Temperature Impact on the In-Situ S-Parameter
Calibration in Advanced SiGe Technologies
Andrej Rumiantsev 1), 2)

Ralf Doerner

1)

MPI Corporation,
Chu-Pei City, Hsinchu County, Taiwan
2)
Brandenburg University of Technology (BTU),
Cottbus-Senftenberg, Cottbus, Germany
a.rumiantsev@ieee.org

Ferdinand-Braun-Institut (FBH),
Leibniz-Institut fuer Hoechstfrequenztechnik,
Berlin, Germany
ralf.doerner@fbh-berlin.de

Falk Korndoerfer
Innovations for High Performance Microelectronics (IHP)
Leibniz-Institut fuer innovative Mikroelektronik,Frankfurt (Oder), Germany
korndoerfer@ihp-microelectronics.com
Abstract—This paper analyzes the in-situ S-parameter
multiline TRL and the transfer TMR calibration methods for thesensitivity to the thermal variation of electrical characteristics ofcalibration standards. The standards were realized in IHP’s
SG13 130 nm SiGe:C BiCMOS process. The measurement
experiment was performed for the frequency range up to
110 GHz. We demonstrate that the calibration error caused bythermal instability of electrical characteristic of standards is inorder of magnitude of the system drift error and, thus, negligible.
Keywords—S-parameter calibration, device characterization,
mm-wave measurements, BiCMOS.

I.

INTRODUCTION

Increasing demand for more content, higher data transfer
rates and cost reduction pushes the development of advanced
SiGe technologies operating at mm-wave and sub-THz ranges.
Optimization of device models over extremely wide frequency
ranges and across multiple temperatures as well as verificationof the results with highest level of accuracy and confidence
becomes more and more challenging. Therefore, accurate andconsistent in-situ S-parameter calibration procedures covering
wide frequency and temperature ranges are the critical successfactor for development of advanced SiGe technologies.
The state-of-the-art in-situ S-parameter calibration
techniques for Silicon processes were reviewed in [1]. It
recommended implementation of two comparable calibration
concepts: 1) the probe-tip calibration performed on thecommercially available Alumina substrate, followed by theadvanced six-step de-embedding procedure, and 2)
straightforward in-situ multiline Thru-Reflect-Line (TRL) or
transfer Thru-Match-Reflect (TMR, also known as LRM+).
However, [1] presented results for the room temperature only.
Possible variation of electrical characteristics of calibration
standards with the change of the measurement temperature,and, as a result, the accuracy of the over-temperature
calibration remained unclear.
Later, the work in [2] addressed this topic for the firstcalibration concept. It proposed a method for accuracy analysisof the over-temperature probe-tip calibration. It wasdemonstrated that the temperature variation has a marginal
impact on the electrical characteristic of the evaluatedcommercially available Alumina calibration standards. In thispaper, we present the investigation results for the second
calibration concept applying custom on-wafer standards andthe multiline TRL and the transfer TMR. The objective of thiswork is to identify standards parameters that are most sensitive
to the temperature variation as well as to propose a practicalmethod for compensation of possible calibration error.
II.

ANALYSIS METHOD

Multiline TRL and TMR calibration methods differently
define calibration reference impedance ZREF : For themultiline TRL, the reference impedance is set to thecharacteristic impedance ZLIN E of the line standard.
Assuming that the conductive loss of the microstrip-designed
transmission line is negligible in the frequency range ofinterest, we calculated ZLIN E from the measured capacitance
per unit length C 0 and propagation constant ° , as proposed in[3, 4]. Once ZLIN E is known, the calibration reference
impedance can be transformed to the desired value of
ZREF = 50 Ð.
The ZREF for TMR depends on the impedance of thematch (load) as well as ° and ZLIN E of the thru. Therefore,
multiline TRL and the transfer TMR may show different
calibration residual error across the temperature range.
As it was already proposed in [2], the maximum error
bounds for measured S-parameters of a passive device are a© 2014 IEEE. Reprinted, with permission, Bipolar/BiCMOS Circuits and Technology Meeting (BCTM); DOI: 10.1109/BCTM.2014.6981307

reliable figure of merit (FoM) of the calibration accuracy,
calculated by the calibration comparison technique at given
temperature. The benchmark calibration conditions were
established by using pre-characterized temperature-dependent
electrical properties of standards. The test calibration was
performed at the test temperature, but using electrical modelsof standards extracted at the room temperature. Thus, themaximum error bounds can be calculated for each temperaturepoint and calibration method used.

IV. RESULTS AND DISCUSSIONFirst, the propagation constant ° (Fig. 2) and thecapacitance per unit length C 0 were determined using themultiline TRL method for every temperature point. The
extracted characteristic impedance of the line ZLIN E (Fig. 3),
as well as other parameters of the calibration standards are
given in the Table I.

10

III. EXPERIMENTAL SETUP

We designed test structures consisting of open, short, load,
thru, and 10 microstrip lines (Fig. 1). Their lengths vary from
0.4 mm to 15.1 mm. The length ratio between two lines isalways non-integer. We decided for microstrip lines tocircumvent influences of substrate losses in the silicon wafer.
The signal line is designed in the topmost metallization
layer (TM2) and the ground plane in the lowest (M1). The
signal line is 15 µm wide. The ground plane has a width of
90 µm. The insulator between signal line and ground plane is
9.8 µm thick with a dielectric constant of εr = 4.1. The
expected line impedance is about 50 Ω with that dimensions.
All structures are placed in GSG pads with 100 µm pitch.
We added 65 µm feeding lines between contact pad and lines
to allow a homogenization of the fields.

233K
300K
398K

Attenuation (dB/cm)

8

6

4

2

0
0

20

40

60

80

Frequency (GHz)
2.00

Relative Phase Constant (unitless)

A. Calibration Standards
The test structures were realized in IHP’s SG13 process. It
is a 130 nm SiGe:C BiCMOS process with 5 thin and 2 thickaluminum metallization layers [5]. The top metallization layers
have 2 µm and 3 µm thickness, respectively. Two types ofbipolar transistors are available in the process. The high speed
HBTs feature fT/fMAX of 240 GHz/330 GHz at a breakdown
voltage BVCEO of 1.7 V. The high voltage HBTs
BVCEO of 3.7 V with cut-off frequencies fT/fMAX of
50 GHz/130 GHz.

233K
300K
398K

1.95

1.90

1.85

1.80
0

20

40

60

80

Frequency (GHz)

Fig. 2. Attenuation constant (top) and the relative phase constant (bottom) of
the line standard measured across the temperature.

Fig. 1. Selected layouts of the designed calibration standards (from left toright: open, short, load, thru, and line).

B. Measurement Setup
The experimental setup included a semi-automatic thermalprobe system PA200 and Agilent PNA 67 GHz vector network
analyzer (VNA). Experiments were conducted for threetemperature points: 233 K, 300 K, and 398 K covering typicaldevice modeling temperature range. All measured data ofcalibration standards and the device under test were acquired
uncorrected, in one series, and saved for further analysis. Thus,
uncertainty caused by contact repeatability is minimized.

With the measurement temperature variation from 233 K to
398 K, the maximum variation of key standard parameterscompared to room temperature (300 K) is: 1.8% for the load
resistance, 33% for the M1 sheet resistance, 1.4% for the line
capacitance per unit length C 0 , 14% for the attenuation
constant ® , and is marginal (0.4%) for the relative phase
constant ¯=¯0 . As a result, the maximum variation of thecharacteristic impedance ZLIN E is 1.7% for its real and 15%
for its imaginary part respectively (for 40 GHz frequency). We
attributed measured variations in the electrical parameters ofcalibration standards to the temperature impact on the sheet
resistance and the permittivity of dielectric. Once ZLIN E (T ),RLOAD (T ) and ° (T ) are defined, the impact of each of themon the calibration accuracy of the multiline TRL and thetransfer TMR can be estimated.

© 2014 IEEE. Reprinted, with permission, Bipolar/BiCMOS Circuits and Technology Meeting (BCTM); DOI: 10.1109/BCTM.2014.6981307

233

300

398

® @ 40 GHz, dB/cm

4.22

4.85

5.53

¯=¯0

1.856

1.864

1.870

C0, pF/cm

1.248

1.241

1.224

<(ZLINE ) @ 40 GHz, Ω

49.61

50.10

50.96

=(ZLINE ) @ 40 GHz, Ω

-1.55

-1.79

-2.06

RLOAD;P 1, Ω

51.64

50.77

49.99

RLOAD;P 2 Ω

51.33

50.43

49.76

M1 sheet resistance, Ω/¤

0.08350.10860.1439TM2 sheet resistance, Ω/¤

0.00820.01110.0151

56

233K
300K
398K

Real(ZLINE) (Ohm)

54

0.06

233K:
398K:

mTRL
TMR
mTRL
TMR
System drift

0.04

'

Temperature, K

Parametertypical drift of the on-wafer setup and, thus, negligible (Fig. 4).
The setup drift was obtained from a separate experiment.
Therefore, the extensive characterization of the electricalproperties of both the lumped and the distributed calibration
standards is not required. This founding significantly simplifies
implementation of the over-temperature in-situ calibration foradvanced SiGe technologies.

Max Error Bounds |S ij-Sij|/|Sij|

TABLE I. STANDARD PARAMETERS VARIATION OVER TEMPERATURE

0.02

0.00
0

20

40

60

80

Frequency (GHz)52

Fig. 4. Maximum error bounds calculated for multiline TRL, and transfer
TMR for TT EST = 233 K and TT EST = 398 K with benchmark andworst case definition of standard properties. Typical experimental drift of acomparable setup is added for reference.

50

10

233K
398K

48
0

20

40

60

80
9

Capacitance (fF)

Frequency (GHz)
5.0

233K
300K
398K

2.5

Imag(ZLINE) (Ohm)

233K (simp)
398K (simp)

8

7

0.0
6
0

20

40

60

80

Frequency (GHz)

-2.5

-5.0
0

20

40

60

80

Frequency (GHz)

Fig. 3. Real (top) and imaginary (bottom) parts of the characteristic
impedance ZLIN E of the line standard measured across the temperature.

We calculated the maximum error bounds for both
calibration methods for simplified (T = 300 K ) andcharacterized (T = TT EST ) models of calibration standards
for every temperature point TT EST using the method from [2].
The maximum error bounds are 0.02 for the multiline TRL for
TT EST = 398 K and 0.027 for the transfer TMR for
TT EST = 233 K at 67 GHz, respectively. It is lower than theFig. 5. CBE of a test DUT extracted from the cold S-parameter conditions
for the benchmark and simplified multiline TRL at TT EST = 233 K and
TT EST = 398 K . The results extracted for the transfer TMR are similar.

The calibration residual error of the simplified multiline
TRL stems from the error of the characteristic impedance ofthe line ¢ZLIN E that we found to be frequency independent.
Thus, we observed constant maximum error bound0
jSij¡ Sij j=jSij j. The transfer TRM residual errors are the sumof errors of the characteristic impedance ¢ZLIN E and the
propagation constant ¢° of the line, as well as of the
impedance of the load ¢ZLOAD . The individual impact ofeach of the errors depends on the frequency range: The error in
the load resistance and the line characteristic impedancecontribute the most at lower frequencies, while the impact of© 2014 IEEE. Reprinted, with permission, Bipolar/BiCMOS Circuits and Technology Meeting (BCTM); DOI: 10.1109/BCTM.2014.6981307

errors in the load reactance and line propagation constantpredominate at higher frequencies.

mTRL
TMR
System drift
0.08

V.

CONCLUSION'

Max Error Bounds |S ij-Sij|/|Sij|

0.12

comparable with those for the 67 GHz probe system (Fig. 6,7). However, we observed a minor deviation of the extracted
CBE from the expected value above 60 GHz for the TMR
calibration (up to 13% at 110 GHz). This error can be
attributed to insufficiencies of the load standard model. It canbe decreased by an appropriate description of the load
impedance [6] what was out of the scope of this experiment.

0.04

0.00
0

20

40

60

80

100

120

Frequency (GHz)

Fig. 6. Maximum error bounds calculated for multiline TRL, and transfer
TMR for the 110 GHz setup and for TT EST = 358 K with benchmark andworst case definition of standard properties. Typical experimental drift of acomparable setup is added for reference. Measurement data were obtained on
the second experimental system.
16

Capacitance (fF)

TMR
mTRL

TMR (simp)
mTRL (simp)

For the first time, sensitivity analysis of the in-situ overtemperature calibration was performed for the multiline TRL
and the transfer TMR implemented in the advanced SiGe
BiCMOS process up to 110 GHz. The obtained results
demonstrated that temperature variations of the electricalcharacteristics of load and line standards lead to different
calibration residual errors depending on the calibration methodused.
For the considered experimental setup, we found that themultiline TRL calibration method was less sensitive totemperature. However, the worst-case error bound for bothmethods were three times less than the typical drift of themeasurement setup. Therefore, complicated and timeconsuming experiments for characterization of the temperature
coefficients of custom calibration standards are not required.
Extracted CBE of a test HBT proved this statement. Results ofthis investigation significantly simplify implementation of theadvanced in-situ calibration methods into the conventional
characterization workflow of advanced SiGe devices.

12

REFERENCES[1]

N. Derrier, A. Rumiantsev, and D. Celi, "State-of-the-art and future
perspectives

8

incalibration

andde-embedding

techniquesforcharacterization of advanced SiGe HBTs featuring sub-THz fT/fMAX,"in Bipolar/BiCMOS Circuits and Technology Meeting (BCTM), 2012.
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[2]

4
0

20

40

60

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A. Rumiantsev, G. Fisher, and R. Doerner, "Sensitivity analysis ofwafer-levelover-temperatureRF

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Measurement Symposium (ARFTG)-Fall, 80th, San Diego, CA, USA,

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Fig. 7. CBE of a test DUT extracted from the cold S-parameter conditions
for the benchmark and simplified multiline transfer TMR at
TT EST = 358 K: Measurement data were obtained on the second
experimental system.

Finally, the capacitance CBE of a test HBT at
TT EST = 233 K and TT EST = 398 K was extracted from thecold S-parameters corrected with the benchmark and thesimplified calibrations (Fig. 5). In both cases, the difference
between the extracted value from the benchmark and thesimplified calibration is negligible. Fig. 5 shows the results forthe multiline TRL calibration. The results for the transfer TMR
calibration are similar.
We repeated the experiment for the same device on a
110 GHz system, which allowed a temperature variation from300 K to 358 K. The obtained results are, in general,[3]

R. B. Marks and D. F. Williams, "Characteristic impedance
determination

using

propagation

constant

measurement,"IEEE

Microwave and Guided Wave Letters, vol. 1, pp. 141-143, June 1991.
[4]

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[5]

H. Rucker, B. Heinemann, W. Winkler, et al., "A 0.13 um SiGe
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[6]

A. Rumiantsev, “On-Wafer calibration techniques enabling accuratecharacterization of high-performance silicon devices at the mm-wave
range and beyond,” Fakultät für Maschinenbau, Elektrotechnik und
Wirtschaftsingenieurwesen, BTU Cottbus, Cottbus, 2014.

© 2014 IEEE. Reprinted, with permission, Bipolar/BiCMOS Circuits and Technology Meeting (BCTM); DOI: 10.1109/BCTM.2014.6981307