Advancements in mm-wave On-Wafer Measurements: A Commercial Multi-Line TRL Calibration Author: Leonard Hayden Presenter: Gavin Fisher
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1 Advancements in mm-wave On-Wafer Measurements: A Commercial Multi-Line TRL Calibration Author: Leonard Hayden Presenter: Gavin Fisher The title of this section is A Commercial Multi-Line TRL Calibration 1
2 Outline Motivation On-Wafer vs. Off-Wafer Standards & Calibration TRL / ML TRL Calibration Overview Multi-Line TRL Implementation in WinCal XE Example Results 2 We will start with a brief discussion of the motivation of this work and then discuss the idea of on-wafer vs. off-wafer standards and calibration. We will then take a quick look at the nuts and bolts of the TRL calibration and how it is implemented in WinCal XE. A quick example comparison of automated multi-line TRL with traditional methods will be followed by a brief conclusion. 2
3 Motivation NIST Multi-Line TRL Established reference calibration Minimal knowledge of standards needed Limited software support from NIST (HP Basic, Labview) WinCal XE Implementation Supported application with broad array of calibration and measurement tools Fully automated calibration using automated probe positioners Broad selection of supported VNAs 3 The NIST multi-line TRL algorithm has become established as a reference calibration method. Its primary value is the need for minimal knowledge of the electrical behavior of the standards. It is provided from NIST as an HP Basic or Labview application. WinCal is a supported commercial application with a broad array of additional calibration methods and measurement tools. Fully automated calibration is supported, including for TRL when using automated probe positioners. A broad selection of modern VNAs is supported. 3
4 On-Wafer vs Off-Wafer Calibration On-wafer calibration Custom standards on the wafer Identical launch for DUT and Standards Need simple standards and cal requiring minimal knowns - E.g., known loads usually hard, transmission lines often easy Off-wafer calibration Commercial impedance standard substrate - Process supporting precision standards (e.g., trimmed loads) Launch differences absorbed as additional uncertainty - Pad layout and/or substrate dielectric differences (delay error often dominates) or corrected by intrinsic device de-embedding method - Limited at high freq or when precision phase is needed (T-lines) 4 TRL is particularly of value for on-wafer calibration. In on-wafer calibration the standards are fabricated on the same wafer as the DUT. Note that the term wafer can really mean any substrate, not just a semiconductor in wafer form. The standards are created with the identical launch as the DUT with the same metal pad pattern and substrate dielectric. The standards need to be very simple so that they can be created using the process used for the DUT. Transmission line standards require only metal patterns making them particularly well suited for on-wafer calibration. Off-wafer calibration is the name used to describe the use of a separate impedance standard substrate with standards. This cal substrate is usually created in a process optimized for making precision standards typically on a very low-loss Alumina substrate with precisely trimmed load resistors. Launch differences between the cal substrate and the DUT result in additional measurement uncertainty. In the most benign cases this error results in only a delay error (reference plane location). This is often adequate for circuit measurement where the return loss, gain, and relative delay (flatness) of the circuit are of greatest concern. In device measurement (such as a transistor on a semiconducter wafer) the goal will be to get the intrinsic device without pads. The de-embedding steps needed to remove the parasitic pad behavior also serves to remove the launch difference associated with using off-wafer standards. These methods often used lumped element models for the parasitics and become less effective at higher frequencies. Measurement of transmission line structures where the absolute phase is of great interest would also be significantly effected by launch differences. 4
5 What is TRL Calibration? What is calibration? A long story, but the idea is to characterize the non-ideal VNA + cables + probes system by measuring known and partly known standards What about TRL? With TRL the standards are: - Thru (short transmission line) - Reflect (unknown but equal reflect on both ports, sign known) - Line (transmission line with electrical length ~ degrees) Lines cannot be 0 or 180 degrees long (or near there) since the electrical behavior is not distinguishable from the Thru Multiple lines are required, each covers a subset frequency range - Data discontinuities occur at band edges Resulting S-parameter measurements are referenced to the unknown (and sometimes complex) characteristic impedance of the lines Thru Reflect Lines 5 The basic calibration concept is probably familiar to this audience so I simply remind that the goal is to characterize the non-ideal VNA and fixturing using known and partly known standards so that a measurement may be corrected to a specific corrected reference plane. TRL calibration uses transmission lines a short Thru and a longer Line along with an unknown reflection that is equal at both ports. The Line structure cannot be too short or near 180 degrees of electrical length since at these locations it can be inadequately distinguished from the Thru s electrical behavior. So to cover a wide frequency range a number of lines are required with each covering an appropriate frequency band. In VNA based TRL the measured DUT S-parameters are normalized to the (often) unknown characteristic impedance of the lines. 5
6 How does TRL work? Start with switch-corrected measurement data so that we have an 8-term error model Error boxes A and B represent all errors associated with ports 1 and 2 A & B are transmission scattering parameters (T-parameters) 1 A = S A 21 S S A A 22 S 1 Reference plane is the center of the thru thru is identity A 11 A A A A A S = S11 S22 S12 S21 A B M T = A T B = A B 6 TRL is an advanced calibration using the 8-term error model created by switch-correcting all measurement data. The error boxes A and B represent all of the errors of the system down to the center of the Thru line, the initial measurement reference plane. By using the transmission scattering parameter representation of A and B we find that the measured T matrix is given by the matrix product of A and B. 6
7 Transmission Line Equations Line impedance is reference impedance Transmission is line loss and delay γ = propagation constant L S 12 = S In T-parameters: + γ l = e 0 L M γ l L = A L B 0 e Key equation: Q M L ( M = A L B B T ) 1 1 A 1 1 L 21 = A L B ( A B) = A L A = e 1 Q = ALA -1 is called a similarity transform of Q L is a diagonal matrix with elements known as eigenvalues p ii of Q A is a matrix made up of columns that are eigenvectors v i of Q (direction, any magnitude) S L S 11 = L 22 = γ l 0 Q p I = 0 ii [ Q p I ] v = 0 ii A L B i 7 The line standard is inherently matched since its impedance is the reference impedance of the error box S-parameters. The line transmission behavior is set by the propagation constant and physical length resulting in a diagonal T- matrix. The Line measurement is simply the matrix product of A, L, and B. The key to TRL is to formulate the matrix Q which is the product of the line and the inverse of the thru measurement (as T-parameters). This reduces to the A-L-A inverse form. This form is called a similarity transform of Q allowing the diagonal matrix L to be found from the eigenvalues of Q (by finding the roots of this determinant equation) and A is known to be composed of vectors of direction given by the eigenvalues of Q (using the roots of the matrixvector product equation for each eigenvalue). 7
8 TRL Details Propagation constant given directly by the eigenvalues The eigenvectors give columns of A to multiplicative constants, a i 1 A = [ v1 v2 ] a1 a2 a 1 B -1 is likewise known to these same constants B = a2 a 1 A measurement of a DUT is given by: 1 1 ( M T ) A = [ M T ] [ v1 v2 ] a1 1 1 A DUT B M DUT = A DUT B So correction is obtained from: a 1 drops out of the equation DUT = A M B 1 1 DUT We only need to know a 2 /a 1 Finding a 2 /a 1 comes from equal reflects, but we won t go into this... 8 The line propagation constant is given directly by the eigenvalues (which will be handy later for moving the reference plane). The eigenvectors give the columns of A to multiplicative constants a1 and a2. By using this form we will find when we go to correct a DUT measurement that the a1 constant drops out entirely leaving only one complex unknown (the a2/a1 ratio) to fully determine the correction equation. This term is determined using the equal reflects measurement, but time is too short to go into this 8
9 Example TRL Measurement: Load GHz Scale= S-Parameters referenced to line impedance, not 50 Ω GHz Band Breaks :57: Complex Zo at low frequencies Mismatch from 50 Ω 270 [db] [GHz] 9 When measuring a low-inductance load after a TRL calibration we see a poormatch at low-frequency and band breaks at higher frequency. This is the behavior one sees with conventional TRL such as is found in most VNAs. 9
10 Characteristic Impedance TRL From per-unit-length resistance, inductance, conductance, and capacitance (r, l, g, c) ( r + jωl) ( g jωc) γ = + L R Z o = ( r + jωl) ( g + j ω c) G C Z o freq high l c Z o freq low r + jωl jωc = complex! ω = 2 π freq 10 Some people mistakenly refer to this low-frequency behavior as caused by skin-effect. This is not the case. Instead the resistance and conductance of a line is swamped by the inductive reactance and capacitive susceptance resulting in a real Zo at high frequencies. But at low frequencies this doesn t occur. For the low substrate loss case where g 0, the line Zo is complex in the frequency range where r is equal to or greater than the omega-l inductive reactance. 10
11 What is Multi-line TRL? Uses all lines at all frequencies not banded Optimally weights data from line pairs according to how distinguishable they are 90 degree differences maximally weighted 0 or 180 degree differences minimally weighted No data discontinuities due to band breaks Provides the ability to: Position the reference plane locations to a specific physical offset distance from the center of the thru Renormalize the reference impedance to 50 ohms 11 Multi-line TRL was developed by Roger Marks, a distinguished NIST/ARFTG/IEEE alum. The data from all lines is used at each frequency eliminating banding. A weighted averaging process is used that maximally weights when the lines are electrically 90 degrees different and most distinguishable, and minimally weighted at 0 or 180 degrees where they are least distinguishable. The continuously varying weighting eliminates the abrupt band breaks of conventional TRL which uses only a single line pair at each frequency but must change lines to cover broad bands. Additionally, the NIST multi-line TRL implementation allows relocation of the reference places to specific physical offsets from the center of the thru and the renormalization of the measurement reference impedance to a specific value like 50 ohms. 11
12 Characteristic Impedance ML TRL Z o = ( r + jωl) γ = ( g + jωc) ( g + j ω c) When g << ωc Z o = γ/(jωc) True for low-loss lines on Alumina, SiO 2, GaAs, Quartz - And the capacitance, c, is constant with frequency, c(f) = c dc Not true for Silicon, Polyimide, Epoxy With known Zo, the S-parameters may be renormalized to 50 ohms L R G 0 C 12 When the substrate loss is low then knowledge of the frequency independent capacitance per-unit-length at a single frequency (such as dc) allows full determination of the line characteristic impedance. [See the Dylan Williams bibliography on the NIST web site for many references covering the more complex general cases for lossy substrates). 12
13 Characteristic Impedance Correction With known Zo, the S-parameters may be renormalized to 50 ohms 50 Ohm Load S-Parameter Normalized to Complex Line Zo Normalized to 50 Ohms 13 The WinCal XE implementation of TRL includes a number of options for handling the reference transmission line impedance. 1. Treat the Zo of the reference line as unknown, leaving the DUT S- parameter normalizing impedance that of the line. In this case the Zo and system impedance are set to 1 indicating the normalization. This is how VNA front panel TRL calibrations normally work. The resultant S- parameters can have a complex reference impedance (particularly at low frequencies) resulting in non-intuitive behavior demanding careful use. 2. Treat the line as having a constant, real Zo that is known and entered. The line impedance may differ from the target system impedance (often 50 ohms). This is most useful when the data is for frequencies where the line behavior is dominated by the distributed inductive reactance and capacitive susceptance resulting in a real Zo. This is a good choice for a narrow band or measurements only at higher frequencies. 3. Treat the line as having a known, frequency-dependent complex Zo. The Zo is provided in the form of a reflection coefficient (in an S1P file) with a real (typically 50 ohm) normalizing impedance. This approach is very general compatible with even the most complex means of determining the line Zo (even simulation). 4. The line Zo is determined using the small G and constant C assumption and an entered value of C (per-unit-length). This method is suited for lowloss dielectrics such as Alumina, GaAs, etc. If a known DC resistance load is available one can start with an estimated C value and observe the impact when applying the correction to the load. If the load R is incorrect the C estimate is adjusted until the correct load resistance is found. 13
14 WinCal MLTRL Implementation TRL calibration standards are defined by physical dimensions The Location Manager tool provides a way to conveniently record a set of device locations including moves with probe position changes 14 Since the most useful use of TRL and ML-TRL calibration is with custom onwafer standards, WinCal makes it convenient to describe the calibration standards from physical dimensions and locations. Automated moves are facilitated by the location manager tool. The location manager provides a way to record and move to any user artifacts, including repositioning the probes (when an automated probe positioner is available). These moves may be defined as relative to a single reference location. This makes it easy to realign for a new sample since one finds the reference location and optionally a second to provide a software angle correction. Simple calibration routines insure that the stage and positioner move axes are aligned to the DUT. 14
15 WinCal Calibration Measurement Plan Moves to any location manager recorded location Measure in an automated sequence or one-at-a-time Additional measurement for: Pre-cal repeatability test Post-cal validation measurement comparison Post-cal monitoring reference 15 The WinCal measurement plan is very flexible for selecting locations and stepping through the calibration. With programmable positioners a fully automated, one-button MLTRL on-wafer calibration becomes very practical. Manual TRL with repeated repositioning of the probe positioner is error-probe and subject to small probe positional errors, significantly degrading the speed and accuracy. 15
16 Default MLTRL Calibration Report Calibration report format is defined by customizable template 16 The calibration report provides several views of useful information about the standards. The template is easily customized if other or additional displays are desired. 16
17 Error Set Manipulation & Comparison Error Set Management selection and application Error Set Manipulation augmentation (1 st tier/2 nd tier) Error Set Comparison error bounds and direct comparison of terms 17 WinCal include other useful tools for managing, manipulating, and comparing error sets. 17
18 Example: Comparison Study SOLT Manual MLTRL Auto MLTRL Cal Method SOLT Manual MLTRL Auto MLTRL Time 1.25 minutes >10 minutes <2 minutes Agilent 8364A PNA GHz, 200pts, 100Hz IF BW Cascade Microtech Summit 12861B probe station 200mm wafer chuck Aux chuck for off-wafer stds MS-1 programmable positioner Infinity i40a-gsg-150 RF Probes C Imp. Standard Substrate Reference Automated MLTRL One-button Cal! = Fast Very repeatable SOLT Inaccuracy Ref Plane error? 18 A quick study compared the SOLT calibration with the manual and automated multi-line TRL calibrations. 18
19 Conclusion A commercial implementation of Multi-Line TRL is now available Programmable probe positioning enables automated one-button MLTRL calibration Automated MLTRL is quick and very repeatable Cal Method SOLT Manual MLTRL Auto MLTRL Time (minutes) 1.25 >10 <2 Error Bound (@40GHz) > >5x Faster >12x Repeatability Improvement 19 19
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