Chapter 3 Characterizing RF MOSFET’s by Four-Port Measurement
4.3 Parameter Extraction
4.3.1 Extraction of Extrinsic Parasitic Components in the Equivalent circuit
m g GD m g
g v − C +C dv dt . Note that not only is there a conductive current but also a capacitive current different form −CGD(dvd dt). Thus CGD+Cm represent the effect of gate on drain and is different from CGD. Cm is an element models the different effect of the gate and drain on each other in terms of charging currents [32].
4.3 parameter extraction
4.3.1 Extraction of Extrinsic Parasitic Components in the Equivalent circuit of Cold MOSFET’s
The intrinsic part or say the voltage-controlled current sources of a MOSFET will exist only if the device is biased properly. Considering a MOSFET with no DC bias applied, the intrinsic part of the MOSFET will vanish. The remained components in the small-signal equivalent circuit will be the extrinsic part of the device. The equivalent circuit shown in Fig.4.2 then can be simplified by removing the voltage-controlled current sources and becomes the equivalent circuit shown in Fig.4.3. Below a certain operation frequency range, an assumption is given that the values of RS and RD are much smaller than the impedance of CGSO, CGDO, CSBO, CDBO, and CGBO. According to this assumption, RS and RD can be neglected while the test frequency below a certain value. Therefore, the equivalent circuit in Fig.4.3 was further simplified to the circuits in Fig.4.4. The y-parameters of this equivalent circuit can be easily derived according the definition. There will be sixteen y-parameters and nine of them are independent for a four-terminal circuit. However, since this is an equivalent circuit consists of passive
components, it is reciprocal. The transadmittances between any two terminals in both directions will equal to each other. Therefore, only six of the sixteen y-parameters are independent, another ten can be derived from these six y-parameters. Five independent and one dependent y-parameters of the equivalent sown in Fig4.4 were derived as below.
( )
a test voltage source was placed at body terminal, it will be foreseen that the RDSB can be neglected while calculating YDB and YSB since the voltage drop across RDSB is neglected.According to simulation results, it’s also found that the RDSB has minor effect on YBD and YBS. Therefore, it was neglected while deriving the YBD and YBS and the resulting expression are shown in Eq.4-14 and Eq.4-15.
2 2
Equations 4-10 to 4-15 are the exact expression of the six corresponding y-parameters of the equivalent circuit. However, the expanding expression will very complex and enormous to
solve the contained components. Therefore, further simplification is required. At appropriate frequencies, it can be assumed that the higher order terms of ωCxRx are neglected while compared with the constant one and first order terms in these equations. Then the YGG, YSG, YDG can be simplified to Eq.4-17 to Eq.4-19.
According to Eq.4-18 and Eq.4-19, CGSO and CGDO can be expressed as Eq.4-20 and Eq.4-21.
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Substituting Eq.4-18 and Eq.4-19 into Eq.4-17, the CGBO can be derived as Eq.4-22.
[ ] [ ] [ ]
According to Eq.4-17, the gate resistance RG can be approximately derived by dividing the real part of YGG by imaginary part of YGG. According to Eq.4-14, at low frequency range, the imaginary part of YBD is approximated to the sum of ωCDBO and ωCDBE. They could not be separated if no further information provided. It’s also found that the real part of YBD is independent of CDBE but only the function of CDBO and RDB. Therefore, the values of CDBO and RDB can be extracted from the real part of YBD at different frequencies, in theory. The deduction is demonstrated below.
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2 2Re CDBO RDB Y = − ω
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2 2 2 2 2Re YBD +Re YBD ω CDBO RDB +ω CDBO RDB = 0 (4-24) Equation 4-24 corresponds to two different frequencies ω1 and ω1 can be expressed as:
[
1] [
1]
12 2 2 12 2The value of RDB can be obtained by dividing Eq.4-27 to 4-28. Then, substituting RDB to Eq.4-27 or Eq.4-28, the CDBO can also be extracted. Since the sum of CDBO and CDBE is approximately equals to the value of YBD at low frequencies, the CDBE can also be obtained.
Similarly, the CSBO, CSBE and RSB can be extracted by this approach, so do the CGBO, CGBE and RGB.
The expression of RDSB is very complex and difficult to simplify, therefore it cannot be extracted by a compact equation. However, since the value of other components in Fig.4.4 are known, they can be de-embedded out from the measured data and the value of RDSB can be obtained.
According to the data measured from a cold DUT and the simplified equivalent circuit, the method of extracting extrinsic components in Fig.4.4 are deduced. According to some literature [33]-[35], the substrate resistances of a NMOSFET are almost unchanged when negative or low positive gate bias voltage was applied. The CGSO and CGDO are also independent of bias condition. Therefore, they may be used for the small-signal equivalent
circuit of an active NMOSFET. This will be checked later. However, the RG, CDB, CSB, and CGB will influent by the applied voltage, they must be re-extracted for the case of active DUT.
4.3.2 Extraction of Components in the Equivalent Circuit of MOSFET’s in Linear