Free Space Dielectric Techniques for Diamond Composite Characterization

At a Glance

Metadata	Details
Publication Date	2023-12-19
Journal	IEEE Journal of Microwaves
Authors	Shu-Ming Chang, Chelsea Swank, Andrew C. Kummel, James F. Buckwalter
Institutions	University of California, Santa Barbara, University of California, San Diego
Citations	3
Analysis	Full AI Review Included

Executive Summary

Core Problem Addressed: Compact D-band (110-170 GHz) millimeter-wave arrays require novel packaging materials that simultaneously offer high thermal conductivity (> 100 W/mK) and low dielectric loss tangent.
Proposed Solution: Ultradense Diamond Composites (UDC), formed from 10 µm synthetic diamond particles embedded in polymer matrices (TMPTA or PDMS), are investigated as a low-cost, high-performance dielectric heat spreader.
Measurement Technique: Dielectric properties were characterized in the 120-160 GHz range using a free-space focused beam system, which avoids the significant conductor loss uncertainties associated with transmission line methods at D-band.
Calibration and Processing: The NIST iterative extraction method was employed, combined with time-domain gating, to eliminate measurement artifacts, including sample positioning uncertainty and non-line-of-sight (NLOS) reflections.
Key Dielectric Performance (TMPTA-UDC): The TMPTA-based UDC (50% diamond volume fraction) exhibited a relative permittivity (ε_r) of approximately 3.75 and a loss tangent (LT) ranging from 0.027 to 0.048 across the D-band.
Conclusion: The UDC material successfully achieves a low permittivity (roughly 50% of bulk diamond) and an acceptable loss tangent, positioning it as a viable candidate for thermally conductive dielectric packaging in high-frequency RF systems.

Technical Specifications

Parameter	Value	Unit	Context
Target Frequency Band	110-170	GHz	D-band operation.
Reliable Measurement Range	120-160	GHz	Range used after time-domain gating.
Target Thermal Conductivity	> 100	W/mK	Required for PA temperature rise < 100 K (at 30% PAE).
Bulk Diamond Thermal Conductivity	~2000	W/mK	Ideal reference material.
TMPTA-Diamond ε_r (Avg.)	3.75	N/A	Measured at 140 GHz (50% diamond volume fraction).
TMPTA-Diamond Loss Tangent (Min)	0.027	N/A	Polished sample result at D-band.
Pure TMPTA ε_r (Avg.)	2.54	N/A	Measured at 140 GHz.
Pure TMPTA Loss Tangent (Max)	0.052	N/A	Measured at 140 GHz.
PDMS-Diamond ε_r (Avg.)	3.28	N/A	Measured at 140 GHz (30% diamond volume fraction).
PDMS-Diamond Loss Tangent (Max)	0.067	N/A	Measured at 140 GHz.
Quartz Reference ε_r (Avg.)	4.8	N/A	Measured baseline (Manufacturer value 4.68).
Measurement Floor (Loss Tangent)	5 x 10^-3	N/A	Lowest measurable loss tangent in the D-band setup.
Focused Beam Spot Diameter (e^-2)	5.7	mm	Simulated size enclosing 87% of power.
UDC Processing Temperature (Max)	140	°C	Maximum curing temperature for TMPTA.

Key Methodologies

Material Synthesis (Ultradense Diamond Composite - UDC):
- Components: 10 µm synthetic diamond particles mixed with polymer matrices (Trimethylpropane Triacrylate, TMPTA, or Polydimethylsiloxane, PDMS).
- Packing Density: Diamond slurry deposited into a 20-mm Al mold. Pressure was applied using an ultrasonicator while processing at 60 °C to increase packing density.
- Curing: The diamond matrix was cured at 120 °C for 1 hour, followed by TMPTA deposition and final curing at a maximum of 140 °C for 20 minutes.
Free-Space Measurement Setup:
- System: D-band (110-170 GHz) focused beam system utilizing a Keysight PNA, frequency extenders, 25 dBi horn antennas, and bi-convex lenses.
- Lenses: Two 50-mm diameter PTFE plano-convex lenses were combined to form an effective bi-convex lens with a focal length of approximately 50 mm.
- Beam Optimization: Zemax simulation was used to optimize element distances, resulting in a focused beam spot diameter of 5.7 mm (e^-2 point) at the sample plane.
Calibration Procedure:
- Method: Free-space Through/Reflect/Line (TRL) calibration was performed.
- Reference Plane: During sample measurement, Port 2 elements were shifted based on the sample thickness to ensure the calibration plane remained accurately positioned at the sample-air interface.
Dielectric Extraction and Error Mitigation:
- Extraction Algorithm: The NIST iterative method was used to calculate permittivity and loss tangent from the four measured S-parameters (S₁₁, S₂₂, S₁₂, S₂₁). This method is mathematically immune to sample position uncertainty.
- Signal Filtering (Time-Domain Gating): A Fast Fourier Transform (FFT) was used to move the frequency data into the time domain. A Kaiser-Bessel Window (order 6, span 0.2 ns) was applied to isolate the desired signal peak and suppress NLOS reflections and multiple internal system reflections.
- Uncertainty Handling: Sample thickness uncertainty was measured (six times around the sample) and incorporated into the dielectric constant plots as a shaded uncertainty area.

Commercial Applications

High-Frequency RF Packaging: Used for packaging compact millimeter-wave arrays operating in the D-band (110-170 GHz), specifically for radar and backhaul communications.
High-Power Density Electronics: Serves as a thermally conductive dielectric layer for heat spreading in systems where high-power amplifiers (PAs) dissipate significant power in constrained spaces (< 1 mm antenna spacing).
Low-Cost Interposer Technology: Provides a potential low-cost alternative to traditional insulating interposers (like silicon or aluminum nitride) that rely on expensive copper thermal vias to achieve necessary thermal performance.
Advanced Material Development: The free-space focused beam technique enables accurate characterization of novel, non-standard materials (like UDC) in early development stages, where surface roughness prevents the use of standard transmission line test structures.
Heterogeneous Integration: Supports packaging schemes that integrate III-V front-end components (PAs, LNAs) with silicon RFICs, requiring materials that withstand low-temperature processing.

View Original Abstract

Compact millimeter-wave arrays demand novel packaging solutions that feature low-cost dielectric materials with significant thermal conductivity (<inline-formula><tex-math notation=“LaTeX”>$\sim$</tex-math></inline-formula>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.

Tech Support

Original Source

DOI: https://doi.org/10.1109/jmw.2023.3339255

References

2021 - Fabrication of extreme density microdiamond composites for RF and logic heat spreaders
**** - The CVD diamond booklet