With the advent of ever increasing operation frequencies, Silvaco is introducing a new high frequency model for MOSFETs that will be implemented into the SmartSpice code. This article describing these new models will be in two parts. The first part describes the mathematical detail concerning the extraction of the "Y" parameters that contain the necessary frequency terms and part two, in the July issue, describes the conversion of the "Y" parameters into the required elements for the Spice model itself.

Figure 1. The proposed common-source equivalent circuit of
a MOSFET after de-embedding parasitics of on-wafer pads and
interconnection lines. Four independent intrinsic capacitances
Cgs, Cgd, Cdg, and Cds are needed for charge
conservation. The definitions of each capacitance are also shown.

When extracting frequency dependent parameters for high frequency MOSFETs and other active devices from measured data, it is important to isolate the elements that are due to the device alone, from the "parasitics" that are inevitably present from bonding pads, packaging and the like. To this end, the user has to have two types of structure. One structure type contains all the active elements and the other structure type consists of identical bond pads and packaging but without the active devices. By measuring both types of structure, the frequency dependent parameters of the active device can be isolated by subtracting the effects of the package without the active devices. This procedure is called "de-embedding. The following article describes the method for extracting an accurate high frequency Spice model from just such measured data.

1.1 Parameter Extraction Requirement
Measured S-parameters of MOSFET devices and S-parameters of de-embedding patterns (open, short) are needed to extract small signal parameters of RF MOSFET. De-embedding patterns are used to de-embed parasitics of pad and interconnection line. Gate is port 1 and drain is port 2. Source and body are grounded. The characteristic impedance is 50 Ohm.

The data is stored in standard sequential ASCII files. One line of data is a set of data for one frequency and, for example, can be written as

Frequency Mag(S11) Phase(S11) Mag(S21)
Phase(S21) Mag(S12)
Phase(S12) Mag(S22) Phase(S22)

In an S-Parameter file, a typical line might be

500 0.64 -23 12.5 98 0.03 70 0.8 -37

In this case, 500 is the frequency in megahertz. The magnitudes of S11, S21, S12 and S22 are 0.64, 12.5, 0.03 and 0.8, and the phases are -23, 98, 70 and -37 degrees, respectively.

S-parameter of devices will have to be measured under DC bias condition of Vgs, Vds. One routine of extraction procedure extracts small-signal parameters under one DC bias condition of Vgs, Vds. De-embedding patterns (open, short) are measured under zero DC bias condition of Vgs = 0 V, Vds = 0 V.

The symbol definitions for the de-embedding procedure are listed in Table 1.

Table 1. The symbol definitions for the de-embedding procedure.

1.2 S-parameter Measurement
(1) S-parameters of MOSFET device are represented as

The magnitudes and the phases of S11D, S21D, S12D and S22D are converted to real and imaginary format.

Then, S11D, S21D, S12D and S22D are represented as real and imaginary format as following.

(2) S-parameters of open de-embedding pattern are represented by

The magnitudes and the phases of S11O, S21O, S12O and S22O are converted to real and imaginary format.

Then, S11O, S21O, S12O and S22O are represented as real and imaginary format as following.

(3) Measured S-parameters of short de-embedding pattern are represented by

The magnitudes and the phases of S11S, S21S, S12S and S22S are converted to real and imaginary format.

Then, S11S, S21S, S12S and S22S are represented as real and imaginary format as following.

1.3 De-embedding Procedure
(1) Measured S-parameters of MOSFET device are converted to Y-parameters. (([SD]

[YD] ) )

Then, MOSFET device Y-parameters are represented as real and imaginary parts.

(2) Measured S-parameters of open de-embedding pattern are converted to Y-parameters. ([S0]

[Y0])

Then, open pattern Y-parameters are represented as real and imaginary parts.

(3) Subtract open pattern Y-parameters from MOSFET device Y-parameters. ([YDO] = [YD] - [YO] )

If only open de-embedding pattern is used without using short-pattern, following (4)-(9) procedures are omitted. In this case, Y11DO, Y21DO, Y12D0, Y22DO are used for parameter extraction.

(4) Measured S-parameters of short de-embedding pattern are converted to Y-parameters. ([SS]

[YS] )

Then, short pattern Y-parameters are represented as real and imaginary parts.

(5) Subtract open pattern Y-parameters from short pattern Y-parameters. ([YSO] = [YS] - [YO] )

(6) ([YSO]

[ZSO] )

(7) ([YDO]

[ZDO] )

(8) ([ZF] = [ZDO] - [ZSO] )

(9) ([ZF]

[YF] )

De-embedding procedure using open and short de-embedding pattern is finished.

Note that, Y11F, Y21F, Y12F, Y22F are used in the following parameter extraction procedure and Y-parameters in the extraction equation is same as Y11F, Y21F, Y12F, Y22F . (i.e. [Y] = [YF] )

If only open pattern is used, Y11DO, Y21DO, Y12DO, Y22DO are used instead of Y11F, Y21F, Y12F, Y22F. (i.e. [Y] = [YDO] )

For the parameter extraction, Y-parameters are represented as real and imaginary format as follows.

Conclusion

This concludes the extraction of the "Y" parameters that are required for generating the equivilent circuit elements in the high frequency Spice model for MOSFETs. In the July issue, the conversion of the de-embedded "Y"parameters into the frequency dependent circuit elements is described.