IEICE TRANS. ELECTRON., VOL.E82–C, NO.11 NOVEMBER 1999
1968
PAPER
Special Issue on High Frequency/Speed Devices in the 21st Century
A Technique for Extracting Small-Signal
Equivalent-Circuit Elements of HEMTs
Man-Young JEON†a) , Byung-Gyu KIM† , Young-Jin JEON†† ,
and Yoon-Ha JEONG† , Nonmembers
SUMMARY We propose a new technique that is able to extract the small-signal equivalent-circuit elements of high electron
mobility transistors (HEMTs) without causing any gate degradation. For the determination of extrinsic resistance values, unlike
other conventional techniques, the proposed technique does not
require an additional relationship for the resistances. For the
extraction of extrinsic inductance values, the technique uses the
R-estimate, which is known to be more robust relative to the measurement errors than the commonly used least-squares regression.
Additionally, we suggest an improved cold HEMT model that
seems to be more general than conventional cold HEMT models.
With the use of the improved cold HEMT model, the proposed
technique extracts the extrinsic resistance and inductance values.
parameter extraction, HEMT characterization,
key words:
equivalent-circuit, cold HEMT
1.
Introduction
The cold FET method is widely used to extract FET
equivalent-circuit elements quickly and accurately [1]–
[6]. The method generally needs to apply a strong forward bias to the gate of the cold FET in order to extract
external extrinsic resistance and inductance values. In
the case of HEMTs, however, application of forward
bias to the gate may cause gate degradation due to the
large gate current through the Schottky junction. To
avoid gate degradation, other techniques using minimum forward bias or zero bias have been attempted in
Refs. [7] and [8]. Instead of a srong forward bias, these
techniques apply a minimum forward bias or zero bias
to the gate and reliably extract the extrinsic element
values without any damage to the gate.
In this paper, we present a technique to reliably
extract extrinsic element values of a HEMT without
causing any gate degradation. Our method is similar
to Refs. [7] and [8] from the standpoint that there is no
application of a forward bias to the gate, but it differs
from them with respect to the following two points.
First, it biases the gate with a voltage slightly below
Manuscript received March 18, 1999.
Manuscript revised May 20, 1999.
†
The authors are with the Department of Electronic and
Electrical Engineering, Pohang University of Science and
Technology, San-31 Hyoja-dong, Nam-gu, Pohang, Kyungbuk, 790-784, Republic of Korea.
††
The author is with Memory Design Department, 1,
LG Semicon., 1, Hyangjeong-dong, Hungduk-gu, Cheongju,
Chungbuk, 361-480, Republic of Korea.
a) E-mail: myjeon@postech.ac.kr
the pinch-off point instead of using a minimum forward
or zero bias. By applying such a voltage to the gate,
our technique does not need an additional relationship
between extrinsic resistances, whereas the techniques
of Refs. [7] and [8] as well as Refs. [1]–[6] require the
relationship in order to completely determine the external resistance values. Second, for the extraction of
the extrinsic inductance values, we use the R-estimate
[9] instead of the conventionally used least-squares regression. The R-estimate is known to be more robust
relative to the measurement error because its objective function behaves in a linear fashion rather than a
squared fashion [9].
In general, the cold HEMT model proposed in
Ref. [1] fails to explain the frequency behavior of the
cold HEMT as the gate bias decreases toward the pinchoff voltage [4]. To resolve the problem, in this paper, we
suggest an improved cold HEMT model that is able to
explain all of the frequency characteristics of the cold
HEMT under any gate biasing condition.
For the extraction of the equivalent-circuit, we
used T-gate AlGaAs/GaAs HEMT which has a gate
length of 0.35 µm, gate width of 100 µm, and pinch-off
voltage of −0.8 V. It was fabricated and measured at
the Fujitsu Laboratory in Kawasaki, Japan.
2.
Extrinsic Element Extraction
For the information of dc-characteristics of the cold
HEMT at Vds = 0 V, the Ids -Vgs curve at Vds = 0 V
is shown in Fig. 1. The drain-to-source current(Ids )
was sampled at eight gate-to-source voltages with the
step size of 0.1 V. The current Ids flows out from the
drain with 0.01 µA at Vgs = −0.9 V and 0.2 µA at
Vgs = −0.8 V even though it is not clearly shown in
Fig. 1. Ideally, the drain current must not flow since
Vds = 0 V, but actually it flows due to an imperfect
zero voltage applied to the drain. As shown in the figure, the current grows up as the Vgs increases from the
pinch-off voltage since more free electrons are available
in the channel according as the increase of Vgs .
Under the assumption that gate and drain pad
capacitance are so small that they can be neglected,
Figure 2 shows the small-signal equivalent circuit of
the HEMT adopted for the equivalent-circuit parameter extraction under the RF wafer probe measurement
JEON et al: A TECHNIQUE FOR EXTRACTING SMALL-SIGNAL EQUIVALENT-CIRCUIT ELEMENTS
1969
Fig. 1 Ids -Vgs curve of the cold HEMT used for the extraction
of equivalent-circuit elements.
Fig. 3 Proposed equivalent-circuit of the cold HEMT
(Vds = 0 V).
Fig. 2 Equivalent-circuit of the HEMT. The part surrounded
= g exp(−jωτ ).
by dashed box denotes the intrinsic part: gm
m
environment.
2.1 Suggested Cold HEMT Model
Figure 3 shows the suggested cold HEMT model. As
shown in the figure, the intrinsic gate region surrounded
by the dashed line is represented by a distributed RC
Network. ∆Cy , ∆Ry , Cy , and Ry are infinitesimal capacitance, infinitesimal resistance, equivalent lumped
capacitance, and equivalent lumped resistance of Schottky barrier, respectively; ∆Cch , ∆Rch , Cch , and Rch
denote infinitesimal channel capacitance, infinitesimal
channel resistance, equivalent lumped channel capacitance, and equivalent lumped channel resistance, respectively. In the figure, n is the number of division
of the intrinsic gate region and very large number converging to infinity. The relationships between infinitesimal elements and corresponding lumped elements are
expressed by the equations in Fig. 3.
The model is an extension of that of Ref. [1] in that
∆Cch is attached parallel to ∆Rch . The channel capacitance has been introduced to explain the frequency dependent characteristics of the measured Z-parameters
of a weakly pinched-off cold HEMT . A weakly pinchedoff cold HEMT means a cold HEMT that is biased at
a gate voltage slightly below the pinch-off point (in
this paper, −0.9 V) and drain voltage of 0 V. In the
suggested model, the channel resistance has been replaced by a channel impedance. By the replacement,
we can explain all of the frequency characteristics of
the cold HEMT for any gate biasing condition including the strong forward bias and strong pinched-off bias.
A more detailed description of the consistency of our
cold HEMT model will be given in Sect. 2.4.
For the extraction of extrinsic elements without
any gate degradation, the gate may be considered to
be biased with a strong pinched-off voltage, e.g., −3 or
−4 V, which reduces the equivalent circuit of the cold
HEMT to a simpler topology used in Refs. [6] and [10].
However, since extrinsic resistances may be gate-bias
dependent [11]–[13], it is more desirable to bias the gate
as close to the real operating voltage as possible.
Deducing from Refs. [1], [14], [15], and [16], we assume that the impedance parameters zij of the intrinsic
gate region shown in Fig. 3 can be expressed as follows:
z11 = αZch + Zy
Rch
Ry
= α
+
1 + jωCch Rch
1 + jωCy Ry
z12 = z21 = βZch = β
z22 = Zch =
Rch
1 + jωCch Rch
Rch
,
1 + jωCch Rch
(1)
(2)
(3)
where α and β are constants to take into account the
distributed RC Network under the intrinsic gate; Zch =
Rch //Cch is the equivalent lumped channel impedance;
Zy = Ry //Cy is the equivalent lumped impedance of
the Schottky barrier.
2.2 Extraction of Extrinsic Resistances
In the case of a weakly pinched-off cold HEMT, Zy in
IEICE TRANS. ELECTRON., VOL.E82–C, NO.11 NOVEMBER 1999
1970
Eq. (1) is nearly equal to −j/ωCy because Ry is extremely high. By adding the external extrinsic resistances Rs , Rg , and Rd as well as inductances Ls , Lg ,
and Ld to Eqs. (1)–(3), and then arranging real and
imaginary parts separately, we have the following expressions for the Z-parameters of a weakly pinched-off
cold HEMT:
Rch
Z11 = Rg +Rs +α
2 R2
1+ω 2 Cch
ch
2
1
ωCch Rch
+j ω (Lg +Ls )−
−α
(4)
2 R2
ωCy
1+ω 2 Cch
ch
Rch
Z12 = Z21 = Rs +β
2 R2
1+ω 2 Cch
ch
2
ωCch Rch
+j ωLs −β
2 R2
1+ω 2 Cch
ch
Rch
Z22 = Rd + Rs +
2 R2
2
1+ω Cch
ch
2
ωCch Rch
+j ω (Ld + Ls ) −
.
2 R2
1+ω 2 Cch
ch
(a)
(5)
(6)
2
2
Rch
> 1 for the measureIf we assume that ω 2 Cch
ment frequency range of 1 to 62 GHz, we know that
the real parts of Eqs. (4)–(6) have strongly decreas2
2
2
2
Rch
), βRch /(1 + ω 2 Cch
Rch
)
ing terms αRch /(1 + ω 2 Cch
2
2
Rch
), which result from a parallel
and Rch /(1 + ω 2 Cch
addition of infinitesimal channel capacitance ∆Cch to
the infinitesimal channel resistance ∆Rch as shown in
the suggested cold HEMT model in Fig. 3. Therefore,
we know that the real parts strongly decrease as frequency increases and finally arrive at constant values
of Rg + Rs , Rs , and Rd + Rs .
Figure 4(a) shows the measured real parts of the
weakly pinched-off cold HEMT biased at Vgs = −0.9 V
and Vds = 0 V. From Fig. 4(a), it can be seen that the
measured real parts strongly decrease as the frequency
increases and then remain almost constant over the region above 18 GHz. The close agreement between the
real parts of Eqs. (4)–(6) and their measured counterparts supports the validity of our model for a weakly
pinched-off cold HEMT. Figure 4(a) indicates that the
strongly decreasing terms actually disappear as the frequency enters the high frequency region above 18 GHz.
Therefore, Rg +Rs , Rs and Rd +Rs can be calculated by
averaging the limiting values of Re(Z11 ), Re(Z12 ) and
Re(Z22 ) over the range above 18 GHz. By averaging
the values, Rg + Rs , Rs and Rd + Rs were determined
to be 4.3, 1.2 and 3.6 Ω, respectively; thus, the extrinsic resistances of Rs , Rg and Rd were determined to be
1.2, 3.1 and 2.4 Ω, respectively.
When the gate voltage of a cold HEMT is more
than 500 or 600 mV above the pinch-off point, the chan2
2
Rch
1.
nel resistance becomes so small that ω 2 Cch
2 2
2
Therefore, the terms αRch /(1 + ω Cch Rch ), βRch /(1 +
(b)
Fig. 4 (a) Measured real parts of Z-parameters of the weakly
pinched-off cold HEMT (Vgs = −0.9 V, Vds = 0 V) over the frequency range of 1 to 62 GHz. (b) Measured imaginary parts of
Z-parameters over the frequency range of 1 to 62 GHz for the
same bias conditions as (a).
2
2
2
2
ω 2 Cch
Rch
) and Rch /(1 + ω 2 Cch
Rch
) are reduced to
αRch , βRch , and Rch , respectively. Therefore, in this
case, the real parts of Eqs. (4)–(6) include terms related to the channel resistance (αRch , βRch , and Rch ).
This corresponds to the case of conventional techniques
of Refs. [1]–[6] and the techniques of Refs. [7] and [8].
These techniques need one additional relationship between the resistances to determine the extrinsic resistances because they have only three equations for the
determination of four unknowns: Rs , Rg , Rd , and Rch .
The relationship is usually obtained by an extra measurement or device process parameters. However, our
technique does not need such a extra measurement or
device process parameters due to disappearance of the
terms related to Rch in the high frequency region.
Equations (4) and (6) indicate that α can be calculated by the ratio of [Re(Z11 ) − Rg − Rs ]/[Re(Z22 ) −
Rd − Rs ]. In Fig. 4(a), by averaging this ratio in
the low frequency region (typically below 5 GHz) in
2
2
Rch
) and
which decreasing terms of αRch /(1 + ω 2 Cch
2
2
Rch
) dominate, α was obtained to be
Rch /(1 + ω 2 Cch
about 0.2, which is less than the conventionally used
value of 1/3. From Eqs. (5) and (6), we know that there
JEON et al: A TECHNIQUE FOR EXTRACTING SMALL-SIGNAL EQUIVALENT-CIRCUIT ELEMENTS
1971
are two methods for the calculation of β. One is by the
ratio of [Re(Z12 ) − Rs ]/[Re(Z22 ) − Rd − Rs ] and the
other is by the ratio of Im(Z12 )/Im(Z22 ) in the low frequency region because the reactance by inductance Ls
or Ld +Ls is negligible in the low frequency region. In
Figs. 4(a) and (b), by averaging these ratios in the low
frequency region, β obtained by the former method was
found to be 0.41, while β obtained by the latter method
was found to be 0.42. These values are also less than
the conventionally used value of 1/2. The fact that β
values by both methods are nearly equal again confirms
the validity of our model for a weakly pinched-off cold
HEMT because Eqs. (5) and (6) derived from our model
indicate that β values by both methods are almost the
same.
2.3 Extraction of Extrinsic Inductances by REstimate
2
2
Rch
1 over the
Under the assumption that ω 2 Cch
frequency region of 5 to 62 GHz, the imaginary parts of
Eqs. (4)–(6) are reduced to the following forms because
2
2
2
2
Rch
+1∼
Rch
:
ω 2 Cch
= ω 2 Cch
1
1
0.2
+
(7)
Im(Z11 ) = ω(Lg + Ls ) −
ω Cy
Cch
Im(Z12 ) = Im(Z21 ) = ωLs −
Im(Z22 ) = ω(Ld + Ls ) −
0.4
ωCch
1
,
ωCch
(8)
(9)
where α and β in Eqs. (4) and (5) were replaced by
their respective values obtained in the preceding subsection. The imaginary parts of Eqs. (7)–(9) were measured up to the high frequency of 62 GHz, and are depicted in Fig. 4(b). From the curves, inductances can
be extracted without having large errors because the reactances by inductances in Eqs. (7)–(9) are somewhat
conceivable in the high frequency region. We know that
the curves in Fig. 4(b) are in good agreement with their
counterparts in Eqs. (7)–(9). Particularly, The measured Im(Z12 ) and Im(Z22 ) manifestly show that there
is a capacitance component in the channel, which once
more supports the validity of our model including channel capacitance. The conventional cold HEMT model
in Ref. [1] fails to explain these frequency behaviors of
Im(Z12 ) and Im(Z22 ).
If we arrange Eq. (8) in terms of 0.4/Cch , we have
0.4
= ωi2 Ls − ωi Im(Z12 )i
(10a)
Cch i
0.4
= ωi2 Ls − ωi Im(Z21 )i ,
(10b)
Cch i
where Im(Z12 )i is the imaginary part value of Z12
measured at ωi , and (0.4/Cch )i is the value at the ith sampled angular frequency ωi (i = 1, 2, · · · N ). N
denotes the total number of sampled frequency points.
Similarly, if we arrange Eqs. (7) and (9) in terms of
(1/Cy + 0.2/Cch ) and 1/Cch , respectively, we have the
following equations:
1
0.2
+
= ωi2 (Lg + Ls ) − ωi Im(Z11 )i (11)
Cy
Cch i
1
Cch
= ωi2 (Ld + Ls ) − ωi Im(Z22 )i
(12)
i
If we denote the measure of dispersion of fi by
M.D.(fi ), the measure of dispersion of (0.4/Cch )i in
Eq. (10a) is defined as follows [9]:
N
0.4
0.4
M.D.
a(Ri )
≡
Cch i
C
ch i
i=1
N
=
a(Ri )[ωi2 Ls −ωi Im(Z12 )i ],
i=1
(13)
where Ri is the rank of a (0.4/Cch )i when sorting
(0.4/Cch )i (i = 1, 2, . . . N ) in ascending order, and
a(Ri ) = Ri /(N + 1) − 0.5 is a score function. Equation (13) indicates the extent of dispersion of (0.4/Cch )i
along the frequency ωi . Since (0.4/Cch )i have to be constant along the frequency, the Ls that makes Eq. (13)
minimum is the extrinsic source inductance value that
we want to find. As Eq. (13) is a concave function of
Ls , the minimal point of the function can be searched
by the well-known Steepest Descent method using the
gradient
N
0.4
d
∇=
a(Ri )ωi2 . (14)
M.D.
=
dLs
Cch i
i=1
The estimation of unknown variables by minimizing the
objective function like Eq. (13) is called R-estimate.
The R-estimate is known to be more robust relative
to measurement errors than the least-squares regression because its objective function behaves in a linear
fashion rather than a squared fashion [9]. Our method
is similar to Ref. [17] in which, to extract the extrinsic element values, Shirakawa et al. suggested a novel
method that uses the condition that intrinsic element
values must be constant along frequency. However, our
method differs from Ref. [17] in that it uses the measure of dispersion instead of the variance that was used
as an optimization criterion in Ref. [17]. Since variance
behaves in a squared fashion, it may be more vulnerable
to the measurement error than the measure of dispersion.
The Ls extracted by the minimization of Eq. (13)
was 1.422 pH, while the Ls determined by the minimization of the measure of dispersion of Eq. (10b) was
IEICE TRANS. ELECTRON., VOL.E82–C, NO.11 NOVEMBER 1999
1972
0.967 pH. By averaging these two values, Ls was determined to be 1.195 pH. By minimizing M.D.[(1/Cy +
0.2/Cch )i ] and M.D.[(1/Cch )i ], (Lg +Ls ) and (Ld +Ls )
were found to be 35.152 and 23.012 pH, respectively.
M.D.[(1/Cy + 0.2/Cch )i ] and M.D.[(1/Cch )i ] are obtained from Eqs. (11) and (12) by the same definition
as Eq. (13). From the difference of (Lg +Ls ) and Ls , we
obtained Lg = 33.957 pH. Similarly, from the difference
of (Ld + Ls ) and Ls , we obtained Ld = 21.817 pH.
The channel capacitance Cch is calculated by the
following equation:
1
Cch = {E[(Cch,12 )i ]
3
+E[(Cch,21 )i ]+E[(Cch,22 )i ]},
(15)
where E[(Cch,kl )i ] denotes the average of (Cch,kl )i (i =
1 ,2, . . . N ). E[(Cch,12 )i ], E[(Cch,21 )i ], and E[(Cch,22 )i ]
are calculated from Eqs. (10a), (10b) and (12), respectively, when the extracted Ls is replaced into these
equations. E[(Cch,12 )i ], E[(Cch,21 )i ] and E[(Cch,22 )i ]
were found to be 59.21, 59.69 and 58.36 fF respectively.
Therefore, from Eq. (15), the channel capacitance Cch
was found to be 59.09 fF. The Schottky barrier capacitance Cy is determined by averaging the (Cy )i that
are calculated from Eq. (11) when the extracted Lg , Ls
and Cch values are inserted into the equation. The
obtained Schottky barrier capacitance Cy was 80.61 fF.
Channel resistance Rch is calculated from the real parts
of Eqs. (4)–(6) when the extracted values of α, β, Cch ,
Rs , Rg , and Rd are substituted into the real parts. By
averaging the calculated results over the region below
5 GHz we obtained Rch = 5.4 kΩ.
forward gate bias condition.
When we bias the gate of a cold HEMT with a
strong pinched-off voltage, e.g., Vgs = −3 or −4 V, the
Ry and Rch in Fig. 3 become extremely high so that
Zy and Zch can be reduced to 1/jωCy and 1/jωCch ,
respectively. Therefore, Eqs. (1)–(3), the impedance
parameters of the intrinsic gate are given by z11 =
α/jωCch + 1/jωCy , z12 = z21 = β/jωCch and z22 =
1/jωCch , respectively. Hence, in this case, by including
extrinsic resistances and inductances, the Z-parameters
of a cold HEMT biased with strong pinched-off gate
voltage are obtained as follows:
α
1
1
+
Z11 = Rg +Rs +j ω(Lg +Ls )−
ω Cch Cy
1
= Rg + Rs + j ω(Lg + Ls ) −
(19)
ωCa
Z12 = Z21 = Rs + j ωLs −
Z22
β
ωCch
= Rd + Rs + j ω(Ld + Ls ) −
(20)
1
,
ωCch
(21)
where Ca is the total series capacitance of Cch /α and
2.4 Consistency of the Suggested Cold HEMT Model
In the case of a cold HEMT biased with a strong forward gate voltage, the dynamic resistances of the Schottky barrier Ry and channel resistance Rch in Fig. 3 are
so small that the impedance of Schottky barrier Zy
and channel impedance Zch is reduced to Ry and Rch ,
respectively. Therefore, in this case, Eqs. (1)–(3), the
impedance parameters of the intrinsic gate region are
reduced to z11 = αRch + Ry , z12 = z21 = βRch and
z22 = Rch , respectively. Hence, by including extrinsic
resistances and inductances, the Z-parameters of a cold
HEMT with a strong forward bias are given by
Z11 = Rg +Rs +αRch +Ry +jω(Lg +Ls )
(16)
Z12 = Z21 = Rs + βRch + jωLs
(17)
Z22 = Rd + Rs + Rch + jω(Ld + Ls ),
(18)
where Ry = ηVT /Ig (Ig : forward DC current). When α
and β of Eqs. (16) and (17) are substituted with 1/3 and
1/2, respectively, they becomes the very Z-parameter
expressions of Eqs. (15)–(17) of Ref. [1] for the strong
(a)
(b)
Fig. 5 (a) Equivalent-circuit represented by Eqs. (19)–(21).
(b) Equivalent-circuit converted from (a); equivalent-circuit of
the strongly pinched-off cold HEMT.
JEON et al: A TECHNIQUE FOR EXTRACTING SMALL-SIGNAL EQUIVALENT-CIRCUIT ELEMENTS
1973
Cy . The above Z-parameters represent the equivalentcircuit in Fig. 5(a). If we convert the T -Network surrounded by dashed box into Π-Network as shown in
Fig. 5(b), then Fig. 5(b) is the very equivalent-circuit of
the strongly pinched-off cold HEMT used in Refs. [6]
and [10]. Therefore, it can be said that the suggested
cold HEMT model in Fig. 3 well reflects the frequency
behaviors of the cold HEMT at the extreme cases of
strong forward and strong pinched-off gate bias.
For the gate voltage from −0.9 V to 0 V, we also
found that the suggested cold HEMT model agrees well
with the measured Z-parameters of our cold HEMT
at Vds = 0 V. For example, we analyze the frequency
characteristics of Z22 for the three gate bias conditions
of −0.9, −0.8, and −0.6 V. If we assume that, for the
three gate biases the channel resistance Rch is so large
that the first term in the imaginary part of Eq. (6) is
negligible compared to the second term, the imaginary
part Im(Z22 ) is approximated as follows:
Im(Z22 ) = −
2
ωCch Rch
2
2 .
2
1 + ω Cch Rch
(a)
(22)
After differentiating Eq. (22) with respect to ω and setting its derivative to zero, the negative peak value Xp
of Eq. (22) and the frequency fp for the value are respectively found to be
Rch
Xp = −
2
(23)
and
fp =
1
.
2πRch Cch
(24)
The channel resistance Rch decreases as the gate bias
increases because more free electrons in the channel
are available. If we assume that the channel capacitance Cch does not vary so much when the gate bias
increases, from Eqs. (23) and (24) we know that as the
gate bias increases, fp will increase, while −Xp will
decrease due to reduction of channel resistance Rch .
In fact, from Fig. 6(a), we observe that the fp shifts
to the right along the frequency axis as the gate bias
increases from −0.9 through −0.8 to −0.6 V (in this
figure, we know that the negative peak of Im(Z22 ) at
Vgs = −0.9 V will exists somewhere below 1 GHz even
though it was not measured in such a low frequency
region). We also observe that as the gate bias increases, −Xp abruptly decreases due to the abrupt drop
of channel resistance. From Eq. (6), we know that as
the channel resistance decreases, Re(Z22 ) will decrease
more slowly starting from a smaller value at the low
frequency (1 GHz). From Fig. 6(b), we can see that the
measured frequency behaviors of Re(Z22 ) for the three
gate bias conditions well reflect the frequency response
of Re(Z22 ) in Eq. (6). For other Z-parameters, such as
Z11 , Z12 and Z21 , we also observed that their measured
frequency characteristics at the above three gate bias
(b)
Fig. 6 (a) Frequency characteristics of Im[Z22 ] measured from
1 GHz to 62 GHz for the three gate bias conditions of −0.9, −0.8
and −0.6 V; Im[Z22 ] at Vgs = −0.9 V and Im[Z22 ] at Vgs =
−0.8 V were divided by 20 and 8 respectively. (b) Frequency
characteristics of Re[Z22 ] measured from 1 GHz to 62 GHz for the
same gate bias conditions as (a). In both (a) and (b), Vds = 0 V.
conditions agree well with the frequency behaviors of
Eqs. (4)–(5).
In conclusion, it can be said that the suggested cold
HEMT model in Fig. 3 well reflects all of the frequency
characteristics of a cold HEMT under any gate bias
condition.
3.
Intrinsic Element Extraction
The equivalent-circuit for the intrinsic part of the
HEMT may be different from that of the MESFET
because the HEMT has a different device structure
from the MESFET. Nevertheless, we adopted the same
equivalent-circuit with MESFET as shown in Fig. 2
because, to our knowledge it is one of the widely
used equivalent-circuits for the parameter extraction
of GaAs-based HEMTs and produces good extraction
results [8], [17]. The intrinsic elements in Fig. 2 were
determined using conventionally used analytical relationships between intrinsic elements and intrinsic yparameters that are obtained by subtracting the extrinsic elements calculated in Sects. 2.2 and 2.3 from
IEICE TRANS. ELECTRON., VOL.E82–C, NO.11 NOVEMBER 1999
1974
Table 1 Extracted extrinsic and intrinsic element values for
the HEMT (Vgs = −0.2 V, Vds = 0.2 V, W = 100 µm, and
L = 0.35 µm), and intrinsic elements of a weakly pinched-off cold
HEMT (Vgs = −0.9 V, Vds = 0 V).
(a)
(b)
Fig. 7 (a) Extracted intrinsic capacitances Cgs , Cgd and Cds
versus frequency for the HEMT. Frequency: 1–62 GHz, Bias:
Vgs = −0.2 V and Vds = 0.2 V. (b) Extracted intrinsic transcon−1
, transit
ductance gm , drain-to-source conductance gds = rds
time τ , and resistance Ri versus frequency. Frequency: 1–
62 GHz, Bias: Vgs = −0.2 V and Vds = 0.2 V.
measured S-parameters.
Figure 7 shows the extracted intrinsic element values of the HEMT biased with normal operating voltages
of Vgs = −0.2 V and Vds = 2.0 V. All the element values are almost constant over the frequency region that
ranges from 1 to 62 GHz, except that Ri shows some
dispersions for the low and high frequency region. This
indicates that the extracted extrinsic element values in
Sect. 2 are accurate and reliable. Table 1 summarizes
the extracted extrinsic and intrinsic element values of
the HEMT, and the intrinsic element values of a weakly
pinched-off cold HEMT. The intrinsic element values
of the HEMT were determined by selecting the median
of all calculated values over the frequency from 1 to
62 GHz.
Figure 8 compares the modeled and measured Sparameter values for the HEMT in the frequency range
of 1 to 62 GHz under the bias condition of Vgs = −0.2 V
and Vds = 2 V. The modeled S-parameters agree well
with the measured S-parameters from 1 GHz to 62 GHz,
except that the modeled phase response of S12 deviates
from the measured one in the high frequency region.
Fig. 8 Comparison of modeled and measured S-parameters of
the HEMT (Wg = 100 µm, Lg = 0.35 µm). Frequency: 1–
62 GHz, Bias: Vgs = −0.2 V, Vds = 2 V. Crosses indicate measured values and lines indicate modeled values.
Considering that no optimization was performed and
the measurement errors in the high frequency limit, it
can be said that the agreement between the modeled
and measured S-parameters is quite good. We also observed that for other normal operating bias points, the
modeled S-parameters are in good agreement with the
measured S-parameters.
4.
Conclusion
We proposed a technique that is able to reliably extract
JEON et al: A TECHNIQUE FOR EXTRACTING SMALL-SIGNAL EQUIVALENT-CIRCUIT ELEMENTS
1975
HEMT small-signal equivalent-circuit elements without
any gate degradation. The proposed technique biases
the gate of the HEMT at a voltage slightly below the
pinch-off voltage. By applying such a bias voltage, the
technique can determine the extrinsic resistance values
completely without an additional relationship for the
resistances.
We used the R-estimate for the extraction of extrinsic inductance values instead of the conventionally
used least-squares regression. The R-estimate is more
robust relative to measurement errors than the leastsquares regression.
We suggested an improved cold HEMT model by
which the extrinsic resistance and inductance values
are extracted. We confirmed that the suggested cold
HEMT model well reflects the frequency characteristics of a cold HEMT under various gate bias conditions
including strong forward and strong pinched-off gate
bias.
The intrinsic element values determined by the deembedding procedure were almost constant over the frequency range of 1 to 62 GHz, which indicates that the
extrinsic resistance and inductance values extracted by
the proposed technique are accurate and reliable.
For the extraction of the equivalent-circuit elements, the proposed technique requires only one additional RF measurement of the cold HEMT and uses
no optimization. Therefore, the technique is suitable
for the extraction of the small-signal equivalent-circuit
of the HEMT in a wafer-probe measurement environment.
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
Acknowledgement
[16]
The authors would like to thank Dr. K. Shirakawa of
Fujitsu Laboratories Ltd. and Professor Y. Daido of the
Kanazawa Institute of Technology, Japan, for providing
the measured S-parameters of the HEMT. This work
has been partially supported by Microwave Application
Research Center in POSTECH, Optical Electronics Research Center in KAIST and Hyundai Electronics Industries Co., Ltd., Republic of Korea.
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IEICE TRANS. ELECTRON., VOL.E82–C, NO.11 NOVEMBER 1999
1976
Man-Young Jeon
was born in Kimcheon, Korea, in 1959. He received the
B.S. and M.S. degrees in electronic engineering from Kyungpook National University, Taegu, in Korea, in 1987 and
1991, respectively. From 1987 to 1989,
he was a member of research staff at the
Electronics and Telecommunications Research Institute (ETRI), where he was involved in the VLSI design project for the
TDX-10 switching system. From 1991 to
1992 he was with Telecommunications Research Center, Samsung Electronics Co., Ltd., where he participated in the development of ASICs for the TDX-10 switching system. He rejoined
the ETRI in 1993, and was involved in ATM switch development project. He was a senior member of research staff of the
ATM access section at the ETRI. From 1997, he is pursuing toward the Ph.D. degree in electronic and electrical engineering in
Pohang University of Science and Technology (POSTECH), Pohang, Korea. His current research interests are equivalent-circuit
parameter extraction of HEMT and MESFET, and MMIC design. He is also interested in ATM traffic control, ASIC design
for communication system, and adaptive filter theory.
Byung-Gyu Kim
was born in Taegu,
Korea, in 1974. He received the B.S. degree in elctronic engineering from Kyungpook National University, Taegu, in Korea, in 1997, and the M.S. degree in electronic and electrical engineering from the
Pohang University of Science and Technology (POSTECH), Pohang, Korea, in
1999. He is now pursuing toward the
Ph.D. degree in electronic and electrical
engineering in the same university. His
current research interests are the fabrication of HEMT and
MMIC design.
Young-Jin Jeon
was born in Kimcheon, Korea, in 1970. He received the
B.S. degree in electronic engineering from
Kyungpook National University, Taegu,
in Korea, in 1993, and the M.S. and Ph.D.
degree in electronic and electrical engineering from the Pohang University of
Science and Technology (POSTECH), Pohang, Korea, in 1995 and 1998, respectively. He is now a member of research
staff at the LG Semicon, where he is involved in the development of DDR SDRAMs. His current research interests include analog integrated circuits design and Si
RF integrated circuit design.
Yoon-Ha Jeong
was born in
Youngchun, Kyungbuk, Korea. He received the B.S. and M.S. degrees in electronic engineering from Kyungpook National University, Taegu, Korea, in 1974
and 1976, respectively, and the Ph.D. degree in electronic engineering from the
University of Tokyo, Japan, in 1987.
From 1976 and 1981, he was an assistant professor in electronic engineering,
Kyungnam College of Technology, Pusan,
Korea. From 1982 and 1987, he was a research assistant, department of electronic engineering, University of Tokyo, where
he pioneered in situ vapor phase deposition and development of
photo-CVD Technology for InP MISFET’s. He joined as an assistant professor in 1987, and became an associate professor in
1992, and a professor in 1997, department of electronic and electrical engineering, Pohang University of Science and Technology
(POSTECH), Pohang, Korea. During 1990 and 1991, he was
a visiting research fellow, Bell Communications Research (Bellcore), Red Bank, NJ, U.S.A, where he was engaged in development of delta-doped FET’s and HEMT’s. He was also a visiting
professor at the University of Washington, Seattle, Washington,
U.S.A, from 1997 to 1998. His research interests include microwave and millimeterwave device fabrication, characterization,
modeling, and circuit design, based on GaAs and InP compound
semiconductors, and single electron transistors. Dr. Jeong received the graduate excellent award from Rotary International
Foundations in 1984, a research fellowship award from Japanese
government from 1985 to 1987, and a research fellowship award
from Korean government in 1990. He is a senior member of the
IEEE Electron Device Society, a member of the IEEE Microwave
Theory and Techniques, Japan Society of Applied Physics, and
the Institute of Electronics Engineers of Korea.