functionMOSeq3

Computation of injected drain-source current for Level=3

Information

This function implements a Spice-style Level-3 model of the current flowing between drain and source of a MOSFET. It is is an empirical model that computes the current in its linear, saturation, and weak inversion regions. Various channel modulation effects are also considered.

The model offers a compromise between the much more sophisticated Level-2 model that, however, simulates very slowly, and the often too simple Level-1 model that doesn't allow many questions to be answered, such as what is the highest possible switching frequency reachable, how much power is being dissipated at high frequency operation, what is the amount of substrate cross-talk, etc.

The model comments the equations by providing the corresponding equation numbers from [1].


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)

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

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

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

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

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

 LD:      Lateral diffusion (default value = 0 m)

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

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

 VMAX:    Maximum drift velocity of carriers (default value = 0 m/s)

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

 KAPPA:   Saturation field factor (default value = 0.2)

 ETA:     Static feedback on threshold voltage (default value = 0)

 THETA:   Mobility modulation (default value = 0 1/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)

 vpof:    Pinch-off voltage (Volt)


References:

  1. 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)
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
RealCOXSpecific capacitance of SiO2
RealNFSSurface fast state density
Modelica.SIunits.LengthXJMetallurgical junction depth
Modelica.SIunits.LengthLEffective hannel length
Modelica.SIunits.LengthWEffective channel width
Modelica.SIunits.LengthLDLateral diffusion
RealXDDepletion factor
RealU0Surface mobility at reference temperature
Modelica.SIunits.VelocityVMAXMaximum drift velocity of carriers
RealDELTAWidth effect on threshold voltage
RealKAPPASaturation field factor
RealETAStatic feedback on threshold voltage
Modelica.SIunits.InversePotentialTHETAMobility modulation
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.VoltagevpofPinch-off voltage