Microwave plasma modelling in clamshell chemical vapour deposition diamond reactors

At a Glance

Metadata	Details
Publication Date	2022-02-17
Journal	Diamond and Related Materials
Authors	Jerome A. Cuenca, Soumen Mandal, Evan L. H. Thomas, Oliver A. Williams
Institutions	Cardiff University
Citations	31
Analysis	Full AI Review Included

Executive Summary

This study presents a coupled electromagnetic (EM), plasma fluid, and heat transfer model to optimize diamond growth uniformity in a clamshell Microwave Plasma Chemical Vapor Deposition (MPCVD) reactor (Seki Diamond 6K style).

Core Problem Addressed: Achieving spatial homogeneity of polycrystalline diamond (PCD) growth over small (1-inch) Si wafers, which is highly sensitive to sample holder geometry.
Modeling Approach: A multi-physics Finite Element Model (FEM) was developed to simulate the plasma activation region and substrate temperature as a function of Molybdenum (Mo) sample holder “puck” height.
Geometric Impact: Taller pucks (15 mm vs. 5 mm) significantly perturb the reactor’s resonant frequency (up to ~66 MHz shift) and cause the E-field and plasma to focus intensely towards the sample edges.
Optimal Result: The 10 mm puck height yielded the most spatially uniform diamond films, correlating directly with the most uniform and optimal modeled substrate temperature (~790 °C).
Shallow Puck Limitation: Shallow pucks (5 mm) resulted in highly non-uniform growth (large radial variation in grain size and sp³/sp² ratio) due to excessive thermal cooling by the underlying stage.
Key Conclusion: Accurate spatial growth optimization requires coupling plasma fluid and heat transfer solutions, as simple EM field models alone are insufficient for predicting growth rate variations across small substrates.

Technical Specifications

Parameter	Value	Unit	Context
Reactor Topology	TM_0(n>1)p Clamshell	N/A	Seki Diamond/ASTEX SDS 6K style
Substrate Material	Silicon (Si) Wafer	N/A	Diameter = 1”, Thickness = 0.5 mm
Sample Holder Material	Molybdenum (Mo)	N/A	Puck diameter 40 to 60 mm
Optimal Puck Height	10	mm	Yielded most uniform film quality
Puck Height Range Tested	5, 10, 15	mm	Experimental validation
Unperturbed Resonant Frequency	~2.45	GHz	Initial EM model calculation
Maximum Frequency Shift	~-66	MHz	Observed for 20 mm puck height
High MWPD (Growth Power)	5.0	kW	Forward microwave power
High Pressure (Growth)	160	mbar	Plasma fluid model and experiment
Gas Mixture	3% CH₄ in H₂	N/A	Total flow rate 300 sccm
Optimal Substrate Temperature	~790	°C	Measured for 10 mm puck
Lowest Substrate Temperature	~760	°C	Measured for 5 mm puck
Modeled Electron Density (High MWPD)	10 x 10¹⁷	m^-3	Calculated plasma fluid density
Cooling Flux (Modeled)	850	W m^-1 K	Fixed systematic heat transfer coefficient
Raman Laser Wavelength	532	nm	Used for sp³/sp² analysis

Key Methodologies

1. Finite Element Modeling (FEM) Process

The multi-physics simulation was performed in three sequential, coupled steps using COMSOL Multiphysics®:

EM Eigenfrequency Analysis:
- Calculated the Electric (E) field distribution of the resonant mode (TM_0(n>1)p) without plasma.
- Determined how varying puck height and diameter perturbed the resonant frequency, confirming that taller pucks cause significant frequency shifts.
Frequency-Transient EM/Plasma Fluid Solution:
- Modeled the collective behavior of electrons, ions (H₂⁺, H₃⁺), and neutrals using continuity equations.
- Used a simplified H₂ reaction cross-section set (Itikawa database) to model electron-impact reactions (elastic scattering, excitation, ionization).
- Simulated the plasma evolution from ignition (1.5 kW, 27 mbar) to steady state growth conditions (5 kW, 160 mbar) over 1 hour.
Transient Heat Transfer Solution:
- Calculated the spatial gas and substrate temperature distribution over time.
- Used the microwave power dissipated (Q_mw) by the plasma as the heat source.
- Boundary conditions included fixed heat flux simulating cooling and a target substrate temperature of approximately 800 °C.

2. Experimental Growth and Characterization

Substrate Seeding: 1-inch Si wafers were seeded using an ultrasonic process in a nanodiamond colloidal solution to ensure high nucleation density.
Puck Testing: Three Mo pucks (5 mm, 10 mm, 15 mm height) were used; a 20 mm puck was tested but failed to ignite a stable plasma due to excessive frequency perturbation.
Growth Parameters:
- Power: 5 kW (High MWPD).
- Pressure: 160 mbar.
- Gas: 3% CH₄ in H₂ (300 sccm total flow).
- Duration: 30 minutes.
Temperature Measurement: Substrate temperature was monitored using a Williamson dual wavelength pyrometer.
Film Analysis:
- Raman Spectroscopy: Line scans (20 points over 22 mm) were taken across the wafer to map the spatial variation of the diamond quality (d/G ratio, or sp³/sp² content).
- SEM: Used to observe radial variations in grain size and film morphology.

Commercial Applications

The findings are critical for optimizing CVD processes, particularly for small-scale, high-value diamond applications where spatial uniformity is paramount.

Quantum Sensing and Computing:
- Growth of Single Crystal Diamond (SCD) required for creating high-quality Nitrogen-Vacancy (NV) centers, which demand extremely uniform growth conditions over small areas.
Thermal Management (Heat Spreaders):
- Production of high-quality PCD films used as heat sinks in high-power electronic devices (e.g., GaN/III-Nitride membranes), where thermal uniformity across the substrate is essential.
Advanced Optical Components:
- Manufacturing diamond windows and optics, where film thickness and quality homogeneity directly impact performance.
Micro/Nano-Crystalline Diamond Films:
- Optimization of reactor conditions for growing specialized films like Nano-Crystalline Diamond (NCD) and Ultra-Nano-Crystalline Diamond (UNCD), which often require lower power/pressure regimes.
CVD Reactor Design and Engineering:
- Provides a cost-effective modeling pathway for optimizing reactor geometry (e.g., sample stage, puck design) prior to expensive physical prototyping and machining.

View Original Abstract

A microwave plasma model of a chemical vapour deposition (CVD) reactor is presented for understanding spatial heteroepitaxial growth of polycrystalline diamond on Si. This work is based on the TM0(n>1) clamshell style reactor (Seki Diamond/ASTEX SDS 6K, Carat CTS6U, ARDIS-100 style) whereby a simplified H2 plasma model is used to show the radial variation in growth rate over small samples with different sample holders. The model uses several steps: an electromagnetic (EM) eigenfrequency solution, a frequency-transient EM/plasma fluid solution and a transient heat transfer solution at low and high microwave power densities. Experimental growths provide model validation with characterisation using Raman spectroscopy and scanning electron microscopy. This work demonstrates that shallow holders result in non-uniform diamond films, with a radial variation akin to the electron density, atomic H density and temperature distribution at the wafer surface. For the same process conditions, greater homogeneity is observed for taller holders, however, if the height is too extreme, the diamond quality reduces. From a modelling perspective, EM solutions are limited but useful for examining electric field focusing at the sample edges, resulting in accelerated diamond growth. For better accuracy, plasma fluid and heat transfer solutions are imperative for modelling spatial growth variation.

Tech Support

Original Source

DOI: https://doi.org/10.1016/j.diamond.2022.108917

References

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