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A molecular dynamic study of change in thermodynamic functions of silicon FCC cell with the change in temperature

MetadataDetails
Publication Date2017-12-28
JournalJournal of Naval Architecture and Marine Engineering
AuthorsA.B.M. Mainul Bari, Saeed Rubaiee, Anas Ahmed, Akm Masud
InstitutionsBangladesh University of Engineering and Technology, University of Jeddah
AnalysisFull AI Review Included

Technical Documentation and Collateral: Advanced Thermal Management in Next-Generation Electronics

Section titled “Technical Documentation and Collateral: Advanced Thermal Management in Next-Generation Electronics”

Analysis of Molecular Dynamics Study of Thermodynamic Functions in FCC Silicon


This research confirms the critical role of thermodynamic properties (specifically molar heat capacity, enthalpy, and Debye temperature) in designing stable and long-lasting electronic semiconductor devices. The simulation results for silicon highlight the thermal limitations that 6CCVD’s engineered diamond materials are specifically designed to overcome.

  • Thermal Challenge Validation: Molecular Dynamics (MD) simulation confirms that silicon’s molar heat capacity ($C_{p}$) approaches 24.2 J K-1 mol-1 near 1000 K, contributing to excessive heating and reduced chip life.
  • Debye Temperature (TD) as Key Metric: The paper establishes TD as a crucial indicator for crystal stiffness and thermal stability, noting that diamond’s TD is inherently required to exceed that of silicon. Silicon’s TD peaks at only 722 K in the simulated range.
  • The Diamond Advantage: A crystal with a large Debye temperature provides superior thermal management and structural stiffness compared to silicon, making MPCVD diamond the necessary substrate for high-density, high-power electronics.
  • Methodological Rigor: The study successfully used CASTEP/COMPASS (Kohn-Sham potential) and NPT ensemble heating to model Si behavior from 0 K to 1000 K, validating simulation results against experimental data.
  • Strategic Opportunity: The need for better thermal design directly aligns with 6CCVD’s expertise in providing high-thermal-conductivity (HTC) Single Crystal Diamond (SCD) and Polycrystalline Diamond (PCD) wafers, which possess a Debye temperature exceeding 2000 K.

The following hard data was extracted from the simulation parameters and results detailing the behavior of Silicon FCC cells:

ParameterValueUnitContext
Simulation MethodMolecular Dynamics (MD)N/AUtilized Accelrys Materials Studio (v5.0)
Simulation ToolCASTEPN/AUsed for molecular level thermodynamic analysis
Atomic Potential UsedKohn-Sham PotentialN/AExpressed interaction between silicon atoms
Structure SimulatedSilicon FCC DiamondN/AConstructed using 19 silicon atoms per unit cell
Simulation Temperature Range0 to 1000KHeating cycle for NPT ensemble stabilization
Lattice Parameter (Input)5.43A°Used for model construction
Maximum Molar Enthalpy~335KJ mol-1Observed at 1000 K
Peak Molar Heat Capacity (Cp)24.2J K-1 mol-1Achieved at 1000 K, confirming thermal limit
Peak Debye Temperature (TD)722KAchieved at 1000 K in simulation
Low Temperature TD Limit50KObserved at 0 K

The molecular dynamics simulation was conducted under the following optimized steps and conditions:

  1. Model Construction: A unit cell consisting of 19 silicon atoms in an FCC diamond structure was constructed using a lattice parameter of 5.43 A°.
  2. Interaction Potential: The interaction between silicon atoms was modeled using the standard Kohn-Sham potential, specifically constructed to reproduce the crystalline silicon structure just above the melting point.
  3. Force Field Selection: The COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) force field was selected for its proven validation in modeling organic and inorganic materials.
  4. Ensemble and Heating: The Isothermal-Isobaric (NPT) ensemble was used for heating cycles to stabilize the system to equilibrium. Heating was simulated between 0 K and 1100 K.
  5. Integration Parameters: Equations of motion were integrated with a 1 fs time interval using a fifth-order predictor-corrector algorithm.
  6. Analysis: Thermal properties (heat capacity, enthalpy, Debye temperature) were analyzed using the CASTEP thermodynamic analysis tool.

This research reinforces the growing consensus that silicon substrates are thermally limited in next-generation high-density power and electronic devices. The requirement for a “stiffer crystal” with a significantly larger Debye temperature points directly to MPCVD diamond as the necessary material solution.

To replicate or, more importantly, advance the thermal management and stiffness of high-power electronics described in this study, 6CCVD recommends:

6CCVD Material GradeThermal Property FocusDimensions & PolishingTarget Application
Optical Grade SCD (Intrinsic)Highest Thermal Conductivity (> 2000 W/mK) and Highest TD (> 2000 K).Thicknesses from 0.1 ”m to 500 ”m. Ultra-polished Ra < 1 nm for chip interfaces.Heat spreading layers, semiconductor coolers, high-power electronics substrates (where maximum heat extraction is critical).
Polycrystalline Diamond (PCD)High mechanical stiffness, excellent heat capacity transition, and customizable dimensions.Plates/wafers up to 125 mm diameter. Ideal for large-area heat sinks or deposition platforms.Advanced thermal stacks, deposition substrates for novel 2D materials, mechanical components.
Boron-Doped Diamond (BDD)Required if the research scope expands to include charge conduction or electrochemical applications alongside thermal management.Customizable doping levels (light to heavy).Sensors, electrodes, active thermal management devices.

The complexity of designing thermal interface materials (TIMs) or novel semiconductor architectures requires precise material customization, a core strength of 6CCVD.

  • Large Format & Precision: 6CCVD offers custom PCD and SCD substrates up to 125 mm (inch-size wafers), enabling scaling from unit cell simulation to industry-relevant device fabrication.
  • Advanced Polishing: Achieving Ra < 1 nm surface roughness on SCD is essential for atomic-scale fidelity at the interface between the diamond substrate and subsequently deposited device layers (e.g., in modeling phonon transport across heterogeneous interfaces).
  • Integrated Metalization: If future studies require contacts or interlayers (e.g., Ti/Pt/Au, as commonly used in diamond device fabrication), 6CCVD provides in-house metalization services, ensuring turnkey, research-ready materials.
  • Dimensional Flexibility: We provide substrates up to 10 mm thick for robust engineering components or ultra-thin SCD films (0.1 ”m) for complex thermal barrier applications.

6CCVD’s in-house team of PhD material scientists specializes in the growth, characterization, and application of CVD diamond with respect to phonon transport, thermal boundary resistance, and wide bandgap physics. We are uniquely positioned to assist researchers and engineers focused on next-generation High-Efficiency Chip Design and Phase Transition Modeling who require materials with inherent thermal stability well beyond silicon’s TD limit of 722 K.

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

View Original Abstract

In modern days silicon is being extensively used in making electronic semiconductor-based chips and IC’s. In this research, the change in different thermodynamic properties of silicon like lattice heat capacity, molar enthalpy and Debye temperature at constant pressure, with the change in temperature, has been investigated by using molecular dynamics (MD) simulation method. Knowing silicon’ thermodynamic functions are quite important, because many electronic companies are nowadays trying a lot to reduce the heat generated by their semiconductor chips as excessive heating of the chip not only warms up the device quickly but also reduces the chip life. The results obtained from this simulation help engineers to design electronic chips more efficiently. For simulation “Accelrys Materials Studio” (Version 5.0) software has been used. The simulation was run for silicon FCC diamond structured cell. The analysis tool used in the simulation is known as CASTEP (Cambridge Sequential Total Energy Package). This tool is specialized for performing molecular level thermodynamic analysis to generate data and graphs for the change in different temperature dependent properties of the molecular system. The interaction between silicon atoms was expressed by the Kohn-Sham potential and MD calculation was conducted on crystalline state of silicon at temperatures between 0 and 1000 K. Here, density function theory (DFT) based tool has been used to derive density of state relations. Results obtained by the simulation were compared with published experimental values and it was found that the simulation results were close to the experimental values.