Subsections

# MOS Field-Effect Transistor

There are four different types of MOS field effect transistors as shown in fig. 10.17 all covered by the model going to be explained here. The First Order Model'' is a physical model with the drain current equations according to Harold Shichman and David A. Hodges [13].

The following table contains the model and device parameters for the MOSFET level 1.

 Name Symbol Description Unit Default Typical Is bulk junction saturation current N bulk junction emission coefficient Vt0 zero-bias threshold voltage Lambda channel-length modulation parameter Kp transconductance coefficient Gamma bulk threshold Phi surface potential Rd drain ohmic resistance Rs source ohmic resistance Rg gate ohmic resistance L channel length Ld lateral diffusion length W channel width Tox oxide thickness Cgso gate-source overlap capacitance per meter of channel width Cgdo gate-drain overlap capacitance per meter of channel width Cgbo gate-bulk overlap capacitance per meter of channel length Cbd zero-bias bulk-drain junction capacitance Cbs zero-bias bulk-source junction capacitance Pb bulk junction potential Mj bulk junction bottom grading coefficient Fc bulk junction forward-bias depletion capacitance coefficient Cjsw zero-bias bulk junction periphery capacitance per meter of junction perimeter Mjsw bulk junction periphery grading coefficient Tt bulk transit time Kf flicker noise coefficient Af flicker noise exponent Ffe flicker noise frequency exponent Nsub substrate (bulk) doping density Nss surface state density Tpg gate material type (0 = alumina, -1 = same as bulk, 1 = opposite to bulk) Uo surface mobility Rsh drain and source diffusion sheet resistance square Nrd number of equivalent drain squares Nrs number of equivalent source squares Cj zero-bias bulk junction bottom capacitance per square meter of junction area Js bulk junction saturation current per square meter of junction area Ad drain diffusion area As source diffusion area Pd drain junction perimeter Ps source junction perimeter Temp device temperature Tnom parameter measurement temperature

## Large signal model

Beforehand some useful abbreviation are made to simplify the DC current equations.

 (10.167) (10.168)

The bias-dependent threshold voltage depends on the bulk-source voltage or the bulk-drain voltage depending on the mode of operation.

 (10.169)

The following equations describe the DC current behaviour of a N-channel MOSFET in normal mode, i.e. , according to Shichman and Hodges.

• cutoff region:

 (10.170) (10.171) (10.172) (10.173) saturation region: (10.174) (10.175) (10.176) (10.177) linear region: (10.178) (10.179) (10.180) (10.181)

with

 (10.182)

In the inverse mode of operation, i.e. , the same equations can be applied with the following modifications. Replace with , with and with . The drain current gets reversed. Furthermore the transconductances alter their controlling nodes, i.e.

 (10.183)

The current equations of the two parasitic diodes at the bulk node and their derivatives write as follows.

 (10.184) (10.185)

with

 (10.186)

With the accompanied DC model shown in fig. 10.19 it is possible to form the MNA matrix and the current vector of the intrinsic MOSFET device.

 (10.187)

 (10.188) (10.189) (10.190)

## Physical model

There are electrical parameters as well as physical and geometry parameters in the set of model parameters for the MOSFETs First Order Model''. Some of the electrical parameters can be derived from the geometry and physical parameters.

The oxide capacitance per square meter of the channel area can be computed as

 (10.191)

Then the overall oxide capacitance can be written as

 (10.192)

The transconductance coefficient can be calculated using

 (10.193)

The surface potential is given by (with temperature voltage )

 (10.194)

Equation (10.194) holds for acceptor concentrations () essentially greater than the donor concentration . The bulk threshold (also sometimes called the body effect coefficient) is

 (10.195)

And finally the zero-bias threshold voltage writes as follows.

 (10.196)

Whereas denotes the flat band voltage consisting of the work function difference between the gate and substrate material and an additional potential due to the oxide surface charge.

 (10.197)

The temperature dependent bandgap potential of silicon (substrate material Si) writes as follows. With the bandgap is approximately .

 (10.198)

The work function difference gets computed dependent on the gate conductor material. This can be either alumina ( ), n-polysilicon ( ) or p-polysilicon ( ). The work function of a semiconductor, which is the energy difference between the vacuum level and the Fermi level (see fig. 10.20), varies with the doping concentration.

 (10.199)

 (10.200)

The expression in eq. (10.199) is visualized in fig. 10.20. The abbreviations denote

 electron affinity of alumina electron affinity of silicon vacuum level conduction band valence band Fermi level intrinsic Fermi level bandgap of silicon at room temperature

Please note that the potential is positive in p-MOS and negative in n-MOS as the following equation reveals.

 (10.201)

When the gate conductor material is a heavily doped polycrystalline silicon (also called polysilicon) then the model assumes that the Fermi level of this semiconductor is the same as the conduction band (for n-poly) or the valence band (for p-poly). In alumina the Fermi level, valence and conduction band all equal the electron affinity.

If the zero-bias bulk junction bottom capacitance per square meter of junction area is not given it can be computed as follows.

 (10.202)

That's it for the physical parameters. The geometry parameters account for the electrical parameters per length, area or volume. Thus the MOS model is scalable.

The diffusion resistances at drain and gate are computed as follows. The sheet resistance refers to the thickness of the diffusion area.

 (10.203)

If the bulk junction saturation current per square meter of the junction area and the drain and source areas are given the according saturation currents are calculated with the following equations.

 (10.204)

If the parameters and are not given the zero-bias depletion capacitances for the bottom and sidewall capacitances are computed as follows.

 (10.205) (10.206) (10.207) (10.208)

## Small signal model

The bulk-drain and bulk-source capacitances in the MOSFET model split into three parts: the junctions depletion capacitance which consists of an area and a sidewall part and the diffusion capacitance.

 (10.209) (10.210) (10.211) (10.212)

The diffusion capacitances of the bulk-drain and bulk-source junctions are determined by the transit time of the minority charges through the junction.

 (10.213) (10.214)

Charge storage in the MOSFET consists of capacitances associated with parasitics and the intrinsic device. Parasitic capacitances consist of three constant overlap capacitances. The intrinsic capacitances consist of the nonlinear thin-oxide capacitance, which is distributed among the gate, drain, source and bulk regions. The MOS gate capacitances, as a nonlinear function of the terminal voltages, are modeled by J.E. Meyer's piece-wise linear model [15].

The bias-dependent gate-oxide capacitances distribute according to the Meyer model [15] as follows.

• cutoff regions:
•  (10.215) (10.216) (10.217) (10.218) (10.219) (10.220) (10.221) (10.222) (10.223)

• saturation region:

 (10.224) (10.225) (10.226) linear region: (10.227) (10.228) (10.229)

with

 (10.230)

In the inverse mode of operation and need to be exchanged, changes its sign, then the above formulas can be applied as well.

The constance overlap capacitances compute as follows.

 (10.231) (10.232) (10.233)

With these definitions it is possible to form the small signal Y-parameter matrix of the intrinsic MOSFET device in an operating point which can be converted into S-parameters.

 (10.234)

with

 (10.235) (10.236) (10.237) (10.238) (10.239) (10.240)

## Noise model

The thermal noise generated by the external resistors , and is characterized by the following spectral density.

 (10.241)

Channel and flicker noise generated by the DC transconductance and current flow from drain to source is characterized by the spectral density

 (10.242)

The noise current correlation matrix (admittance representation) of the intrinsic MOSFET can be expressed as

 (10.243)

This matrix representation can be easily converted to the noise-wave representation if the small signal S-parameter matrix is known.

## Temperature model

Temperature affects some MOS model parameters which are updated according to the new temperature. The reference temperature in the following equations denotes the nominal temperature specified by the MOS transistor model. The temperature dependence of and is determined by

 (10.244) (10.245)

The effect of temperature on and is modeled by

 (10.246)

where the dependency has already been described in section 10.2.4 on page . The temperature dependence of , , and is described by the following relations

 (10.247) (10.248) (10.249) (10.250)

The temperature dependence of is given by the relation

 (10.251)

An analogue dependence holds for .

This document was generated by Stefan Jahn on 2007-12-30 using latex2html.