Study of detailed balance between excitons and free carriers in diamond using broadband terahertz time-domain spectroscopy

At a Glance

Metadata	Details
Publication Date	2020-06-08
Journal	Applied Physics Letters
Authors	T. Ichii, Y. Hazama, N Naka, K. Tanaka, T. Ichii
Institutions	Kyoto University
Citations	20
Analysis	Full AI Review Included

Technical Documentation & Analysis: Exciton-Free Carrier Balance in Pristine Diamond

This documentation analyzes the findings of “Study of detailed balance between excitons and free carriers in pristine diamond using terahertz spectroscopy” to highlight 6CCVD’s capability in supplying the advanced MPCVD diamond materials necessary for replicating and extending this fundamental research in diamond photonics and electronics.

Executive Summary

This study successfully employed deep-ultraviolet (DUV) pump-terahertz (THz) probe spectroscopy to accurately determine the chemical equilibrium constants governing exciton and free-carrier populations in pristine diamond.

Fundamental Constant Determination: The equilibrium constant ($A$) in the Saha equation was experimentally determined to be $(4.4 \pm 2.7) \times 10^{14}$ cm$^{-3}$ K$^{-3/2}$, confirming theoretical estimates.
New Exciton Binding Energy: A revised exciton binding energy ($E_{ex}$) of $93.8 \pm 8.2$ meV was determined, which is significantly larger than the conventional 80 meV value, attributed to fine-structure splitting.
High-Purity Material Requirement: The experiment relied on high-quality, low-impurity CVD diamond (N < 5 ppb, B $\approx$ 1 ppb) to minimize trapping and surface recombination effects.
Advanced Spectroscopy: The research utilized a custom THz-TDS system capable of generating and detecting broadband THz pulses (2-25 THz) to observe the exciton internal transition (1s-2p) at approximately 15 THz.
Device Relevance: These precise fundamental findings are crucial for optimizing the design and efficiency of next-generation diamond-based photonic and electronic devices, particularly DUV light-emitting diodes (LEDs).
6CCVD Capability: 6CCVD specializes in providing the required high-purity, thick Single Crystal Diamond (SCD) wafers (up to 500 µm) necessary for high-fidelity optical and THz transmission studies.

Technical Specifications

The following hard data points were extracted from the experimental results and material characterization:

Parameter	Value	Unit	Context
Material Purity (Nitrogen)	< 5	ppb	Unintentionally incorporated dopant
Material Purity (Boron)	$\approx$ 1	ppb	Unintentionally incorporated dopant
Sample Thickness	500	µm	CVD-grown diamond
Exciton Binding Energy ($E_{ex}$)	$93.8 \pm 8.2$	meV	Derived from Saha equation fitting
Saha Coefficient ($A_{exp}$)	$(4.4 \pm 2.7) \times 10^{14}$	cm$^{-3}$ K$^{-3/2}$	Experimental value, consistent with theory
Initial Free-Carrier Density ($n_{eh}$)	$4.9 \times 10^{15}$	cm$^{-3}$	Measured at 10 ps delay, 100 K
Total Carrier Density ($n_{total}$)	$1.06 \times 10^{15}$	cm$^{-3}$	Used for Saha fitting (at 160 K)
Exciton Internal Transition Frequency	$\approx 15$	THz	Observed 1s-2p transition
DUV Pump Wavelength	267	nm	Generated via Third Harmonic Generation (THG)
Excitation Density	2.5	mJ/cm$^{2}$	DUV pulse energy density
THz Probe Spectral Range	2-25	THz	Broadband measurement capability
Lattice Temperature Range ($T_L$)	100 to 300	K	Range for dynamics and equilibrium studies

Key Methodologies

The experiment utilized a sophisticated DUV pump-THz probe spectroscopy system to measure the complex dielectric function ($\Delta\epsilon$) and track the time evolution of free carriers ($n_{eh}$) and excitons ($n_{ex}$).

Material Selection: High-purity, low-dopant CVD diamond (500 µm thick) was used to ensure intrinsic behavior and minimize impurity trapping effects.
Excitation Source: An 800 nm Ti:sapphire amplifier was used to generate a 267 nm DUV pump pulse via third harmonic generation (THG).
Carrier Generation: The DUV pulse was incident at 45° and generated transient free carriers ($n_{eh} \approx 10^{15}$ cm$^{-3}$) via a two-photon absorption process.
THz Generation/Detection: A broadband THz pulse (2-25 THz) was generated using a collinear air plasma method and detected via air-biased coherent detection (ABCD) to cover the critical 15 THz exciton transition region.
Spectroscopic Analysis: The photoinduced change in the complex dielectric function ($\Delta\epsilon$) was measured at various time delays ($\Delta t$) and lattice temperatures ($T_L$).
Modeling: Data was fitted using a combination of the Drude model (for free carriers) and the Lorentz oscillator model (for excitons) to determine absolute densities ($n_{eh}$ and $n_{ex}$).
Equilibrium Determination: The temperature dependence of the free-carrier density at chemical equilibrium ($\Delta t = 550$ ps) was analyzed using the Saha equation to extract the equilibrium constant ($A$) and the exciton binding energy ($E_{ex}$).

6CCVD Solutions & Capabilities

This research demonstrates the critical need for ultra-high-quality, thick SCD material for fundamental studies in solid-state physics and advanced device development (e.g., DUV emitters). 6CCVD is uniquely positioned to supply the exact specifications required to replicate and advance this work.

Applicable Materials

The study required diamond with extremely low nitrogen and boron content to ensure pristine, intrinsic behavior.

Research Requirement	6CCVD Material Solution	Key Specification Match
Pristine, Low-Impurity Diamond	Optical Grade Single Crystal Diamond (SCD)	N < 5 ppb, B $\approx$ 1 ppb purity levels achievable. Essential for minimizing non-radiative recombination and trapping.
Thickness for THz Transmission	SCD Wafers and Substrates	The paper used 500 µm thickness. 6CCVD offers SCD up to 500 µm and substrates up to 10 mm, providing flexibility for future experiments requiring thicker samples or specific thermal management.
High-Quality Surface	Precision Polished SCD	6CCVD guarantees Ra < 1 nm polishing on SCD, crucial for minimizing surface recombination effects that complicate carrier dynamics analysis.

Customization Potential

To move this fundamental research toward practical device prototypes (such as DUV LEDs or high-power switches), custom engineering is essential. 6CCVD offers comprehensive services to bridge this gap:

Custom Dimensions: While the paper used a standard size, 6CCVD can provide custom-cut SCD plates and large-area Polycrystalline Diamond (PCD) wafers up to 125 mm for scaling up device fabrication.
Advanced Metalization: If future experiments require electrical contacts for conductivity measurements or device integration, 6CCVD offers in-house deposition of standard and custom metal stacks, including Ti/Pt/Au, W, Cu, and Pd.
Boron Doping for Conductivity: For extending the research into high-field transport or creating p-n junctions, 6CCVD provides Boron-Doped Diamond (BDD) materials, allowing precise control over conductivity and carrier density.

Engineering Support

The accurate determination of fundamental constants like $A$ and $E_{ex}$ is vital for predictive modeling in diamond device design. 6CCVD’s in-house team of PhD material scientists specializes in the properties of MPCVD diamond.

Material Selection Consultation: Our experts can assist researchers in selecting the optimal SCD grade, thickness, and orientation necessary for high-fidelity Terahertz Spectroscopy and DUV Photonic projects, ensuring minimal parasitic effects from impurities or surface defects.
Process Optimization: We provide technical support regarding material preparation (e.g., specific surface terminations or polishing requirements) to meet the stringent demands of ultrafast pump-probe experiments.

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

View Original Abstract

A fundamental understanding of the photoexcited carrier system in diamond is crucial to facilitate its application in photonic and electronic devices. Here, we report the detailed balance between free carriers and excitons in intrinsic diamond by using a deep-ultraviolet pump in combination with broadband terahertz (THz) probe spectroscopy. We investigated the transformation of photoexcited carriers to excitons by using an internal transition of excitons, which is found to occur at a frequency of 16 THz. We determined the equilibrium constant in the Saha equation from the temperature dependence of the free-carrier density measured at chemical equilibrium. The derived exciton binding energy is larger than the conventional value, which indicates an energy shift due to the fine-structure splitting of the exciton states.