functionMOSeq2

Computation of injected drain-source current for Level=2

Information

This function implements a Spice-style Level-2 model of the current flowing between drain and source of a MOSFET. It is one of the most complex models currently available that computes the current in its linear, saturation, and subthreshold regions. Various channel modulation effects are also considered. The saturation voltage is computed either in accordance with the Grove-Frohman model [1,2] or using Baum's theory of scattering velocity saturation [3].

The model simulates very slowly, and is probably not useful except for simulating across a single switching event.

The model comments the equations by providing the corresponding equation numbers from [4].


Input variables:

 vds:     Drain-source voltage (Volt)

 vgs:     Gate-source voltage (Volt)

 vbs:     Bulk-source voltage (Volt)

 Tdev:    Device temperature (K)

 sig:     Indicator of operating mode
            sig = +1:  direct mode
            sig = -1:  reverse mode (source and drain are flipped)


Input parameters:

 Type:    Type of MOSFET (default value = 1)
            Type = +1:  NMOS
            Type = -1:  PMOS

 Tnom:    Reference temperature (default value = 300.15 K)

 VFB:     Flat band voltage at reference temperature (default value = 0 Volt)

 KP:      Transconductance parameter at reference temperature (default value = 0 Amp/Volt2)

 GAMMA:   Body-effect parameter (default value = 0 Volt0.5)

 PHI:     Surface inversion potential at reference temperature (default value = 0 Volt)

 LAMBDA:  Channel length modulation  (default value = 0 1/Volt)

 COX:     Specific capacitance of SiO2 (default value = 0 F/m2)

 NFS:     Surface fast state density (default value = 0 1/m2)

 NEFF:    Total channel charge coefficient (default value = 1)

 XJ:      Metallurgical junction depth (default value = 0 m)

 L:       Channel length (default value = 1e-4 m)

 W:       Channel width (default value = 1e-4 m)

 XD:      Depletion factor (default value = 0 m/Volt0.5)

 U0:      Surface mobility at reference temperature (default value = 0 m2/(V*s))

 UEXP:    Exponential coefficient for mobility (default value = 0)

 UTRA:    Transverse field coefficient (default value = 0)

 VMAX:    Maximum drift velocity of carriers (default value = 0 m/s)
            VMAX = 0: Frohman-Grove model of drain current computation
            VMAX > 0: Baum-Beneking model of drain current computation

 ECRIT:   Critical electric field for pinch-off (default value = 0 V/m)

 DELTA:   Width effect on threshold voltage (default value = 0)

 VBP:     Gate to channel critical voltage (default value = 0 Volt)

 PB:      Built-in potential at reference temperature (default value = 0.8 Volt)

 EG:      Energy gap for temperature effect on saturation current at 0 K (default value = 1.11 Volt)

 EMin:    if x < EMin, the exp(x) function is linearized (default value = -100) Levels 1-3

 EMax:    if x > EMax, the exp(x) function is linearized (default value = 40) Levels 1-3


Output variables:

 isd0:    Drain-source current (Amp)

 Vfb:     Flat band voltage at device temperature (Volt)

 Vth:     Threshold voltage (Volt)

 vdsat:   Saturation voltage (Volt)

 vdsat1:  Adjusted saturation voltage (Volt)

 vpof:    Pinch-off voltage (Volt)


References:

  1. Frohman-Bentchkowsky, D. (1968), "On the Effect of Mobility Variation on MOS Device Characteristics," Proc. IEEE, 56, pp.217-218.
  2. Frohman-Bentchkowsky, D. and A.S. Grove (1969), "Conductance of MOS Transistors in Saturation," IEEE Trans. Electron Devices, ED-16, pp. 108-113.
  3. Baum, G. and H. Beneking (1970), "Drift Velocity Saturation in MOS Transistors," IEEE Trans. Electron Devices, ED-17, pp. 481-482.
  4. Massobrio, G. and P. Antognetti (1993), Semiconductor Device Modeling with Spice, 2nd edition, McGraw Hill, New York.

Inputs

TypeNameDefaultDescription
Modelica.SIunits.VoltagevdsDrain-source voltage
Modelica.SIunits.VoltagevgsGate-source voltage
Modelica.SIunits.VoltagevbsBulk-source voltage
Modelica.SIunits.TemperatureTdevDevice temperature
Realsigsign(vds)
IntegerLevel2Level of MOS model
IntegerTypeType=1 for NMOS; Type=-1 for PMOS
Modelica.SIunits.TemperatureTnomReference temperature
Modelica.SIunits.VoltageVFBFlat band voltage at reference temperature
Modelica.SIunits.TransconductanceKPTransconductance parameter at reference temperature
RealGAMMABody-effect parameter
Modelica.SIunits.VoltagePHISurface inversion potential at reference temperature
Modelica.SIunits.InversePotentialLAMBDAChannel length modulation
RealCOXSpecific capacitance of SiO2
RealNFSSurface fast state density
RealNEFFTotal channel charge coefficient
Modelica.SIunits.LengthXJMetallurgical junction depth
Modelica.SIunits.LengthLEffective hannel length
Modelica.SIunits.LengthWEffective channel width
RealXDDepletion factor
RealU0Surface mobility at reference temperature
RealUEXPExponential coefficient for mobility
RealUTRATransverse field coefficient
Modelica.SIunits.VelocityVMAXMaximum drift velocity of carriers
Modelica.SIunits.ElectricFieldStrengthECRITCritical electric field for pinch-off
RealDELTAWidth effect on threshold voltage
Modelica.SIunits.VoltageVBPGate to channel critical voltage
Modelica.SIunits.VoltagePBBuilt-in potential at reference temperature
Modelica.SIunits.VoltageEGEnergy gap for temperature effect on saturation current at 0 K
RealEMinif x < EMin, the exp(x) function is linearized
RealEMaxif x > EMax, the exp(x) function is linearized

Outputs

TypeNameDefaultDescription
Modelica.SIunits.Currentids0Injected drain-source current
Modelica.SIunits.VoltageVfbEffective flat band voltage at device temperature
Modelica.SIunits.VoltageVthThreshold voltage
Modelica.SIunits.VoltagevdsatSaturation voltage
Modelica.SIunits.Voltagevdsat1Adjusted saturation voltage
Modelica.SIunits.VoltagevpofPinch-off voltage