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In this paper, the uncertainty and the impact of imperfect load calibration standard for on-wafer Through-Reflect-Match calibration method are analyzed with the help of 3D electromagnetic simulations. Based on the finding that load impedance can lead to significant errors in calibration, an automatic algorithm to determine the complex impedance of the load standard is proposed. This method evaluates the resistance as well as the parasitic inductance introduced by the misalignment of the probe tip to the substrate pad at mm-wave frequencies or the non-precize load standard. The proposed algorithm was verified by practical measurement, and the results show that by incorporating actual load impedance into the calibration algorithm, the deviations of RF measurement results are greatly suppressed.

In order to research and develop the application of millimeter wave devices in the commercial world, accurate on-wafer measurement is a key requirement since it eliminates the additional errors and uncertainties introduced by the device package [

However, the TRL technique sets the reference impedance after the calibration by the characteristic impedance of the through/lines used. The accurate determination of the frequency-dependent calibration lines’ characteristic impedance thus becomes a key requirement to allow for the correct S-parameter measurement. At lower frequencies, when radiation losses and surface waves can be neglected, the line’s characteristic impedance can be calculated using quasi-static approaches like con-formal mapping [

The issue of accurate characteristic impedance of lines, along with other shortcomings of TRL calibration, such as how multiple lines are required to cover greater than an 8:1 frequency band and the impractically long length of lines at lower frequencies, calls for an alternative calibration approach to TRL calibration [

However, the biggest problem with TRM calibration is its reliance on a precise and predictable load standard. When the assumption of a non-reflecting match standard is not fulfilled, calibration introduces extra residual errors, which degrades the measurement accuracy. However, the ideal load standard to provide a perfect match can never be realized in practice [

In this paper, we propose an improved method to characterize the imperfect match standard for precise on-wafer TRM calibration. Firstly, an uncertainty analysis of TRM calibration using imperfect calibration standards is carried out. Next, a model of the load standard is established using 3D EM simulation. A smart automatic load impedance determination algorithm is thus elucidated. Finally, in

A simplified block diagram of an on-wafer measurement system is shown in _{00},_{11},_{01}, and _{10} are the error terms of block A, and _{22},_{23},_{23}, and _{32} are error terms of bock B. The calibration process can thus be inferred to determine the eight error terms from a set of uncorrected S-parameters measured on a set of calibration standards. For a two-port network, the S-parameter _{
ij
} of calibration items are therefore linearly related to the raw S-parameter measurement data by error terms _{00} _{32}. For TRM calibration, the raw S-parameter measurement data measured by the Vector Network Analyzer can be expressed as_{11} and _{22} are mainly influenced by the deviations _{12} and _{21} are mainly influenced by the deviations _{
m
}, _{
m
}, and _{
m
} correspond to the measured S parameters of the Reflect, Thru, and Match standards, respectively. In the scenario that the calibration standards are not ideal, the deviations of the S parameters are calculated as_{
m
}, _{
m
}, and _{
m
} correspond to the measured S parameters of the Reflect, Thru, and Match standards respectively. In the scenario that the calibration standards are not ideal, the deviations of the S parameters are calculated as follows.

Typical on-wafer measurement system structure:

For non-ideal Reflection standard:

The error comes from the first source and can be minimized by introducing an additional reverse injected active VNA measurement as proposed in Ref.

For on-wafer measurement, the calibration standard is typically fabricated in the form of coplanar waveguide (CPW) geometry. As shown in

The full structure including probes, pad and calibration standard

To better understand the influence of the probe-pad alignment on the load impedance, EM simulation using HFSS software was carried out. In the simulation, the meshed ground planes were simplified considering a continuous metal connection, both vertically and horizontally. This simplification provides a good approximation of the electrical response of the structure, the openings in the metal mesh being much smaller than the wavelength. The signal pad is modeled as a 50*50*3.4 um metal with conductivity of 4.9E7 S/m, and the distance from the signal pad to ground is 100 um. The load consists of two identical zero-thickness rectangular sheets in contact with the signal pad and the ground with a boundary condition of 100 lumped resistance. The CPW line is excited by a wave-guide port considering parasitic effects.

Field distribution of match standard at 100 GHz simulated by Ansoft HFSS Software.

The variation of match standard impedance with different probe tip position on pads.

A lumped elements model, as shown in

The lumped circuit model for probe contacting with the calibration standard in ADS simulation software

As can be seen in

The load impedance using EM simulation, probe misalignment model and simplified model.

From the analysis in _{
act
} will have the measured impedance equals to _{0} = 50 Ω.

The TRM calibration method, by definition, always solves the error terms with the reference plane at the center of the Through standard. The probes-in-air open therefore actually corresponds to a negative-length open stub with a length one-half that of the Through standard and with the reflection coefficient magnitude of unity. If the match standard used in the calibration is offset, it would appear to have a magnitude different from one; additionally, as the on-wafer ISS short standard typically has the same length as the Through line, the short standard will have the reflection coefficient magnitude of unity but in the admittance chart. The open and short calibration standard thus provides a convenient means of determining how far the match standard is offset from the standard 50 Ω.

Returning to the calibration models described in _{
A
} can be represented as_{
M
} represents the impedance of the loads used as the match standard at measurement port. The terms _{
A
} are determined by the raw calibration measurement of Reflect and Through measurement. In the case of measuring match standard, the Y parameter, or the admittance of the match standard, can be expressed as_{
A
} is solely decided by the match standard, for one port, DUT is measured at port 1,

To correct the limitations of the proposed algorithm, an iteration process is thus being introduced, which will take account of the length of the Through and the Short standard. The full calibration steps can thus be summarized as follows:

Make a TRM calibration with the assumption that the load standard is ideal 50 Ω impedance.

Use the calculated error coefficients to measure the S-parameters of the open and short standard.

Calculate the actual impedance of the load standard as the guess value.

Recalculate the error terms from the calculated actual load impedance.

Re-measure the S parameters of the open, short, and through standard with the corrected error terms.

Calculate a difference between the expected reflect coefficient of open, short, and thru standard.

Repeat step 3 to step 6 to minimizes the errors and obtain the desired load impedance.

In order to validate the method proposed, we built a measurement bench composed of a manual probe station, Cascade Summit 11,000, and a Keysight PNA-X Vector Network Analyser. A detailed photo of the measurement bench is shown in

The measurement bench and the imperfect calibration standard used in the experiment.

The real part of load impedance

Next, we drew the S-parameter measurements of the open and short standard, by both the classical TRM calibration method and the impedance correction method proposed in this work. As can be seen in

The re-measured open standard with conventional TRL calibration method (red) and the correction method proposed in this work (blue).

The re-measured short standard with conventional TRL calibration method (red) and the correction method proposed in this work (blue).

In this paper, a comprehensive analysis of the error source of TRM calibration is presented, leading to the conclusion that load impedance is the most important determinant of on-wafer calibration quality. Based on full wave 3D EM simulations, it is shown that the imperfect load impedance was not only caused by the non-precize DC resistance of the load but also by the overlap between the probe tips and the pads on the substrate.

An improved load impedance estimation algorithm has therefore been presented, which automatically calculates the load’s complex impedance in the calibration process. Actual measurements on worn calibration standards up to 40 GHz show that the RF performance due to the variations of imperfect load standard can be corrected by accommodating the calculated load impedance into the TRM calibration method. The novelty of the estimation method lies in is its immune to pad-to-tip discontinuities since it calculates the actual impedance at the time of calibration. Moreover, the dependence on a fully automated probe station or an operator experienced in on-wafer measurement is eliminated with the proposed smart impedance calculation method. The proposed algorithm would find immediate application in the on-wafer characterization of mm-wave or higher frequencies device.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

First Author conceived of the presented idea, JS and JW developed the algorithm and performed the computations. JS and FW. verified the analytical methods with experiment. LS encouraged authors to investigate this calibration issue and supervised the findings of this work. All authors discussed the results and contributed to the final manuscript.

This work is funded by the National Natural Science Foundation of China (No.61827806, No.61871161) and the Key Lab Research Foundation of Science and Technology on Electronic Test & Measurement Laboratory (6142001190103).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.