Improving Wafer-Level Calibration Consistency
with TMRR Calibration Method
Andrej Rumiantsev1, Tony Fu1, and Ralf Doerner2
1

2

MPI Corporation, Advanced Semiconductor Test Division, Chu-Pei City, Taiwan
Ferdinand-Braun-Institut (FBH), Leibniz-Institut fuer Hoechstfrequenztechnik, Berlin, Germany

Abstract — This paper presents the new calibration algorithm
TMRR (Thru-Match-Reflect-Reflect), the extension of the ThruMatch-Reflect (TMR) method with one extra Reflect standard.
The algorithm was developed to reduce the impact of anasymmetrical placement of RF probes on coplanar probe-tip
calibration standards on consistency and reproducibility ofcalibration results often observed for an inexperienced system
operator. The introduction of an additional Reflect calibration
element to the TMR algorithm increases the measurement
information redundancy, and thus reduces the calibration error
caused by possible asymmetry in reflection coefficients of lumped
standards. The new method was verified for simulated data as
well as for an InP DHBT device operating in the “off-state”
regime.
Index Terms — S-parameters, calibration, on-wafer
measurements.

I. INTRODUCTION
The operation frequencies of semiconductor devices andcircuits continuously increase and confront characterizationengineers with new challenges: the device under test (DUT)
pad de-embedding methods turn out to be complex and require
additional dummy elements; the positioning of RF probe on
calibration standards and DUT contact pads has to be more
precise. It becomes hard to ensure accuracy, repeatability, andreproducibility of the system RF calibration and measurement
data.
Implementing calibration standards into the device test chipsignificantly reduces back end of line (BEOL) parasitics,
simplifies device parasitic de-embedding step and eliminates
impact of the RF probe misplacement error on calibration
standards [1]. However, is not always possible to scarify wafer
real estate for custom calibration kits. Therefore, thealternative solution involves improving accuracy andconsistency of the probe-tip calibration process conducted oncommercially available alumina calibration substrates [2].
The calibration method of [3] enabled asymmetry of the
Load equivalent impedance. As is was later demonstrated in[4], it is essential to measure Load standard on each VNA port
during the calibration process. However, possible asymmetryin Reflect impedance (e.g. due to misplacement of RF probes
on the standard) still remains the main contributing factor tothe overall accuracy of the system calibration. This work
extends the method of [4] by introducing additional Reflect
standard to the conventional TMR calibration algorithm. The
new TMRR method uses redundancy of standard
978-1-5386-5450-7/18/$31.00 ©2018 IEEE

measurements to reduce the impact of this type of error on
accuracy and consistency of the system calibration.
The next chapter briefly describes the theoreticalbackground of the TMRR calibration solution. The Chapter III
presents verification results for the numerical experiment aswell as for an active DUT.
II. THEORETICAL BACKGROUND
The systematic measurement errors of a modern two-port
double-reflectometer VNA can be fully described by thedenote theseven-term error model given by Fig. 1, where
wave quantities measured by an ideal th VNA receiver;are the 2x2 matrices of error terms;
and are theandth port of the DUT, andis thewave quantities at the-parameter matrix of the DUT [5]. Self-calibration
andfrom measurement data ofalgorithms calculate
partly-known calibration standards, such as the Line and theReflect for the TRL1 method; reflect for the TMR, LRM2.

Fig. 1. The seven-term systematic error model of a two-port double
reflectometer VNA.

Usually, the solution for the seven error terms consists of
two steps: 1) calculation of the a priori unknown electricalcharacteristics of partly-known standards (i.e. “self-calibration
step”); 2) calculation of the error terms based on the measured
data of calibration standards and their now fully known
electrical characteristics.
The relationship between the actual and measured parameters of a two-port DUT is given by:
,
where

1
2

is the measurement matrix:

Thru-Reflect-Line
Line-Reflect-Match(1). (2)
Prime and double-prime
denote data acquired in forward
and reverse direction, respectively. The measurement of a oneon the first andport device with the reflection coefficientand:the second VNA port yields
,

(3)

,

(4)

where :

This is particularly beneficial for on-wafer calibration: thereactance of the on-chip match standard is usually different
between its ports due to asymmetry in the via stack.
The measurement, self-calibration and calibration steps canbe extended by adding the third partly-known one-port. Its reflection coefficient can be found in theelement
same way as . Thus, the three-standard calibration solution
TMR is expanded to the four-standard method TMRR with ahigher grade of measurement information redundancy.
III. EXPERIMENTAL RESULTS AND ANALYSIS
A. Worst-Case Scenario of CPW Standards Asymmetry

.

(5)

and
can beAs shown in [5], the error-term matrixes
derived from measurements of at least three different(e.g., Thru),
standards: one fully known two-port element
one fully known element(e.g. Match,), and one partly
known
one-port element (e.g. Reflect, ).
For the Thru standard, we have:, and therefore:.

(6)

Re-composing (2)-(4) and taking into account (6), we arrive
at:
,
,
,
,

(7)
(8)
(9)
(10)

,
are measured results for the first
, and
where
,
for the second
one-port standard, respectively,
with:
,
,
,
.

We conducted several experiments to verify the capabilityof the proposed calibration method. First, we defined the
maximum possible asymmetry in equivalent impedances of
lumped coplanar calibration standards. It is caused bymisplacement of RF probes on the standard (Fig. 2). Theseerrors usually occur in case of inexperienced system operators,
entry-level manual wafer probe systems equipped with lowresolution microscopes, inaccurate or unstable chuck stages
and imprecise RF probe positioners. For a paired symmetrical
one-port standard, the maximum asymmetry of its equivalent
impedance corresponds to the maximal lateral shift of both RFprobes either to the left or to the right [6]. So, one probe
entirely overlaps the standard contact pad while the otherprobe barely touches the edge of the pad (Fig. 3).

a)

b)

c)

Fig. 2. Equivalent impedance models of lumped standards: a) Load,b) Open, c) Short(11)

Equations (7)-(10) can be solved for a priory unknown. Thus, the unknown reflection
and forcing
coefficient of the second one-port calibration standard can befound without calculating error terms.
It is important to note, (7)-(10) do not impose any specific. In the mostrequirements to the first one-port standard
general case, it can be realized as an asymmetrical elementwith known arbitrary impedance, i.e. it is allowed:
(12)

a)

b)

Fig. 3. From left to right: probe-tip coplanar Load, Open, and Shortstandards in ground-signal-ground (GSG) configuration withcentral RF probe contact points, i.e. nominal equivalent
impedance, a), and same standards contacted with maximal
lateral shift of RF probes to the left, i.e. maximum asymmetryof the standard equivalent impedance, b).

In this experiment, we used an AC2 calibration substratefrom MPI Corporation that includes Open, Short, Load, Thru
and five calibration Lines in CPW design. It can be used forcalibrating RF probes in GSG configuration of pitches from100 µm to 250 µm. The lumped standard width is 50 µm andthus, the maximal possible lateral shift of RF probes is 25 µm.
Table I presents the nominal equivalent model parameters ofcalibration standards as well as the extracted model
parameters for the shifted configuration of the probes.
Because the probe-to-probe distance remained unchanged,
we did not observe any variations in extracted model
parameters for the thru standard.

Our experiment focused on the worst-case scenario with
off-wafer standards (located directly under the probe tips) andthe maximum lateral shift of the probes. In this case we havethe highest asymmetry between standard impedances. Onwafer calibration standards, however, are located relatively far
from the probe tips. Thus, they are significantly less sensitive
to the RF probe placement error.

2.
0

1.0

0. 6

0.8

10.0

3.0
4.0
5.0

2.0

0.8
1.0

0.6

0.4

0

0.2

10.0

2
- 0.

.0
-2

.4

Sw p Min
0.1GHz

-1.0

-0.8

-0

.6

-0

-3
.0
-4
.
- 5. 00

Shifted
P1
P2
5.1
6.5
0.5
-11.7
6.5
-5.0

5.0

-10.0

Open, fF
Load, pH
Short, pH

Nominal
P1
P2
5.8
5.8
-6.0
-6.0
0.8
0.8

3.

DUT C1 - model
4. 0

0.2

Standard

Sw p Max40GHz

DUT RiL1 - model
0

0.
4

TABLE IEXTRACTED MODEL PARAMETERS OF EQUIVALENT IMPEDANCEOF CPW STANDARDS USED IN THE EXPERIMENT

S11, S22

Fig. 4. S-parameters of the verification DUT-PAD-SHORT and
DUT-PAD-OPEN devices.

Reflection Magnitude, dB

-0.8

-0.9

DB(|S[1,1]|)
TMR_O

DB(|S[1,1]|)
TMRR

DB(|S[2,2]|)
TMR_O

DB(|S[1,1]|)
TMR_S

DB(|S[1,1]|)
Model

DB(|S[2,2]|)
TMR_S

200

180

-1

160

-1.1

140

-1.2
0

10

20
Frequency (GHz)

Reflection Phase, Degrees

DB(|S[2,2]|)
TMRR

30

40

Ang(S[1,1])
TMR_O

Ang(S[1,1])
TMRR

Ang(S[2,2])
TMR_O

Ang(S[1,1])
TMR_S

Ang(S[1,1])
Model

Ang(S[2,2])
TMR_S

120
0

10

20
Frequency (GHz)

Ang(S[2,2])
TMRR

30

40

Fig. 5. S11 and S22 of the DUT_PAD_SHORT device corrected withthe respect to TMR(O), TMR(S) and TMRR methods.

B. Evaluation of Calibration Error Caused by Standards
Asymmetry
Next, we evaluated the measurement error of theverification devices caused by the maximum positioning errorof RF probes on lumped CPW standards during systemcalibration. This experiment used synthesized raw data seriesof calibration standards and verification elements, DUT-PADOPEN and DUT-PAD-SHORT, respectively. The DUT-PADOPEN is a capacitor of CO=270 fF and the DUT-PADSHORT is a series connection of a resistor RS=3  and an
inductor LS=20 pH. Similar elements are commonly used asdummy structures for de-embedding of the back end of line
parasitics of silicon processes (Fig. 4).
We modeled two sets of calibration standard raw Sparameters: the “reference set” – using nominal standard
model coefficients, and the “shifted set” – representing theworst-case probe positioning error on all lumped-element
standards (Fig. 2-3, Table I). Next, we executed threecalibrations series and respectively corrected verification
DUTs: TMR with Short as the Reflect (TMR(S)), TMR with
the Open as the Reflect (TMR(O)), and TMRR, with the same
Short standard as the first Reflect and the Open as the second
Reflect element. Fig. 5-6 show the experimental results.

0.5

0.25

Reflection Magnitude, dB
DB(|S[1,1]|)
TMR_O

DB(|S[1,1]|)
TMRR

DB(|S[2,2]|)
TMR_O

DB(|S[1,1]|)
TMR_S

DB(|S[1,1]|)
Model

DB(|S[2,2]|)
TMR_S

-40

-80

0

-120

-0.25

-160

-0.5
0

10

20
Frequency (GHz)

Reflection Phase, Degrees

DB(|S[2,2]|)
TMRR

30

40

-200
0

Ang(S[1,1])
TMR_O

Ang(S[1,1])
TMRR

Ang(S[2,2])
TMR_O

Ang(S[1,1])
TMR_S

Ang(S[1,1])
Model

Ang(S[2,2])
TMR_S

10

20
Frequency (GHz)

Ang(S[2,2])
TMRR

30

40

Fig. 6. S11 and S22 of the DUT_PAD_OPEN device corrected withrespect to TMR(O), TMR(S) and TMRR methods.

This experiment demonstrated that the asymmetry error inlumped standards affects the accuracy of all evaluatedmethods. However, if only one reflect element (Open or
Short) is used for calibration, the measurement error becomesdominant at the opposite site of the Smith chart. For instance,
error is less for the DUT-PAD-SHORT element for TMR(S),while TMR(O) shows the largest error for this device. For thesame data set, the TMRR error is significantly smaller for bothdevices. Also, the measurement error is dominant for themagnitude of the reflection coefficient of the verification
DUTs. One the other hand, it is negligible for the phase.
Also, we observed a larger calibration error for the TMR(O)than for the TMR(S). While this effect requires further
detailed analysis, we anticipate that it may be related tosimilarities in design of the probe tip Load and Shortstandards.
C. Verification for an Active DUT
Finally, we verified the new TMRR method by evaluating
an HBT device. The HBT was fabricated in InP DHBT
transferred-substrate technology from FBH. The off-wafer
TMRR corrected measurements using a commercial
calibration substrate were compared with the multiline TRL(mTRL) as well as the TMR method.
Accurate model parameter extraction is a crucial task forsuccessful circuit design. We found, that special bias point
measurements, which enable the extraction of certain
important model parameters of an HBT [7], are extremely
sensitive to the system calibration.

provides the most trustable measurement results for the test
HBT under considered bias conditions. This ensures that theextraction of model parameters yields reasonable and reliable
results.
IV. CONCLUSION
In this paper we introduced and verified the new calibration
algorithm TMRR. This method extends the TMR procedureby an additional symmetrical Reflect element. The extra
measurement step increases the information redundancy andthus reduces the calibration error caused by possible
asymmetry in reflection coefficients of lumped standards.
Such asymmetry is usually observed for probe-tip calibrationon commercially available alumina coplanar standards.
Experimental results demonstrated that TMRR outperforms
conventional methods that use only one Reflect standard. The
new method is a good candidate for both probe tip and onwafer system calibration.
REFERENCES

0.04
0.02

Reflection Magnitude, dB
DB(|S[1,1]|)mTRL

DB(|S[1,1]|)
TMR

DB(|S[1,1]|)
TMRR

0
-0.02
-0.04
-0.06
-0.08
0

0.04

5

10
Frequency (GHz)15

20

Reflection Magnitude, dB

0.02
0
-0.02
-0.04
-0.06
-0.08
0

DB(|S[2,2]|)mTRL

5DB(|S[2,2]|)
TMR

10Frequency (GHz)

DB(|S[2,2]|)
TMRR

15

20

Fig. 7. Measurement results of an active DUT corrected withrespect to off-wafer TMRR, multiline TRL, and TMR(S)calibration methods: S11 (top) and S22 (bottom).

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