFET current never changes sign, such as in a small-signal amplifier, set this parameter to 0 to increase the simulation speed.
Units
A | pA | nA | uA | mA | kA | MA
Default value
5.2e-13 A
Program usage name
I_sat_reference
Evaluatable
Yes
#Built-in voltage —
voltage of the built-in diode
V | uV | mV | kV | MV
Details
Voltage of the built-in diode in the equations for the built-in diode. This voltage only affects the junction capacitance equation. It does not affect the conduction current.
The coefficient of ideality in the equations for the built-in diode.
Default value
1.0
Program usage name
ideality_factor
Evaluatable
Yes
#Zero-bias junction capacitance —
transition capacity at zero offset
F | pF | nF | uF | mF
Details
The capacitance between the drain and the substrate at zero bias, due only to the built-in diode, in the equations for the built-in diode.
Units
F | pF | nF | uF | mF
Default value
480.0 pF
Program usage name
C_j0
Evaluatable
Yes
#Transit time —
Transit time
s | ns | us | ms | min | hr | d
Details
Time in the equations for the built-in diode.
If the values of the Reverse saturation current and Transit time parameters are non-zero, then the block enables reverse recovery to the built-in diode model.
Units
s | ns | us | ms | min | hr | d
Default value
50e-9 s
Program usage name
transit_time
Evaluatable
Yes
Temperature Dependence
#Parameterization —
parameterization of temperature dependence
None - Simulate at parameter measurement temperature | Model temperature dependence
Details
Choose one of the following methods for parameterizing the temperature dependence:
None - Simulate at parameter measurement temperature — the temperature dependence is not modeled. This is the default method.
Model temperature dependence — simulation of temperature-dependent effects. Specify the temperature value of the device simulation and the coefficients of temperature dependence for other block parameters.
Values
None - Simulate at parameter measurement temperature | Model temperature dependence
Default value
None - Simulate at parameter measurement temperature
Program usage name
enable_temperature_dependence
Evaluatable
No
#Gain temperature exponent —
an indicator of the degree of temperature dependence of the gain coefficient
Details
It is assumed that the gain of the MOSFET exponentially depends on temperature: , where — this is the value of the Gain parameter, and — the value of the Gain temperature exponent parameter.
Dependencies
To use this parameter, set the Parameterization parameter to Model temperature dependence.
Default value
1.3
Program usage name
gain_temperature_exponent
Evaluatable
Yes
#Flatband voltage temperature coefficient —
coefficient in the temperature dependence of the voltage of the flat zone
V/K
Details
It is assumed that the voltage of the flat zone linearly dependent on temperature: , where — this is the value of the Flatband voltage parameter, and — this is the value of the Flatband voltage temperature coefficient parameter.
Dependencies
To use this parameter, set the Parameterization parameter to Model temperature dependence.
Units
V/K
Default value
5e-4 V/K
Program usage name
flatband_voltage_temperature_coefficient
Evaluatable
Yes
#Surface potential at strong inversion temperature coefficient —
coefficient in the temperature dependence of the surface potential under strong inversion
V/K
Details
It is assumed that the surface potential under strong inversion linearly dependent on temperature: , where — this is the value of the Surface potential at strong inversion parameter, and — this is the value of the Surface potential at strong inversion temperature coefficient parameter.
Dependencies
To use this parameter, set the Parameterization parameter to Model temperature dependence.
#Velocity saturation temperature exponent —
an indicator of the degree of temperature dependence of saturation velocity
Details
It is assumed that the saturation of the speed exponentially depends on temperature: , where — this is the value of the Velocity saturation factor parameter, and — the value of the Velocity saturation temperature exponent parameter.
Dependencies
To use this parameter, set the Parameterization parameter to Model temperature dependence.
Default value
1.04
Program usage name
velocity_saturation_temperature_exponent
Evaluatable
Yes
#Surface roughness scattering temperature exponent —
an indicator of the degree of temperature dependence of the scattering coefficient of surface roughness
Details
This parameter leads to a temperature-dependent decrease in the conductivity of the MOSFET at high gate voltage.
It is assumed that the scattering coefficient of the surface roughness exponentially depends on temperature: , where — this is the value of the Surface roughness scattering factor parameter, and — the value of the Surface roughness scattering temperature exponent parameter.
Dependencies
To use this parameter, set the Parameterization parameter to Model temperature dependence.
Default value
0.65
Program usage name
surface_roughness_temperature_exponent
Evaluatable
Yes
#Resistance temperature exponent —
an indicator of the degree of temperature dependence of resistance
Details
It is assumed that the series resistances correspond to semiconductor resistances. Therefore, they decrease exponentially with increasing temperature.: , where — This is , or for the resistance of the source, drain or gate, respectively, is the value of the corresponding parameter Source ohmic resistance, Drain ohmic resistance or Gate ohmic resistance, and — the value of the Resistance temperature exponent parameter.
Dependencies
To use this parameter, set the Parameterization parameter to Model temperature dependence.
Default value
0.95
Program usage name
resistance_temperature_exponent
Evaluatable
Yes
#Body diode reverse saturation current temperature exponent —
an indicator of the degree of temperature dependence of the reverse saturation current
Details
It is assumed that the reverse saturation current for the built-in diode is proportional to the square of the concentration of its own carriers.: , where is the temperature—dependent effective density of states, and is the temperature—dependent band gap for a semiconductor material. In order not to introduce another parameter for the temperature dependence, the block neglects the temperature dependence of the band gap width and uses the silicon band gap at 300 K (1.12 eV) for all types of devices. Thus, the temperature dependence of the reverse saturation current is determined as follows:
where — the value of the parameter Reverse saturation current, — Boltzmann constant, — the value of the Body diode reverse saturation current temperature exponent parameter. The default value is 3 because for silicon, approximately proportionally . It is possible to take into account the temperature dependence of the band gap width by adjusting the value .
Dependencies
To use this parameter, set the Parameterization parameter to Model temperature dependence.
Default value
3.0
Program usage name
reverse_saturation_current_temperature_exponent
Evaluatable
Yes
#Device simulation temperature —
Device simulation temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Details
Temperature , for which the device is being modeled.
Dependencies
To use this parameter, set the Parameterization parameter to Model temperature dependence.
To enable the simulation of thermal effects, select the checkbox for this option.
Default value
false (switched off)
Program usage name
has_thermal_port
Evaluatable
No
#Thermal network —
choosing an internal thermal model
Specify junction and case thermal parameters | Cauer model | Cauer model parameterized with Foster coefficients | External
Details
Choose an internal thermal model:
Specify junction and case thermal parameters;
Cauer model;
Cauer model parameterized with Foster coefficients;
External.
Values
Specify junction and case thermal parameters | Cauer model | Cauer model parameterized with Foster coefficients | External
Default value
Specify junction and case thermal parameters
Program usage name
thermal_network_parameterization
Evaluatable
No
#Junction-case and case-ambient (or case-heatsink) thermal resistances, [R_JC R_CA] —
the vector of thermal resistances
K/W
Details
Vector [R_JC, R_CA] of the two values of thermal resistance. The first value R_JC — this is the thermal resistance between the junction and the housing. The second value, R_CA — this is the thermal resistance between the H port and the device body.
Dependencies
To use this parameter, set the Thermal network parameter to Specify junction and case thermal parameters.
Units
K/W
Default value
[0.0, 10.0] K/W
Program usage name
thermal_resistance_vector
Evaluatable
Yes
#Thermal resistances, [R1 R2 ... Rn] —
the vector of thermal resistances for the Kauer model
K/W
Details
Vector from the values of the thermal resistances represented by the Kauer elements in the heating network. All these values must be greater than zero.
Dependencies
To use this parameter, set the Thermal network parameter to Cauer model.
Units
K/W
Default value
[1.0, 3.0, 10.0] K/W
Program usage name
thermal_resistance_cauer_vector
Evaluatable
Yes
#Thermal resistances, [R1 R2 ... Rn] —
the vector of thermal resistances for the Foster model
K/W
Details
Vector from the values of thermal resistances represented by the coefficients of the Foster model in the heating network. All these values must be greater than zero.
Dependencies
To use this parameter, set the Thermal network parameter to Cauer model parameterized with Foster coefficients.
Units
K/W
Default value
[4.0, 6.0] K/W
Program usage name
thermal_resistance_foster_vector
Evaluatable
Yes
#Thermal mass parameterization —
parameterization of heat capacity
By thermal time constants | By thermal mass
Details
Choose a method for setting the heat capacity:
By thermal time constants — parameterization of heat capacity in terms of thermal time constants. This value is used by default.
By thermal mass — setting the heat capacity values.
Dependencies
To use this parameter, set the Thermal network parameter to Specify junction and case thermal parameters, Cauer model or Cauer model parameterized with Foster coefficients.
Values
By thermal time constants | By thermal mass
Default value
By thermal time constants
Program usage name
thermal_mass_parameterization
Evaluatable
No
#Junction and case thermal masses, [M_J M_C] —
vector of heat capacity values for the Kauer model
J/K | kJ/K
Details
Vector [M_J, M_C] of the two values of the heat capacity. The first value M_J — this is the heat capacity of the transition. The second value, M_C — this is the heat capacity of the case.
Dependencies
To use this parameter, set the Thermal network parameter to Specify junction and case thermal parameters, and for the parameter Thermal mass parameterization the value By thermal mass.
Units
J/K | kJ/K
Default value
[0.0, 1.0] J/K
Program usage name
thermal_mass_vector
Evaluatable
Yes
#Thermal masses, [M1 M2 ... Mn] —
vector of heat capacity values for the Kauer model
J/K | kJ/K
Details
Vector from values of heat capacities, where this is the number of coefficients of the Kauer model in the heat network. All these values must be greater than zero.
Dependencies
To use this parameter, set the Thermal network parameter to Cauer model, and for the parameter Thermal mass parameterization the value By thermal mass.
Units
J/K | kJ/K
Default value
[0.1, 0.3, 1.0] J/K
Program usage name
thermal_mass_cauer_vector
Evaluatable
Yes
#Thermal masses, [M1 M2 ... Mn] —
the vector of heat capacity values for the Foster model
J/K | kJ/K
Details
Vector from values of heat capacities, where this is the number of Foster elements in the heating network. All these values must be greater than zero.
Dependencies
To use this parameter, set the Thermal network parameter to Cauer model parameterized with Foster coefficients, and for the parameter Thermal mass parameterization the value By thermal mass.
Units
J/K | kJ/K
Default value
[1.5, 3.0] J/K
Program usage name
thermal_mass_foster_vector
Evaluatable
Yes
#Junction and case thermal time constants, [t_J t_C] —
vector of thermal time constants
s | ns | us | ms | min | hr | d
Details
Vector [t_J, t_C] of the two values of the thermal time constants. The first value t_J — this is the thermal constant of the transition time. The second value, t_C — this is the thermal time constant of the hull.
Dependencies
To use this parameter, set the Thermal network parameter to Specify junction and case thermal parameters, and for the parameter Thermal mass parameterization the value By thermal time constants.
Units
s | ns | us | ms | min | hr | d
Default value
[0.0, 10.0] s
Program usage name
thermal_time_constant_vector
Evaluatable
Yes
#Thermal time constants, [t1 t2 ... tn] —
vector of thermal time constants for the Kauer model
s | ns | us | ms | min | hr | d
Details
Vector from values of thermal time constants, where this is the number of Kauer elements in the heating network. All these values must be greater than zero.
The value of the heat capacity is calculated as , where , and — heat capacity, thermal time constant and thermal resistance for - the go element of the Cowera.
Dependencies
To use this parameter, set the Thermal network parameter to Cauer model, and for the parameter Thermal mass parameterization the value By thermal time constants.
Units
s | ns | us | ms | min | hr | d
Default value
[1.0, 3.0, 10.0] s
Program usage name
thermal_time_constant_cauer_vector
Evaluatable
Yes
#Thermal time constants, [t1 t2 ... tn] —
the vector of thermal time constants for the Foster model
s | ns | us | ms | min | hr | d
Details
Vector from values of thermal time constants, where this is the number of coefficients of the Foster model in the heating network. All these values must be greater than zero.
The value of the heat capacity is calculated as , where , and — heat capacity, thermal time constant and thermal resistance for - the go element of the Cowera.
Dependencies
To use this parameter, set the Thermal network parameter to Cauer model parameterized with Foster coefficients, and for the parameter Thermal mass parameterization the value By thermal time constants.
Units
s | ns | us | ms | min | hr | d
Default value
[6.0, 18.0] s
Program usage name
thermal_time_constant_foster_vector
Evaluatable
Yes
#Junction and case initial temperatures, [T_J T_C] —
vector of initial temperatures
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Details
Vector [T_J, T_C] of the two temperature values. The first value T_J — this is the initial temperature of the transition. The second value, T_C — this is the initial temperature of the case.
Dependencies
To use this parameter, set the Thermal network parameter to Specify junction and case thermal parameters.
[1] Gildenblat, G., et al. "Introduction to PSP MOSFET model." Proc. the MSM 2005 Int. Conf., Nanotech 2005. 2005.
[2] Van Langevelde, R., A. J. Scholten, and D. B. M. M. Klaassen. "Physical Background of MOS Model 11. Level 1101." Nat.Lab. Unclassified Report 2003/00239. April 2003.
[3] Oh, S-Y., D. E. Ward, and R. W. Dutton. "Transient analysis of MOS transistors." IEEE J. Solid State Circuits. SC-15, pp. 636-643, 1980.