Next: 3.3 Determination of Capacitances
by Quasi Static Approximation Up: 3 Measurement
and Parameter Extraction Previous: 3.1
DC and RF Measurements
3.2 Small Signal Equivalent Circuit
Parameter Extraction
The HEMT can be described by an equivalent circuit model shown in
Figure
3.1. To extract the model parameters from measured Sparameters
a value for each parameter of the model is assumed and Sparameters
are calculated based on the equivalent circuit. The chosen values are then
optimized by minimizing the differences between the calculated and the
measured Sparameters.
Figure 3.1 Equivalent circuit model for parameter
extraction. It includes the intrinsic device, the series resitances to
all three terminals as well as the parasitic capacitances and inductances
of the contacting network.
The transit frequencies f_{T} and f_{max}
can be traced back to equivalent circuit parameters. From the intrinsic
device the well known approximation for the current gain cutoff frequency
f_{T} can be derived as
. 
(10)

Extrinsic values of g_{m} and C_{GS}
can be calculated by g_{m} = g_{mi} /(1+g_{mi}R_{s})
and C_{GS} = C_{GSi} (1+g_{m}R_{s}).
In the active bias region of a HEMT (V_{DS} > 0.5 V and
V_{GS} > V_{T}) C_{GDi} is
only about 15 % of C_{GSi}. Therefore f_{T}
can also be approximated using the extrinsic g_{m} and the
extrinsic total gate capacitance C_{G} = C_{GS} + C_{GDi}
in (10).
According to [37,
38]
f_{max} can also be approximated with equivalent circuit
parameters by:
. 
(11)

For measuring purposes the devices are embedded in a network of coplanar
lines and contacting pads. These will be not included in the simulation
area as described in Chapter 5. The contacting network
can be neglected in first order for DC measurements but must be taken into
account when simulated and measured RF parameters such as f_{T}
and f_{max} are compared. Thus, the parasitic elements L_{G},
L_{D}, L_{S}, C_{PG} and C_{PD}
have to be included in the equivalent circuit model.
Based on the equivalent circuit the parameters can be extracted from
measured Sparameters. In the extraction procedure it is difficult
to distinguish between the parasitic pad capacitances C_{PG}
and C_{PD} and the gate source capacitance C_{GS}
because they are connected in parallel and therefore only their sum can
be determined reliably. In first order C_{PG} and C_{PD}
are the only capacitances which do not scale with the gate width L_{w}.
This can be used to extract these values in a different way.
The measured value of f_{T} includes all capacitances.
The total capacitance can be determined rearranging (10)
to
. 
(12)

As g_{m}, C_{GS} and C_{GD}
scale linearly with L_{w} and both C_{PG}
and C_{PD} are constant for all the devices the sum C_{PG}
+ C_{PD} can be determined by extrapolating C_{tot}
to L_{w} = 0. The calculated C_{tot} using
measured g_{m} and f_{T} for different bias
points is shown in Figure
3.2. The intercept for all linear fits is very close to about 25fF.
This value is used for parameter extraction of all measured devices. More
details of this deembedding procedure are described in [39].
Figure 3.2 Total capacitance of HEMTs versus gate
width at V_{DS}=2.0V. The capacitances are calculated using
(12) with measured g_{m}
and f_{T} of devices with gate widths L_{w}=
80, 180, 360 µm. For all V_{GS} a linear fit can be
found. The intercept determines the constant part of C_{tot},
i. e. C_{PG} + C_{PG}.
The schematic of the extrinsic device used for simulation is shown in
Figure
2.1 It corresponds to the intrinsic device indicated by the dashed
box in Figure
3.1 and the parasitic resistances R_{S}, R_{G},
and R_{D}. The deembedded device parameters will be the
basis for comparison between measured and simulated data.
Next: 3.3 Determination of Capacitances
by Quasi Static Approximation Up: 3 Measurement
and Parameter Extraction Previous: 3.1
DC and RF Measurements
Helmut Brech
19980311