Chapter 3 Characterizing RF MOSFET’s by Four-Port Measurement
4.2 Small-Signal Equivalent Circuits of RF MOSFET’s
In most of the commercially available circuit simulators, MOS transistor models have been originally developed for digital and low frequency analog circuit design [26]-[27], which focus on the DC drain current, conductance, and intrinsic charge/capacitance behavior up to the megahertz range. However, as the operation frequency increases to the gigahertz range, the importance of the extrinsic components rivals that of the intrinsic counter-part. Therefore, a RF model with the consideration of the HF behavior of both intrinsic and extrinsic components in MOSFET’s is important to achieve accurate and predictive results in simulation of a designed circuit. Compared with the MOSFET models for both digital and analog application at low frequency, compact models for high-frequency applications are more difficult to develop due to the additional requirements of bias dependence and geometry scaling of the parasitic components as well as the requirements of accurate prediction of the distortion and noise behavior. A common modeling approach for RF applications is to build sub-circuits based on the intrinsic MOSFET that has been modeled well for analog application [28]-[31]. The accuracy of such model depends on how to establish sub-circuits with the correct understanding of the device physics in high-frequency operation, how to model the
high-frequency behavior of intrinsic devices and extrinsic parasitics, and how to extract parameters appropriately for the elements of the sub-circuits. Since scattering-parameter measurement is the only practical method, and also the measurement method adopted in this study, to characterize the high-frequency performance of devices, circuits, and systems. Thus a RF model and its parameter extraction scheme had better be based on a small-signal model because the scattering-parameter measurement is a small-signal measurement.
Figure 4.1 shows the cross-sectional structure of a four-terminal MOSFET. It can be divided to intrinsic part and extrinsic part. The extrinsic part consists of all the parasitic components, such as the gate resistance RG, gate/source overlap capacitance CGSO, gate/drain overlap capacitance CGDO, gate/bulk overlap capacitance CGBO, source series resistance RS, drain serious resistance RD, source/bulk junction diode DSB, drain bulk junction diode DDB, and substrate resistances RSB, RDB, and RDSB. The intrinsic part is the core of the device without including those parasitics. Even though it is desirable to design and fabricate MOSFETs without these parasitics, they cannot be avoided in reality. Some of them may not be noticeable in DC and low frequency operation. However, they will influence the device performance significantly at high frequency. Equivalent circuits have been an effective approach to analyze the electrical behavior of a device by representing the above components.
Figure 4.2 shows the proposed small signal equivalent circuit of the four-terminal RF MOSFET including the intrinsic and extrinsic part. The RG, RS, RD, RSB, RDB, and RSDB are correspondent to the components shown in Fig.4.1. The CGS including the intrinsic capacitance CGSI not shown in Fig.4.1 and the extrinsic gate/source overlap capacitance CGSO. It can be expressed as Eq.4-1.
GS GSI GSO
C =C +C (4-1)
Similarly, the CGD includes the intrinsic and extrinsic parts and can be expressed as Eq.4-2.
GS GSI GSO
C =C +C (4-2)
and drain/bulk junctions. In addition to the CDB and CSB, there exist two capacitance components, CSBE, CDBE between source/bulk and drain/bulk which are not arisen from the junction capacitances but caused by metal connections or other parasitic capacitances between source/bulk and drain/bulk. Between gate and bulk, there exists an overlap capacitance, CGBE, which is caused by the metal connections and independent of bias condition. In addition to CGBE, there is also a capacitance arisen from the gate oxide and will be in-series with a resistance substrate component, RGB.
The four voltage-controlled current source can be expressed as:
(
The gm, gmb, and gds are the transconductance, bulk transconductance, and channel conductance of the device respectively. Cm is the transcapacitance between the gate and drain terminal. Cmb is the transcapacitance between the drain and body terminal. Cmgb is the transcapacitance between the gate and body terminal. These transcapacitances can be expressed as Eq.4-7, Eq.4-8, and Eq.4-9.
m DGi GDi
These transcapacitances arise from the operation of the MOSFET. For example, if a small-signal voltage is applied at the drain, the resulting small-signal current entering the gate will be −CGD(dvd dt) . CGD actually represent the effect of drain terminal on gate terminal.
However, although the capacitance CGD is connected between gate and drain, it does not
model the total effect of gate on drain. Since if a small-signal voltage is applied at the gate, the amount of charge in the inversion layer will be changed, which will also change the small-signal drain current. The small-signal current entering the drain indeed is
( ) ( )
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].