An On-Wafer Deembedding Procedure for Devices under Measurement with Error-Networks Containing Arbitrary Line Lengths

Transcription

1 An On-Wafer Deembedding Procedure for Devices under Measurement with Error-Networks Containing Arbitrary Line Lengths Thomas-Michael Winkel, Lohit Sagar Dutta, Hartmut Grabinski Laboratorium fur Informationstechnologie, University of Hannover, Schneiderberg 32,30167 Hannover, Germany Abstract Error networks that include contact structures and which embed devices under measurement (DUM) can often be partitioned into different line segments having constant line widths. The basic idea of the here proposed deembedding procedure is the calculation of the error network from a piece by piece characterization of the line segments. In the first step of the proposed deembedding method, the propagation constants and the characteristic impedances of the various line segments are calculated from high frequency S-parameter measurements. In the second step, the chain parameter matrix A,, of the different line segments are then calculated. The third step consists of the calculation of the chain parameter matrix A,, of the complete error network. Finally, one can calculate the scattering chain parameter matrix Terror from the related chain parameter matrix A Lmor of the complete error network. The main advantage of this method lies in the fact that only thru lines with different line lengths have to be measured. A further advantage of this deembedding procedure is that the error networks embedding different DUM's can contain line segments of arbitrary line lengths. Therefore, the proposed deembedding procedure can be used for DUM's that are embedded in error networks that consist of different line segments with constant line widths. Introduction Most common deembedding procedures are usually based on S-parameter measurements of different reference standards with known or partially unknown characteristics, for example different combinations of loads, reflects (shorts, opens) and thru or delay lines with different line lengths [ The quality of these deembedding procedures depend heavily on the accuracy with which these reference standards can be fabricated. The fabrication of high quality loads and shorts with constant values over a wide frequency range is problematic, especially on semiconductor substrates. In general, for the characterization of a multiple number of different devices a correct deembeddjng is only possible when the devices are embedded in exactly the same error networks as was measured during the on wafer calibration procedure. This means, that all line lengths in the error networks have to be always the same. This restriction is not necessary anymore in the here proposed procedure, since variable line lengths can easily be taken into consideration during the calculations of the chain parameter matrices of the error networks. This is possible without having to measure any new reference structures. 102

2 The here proposed deembedding procedure for on-wafer measurements employs only S- parameter measurements of thru lines with different line lengths, together with an additional reflection measurement of a separate pad structure. The method described is applicable under the assumption that the network analyzer, the microwave cable and the microwave probes employed during measurements have already been previously calibrated by using a common calibration procedure (i.e. LRM, TRL, SOLT ect.) with well known reference standards. In this work reference standards on an LRM impedance substrate (fabricated by Cascade Microtech) were used. Measurement Setup In the case of high frequency signal propagation on lines, the currents and voltages can not be measured directly, since these quantities have a wave character and are only well defined for purely TEM wave propagation. Instead the amplitudes and phases of the signals can be determined using scattering parameter (S-parameter) measurements. The S-parameter measurements were performed with a HP 8720B 2 port network analyzer in a frequency range from 200 MHz to 20 GHz. The network analyzer was connected through special flexible microwave cable to cascade coplanar microwave probes with characteristic impedances of 50 Q. The short-gpen-load-through (SOLT) calibration, as was proposed by cascade microtech for the HP 8720B network analyzer [7], was used to calibrate the network analyzer in combination with the flexible microwave cables and microwave probes. The reference standards used for the calibration were fabricated by cascade microtech on special alumina substrate. As a result of the calibration procedure, the reference planes of the measurements had to be taken at the contact points of the microwave probes. Due to the usage of coplanar microwave probes, special contact structures had to be designed for the measurements as depicted in figure 1. Theory In order to characterize a DUM that is Contactpads embedded in structures containing connecting lines and contact pads for the measurement probes, one has to first determine the scattering chain parameter matrices of the error networks TA and TB (figure. 1). The unknown scattering chain parameter matrix of the error network TA can be given by: TA =,[ I2) tu21 (1) tu22 7 Figure 1 Device under measurement embedded with The network described by TA can be connecting lines and contact structures divided into different line segments as shown in 103

3 figure 2. The chain parameter matrices of these line segments are given by the following equations: These matrices contain the unknown parameters which are the propagation constants ( y,, y,) and the characteristic impedances (Zs, 2,). If these values are known, the chain parameter matrix of the complete error network can be calculated through a simple multiplication A=A, A, A,. The normalized chain parameter matrix A 'can then be calculated from: fi (3) Herin the impedance 2, represents the reference impedance of the microwave probes, in the present case 50 Q. Finally, the scattering chain parameter matrix of the error network TA can be calculated from a simple A to T-parameter transformation. The scattering chain parameter matrix TB can be calculated similar to TA. open!pad padline i line i segment contact plane of the microwave probes (=reference plane) single line segment Figure 2 Subdivided signal line of the error network TA In order to characterize the error networks TA and TB one has to determine the unknown parameters ys, y, Z,, Z,. As mentioned above, this can be achieved by 5 measurements: 4 t h line ~i~~~ 3 Geometry of the reference line smcmeasurements and 1 reflection mesurement. ture including the emor networks and the Therefore, the DUM must be substituted by a single line segments transmission line that connects TA with TB. In figure 3 the geometry of a reference line structure is shown which was used for the on-wafer deembedding procedure. All reference structures were fabricated on silicon substrates. The first reference line structure is partitioned into error networks, that represented by the scattering chain parameter matrices TA and TB and into a single line section T, of line length I, and line width w,. The single line section T, of the second reference line structure has the line length I, with 12+I,..In contrast to the first and second reference line, the third and fourth reference lines on the other I 104

4 hand, must have the same line widths wp as the contact pad structures. The line lengths of these reference lines are l3 and l4 with One can now calculate the propagation constants and the characteristic impedances of the lines with the line widths wp and w, using the new method as proposed in [6], which we will call the twin reference line method. A short summary of the method is presented in the appendix and [6]. The fringing effects of the pad structures can be taken into account by a simple reflection measurement of a separate pad structure. One important advantage of this method is that one can use arbitrary line lengths of the single line segments (figure 3) connecting the contact pad to the DUM. The only thing one has to do is to calculate the chain parameter matrix A, (equation 1) of the single line segment using the actual line length 1, and the appropriate values of A, A and TA. This means that no new measurements for the characterization of the error networks are needed anymore! Another important advantage of the presented method lies in the fact that only thru lines of different line lengths have to be measured. In contrast to the reference standards (loads and shorts) normally employed during calibration, these reference lines can be easily fabricated in a high quality for high frequency measurements, especially on semiconductor substrates. Measurement Results In order to proof the accuracy of the above described deembedding method we will compare the measured S-parameter SI, of an embedded thru line with 5 mm line length with the S-parameter SlZc of the deembedded thru line together with the S-parameter S]Zb of the pure line calculated with the help of its propagation constant. The S-parameter matrix of such a line that is terminated by its characteristic impedance 2, is given by: where y is the propagation constant and 1 the line length. The propagation constant can be easily and very accurately determined by the method proposed in [8]. Therefore, the S-parameter SlZc of a deembedded line must be equivalent to the S-parameter calculated with the help of the propagation constant as given by (4). In order to perform a deembedding of a measured thru line one has to first calculate the scattering chain parameter matrix T, from the measured S-parameter matrix S, where Tm = TA. Ti TB The error network TA has to be calculated as described above. The calculation of the error network TB will be described in the following. The chain parameter matrix A, is given by: 105

5 0.01 I I I I I 1 I I I I I I I I I I I I I I Frequency (GHz) Figure 4 Magnitude of S12: a) for the line embedded with contact structures (SI,=), b) for the pure line (S,,,), c) for the deembedded line (S,J Frequency (GHz) Figure 5 Phase of S,,: a) for the line embedded with contact structures (S,,,), b) for the pure line (S,), c) for the deembedded line (S12J 106

6 The normalized chain parameter matrix A, 'can be calculated from: The scattering chain parameter matrix T, can now be calculated by a simple A to T-parameter transformation. In figures 4 and 5 the magnitude and phase of the measured S-parameter S12a of a line embedded in contact structures (a) is compared to the S-parameters S,,, of a line terminated by its characteristic impedance (b), as well as to the S-parameter SIZc of a deembedded line (c). In contrast to the expected difference between Slta and S,2c the magnitude and phase of the S- parameter SlZc of the deembedded line shows a nearly perfect agreement with the S-parameters SIZb as calculated for the pure line. Conclusion and further work A new on-wafer deembedding procedure, that can be performed with lossy lines on ICs in a high frequency range has been presented. The major advantages of this method are: - The characterization of the error networks can be performed using only thru lines and a separate pad structure which are easily fabricated even on silicon substrates. - The position of the reference plane can be shifted by only choosing a different line length for the single line segment as depicted in figure 2 during the calculation of the chain parameter matrix of the complete error network, i.e. without additional measurements. This deembedding procedure presents measurement results which are extremly accurate. This method can be extended further to also include 4 port measurements of DUMs with coupled line segments and which will be published in the near future. Appendix The chain parameter matrix A of a single line terminated by its characteristic impedance Z, is given by: 107

7 1 A = f sinh[y* I ] cosh[y- I ] y denotes here the propagation constant of the line and I the line length. If the chain parameter matrix in equation (8) is given, the characteristic impedance of a single line can then be calculated from: zs = J" I a21 In general, the chain parameter matrix of a line as given in equation (8) cannot directly be measured, since all measured transmission lines are embedded in appropriate contact structures (figure 3), which are described by the unknown 2x2 matrices TA and TB, that represent the error networks. Therefore, one can formulate the matrix of the measured (index m) scattering chain parameter matrix T,,, as follows: (9) where is the scattering chain parameter matrix of the line. Thus, one can ascertain two scattering chain parameter matrices, denoted by T,, and TmZ, of two lines with different lengths, from measurements: In order to eliminate e.g. TB one has to first calculate the inverse matrix of T,,,, and then multiply the result with Tm2 from the left: where 108

8 The unknown matrix TA is given in equation 1. As mentioned above, the matrix TA describes the error network (e.g. pad structures ect.) consisting of only line segments as depicted in figure 2 and figure 3. The chain parameter matrices of the line segments are A, for the open pad line, A, for the pad line segment, and A, for the single line segment and are given in equation 2, where ys and y, are the propagation constants of a single line (line width w,) and of a line with the same width as the pad, respectively. 2, and 2, are the characteristic impedances of these two lines. I,, I, and are the line lengths as depicted in figure 2. The unknown matrix TA can be calculated through a simple transformation (A- to T-parameter transformation) from the normalized chain parameter matrix A '(equation 3). In a similar manner to equation (9), one can in the next step calculate the measured characteristic impedance. Therefore, the chain parameter matrix can be calculated from the left hand side of equation (14), i.e from the scattering chain parameter matrix Tm2Tml*', with the help of a known matrix transformation (T-parameter to A-parameter). The impedance Zmub, which we want to define as the "measured substitute impedance", is then calculated from Amrub by the following expression (cf. equation (9)): Zmub = 4% I am2 I Zmub still includes the influences of the pad. In order to calculate the true characteristic impedance 2, from the measured substitute impedance, one has to now calculate Zmub analytically, in addition to (17), from the right hand side of equation (14) by using equations (1, 9, 14, 15) in a similar way to (17): Notice that (18) includes only the elements of TA. The radical of the right hand side in equation (1 8) is a rational fraction with the numerator N and the denominator D represented by polynomials that include only the unknown parameter y,, yp, Z, and Zp (cf.(2) and (3)). 109

9 (17) with (18) and eliminate y,, y,, and Z, from this expression. The propagation constant y, can be determined after equating coshys.(12- I,) = amll (19) do++z,,~-zs I a!!!!!, I, \ coshy,,. I,, I Zp. sinhy; Ip t coshyp. Ip I and I, /=l,+l,. Using equations (3) and (20) the characteristic impedance Z, of the pad line can be expressed by: 2 2 Zp = Zmubp. Zn2- (1 - (tanhy; 1J2) (21) where Zmubp is now the measured substitute impedance of the transmission line with line width w,=50 pm (similar to (17)). Thus, equation (17) and (18) can be converted into a polynomial with only one unknown parameter, namely, the characteristic impedance Z,: Since the largest power of Z, in (22) is 2, the solution of this polynomial with respect to Z, is simple. Nevertheless, the constants of the polynomial are very complex and will therefore not be presented in this paper. The fringing fields of the open pad line and the step (transition pad line segment to single line segment) behave like additional small virtual lines, which can be characterized by an additional S-parameter measurement (reflection coefficient S,) on a seperate pad structure. These 110

10 calculated virtual additional line lengths lvi, have to be added, in equation (2), to the line lengths I, and Zp, respectively. Therefore, one has to replace I, and Ip in equation (2) by I* = lo + lvirt and ws $. = lp + lyirl. (1 --) (24) wp respectively. The consideration of the virtual additional line lengths is important, especially when the line width of the single line segment is very small in comparision to the width of the pad line segment. Due to the negligible influence of the virtual additional line lengths on the calculated characteristic impedance of the pad line segment Zp, the line length I, is usually not replaced by 1, in equation (21). References Norman R. Franzen and Ross A. Speciale, A New Procedure for System Calibration and Error Removal in Automated S-Parameter Measurements, European Microwave Conference Proceedings, pp , 1975 G. F. Engen and C. A. Hoer, Thru-reflect-line, an improved technique for calibrating the dual six-port automatic network analyzer,leee Transactions on Microwave Theory and Techniques, vol. MTT-27, pp , Dec Gmmo J. Silvonen, A general approach to network calibration, IEEE Transactions on Microwave Theory and Techniques, ~01.40, pp , April 1992 H.-J.Eul and B. Schiek, A Generalized Theory and New Calibration Procedures for Network Analyzer Self-Calibration, IEEE Transactions on Microwave Theory and Techniques, ~01.39, pp , April 1991 H. Van Hamme and M. Vanden Bossche, Flexible Vector Network Analyzer Calibration with Accuracy Bounds Using an 8-Term or a 16-Term Error Correction Model, IEEE Transactions on Microwave Theory and Techniques, vo1.42, no.6, pp , June 1994 Thomas-Michael Winkel, Lohit Sagar Dutta, Hartmut Grabinski, An Accurate Determination of the Characteristic Impedance of Lossy Lines on Chips Based on High Frequency S-Parameter Measurements, IEEE Multi-Chip Module Conference MCMC-96,5-7 February, 1996, Santa Cruz, California, pp Cascade Microtech, Microwave Wafer Probe Calibration Constants, Instruction Manual Jyoti P. Mondal, Tzu-Hung Chen, Propagation constant determination in microwave fixture de-embedding procedure, IEEE Transactions on Microwave Theory and Techniques, Vol. 36, No. 4, April