Free Space Dielectric Techniques for Diamond Composite Characterization

Compact millimeter-wave arrays demand novel packaging solutions that feature low-cost dielectric materials with significant thermal conductivity ($\sim$100 W/m ⋅ K). To characterize the permittivity and loss tangent of the dielectric materials above 100 GHz, free-space characterization is proposed to avoid de-embedding conductor losses. We review current approaches for characterization to investigate the properties of ultradense diamond composite materials at D-band. We compare free-space calibration multiple methods to extract the permittivity and loss tangent. Time-domain gating is employed to reduce the uncertainty in the free space characterization. Material characterizations of the dielectric constant and loss tangent include pure polymer TMPTA, PDMS, TMPTA-based, PDMS-based diamond composites as well as quartz and sapphire wafers for calibration from 120–160 GHz. To the author's knowledge, this is the first characterization of diamond composites for thermally conductive dielectric packaging requirements at D-band.


I. INTRODUCTION
D-band (110-170 GHz) offers opportunities for millimeterwave radar and backhaul communications [1].However, scaling beamformers to higher frequency bands demands reducing spacing between antennas below 1 mm imposing significant space constraints on the power amplifiers (PAs) and heat dissipation.Additionally, the low output power makes heterogeneous solutions with III-V front-end components such as the PA and low-noise amplifier attractive.In Fig. 1(a) [2], a low-cost package would mount a silicon RFIC to a package while transitions through the board couple into a III-V PA microwave monolithic integrated circuits (MMICs) capable of output power exceeding 100 mW.This scheme places two formidable constraints on the package.First, the top side of the package must simultaneously offer excellent thermal dissipation as each PA dissipates significant power.Second, the PAs on the top side must couple directly into antennas on the top side.Consequently, the D-band package requires a low-cost dielectric material that offers both excellent loss tangent as well as high thermal conduction while allowing low-temperature processing.
A basic model of heat flow in a chiplet is based on an assumption of the peak RF output power, power density, and the geometry of the devices.Fig. 1(b) illustrates the temperature rise assuming different power-added efficiency (PAE) for the PA.To reduce the temperature rise of the device to under 100 K, the PAE must be better than 30% and the thermal conductivity should be better than 100 W/m K.
Recently, D-band packaging has focused on glass and other insulating interposers such as silicon and aluminum nitride [3], [4].Glass is not intrinsically a thermal conductor but copper thermal vias are employed since the thermal conductivity of bulk Cu is > 400 W/m K under ideal conditions.However, the thermal vias substantially increase the cost of the interposer.Other materials typically offer some compromise between thermal conductivity, loss tangent, and  amenability with multi-layer packaging.An ideal thermal conductor would behave like bulk diamond (2000 W/m K), but could be processed at low temperature and formed around PA chips.
To attempt to retain the thermal conductivity of diamond in a package that might be molded at or near room temperature, an ultradense diamond composite (UDC) has been proposed [5].Formed from thermally-fused microdiamonds, the UDC comprises 10 μm synthetic diamond particles and trimethylpropane triacrylate (TMP-TA).The relative permittivity ( r ) and loss tangent (δ) of bulk diamond [6], [7] and TMP-TA are 5.7 and 1.78 and 5 × 10 −4 and 0.04, respectively [8].To increase the packing density of the diamond, pressure is applied to a diamond slurry deposited into a 20-mm Al mold inside an ultrasonicator and processed at 60 • C until the diamond composite formed.Once the diamond matrix of the diamond composite was complete, the composite was placed in an oven at 120 • C for 1 hr.Next, TMPTA was deposited into the diamond film and cured at a maximum 140 • C for 20 min.Fig. 2 shows SEM images of the UDC.
This article investigates the dielectric properties of the UDC to understand whether the dielectric characteristics of the original diamond are retained above 100 GHz for packaging beamforming arrays.Section II discusses the free-space focused beam method considerations and Zemax simulation, Section III discusses post processing techniques, Section IV reports quartz, sapphire, and the UDC materials.We measure the materials at D-band using a focused beam free-space measurement to characterize the dielectric properties [9].Compared to earlier work [2], this manuscript explains the methodology for measuring small samples and provides comprehensive measurements of the diamond composite and other materials that might be candidates for high-frequency dielectrics.

II. FREE-SPACE FOCUSED BEAM CHARACTERIZATION
A free-space focused beam system measures scattering (S) parameters from a material specimen.The intrinsic properties of the specimen, including electric permittivity and magnetic permeability, are calculated from the S parameters captured through a focused beam.At lower frequency, the dielectric is characterized using a transmission line [10].At higher frequency, the frequency-dependent conductor losses produce dispersion.Additionally, the surface roughness of the transmission line conductor introduces conductive loss and is difficult to estimate from experimentally printed lines.
The advantage of free-space characterization [11], [12] compared with a transmission line method is eliminating the uncertainty associated with the conductor losses and surface roughness.In an early material development stage, the quality of the material might not yield commercial tolerance which makes the transmission line hard to print on top of the material due to surface roughness.
Alternatives to the transmission line-based structures have been investigated [13].A Fabry-Perot resonator is another method to accurately characterize material properties, and is used commercially in industrial test and measurement.However, the sample under test (SUT) has some requirements for this test.First, the SUT needs to be processed into a plate.Second, the thickness and size are determined by the measurement frequency.The sample size in D-band measurement is recommended to be 50 mm by 50 mm square, which is much larger than standard wafers or sample materials.
On the other hand, the sample size requirements for freespace methods need a diameter of at least 6 wavelengths or more to prevent a diffraction effect.Above 100 GHz, the sample can be closer to 10 mm and much thinner.
The D-band dielectric characterization system comprises a Keysight PNA with D-band frequency extenders, D-band horn antennas, bi-convex lenses, and positioning fixtures that allow free-space TRL calibration as illustrated in Fig. 3.The standard gain horn antenna has 25 dBi gain and 10 • 3-dB beamwidth.The distance between antenna phase center and lens left-side edge is 90 mm, and the distance between lens right-side edge and the sample is 75 mm.Both are optimized by Zemax simulation.

A. CONSIDERATIONS ABOUT MEASUREMENT PROCEDURE
The free-space focused-beam measurement can be analyzed through quasi-optical techniques which involve beams of radiation propagating in free space which are limited in lateral extent when measured in terms of wavelengths and for which diffraction is of major importance [14].Lens design and antenna modeling can found in earlier work, which provides a point of view for modeling antenna using power density [15].
Beam parameters are illustrated with respect to the measurement setup in Fig. 4.During material measurement, a thick specimen that extends outside of depth of focus (DOF) will experience significant phase curvature, which may then reduce the accuracy of the plane wave assumpton.The spot diameter is given in (2), where M is beam quality parameter, f is focal length, and D is the diameter of the beam at the lens surface.Based on (2), we select a lens and decide the positions of each element.To minimize the spot size, a low focal distance lens should be selected, and the input wave diameter located at the lens should be as large as possible.However, it shouldn't exceed the edge of the lens to prevent undesired effects.
Lens design and antenna modeling can be examined with a relative Gaussian intensity versus the normalized radius plot in Fig. 5. Three critical points are indicated: the 3-dB point with a normalized radius of 0.59 which encloses 50% of power, the e −2 point is the conventional definition of Gaussian spot radius where the spot edge relative power encloses around 87% of power, and, finally, the 20-dB point encloses over 99% of power, located at 1.52 of normalized radius.From Fig. 5, the radius ratio between two points is found.The radius ratio are 1.7 and 2.6.Since a standard D-band horn antenna has 3-dB beamwidth of 10 degrees, the other two angles are calculated as θ 3 dB = 10 • , θ 1/e 2 = 17 • , and θ 20 dB = 26 • .These angles are used to position the antenna relative to the lens and prevent the radiated beam from exceeding the lens edge as shown in Fig. 6.
Free-space characterization demands a relatively large sample area relative to the wavelength to minimize the system uncertainty due to the diffraction effect.For small sample sizes, high-gain horn antennas produce a narrow beamwidth, demanding lenses to focus the beam.The distances between antenna, lens and sample are critical to measurement uncertainty.
A bi-convex lens transforms the radiation from the feed antenna into a focused beam.Two 50-mm diameter PTFE plano-convex lenses secured by a metal ring form the biconvex lens.The focal length of a plano-convex lens is 100 mm, which means the effective bi-convex lens focal length is around 50 mm.This arrangement brings the antenna close to the lens while positioning the focal distance at the sample.The uncertainty comes from the metal ring that has a small air gap between lenses.The first plano-convex lens transforms the divergent radiation into a collimated beam and the second plano-convex lens transforms the collimated beam into a focused beam.Therefore, the first lens is designed based on the feed antenna, and the second lens is designed based on the desired spot size located on specimen.To test that the energy has been confined to the small sample area, a metal plate is introduced near the sample edge to characterize the impact on the S parameters.However, the signal spot size and the distances between elements need further optimization through the Gaussian Beam Theory.

B. OPTIMIZATION USING ZEMAX SIMULATION
Due to the combination of two plano-convex lenses to an effective bi-convex lens, the lens used in our D-band system is not optically thin.The center thickness of each Thorlab plano-convex lens is 13.8 mm, and the radius of curvature is 40 mm.To optimize the measurement setup, Zemax was used to simulate the optimized distance between each element and calculate the minimum spot size instead of adopting a thick lens ABCD matrix to calculate the system.Fig. 7 shows the Zemax simulation layout shaded model.Starting from the phase center of the standard gain horn antenna emitting 10 • 3-dB beamwidth angle, the first PTFE lens transforms the divergent radiation into a collimated beam and the second plano-convex lens transforms the collimated beam into a focused beam.This layout provides clear ray transmission paths.Also, it provides the distances between antenna phase center to the first lens and the distance between the second lens to the minimum spot location.Fig. 8 is a simulated normalized irradiance plot that shows energy distribution along with position relative to the center.The spot diameter is 5.7 mm if the whole spot enclosed around 87% of power or the spot edge relative power reaches e −2 .The diameter is around 10.7 mm if the spot size encloses over 99% of power.The beam spread diagram in Fig. 9 also validates the confinement of the beam in the measurement setup.

III. POST PROCESSING A. CALIBRATION
Before calibration, spatial alignment is performed by maximizing S 21 signal.The free-space through/reflect/line (TRL) calibration procedure follows recent work [16], [17] as illustrated in Fig. 10.The through (T) standard is defined by keeping the distance between each lens equal to twice the focal distance.The reflect (R) standard is defined by placing a metal plate at the focal plane of the transmit and receive antenna, respectively.Due to the thickness of the metal, the second port lens and antenna are moved according to the metal thickness, D. Finally, a line (L) standard is achieved by separating the focal plane of the two antennas by a distance equal to a quarter wavelength at the center frequency of the band.During the sample measurement, all the port 2 elements have been shifted based on the sample thickness while keeping the calibration plane at the sample-air interface.

B. EXTRACTION METHOD
In a focused-beam system, the energy is confined to an area within the sample to measure S-parameters.There are multiple extraction methods to characterize the dielectric using measured S-parameters for the sample material and the advantages and disadvantages are briefly discussed.

1) NRW METHOD
The NRW method determines permittivity from S 11 and S 21 [18] [19].The procedure works well off-resonance where the sample length is not a multiple of one-half wavelength in the material.It is ideal for evaluating magnetic materials such as ferrites and microwave absorbers.

2) NIST METHOD
More recently, the NIST iterative algorithm was proposed using four complete two ports S-Parameters measurement data [20], [21].The NIST iterative algorithm was originally demonstrated in waveguide measurement.The key benefit of the NIST iterative method is due to the mathematical property of the matrix determinant.The independent reference plane position doesn't require precise placement of the sample relative to the calibration reference plane which is useful for D-band measurements, where a small distance movement can cause significant phase errors.From basic electromagnetic theory, permittivity is included in the reflection and transmission coefficients.
where is the reflection coefficient at the surface of the sample and T is the transmission coefficient through the sample.
Z and Z 0 are the sample and air characteristic impedance, γ and d represent the propagation constant and thickness of the sample.
From the signal flow chart, the S parameters are related to and T according to and The NIST iterative method utilizes all four S-parameters to determine permittivity from the matrix determinant.
where L 1 and L 2 are the distances from the calibration reference planes to the sample ends.The propagation term is due to waveguide measurement since the measurement ports are in the waveguide air interfaces.However, since we directly clamp the sample at the bottom without using the waveguide, the propagation term can be eliminated.The S-parameters are related to the reflectance and transmission.
Compared with NRW method, the phase error due to sample placement will be eliminated, resulting in better accuracy compared to NRW algorithm.The reflection and transmission can be related to dielectric properties.
3) COMPARISON Fig. 11 compares the NRW and NIST iterative method.As a baseline material with well-defined properties, a quartz wafer ( r ≈ 4) is adopted to verify the overall methodology.Five sets of quartz data are collected at different times with individual calibration data.While the NRW method produced inconsistent results due to positioning uncertainty during the calibration process and due to different metal thicknesses for reflection calibration standards.With using the same five sets of quartz data, the NIST iterative method have better results regarding our measurement setup.However, we encountered a ripple over the narrow band measurement that was not mitigated through averaging across the measurements.

C. TIME DOMAIN GATING
Despite the high-gain lens, multipath scattering introduces a frequency-dependent ripple illustrated in Fig. 11.Consequently, time-domain gating was introduced to the S-parameter measurements to filter out non-line-of-sight (NLOS) path components and improve the accuracy of the extracted permittivity results.By separating different transmission components such as the desired signal, signals from the multiple reflections, and from the discontinuity within the measurement channel.This filter is a window that is convolved with the data to preserve the first strongest desired signal in the time-domain while suppressing other signals at other times and then transferring back to the frequencydomain.Filtering measured data with time-domain gating is effective in cleaning up the measured data.Python module scikit-rf has been adopted to perform time-domain gating.
The measurement data was collected between 110−170 GHz, however, the time gating introduces edge effects near the waveguide band edges.Therefore, data between 110−120 GHz and 160−170 GHz results have been removed, and only leave the reliable 120−160 GHz results.The window function uses Kaiser-Bessel Window with an order equal to 6 which provides a good compromise for most applications.The gating method uses a fast Fourier transform (FFT), the data is transformed into a time-domain using inverse FFT, and the gating is achieved by multiplication with the time-domain gate.The gated time-domain signal is then transformed back into frequency-domain using FFT.As only positive signal frequencies are considered for the inverse FFT, the resulting time-domain signal has the same number of samples as in the frequency-domain but is complex-valued.The filter's center was positioned at the center of the time-domain which is also the peak value position.The time-span is selected as 0.2 ns, the start point is center-span/2 and stop point is center+span/2.Also, using a high number of points is preferred so that the unambiguous range is large enough to avoid aliasing with other undesired signals.
Figs. 12 and 13 show quartz S 11 magnitude data as an example in the frequency-domain and in the time-domain while the iterative method needs all four S parameters, the remaining S parameters also need to adopt time-gating.In Fig. 13, the blue peak at the center is the desired signal that directly transfers  from port 1 to port 2. The secondary blue peak located at −1 and +1 ns might correspond to the reflections from the two lenses in the system, the third peak might correspond to the reflection from the port 2 antenna, and the remaining peaks correspond to multiple reflections.The red curve is reserved for the blue curve around within −0.2 to +0.2 ns.
Time-domain gating indeed has a significant impact on the final permittivity measurement results therefore it also could introduce errors.The temporal window that distorts the impulse response of the sample would impact measured dielectric properties.Accordingly, accurate timing is essential to select the desired portion of the signal in the analysis.A gating window needs to be accurately placed in the center.In addition, different time-span could lead to different results, because a wider span might incorporate undesired signals that come from multiple reflections.If there are errors in the gating process, it can lead to distortions.Moreover, the presence of strong dielectric resonance within the measured frequency range can have a significant impact on the accuracy of the results.Materials with strong dielectric resonances often exhibit strong frequency-dependent behavior.Finally, a frequency-domain convolution associated with time-domain gating could lead to substantial errors in the measured dielectric properties.To mitigate the above two issues, we choose the whole D-band frequency range (110 GHz-170 GHz) to provide a more comprehensive view of dielectric behavior.It reduces the impact of gating-related errors by averaging out the effects of gating over multiple frequency points.

IV. MEASUREMENT RESULTS
These optics and signal processing algorithms are applied to the measurement of the permittivity of the new development diamond composite and compared to other known material such as quartz and sapphire which information are provided on Table 1.The measured quartz dielectric constants in Fig. 14 are around 4.8, which agrees with manufacturer values 4.68.Slight uncertainty comes from different calibration data.The loss tangent in Fig. 15 shows the lowest value in D-band from our setup is around 5 × 10 −3 , and different calibration data can still obtain consistent results.Therefore, this represents a measurement floor, rather than actual material properties.
The manufacturer estimates the loss tangent value at 100 MHz as 2 × 10 −4 .This observation defines the measurement floor for loss tangent at 5 × 10 −3 .PTFE materials used in the dielectric lenses exhibit a loss tangent of 2.2 × 10 −4 although manufacturer data indicates that the lost tangent increases to 1 × 10 −3 in the terahertz regime.Nonetheless, the lenses are not expected to produce a measurement floor.
The measured sapphire dielectric constants in Fig. 14 are around 9.3 for a double-sided polished wafer and 9.5 for a single-sided polished wafer while the manufacturer reports 9.3 below 1 GHz perpendicular to the C-axis.The loss tangent in Fig. 15 shows the lowest loss tangent in D-band is again around 5 × 10 −3 while the manufacturer reports the loss tangent at 1 × 10 −4 at 100 MHz.

A. THICKNESS UNCERTAINTY
To understand the uncertainty in the dielectric characterization, the sources of error in free-space focus-beam measurement are characterized including 1) S-parameters magnitude and phase measurement errors, 2) sample thickness uncertainty, and 3) sample positions uncertainty.
The NIST iterative method is immune from sample position uncertainty due to the property of S-parameters determinant.The magnitude and phase uncertainty could be obtained from Keysight's PNA uncertainty feature.Table 2 shows the sample's measurement thickness information, where each sample thickness has been measured six times around the sample.If the S-parameters uncertainty data could be obtained from network analyzer, the overall permittivity uncertainty can be written as The TMPTA-based diamond composites are mainly composed of polymer TMPTA and microdiamond particles.We measured pure TMPTA samples and also TMPTA-based diamond composites.Two different TMPTA samples are measured.Dielectric constants and loss tangent can be found in Figs.16 and 17.Uneven thickness of the samples are the source of error of permittivity extraction.Thickness plays an important role in the NIST iterative method to extracting dielectric constant.The shaded area of the dielectric constant plots shows the uncertainty comes from the maximum and minimum sample thickness.The loss tangent uncertainty comes from the sample thickness variation is negligible.The dielectric constant is 2.5 for the unpolished sample and 2.7 for the polished sample in good agreement with earlier results [8].The loss tangent ranges from 0.065 to 0.043 for the unpolished sample and from 0.034 to 0.027 for the polished sample.We incorporate these uncertainties into the dielectric characteristics.
Four different TMPTA-based diamond composites are measured.Dielectric constants can be found in Figs.18-21.The dielectric constants extracted from averaging thickness are between 3.5 to 4 while the loss tangent can be found in Fig. 22 and ranges from 0.02 to 0.05 over D-band.The results indicate that the permittivity is roughly 50% of diamond while the loss tangent is limited by the characteristic of the TMPTA.
To investigate other polymer matrix materials, another PDMS-based polymer composite is measured using a pure PDMS sample and also a PDMS-based diamond composites.Two different pure PDMS samples are measured and plotted in Figs.[23][24][25].The dielectric constant is 2.6 for both in agreement with an earlier result [22].The loss tangent is 0.06 to 0.07 indicating a significant loss component to the composite  if the PDMS-based composite is a significant fraction of the material.
Two different PDMS-based diamond composites are also measured and the dielectric constants are plotted in Fig. 26 and 27.Fig. 27 shows the largest uncertainty due to the fact that the sample has thinnest average thickness and largest thickness variation.The loss tangent is plotted in Fig. 28 and ranges from 0.04 to 0.08.The results indicate that is still dominated by the polymer PDMS.

V. COMPOSITE DIELECTRIC MODEL
The properties of the composite dielectric behavior have been studied in many works.The most commonly-used equation is the Lichtenecker logarithmic law [23].If two components are mixing, the effective permittivity can be derived as e f f = ex p{v 1 ln( 1 ) + v 2 ln( 2 )}, (10)  where v is the volume fraction of the composite.We assume diamond has volume fraction of v1, dielectric constant 5.5 and loss tangent 1 × 10 −4 mixes with two types of polymer TMPTA and PDMS with volume fraction of v2.Polymer TMPTA and PDMS are utilizing our measured permittivity.
measurement artifacts in the dielectric and loss tangent characterization.Gaussian beam theory is investigated to acquire more insights into the free-space measurement setup.Spot size can also be estimated through thin lens assumption and even can be simulated with Zemax.We conclude that the diamond composite can offer low dielectric permittivity and acceptable loss tangent while promising a thermal conductivity approximating bulk diamond.

FIGURE 1 .
FIGURE 1.(a) Conceptual diamond composite packaging of CMOS beamformer and antenna (b) Temperature rise for PA die as a function of thermal conductivity.

FIGURE 2 .
FIGURE 2. Ultradense diamond composite deposited at low-temperature on a low-cost printed circuit board to remove heat from PA arrays.A 1000X SEM image shows the packing over time with applied ultrasound and heat during the formation of the diamond composites.(a) Composite is produced without ultrasonication and heat (b) 8 min of applied ultrasound and heat (60 • C) (c) 16 min of applied ultrasound and heat.[2].

FIGURE 3 .
FIGURE 3. D-band free-space focused-beam measurement Setup.Top right plot shows bi-convex lens and the small diamond sample.[2].

FIGURE 5 .
FIGURE 5. Relative Gaussian intensity as a function of the normalized radius.