Vol. 35, No. 5
Journal of Semiconductors
May 2014
Planar Schottky varactor diode and corresponding large signal model for millimeterwave applications
Huang Jie(黄杰)1; 2; Ž , Zhao Qian(赵倩)3 , Yang Hao(杨浩)4 , Dong Junrong(董军荣)4 ,
and Zhang Haiying(张海英)4
1 School
of Engineering and Technology, Southwest University, Chongqing 400715, China
Key Laboratory of Millimeter Waves, Nanjing 210096, China
3 School of Physical Science and Technology, Southwest University, Chongqing 400715, China
4 Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China
2 State
Abstract: A GaAs-based planar Schottky varactor diode (PSVD) is successfully developed to meet the demand
of millimeter-wave harmonic generation. Based on the measured S-parameter, I –V and C –V characteristics, an
accurate and reliable extraction method of the millimeter-wave large signal equivalent circuit model of the PSVD
is proposed and used to extract the model parameters of two PSVDs with Schottky contact areas of 160 m2
and 49 m2 , respectively. The simulated S-parameter, I –V and C –V performances of the proposed physics-based
model are in good agreement with the measured one over the frequency range from 0.1 to 40 GHz for wide operation
bias range from –10 to 0.6 V for these two PSVDs. The proposed equivalent large signal circuit model of this PSVD
has been proven to be reliable and can potentially be used to design microwave circuits.
Key words: planar Schottky varactor diode; large signal equivalent circuit model; millimeter-wave; GaAs
DOI: 10.1088/1674-4926/35/5/054006
EEACC: 2520
1. Introduction
The planar Schottky varactor diode (PSVD) is widely used
as a nonlinear device to generate harmonics for use in solidstate microwave power sources at the millimeter wave and
submillimeter wave frequency ranges due to its fast switching capability and high harmonic conversion efficiencyŒ1; 2 .
Moreover, the corresponding fabrication process is compatible with standard GaAs monolithic microwave integrated circuits (MMICs) technology and an increasing number of applications based on PSVDs have emerged recently in fields such
as radio astronomy, automotive radar, atmospheric science
and wide-band communications, especially in frequency multiplier, voltage-controlled oscillator and phase shiftersŒ3 5 . It
is known that these high-performance MMICs depend on the
characteristics determined by the device epitaxial layer and layout structure, and the knowledge of the large signal equivalent
circuit models is very useful and important for the device performance analysis and accurate design of MMICs. Exact extraction of PSVD device parameters is indispensable for optimizing the PSVD device and its corresponding circuitsŒ6 .
In this paper, an equivalent large signal circuit model of the
PSVD developed by us is proposed. Avoiding the drawbacks
of complex optimization algorithmsŒ7 , a straightforward and
fully analytical technique is used to determine the equivalent
circuit parameters of the PSVD. The proposed physics-based
device model, validated by I –V , C –V and S-parameter characteristics over the frequency range from 0.1 to 40 GHz for a
wide bias range from 10 to 0.6 V for two PSVDs with dif-
ferent Schottky contact areas of 160 m2 and 49 m2 , consists of bias-dependent intrinsic nonlinear elements and biasindependent extrinsic parasitic elements. The proposed equivalent large signal model of the PSVD has been successfully
used to design microwave and millimeter-wave monolithic
ICs, such as a frequency multiplierŒ8; 9 .
2. Device structure and the equivalent large signal circuit model
The epitaxial structure of the PSVD employed in our study
is shown in Table 1. All layers were grown by molecular
beam epitaxial (MBE) technology on a semi-insulating GaAssubstrate. From top to bottom, the basic structure consists of
a 0.6 m-thick n active layer doped with Si at a level of 5 1016 cm 3 , which was determined by a tradeoff between the
power handling ability and the conversion efficiency, and a
1 m-thick nC buffer layer doped with 5 1018 cm 3 , which
was optimized for good ohmic contact and lower parasitical
resistanceŒ10; 11 . In this paper, the PSVDs are fabricated with
Schottky contact areas of 160 m2 (20 8 m2 ) and 49 m2
(7 7 m2 ) by the RFIC Laboratory at the Institute of Microelectronics at the Chinese Academy of Sciences. The schematic
diagram and successfully developed photograph of the PSVD
are presented in Fig. 1, where the anode (Schottky contact) and
cathode (ohmic contact) electroplate are separated by a gap of
4 m.
The proposed large signal equivalent circuit model, shown
in Fig. 2, is based on the fabrication process and physical lay-
* Project supported by the Fundamental Research Funds for Central University of China (No. XDJK2013B004), the Research Fund for the
Doctoral Program of Southwest University of China (No. SWU111030), and the State Key Laboratory for Millimeter Waves of Southeast
University of China (No. K201312).
† Corresponding author. Email: jiehuang@swu.edu.cn
Received 25 September 2013, revised manuscript received 2 December 2013
© 2014 Chinese Institute of Electronics
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Huang Jie et al.
Table 1. The planar Schottky varactor diode epitaxial layer structure.
Layer
Thickness
Dopant
Concentration
(m)
(cm 3 /
n active
0.6
Si
5 1016
C
n buffer
1
Si
5 1018
S.I. GaAs
Fig. 3. Characteristic of the PSVD at large forward-biased voltage.
3. Extraction of the equivalent circuit elements
3.1. Determination of the parasitic anode-to-cathode pad
capacitance Cp
Fig. 1. Schematic diagram and photograph of the PSVD.
Firstly, the anode-to-cathode pad capacitance Cp can be
obtained by measuring a dumbed device based on the device
layout structure after de-embed parasitic capacitance and inductance of the test PAD. Then the capacitance value of 1 fF is
obtained; the parasitic capacitance can not be neglected when
the PSVD is operated at the millimeter-wave frequency.
3.2. Determination of the parasitic inductance Ls
Fig. 2. Large signal equivalent circuit model for the PSVD.
out structure of PSVD, and consists of the bias-dependent intrinsic elements and the bias-independent extrinsic elements.
The intrinsic elements are composed of nonlinear junction resistance Rj characterized by the I –V equation, and nonlinear
capacitance Cj by the C –V equation. The extrinsic elements
are composed of the linear series resistance Rs , the finger-topad linear capacitance Ci and Co , the pad-to-pad linear capacitance Cp , and the finger linear inductance Ls . All these extrinsic component values are related to the physical geometry of
PSVDsŒ11 .
When a large forward-biased voltage is applied to PSVD,
the parasitic pad capacitance Ci and Co can be neglected for frequency up to a few gigahertz (typically f < 5 GHz). As shown
in Fig. 3(a), PSVD can be simplified as impedance elements
composed of parasitic inductance Ls and resistance, which can
be verified in Fig. 3(b) by the fact that the imaginary parts of
Y11 and Y22 nearly equal those of Y12 and Y21 , and that
the imaginary parts of the measured Y parameters increase linearly versus the frequency. According to Eq. (1), the parasitic
inductance Ls can be extracted by linear regression of Im(Y11 /
for f < 5 GHz after the parasitic capacitance and inductance
of the test PAD are de-embed.
054006-2
8
<Rj D 1=Real.Y11 /
:L s
Rj Rj Im.Y11 /=.2freq /
(1)
J. Semicond. 2014, 35(5)
Huang Jie et al.
Fig. 4. Characteristic of the PVSD in a varactor mode.
Fig. 5. C –V and I –V characteristics of the PSVD.
3.3. Extraction of the intrinsic nonlinear capacitance Cj
and extrinsic parasitic capacitance Ci and Co
When the PSVD is operated in a varactor mode, the junction resistance Rj is very large and can be ignored. When the
frequency is low, the parasitic series resistances Rs and inductances Ls have no contribution to the imaginary parts of the Y
parameters, and the capacitance effect is dominant. The simplified equivalent circuit model of the PSVD biased in varactor mode is shown in Fig. 4(a). Figure 4(b) presents a typical
set of plotted measured data for the PSVD at 8 V reversedbias. It can be found in Fig. 4(b) that the imaginary part of Y11
nearly equals that of Y22 due to the symmetrical device layout, and that the imaginary parts of the measured Y parameters
increase linearly versus the frequency. To extract nonlinear capacitances Cj , parasitic capacitance Ci and Co , the measured S
parameters from 0.1 to 40 GHz are converted to Y parameters
at the different bias voltage, and the imaginary part is divided
by !, and then the resulting capacitances can be obtained as
Eq. (2).
Ci D
1
Im.Y11 C Y12 /;
!
Co D
1
Im.Y22 C Y12 /;
!
Cj D
1
Im.Y12 /:
!
(2)
The extracted nonlinear junction capacitance can be formulated as Eq. (3)
M
V
Cj D Cj0 1
;
(3)
Vbi
where Cj0 is zero-bias junction capacitance, Vbi is the barrier
potential and M is a junction doping grading parameter. Finally, the extracted parasitic capacitance Ci and Co are averaged.
3.4. Extraction of the intrinsic nonlinear resistance Rj and
extrinsic parasitic series resistance Rs
In the forward-biased and reversed-biased regions, the
diode can be seen as a variable differential nonlinear resistance.
Generally, the nonlinear resistance Rj is characterized by I –V
Eq. (4), where VT is a thermal voltage of 25.7 mV, Is is the
reverse saturation current, Rs is the parasitic series resistance
and N is the ideality factor. When the current of the diode is
very small, for instance 1–10 A, the voltage across the series
resistance can be ignored, and the Is and N can be experimentally obtained due to the linearity relationship between ln I and
V Œ12 .
V IRs
1 :
(4)
I D IS exp
VT N
The series resistance Rs consists of the resistance in the
active layer, the resistance in the buffer layer as well as the re-
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Fig. 6. Comparison of the measured and modeled S -parameters of 160 m2 PSVD versus frequency at different bias.
sistance of the ohmic contact and Schottky contact, which is
important in evaluating the device performance. After the reverse saturation current Is and the ideality factor N are successfully extracted, the series resistance Rs can be experimentally
obtained by a data fit based on the measured I –V characteristic.
4. Experimental result and discussion
The extracted equivalent large signal circuit model of the
PSVD based on the method mentioned above, is validated by
the good agreement between the measured and modeled I –V ,
C –V and S -parameters achieved up to 40 GHz under different bias conditions. Firstly, the measured capacitance-voltage
characteristics for 20 8 m2 PSVD at 1 MHz by an Agilent 4284A Precision LCR Meter and the extracted one can be
seen in Fig. 5(a), where a good agreement between them is observed. The nonlinear junction capacitance Cj of the PSVD is
given by Eq. (3), where the zero-bias junction capacitance Cj0
is 125.2 fF, the barrier potential Vbi is 0.61 V and the index
factor M is 0.36. The capacitance ratio between the maximum
capacitance Cmax and the minimum capacitance Cmin of the
PSVD over the range of applied voltages (–10 to 0.6 V) is 5.4,
and is usually used to weight the device nonlinearity. The DC
I –V characteristics of the PSVD are measured on an HP4155
semiconductor parameter analyzer. The PSVD has an extracted
ideality factor N of 1.04, series resistance Rs of 3.18  and a
reverse saturation current Is of 31.97 fA. Figure 5(b) shows
the comparison between the measured and modeled I –V performances and a good agreement is also successfully achieved.
The modeled S-parameters based on a large signal model
of 160 m2 PSVD are presented in Fig. 6. A comparison between the measured and the modeled results is performed, and
a excellent agreement over the frequency range from 0.01 to
40 GHz for a wide bias range from –10 to 0.6 V is also observed. In order to further verify the validity of the equivalent
large signal model extraction method, another PSVD with the
same layout and a different Schottky contact area of 49 m2
(7 7 m2 ) is successfully fabricated, and the same extraction method is applied to the 49 m2 PSVD, leading to an excellent agreement between the measured and modeled performances shown in Fig. 7. Finally, based on the model extraction
method above, these equivalent large signal circuit model parameters of the PSVD with Schottky contact areas of 160 m2
and 49 m2 are listed in Table 2. It can be found that a smaller
Schottky contact area, a smaller Cj0 , M and Vbi , and a larger Rs ,
Is , N and Von , induces a stronger nonlinearity. Bias-dependent
nonlinear Capacitance does not present the linear relationship
with the Schottky area and bias-independent parasitic elements
remain constant. The extracted lumped-element model of a
PSVD from the measured C –V , I –V and S -parameter characteristics can be implemented by a symbolically defined device
(SDD) in an Agilent ADS simulator and be used to design microwave and millimeter-wave monolithic ICs.
054006-4
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Fig. 7. Comparison of the measured and modeled I –V , C –V and S -parameters of 49 m2 PSVD versus frequency at different biases.
Table 2. The equivalent large signal model parameters of PSVD with
Schottky contact areas of 160 m2 and 49 m2 (Von referred to as
the turn-on voltage, I @ 1.1 V as the current at 1.1 V forward bias).
Parameter
Cp (fF)
Ci (fF)
Co (fF)
Ls (pH)
Rs (/
Is (fA)
N
Cj0 (fF)
M
Vbi (V)
I @ 1.1 V (mA)
Von (V)
49 m2 PSVD
1.4
1.5
4.5
10.6
6.62
81.19
1.21
45.25
0.2
0.55
24
0.75
160 m2 PSVD
1.4
1.5
4.5
10.6
3.18
31.97
1.04
125.2
0.36
0.61
66
0.62
sitic parameters are bias-independent and show no change with
the Schottky contact area, and that the intrinsic nonlinear elements are bias-dependent and show a nonlinear change with the
Schottky contact area. The implemented PSVD SDD model in
the Agilent ADS simulator can be widely used to design the
microwave and millimeter-wave monolithic ICs needed.
References
5. Conclusion
An equivalent larger signal circuit model of a PSVD selfdeveloped to generate harmonics at the millimeter-wave frequency is successfully proposed, and the validity of the extraction method is effectively verified by the good agreement between the measured and modeled I –V , C –V and S -parameters
from 0.1 to 40 GHz for a wide bias range from –10 to 0.6 V
for two PVSDs with Schottky contact areas of 160 m2 and
49 m2 , respectively. It is observed that the extrinsic para-
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