We examined the scaling effects of a number of gate_fingers (
N
) and gate_widths (
w
) on the highfrequency characteristics of 0.1
μ
m metamorphic highelectronmobility transistors. Functional relationships of the extracted smallsignal parameters with total gate widths (
w_{t}
) of different
N
were proposed. The cutoff frequency (
f_{T}
) showed an almost independent relationship with
w_{t}
; however, the maximum frequency of oscillation (
f_{max}
) exhibited a strong functional relationship of gateresistance (
R_{g}
) influenced by both
N
and
w_{t}
. A greater
w_{t}
produced a higher
f_{max}
; but, to maximize
f_{max}
at a given
w_{t}
, to increase
N
was more efficient than to increase the single gate_width.
Ⅰ. Introduction
Highelectronmobility transistors (HEMTs) have been highlighted as essential highfrequency devices for various stateoftheart microwave or millimeterwave application systems, such as satellite communication, electronic warfare, radiometry, base stations, and smart weapons
[1

3]
. These systems require not only excellent radio frequency (RF) characteristics but also highpower performances for their specific applications
[4]
. The enhancement of power characteristics can be achieved by improving the current level or breakdown voltage of the HEMTs. A variety of methods have been used to increase the power performance of HEMTs these include the GaN/AlGaN material system
[5
,
6]
, the gatefieldplate technique
[7
,
8]
, and the adoption of composite channel systems
[9
,
10]
. Most of these methods have focused on the enhancement of transistor power by increasing the breakdown voltage. These technologies, however, have some drawbacks, such as high cost and difficulty in material growth of the composite channel HEMTs, poor RF characteristics of the GaN HEMTs, and low electron mobility and large increase in the parasitic capacitances of the gatefieldplated HEMTs. As a consequence, in many application achieving a large current level by simply increasing the transistor gate_width (
w
) has been one of the most economic and practical methods in terms of circuit design and device fabrication.
A very long gate width or multifinger gates are effective, but an increase in w gives rise to a large gate resistance (
R_{g}
), thereby causing degradation of noise characteristics
[11]
and the maximum frequency of oscillation (
f_{max}
)
[12]
. Therefore, it preferable to achieve a long effective gate width with no significant increase or even reduction in
R_{g}
. The use of a widehead Tgate was reported
[11]
as an exemplary method for suppressing
R_{g}
; however, this technique has a limit in expanding the gate head because high sourcetodrain channel resistance is unavoidable under increased sourcedrain spacing for accommodating a wide gatehead dimension; consequently, the structural instability of the Tgate increases in this structure. Even though studies
[13

15]
have documented the critical role of
R_{g}
in the highfrequency characteristics of HEMTs based on a smallsignal equivalent circuit model, there has been minimal investigation in reducing
R_{g}
in HEMTs with long gate_ widths or multifinger gates. In this study, we investigated the multifinger structures of the HEMTs affecting
R_{g}
and highfrequency characteristics. Because
R_{g}
is strongly influenced by a number of gate_fingers (
N
) and gate_widths (
w
) of the device structure, we examined the effects of all these parameters on
R_{g}
and the device characteristics by using various combinations of structural parameters for the 0.1
μ
m depletionmode InGa As/InAlAs metamorphic HEMT (MHEMT). To investigate the effects of
N
and
w
, 12 different gate peripheries were fabricated with various gate fingers (2, 4, and 6) and gate widths (25, 40, 50, and 70
μ
m). Except for the variations in
N
and
w
, we maintained the same epitaxial structure, gate length of 0.1
μ
m, and sourcedrain spacing of 2
μ
m for all fabricated devices, as described in the next section.
Micrograph of the fabricated chip with the fourfinger metamorphic highelectronmobility transistors.
The MHEMT micrograph of the HEMT with four fingers is shown in
Fig. 1
.
Ⅱ. Device Fabrication
As shown in
Fig. 2
, the MHEMT epitaxial structure was grown by molecular beam epitaxy on a semiinsulating GaAs substrate. The structures consisted of the following layers from the bottom: a 1000nm In
_{x}
Al
_{1x}
As linearly graded buffer layer with an indium mole fraction, x, linearly graded from 0 to 0.5; a 300nm undoped In
_{0.52}
Al
_{0.48}
As buffer layer; a silicon deltadoped plane (1.3×10
^{12}
/cm
^{2}
), a 4nm undoped In
_{0.52}
Al
_{0.48}
As spacer layer; a 23nm undoped In
_{0.53}
Ga
_{0.47}
As channel layer; a 3nm undoped In
_{0.52}
Al
_{0.48}
As spacer layer; a silicon delta doped plane (4.5×10
^{12}
/cm
^{2}
); a 15nm undoped In
_{0.52}
Al
_{0.48}
As Schottky barrier layer; and a 15nm ntype In
_{0.53}
Ga
_{0.47}
As cap layer (6×10
^{18}
/cm
^{3}
). The grown epitaxial layer showed a twodimensional electron carrier density (
n_{s}
) of about 3.5×10
^{12}
/cm
^{2}
and a Hall mobility of about 9,700 cm
^{2}
/Vsec at room temperature.
To fabricate the MHEMTs, we first isolated active areas by using mesa etching with an etchant of phosphoric acid/H
_{2}
O
_{2}
/H
_{2}
O (1:1:60) to reduce the thickness to 200nm. AuGe/Ni/Au (140/30/160 nm) ohmic metallization showed a specific contact resistance of about 5×10
^{—7}
Ωcm
^{2}
after rapid thermal annealing at 320℃ for 60 seconds in a vacuum. An electron beam lithography system (EBPG4HR, Leica Microsystems Ltd., Buffalo Grove, IL, USA) was used to perform 0.1
μ
m Tshaped gate patterning upon completion gate_recess, gate metallization was performed by evaporating Ti/Au (50/400 nm) followed by metal liftoff. The MHEMTs were passivated with the Si
_{3}
N
_{4}
films (80 nm). Finally, a Ti/Au (30/700 nm) airbridge interconnection was made to connect the source pad.
Epitaxial structure of the metamorphic highelectron mobility transistor.
Ⅲ. Analysis of Device Scaling
The DC characteristics of each MHEMT were measured in an HP 4156 DC parameter analyzer. Drain current (
I_{ds}
) versus gate voltage (
V_{gs}
) and transfer characteristics of the MHEMTs (at a drain voltage [
V_{ds}
] of 1.2 V) were measured at various
N
and
w
values. With the total gate width (
w_{t}
), the saturation drain current (
I_{dss}
) and maximum transconductance (
g_{m,max}
) were linearly increased at constant slopes of about 0.58 mA/
μ
m and 0.57 mS/
μ
m, respectively, as shown in
Fig. 3
. The
w_{t}
is hereafter defined as “total gate width” and given by the product of
N
and
w
. The scaling rules for these parameters are then simply expressed as:
Highfrequency characteristics of the fabricated MHEMTs were measured in the frequency range of 0.5 to 50 GHz using an HP8510C network parameter analyzer (Agilent Technologies, Palo Alto, CA, USA). Cutoff frequency (
f_{T}
) and
f_{max}
were determined by extrapolating the
h_{21}
and
U
gain curves, respectively, at a slope of 6 dB/octave. The DC and RF data were measured from each gate type of the MHEMTs at six different dies a 2.5×2.5 cm
^{2}
specimen. The average
f_{T}
and
f_{max}
from the MHEMTs with 12 different gate types measured from six different dies were plotted respectively in
Fig. 4
with their standard deviations (1
σ
). The
f_{T}
increased slightly in a small
w_{t}
region and was saturated to a frequency of about 100 GHz; on the other hand, the
f_{max}
decreased continuously with the
w_{t}
in our whole experimental range of
w_{t}
, and the reduction ratio was a function of
N
.
I_{dss} and g_{m} versus w_{t} of the metamorphic highelectron mobility transistors at various N.
Average f_{T} and f_{max} as functions of the w_{t} measured from the metamorphic highelectronmobility transistors of twelve different gate types and six different dies (calculation, solid line; measurement, symbols).
Fitting equations of the smallsignal parameters
Fitting equations of the smallsignal parameters
To examine the effects of
N
and
w_{t}
on the smallsignal parameters directly affecting
f_{T}
and
f_{max}
, all the parameters shown in Eqs. (2) and (3)
[16
,
17]
were extracted from the fabricated MHEMTs by the Dambrine method
[18]
and curvefitted to simple functions of
w_{t}
. As shown in
Table 1
, gatetosource capacitance (
C_{gs}
), gatetodrain capacitance (
C_{gd}
), drain conductance (
G_{ds}
), and intrinsic transconductance (
g_{m,int}
) were proportional to
w_{t}
.
However, intrinsic resistance (
R_{i}
) and source resistance (
R_{s}
) were inversely proportional to
w_{t}
. All these parameters were functions of
w_{t}
. But were not functions of
N
; however, one exception was
R_{g}
, which was a function of both
w_{t}
and
N
.
The relationships of the fitted parameters with
w_{t}
can be explained as follows.
C_{gs}
is a function of
C_{gso}
which is gatetosource capacitance per unit gate width, and therefore is expressed as
where
C_{gso}
is about 0.00089 pF/
μ
m in our case. In the case of the
C_{gd}
, yaxis intercepts should also be considered. A nonzero
C_{gd}
at zero
w_{t}
can be formed between the gate bus line and drain pad and this parasitic capacitance, in fact, has been observed in earlier studies
[13
,
19
,
20]
. In our case, the yaxis intercept of
C_{gd}
was about 0.0049 pF, and the proportionality constant was about 0.000087 pF/
μ
m. The linear relationship of
G_{ds}
with
w_{t}
can be understood such that the total sourcedrain conductance is given by (
dI_{ds}
/
dV_{ds}
per unit gate width)×
w_{t}
, and the corresponding proportionality constant was about 0.0355 mS/
μ
m in our case.
R_{s}
and
R_{i}
were inversely proportional to
w_{t}
and curvefitted in the same way with the proportionality constants of about 190 and about 1,580 Ω․
μ
m, respectively. The linear increase of
g_{m,int}
with
w_{t}
can be explained by the linear scaling rule of
g_{m,ext}
with
w_{t}
, as shown in Eq. (1); the proportionality constant was about 0.614 mS/
μ
m.
Extracted R_{g} as functions of w_{t} (fitting, solid line; measurement, symbols).
R_{g}
is a function of both
N
and
w_{t}
, as shown in
Fig. 5
, and can be expressed as Eq. (5) where
ρ_{G}
is the resistivity of the gate metal, and
A
is the crosssectional area of the gate.
R_{o}
is the yaxis intercept obtained by linear curve fitting. This relationship can be obtained by assuming the gradual (linear) reduction in gate current (
I_{g}
) density as the open end is approached, as illustrated in
Fig. 6
, and an essentially uniform displacement current fed from the bottom of the gate to the channel region of the HEMTs
[21]
. In the openended gate structure shown in
Fig. 6
,
I_{g}
and the infinitesimal change of
V_{gs}
(
δV_{gs}
) over
δx
are given by Eqs. (6) and (7),
where
L
and
h
are gatelength and gateheight, respectively. The minus sign in Eq. (7) indicates that gate voltage decreases with increasing
x
. At
x
=0,
V_{gs}
is equal to
V_{gs0}
, gate terminal voltage. Gate voltage
V_{gs}
(
x
) is obtained by integrating Eq. (7) with the boundary condition at
x
=0.
Distribution of gate current in the gatewidth direction.
The average gate voltage is equal to the integral of
V_{gs}
(
x
) from
x
=0 to
W
and then divided by
W
. After carrying out the definition, we find the average value to be
The average intrinsic gate resistance inside the gate electrode region from
x
=0 to
w
is then given by:
Investigations have focused on
R_{o}
,
R_{g}
when
w
approaches zero
[21
,
22]
; however, the model for
R_{o}
, is still not fully understood. In our case, the yaxis intercepts of the MHEMTs (
N
=2, 4, and 6) range from about 0.6 to 0.9 Ω, with the corresponding proportionality constants of about 0.0123, 0.0021, and 0.000515 Ω/
μ
m, respectively, as shown in
Fig. 4
. Therefore, the scaling rules of the smallsignal parameters can be summarized as follows:
f_{T}
and
f_{max}
can be calculated by substituting each smallsignal parameter of Eqs. (2) and (3) with the curvefitting equations in
Table 1
. The calculated results are plotted in
Fig. 4
with measurements at each
N
and
w_{t}
. Good agreement was obtained from the calculated
f_{T}
and
f_{max}
with the measured data over the entire range of measured
w_{t}
. Some discrepancies between the measurements and the calculations are due to the errors associated with the device process in pattern lithography. Because
g_{m}
and
C_{gs}
are both proportional to
w_{t}
, as shown in Eq. (2),
f_{T}
is not a function of
w_{t}
. From our calculations contained in
Fig. 3
,
f_{T}
showed an almost constant frequency of about 100 GHz above a
w_{t}
of about 100
μ
m. Below this
w_{t} f_{T}
a slight increase with
w_{t}
owing to the yaxis intercept effect of
C_{gd}
, as observed in many earlier studies
[23
,
24]
. Since
f_{max}
is a strong function of
R_{g}
as shown in Eq. (3), it is affected by both
N
and
w_{t}
. If we assume that
G_{ds}
is negligible (ideal case without channel length modulation), Eq. (3) is simply expressed as
[25]
:
Because
f_{T}
is almost constant, we therefore obtain:
Eq. (15) shows that a careful combination of
N
and
w_{t}
is required to achieve a maximum
f_{max}
in a given device technology. Obviously, a greater
w_{t}
produces a higher
f_{max}
; however, to increase the number of gatefingers by reducing the unit gate width is more efficient than to simply increase the singlegate_width in order to maximize
f_{max}
at a given
w_{t}
.
Ⅳ. Conclusion
We investigated the effects of
N
and
w
on the RF characteristics of 0.1
μ
m depletionmode multifinger MHEMTs and their smallsignal parameters.
C_{gs}
,
C_{gd}
,
G_{ds}
, and
g_{m,int}
were all proportional to
w_{t}
; however,
R_{i}
and
R_{s}
were inversely proportional to
w_{t}
.
R_{g}
was proportional to both
w_{t}
and 1/
N
^{2}
.
f_{T}
and
f_{max}
were calculated by using the smallsignal models and curvefitting equations from each extracted smallsignal parameters. The calculations showed good agreements with the measurements, and the results demonstrated that a greater
w_{t}
produces a higher
f_{max}
; however, to maximize
f_{max}
at a given
w_{t}
, increasing the number of gate_fingers is more efficient than increasing the singlegate width. On the other hand,
f_{T}
showed an almost independent relationship with
w_{t}
. To our knowledge, this is the first successful demonstration of multifinger gatewidth scaling effects (individual effect of
N
and
w_{t}
) on HEMT devices operating at millimeterwave frequencies.
Acknowledgements
This work was supported by the Industrial StrategicTechnology Development Program (contract no.10038766) funded by the Ministry of Knowledge Economy(MKE, Korea) through ETRI.
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