Comprehensive energy balance analysis of photon-enhanced thermionic power generation considering concentrated solar absorption distribution

At a Glance

Metadata	Details
Publication Date	2021-03-30
Journal	Solar Energy Materials and Solar Cells
Authors	A. N. M. Taufiq Elahi, Devon Jensen, Mohammad Ghashami, Keunhan Park
Institutions	Advanced Cooling Technologies (United States), University of Utah
Citations	15
Analysis	Full AI Review Included

Comprehensive Energy Balance Analysis of Photon-Enhanced Thermionic Power Generation (PETE)

Executive Summary

This technical analysis focuses on the rigorous energy balance modeling of a Photon-Enhanced Thermionic Emission (PETE) device for Concentrated Solar Power (CSP) applications, specifically highlighting the critical role of the diamond collector material and precise geometric optimization.

Application Focus: The study models a realistic PETE device using a boron-doped silicon emitter and a phosphorus-doped CVD diamond collector on tungsten for high-efficiency solar energy conversion.
Optimized Performance: Under optimized conditions (100× solar concentration), the device achieved a maximum electrical power density of 1.61 W/cm² and an energy conversion efficiency of 17.9%.
Material Requirement: The performance relies heavily on the ultra-low work function of the collector ($\Phi_C = 0.9$ eV), achievable using specialized doped CVD diamond films.
Geometric Precision: Optimal performance requires precise control over the inter-electrode vacuum gap, determined to be 2 µm, necessitating ultra-flat, highly polished electrode surfaces.
Key Loss Mechanisms: The analysis reveals that optical loss (17.3%) and far-field radiative heat loss (27.3%) from the glass substrate are the dominant energy sinks, emphasizing the need for optically engineered substrate and emitter materials.
6CCVD Value Proposition: 6CCVD is uniquely positioned to supply the required high-quality, precisely dimensioned, and doped CVD diamond materials (PCD/SCD) necessary to replicate and advance this research.

Technical Specifications

The following parameters represent the optimized geometric and operating conditions derived from the comprehensive energy balance analysis (based on Table 1 and Table 2).

Parameter	Value	Unit	Context
Collector Material	P-doped CVD Diamond on Tungsten	N/A	Optimized low work function collector
Collector Work Function ($\Phi_C$)	0.9	eV	Critical for minimizing back emission
Collector Thickness ($d_C$)	300	nm	Thin film requirement
Emitter Material	B-doped Single Crystal Silicon	N/A	Semiconductor emitter
Emitter Thickness ($d_E$)	50	µm	Optimized for maximum solar absorption
Inter-electrode Gap ($d_G$)	2	µm	Optimal gap balancing space charge and near-field effects
Solar Concentration Factor ($C$)	100	suns	Optimized operating condition
Electrical Power Output ($P_{net}$)	1.61	W/cm²	Maximum achieved power density
Energy Conversion Efficiency ($\eta$)	17.9	%	Optimized efficiency at 100× C
Emitter Temperature ($T_E$)	925	K	Operating temperature at optimal power output
Collector Temperature ($T_C$)	540	K	Optimal cold side temperature
Dominant Heat Loss (Far-field)	2.45 (27.3)	W/cm² (%)	Radiative loss from glass substrate

Key Methodologies

The study employed a rigorous, iterative energy balance analysis (EBA) coupled with advanced thermal and charge transport modeling to accurately predict PETE performance under realistic conditions.

Real Material Property Implementation: Dielectric functions and temperature-dependent thermal conductivities were used for all components (B-doped Si, soda-lime glass, CVD diamond, tungsten) instead of ideal assumptions.
Spectral Solar Absorption: Depth-dependent spectral solar absorption within the multi-layered emitter structure was calculated using the scattering-matrix method.
Charge Transport Modeling: Calculation of current density accounted for both the negative space charge effect and the image charge effect on the potential barrier profile across the vacuum gap.
Radiative Heat Transfer: Near-field radiative heat loss (critical at the optimal 2 µm gap) was calculated using the multi-layer dyadic Green’s function within the fluctuational electrodynamics framework.
Geometric Optimization: Key parameters were optimized through EBA iterations, including:
- Emitter thickness ($d_E = 50$ µm) to maximize solar absorption while suppressing recombination.
- Inter-electrode gap ($d_G = 2$ µm) to balance space charge inhibition and near-field radiative heat loss.
Temperature Dependence: The temperature-dependent narrowing of the Si bandgap (from 1.12 eV at 300 K to 0.91 eV at 925 K) was included for accurate carrier concentration calculation.

6CCVD Solutions & Capabilities

6CCVD provides the specialized MPCVD diamond materials and precision engineering services required to manufacture the high-performance collector electrodes and advance PETE research. The study emphasizes that the low work function of the phosphorus-doped CVD diamond collector ($\Phi_C = 0.9$ eV) is essential for achieving competitive efficiencies.

Applicable Materials for PETE Collectors

Material Requirement (Paper)	6CCVD Solution	Technical Advantage
Phosphorus-Doped CVD Diamond	Polycrystalline Diamond (PCD)	High purity, excellent thermal stability, and customizable doping profiles (including Boron and Nitrogen) to achieve specific low work functions necessary for efficient thermionic emission.
Thin Film Collector ($d_C = 300$ nm)	PCD/SCD Thin Films	We offer CVD diamond films ranging from 0.1 µm up to 500 µm in thickness, perfectly matching the required nanoscale collector layer.
Integrated Substrate (Tungsten)	Custom Metalized Diamond	6CCVD provides internal metalization services (Au, Pt, Pd, Ti, W, Cu) to deposit diamond directly onto customer-specified substrates or apply metal layers to the diamond surface for integration onto the tungsten base.

Customization Potential for Advanced PETE Devices

The optimization of the PETE device relies on precise dimensional control and surface quality, areas where 6CCVD excels:

Precision Thickness Control: We provide SCD and PCD plates with thickness control from 0.1 µm to 500 µm, ensuring the emitter/collector layers meet the exact optimal thickness ($d_E = 50$ µm, $d_C = 300$ nm) required for maximum absorption and minimal recombination.
Ultra-Flat Surfaces for Vacuum Gap: Maintaining the optimal 2 µm inter-electrode vacuum gap demands extremely flat and smooth surfaces. 6CCVD guarantees superior polishing:
- SCD surfaces: Ra < 1 nm.
- Inch-size PCD surfaces: Ra < 5 nm.
Large Area Capability: We can supply custom PCD plates and wafers up to 125 mm in diameter, suitable for scaling up CSP prototypes and commercial devices.
Doping and Work Function Tuning: While the paper used P-doped diamond, 6CCVD’s expertise in controlled doping (BDD, N-doped) allows researchers to explore alternative diamond chemistries to further lower the work function and potentially exceed the 0.9 eV performance benchmark.

Engineering Support

The paper concludes that optimizing the substrate material and structure is a key requirement to maximize PETE performance by balancing photoexcitation and thermalization.

Material Consultation: 6CCVD’s in-house PhD team specializes in the thermal, optical, and electronic properties of CVD diamond. We can assist engineers and scientists in selecting the ideal diamond grade and doping level for similar Photon-Enhanced Thermionic Emission (PETE) projects, focusing on minimizing radiative losses and maximizing carrier transport.
Global Supply Chain: We offer reliable global shipping (DDU default, DDP available) to ensure timely delivery of custom diamond components for critical research timelines.

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

Tech Support

Original Source

DOI: https://doi.org/10.1016/j.solmat.2021.111067

References

2010 - Photon-enhanced thermionic emission for solar concentrator systems [Crossref]
2003 - General temperature dependence of solar cell performance and implications for device modelling [Crossref]
2013 - Photon-enhanced thermionic emission from heterostructures with low interface recombination [Crossref]
2014 - Thermally enhanced photoinduced electron emission from nitrogen-doped diamond films on silicon substrates [Crossref]
2014 - GaAs film for photon-enhanced thermionic emission solar harvesters [Crossref]
2014 - Photon-enhanced thermionic emission from p-GaAs with nonequilibrium Cs overlayers [Crossref]
2017 - Temperature dependence of photon-enhanced thermionic emission from GaAs surface with nonequilibrium Cs overlayers [Crossref]