Effect of thermoelastic damping on silicon, GaAs, diamond and SiC micromechanical resonators

At a Glance

Metadata	Details
Publication Date	2017-05-01
Journal	AIP Advances
Authors	Garuma Abdisa Denu, Jiao Fu, Zongchen Liu, Jibran Hussain Mirani, Hongxing Wang
Institutions	Ethiopian Civil Service University, Xi’an Jiaotong University
Citations	5
Analysis	Full AI Review Included

Technical Documentation and Analysis: High-Q Diamond Micromechanical Resonators

Based on: Effect of thermoelastic damping on silicon, GaAs, diamond and SiC micromechanical resonators AIP Advances 7, 055014 (2017)

Executive Summary

This study numerically compares Thermoelastic Damping (TED) as the primary energy dissipation mechanism across five key MEMS/NEMS materials, providing critical validation for the use of MPCVD Diamond in high-performance resonators and sensing applications.

Diamond Superiority: Single Crystal Diamond (SCD) exhibited the highest simulated Quality (Q) factor—indicating the lowest intrinsic energy dissipation via TED—compared to Silicon (Si), Gallium Arsenide (GaAs), Silicon Carbide (SiC), and Silicon Dioxide (SiO₂).
Modeling Accuracy: Diamond demonstrated the smallest relative difference (1.28%) between the classical Zener model and the more accurate Lifshitz-Roukes (LR) model, proving its material properties align tightly with advanced theoretical predictions.
Low Thermal Diffusion Impact: The largest modeling discrepancy (16.52%, seen in SiO₂) was directly attributed to materials having low thermal diffusion lengths, reinforcing the critical role of diamond’s exceptionally high thermal diffusivity (5.42 cm²s^-1).
Geometrical Optimization: The research validates that resonator performance is highly sensitive to the beam aspect ratio (Length/Width, L/w), providing design constraints essential for optimal high-Q performance.
Application Focus: The findings serve as guidelines for the optimal design of rectangular cantilever beams utilized in high-fidelity micrometer- and nanometer-scale electromechanical systems (MEMS/NEMS) and sensors.

Technical Specifications

The following hard data points were extracted from the simulation parameters and results, highlighting the physical properties that contribute to superior diamond resonator performance.

Parameter	Value	Unit	Context
Material (Optimum Q)	Single Crystal Diamond	N/A	Exhibits lowest Q^-1 (lowest damping)
Young’s Modulus (E, Diamond)	1050	GPa	High intrinsic stiffness
Thermal Conductivity (κ, Diamond)	990	W/mK	Extremely high, key to low TED
Thermal Diffusivity (D, Diamond)	5.42	cm²s^-1	Calculated at 300K
Thermal Diffusion Length (l_T, Diamond)	3.13 x 10^-2	µm	Largest length aids heat dissipation
Simulation Temperature (T₀)	300	K	Equilibrium temperature
Standard Beam Width (w)	5	µm	Fixed dimension for Si, GaAs, Diamond, SiC
Beam Length Range (L)	70 - 520	µm	Analyzed range for aspect ratio variation
Min Q Factor^-1 (Diamond)	0.05 x 10^-3	N/A	Lowest simulated Q-loss for L=170 µm, w=5 µm
Max Model Discrepancy (Diamond)	1.28	%	Difference between Zener and LR models
Max Model Discrepancy (SiO₂)	16.52	%	Observed at L/w aspect ratio of 14

Key Methodologies

The research employed numerical modeling to compare intrinsic energy dissipation (TED) in flexural-mode micromechanical resonators.

Computational Environment: Numerical simulations were performed using Mathematica software to compare the theoretical Quality factors (Q-factors).
Damping Models Compared: Two primary models for thermoelastic damping were utilized:
- Zener Approximation: The classical model based on thermal relaxation time (τ_R).
- Lifshitz-Roukes (LR) Model: An advanced model that accounts for the thermal diffusion length (l_T) and the phonon mean free path, providing a more exact solution for thin beams.
Structural Assumption: All computations assumed a clamped-clamped rectangular beam vibrating in its fundamental flexural resonance mode.
Material and Environment: Simulations used single crystalline material properties for GaAs, Si, Diamond, SiC, and SiO₂ referenced at the equilibrium temperature T₀ = 300K.
Geometric Parameters: Quality factor inverse (Q^-1) was plotted against both normalized frequency (f/f_min) and the dimensionless parameter ξ, which encapsulates the beam aspect ratio (L/w) and the thermal diffusion length (l_T).

6CCVD Solutions & Capabilities

6CCVD is uniquely positioned to supply the advanced MPCVD diamond materials necessary to replicate, optimize, and extend the high-Q resonator performance demonstrated in this research.

Applicable Materials

The paper confirms that the superior thermal and mechanical properties of diamond are essential for achieving maximum Q-factors, directly supporting 6CCVD’s core product offerings.

Optical Grade Single Crystal Diamond (SCD): This material is the definitive choice for replicating the best results found in the paper (E=1050 GPa, κ=990 W/mK). 6CCVD supplies SCD material capable of achieving the highest possible Q-factors required for fundamental physics research and precision sensing.
- Thickness Availability: We offer SCD layers optimized for MEMS/NEMS applications, ranging from 0.1 µm up to 500 µm, precisely matching the requirements for thin-film resonator fabrication.
High-Quality Polycrystalline Diamond (PCD): For applications demanding larger resonant arrays or commercial scale-up, 6CCVD provides PCD wafers up to 125 mm diameter. While SCD offers the highest intrinsic Q, our PCD delivers significantly better thermoelastic performance than Si or SiC at an industrially viable scale.

Customization Potential for Resonator Design

The geometric analysis in the paper (L ranging from 70 µm to 520 µm, w fixed at 5 µm) highlights the need for extreme micro-machining precision.

Requirement from Research	6CCVD Engineering Capability	Benefit to Customer
Specific Dimensions (e.g., L/w aspect ratios up to 104)	High-precision laser cutting and micro-machining services.	Enables fabrication of complex, high-aspect-ratio cantilever beams and arrays post-growth.
High Surface Quality (for reducing extrinsic loss)	Guaranteed SCD surface polish of Ra < 1 nm. Inch-size PCD polish of Ra < 5 nm.	Minimizes surface scattering and anchor losses, complementing the low intrinsic TED characteristics.
Integrated Functionality (for actuation/detection)	Internal metalization capabilities (Au, Pt, Pd, Ti, W, Cu).	Allows for the integration of piezoelectric or electrostatic transduction layers directly onto the diamond film, simplifying device architecture.
Custom Substrates	SCD or PCD wafers available with custom thickness up to 10 mm.	Provides robust platforms for heterogenous integration in MEMS packaging.

Engineering Support

The study emphasizes that selecting the correct material parameters and theoretical models (Zener vs. LR) is critical, particularly when the thermal diffusion length becomes comparable to the system size.

6CCVD’s in-house PhD team provides specialized engineering consultation to assist customers in:

Material Selection: Determining whether SCD or high-purity PCD is the optimal choice based on performance targets, frequency range, and size constraints.
Design Optimization: Assisting with calculating the dimensionless parameter ξ to ensure resonator aspect ratios (L/w) are optimized to minimize TED for specific target frequencies.
Modeling Confidence: Providing data on thermal diffusivity (D) and thermal diffusion length (l_T) relevant to 6CCVD’s specific growth recipes, ensuring researchers utilize the most appropriate damping model for their high-Q NEMS/MEMS resonator projects.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

The effect of thermoelastic damping as a main dissipation mechanism in single crystalline silicon, GaAs, diamond, SiC and SiO2 micromechanical resonators are studied. Numerical simulation is performed to compare quality factors of the given materials. Results using Zener’s well-known approximation and recent developments of Lifshitz and Roukes models were used to model thermoelasticity effects. In the later model, the effect of thermal diffusion length is taken into account for determination of thermoelastic damping. Our results show that larger discrepancy is obtained between the two models for SiO2. The difference is pronounced when beam aspect ratio (L/w) is smaller. Such progresses will find potential applications in optimal design of high quality factor micrometer- and nanometer-scale electromechanical systems.

Tech Support

Original Source

DOI: https://doi.org/10.1063/1.4984288

References

1990 - The effect of thermoelastic internal friction on the Q of micromachined silicon resonators