Study of detailed balance between excitons and free carriers in diamond using broadband terahertz time-domain spectroscopy
At a Glance
Section titled âAt a Glanceâ| 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 |
Executive Summary
Section titled âExecutive SummaryâThis research successfully utilized Deep-Ultraviolet (DUV) pump - Terahertz (THz) probe spectroscopy (THz-TDS) to establish the detailed balance between excitons and free carriers in pristine Chemical Vapor Deposition (CVD) diamond.
- Accurate Equilibrium Constant (A): The experimental equilibrium constant Aexp = (4.4 ± 2.7) à 1014 cm-3 K-3/2 was determined from the temperature dependence of free-carrier density, confirming excellent agreement with the theoretical value (4.5 à 1014 cm-3 K-3/2).
- Revised Exciton Binding Energy (Eex): A more accurate exciton binding energy Eex = 93.8 ± 8.2 meV was derived, significantly higher than the conventional value of ~80 meV. This difference is attributed to the fine-structure splitting of the exciton 1s states.
- Exciton Internal Transition Identified: The 1s-2p internal transition of excitons was newly observed and characterized at approximately 15 THz using broadband THz-TDS (2-25 THz).
- Detailed Balance Equation Established: The derived parameters provide an accurate Saha equation for diamond, crucial for predicting carrier and exciton densities across various temperatures and total carrier concentrations.
- Methodological Advancement: Technical challenges related to broadband THz generation (using air plasma) and cryostat window transparency (custom Ge/Si/quartz windows) were overcome, enabling THz-TDS application to diamond.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Sample Material | Pristine CVD Diamond (Element Six) | N/A | Nitrogen < 5 ppb, Boron ~ 1 ppb |
| Sample Thickness | 500 | ”m | N/A |
| Exciton Binding Energy (Eex) (New) | 93.8 ± 8.2 | meV | Determined via Saha equation fitting |
| Exciton Binding Energy (Eex) (Conventional) | ~80 | meV (930 K) | Previously accepted value |
| Equilibrium Constant (Aexp) | (4.4 ± 2.7) à 1014 | cm-3 K-3/2 | Experimental result, consistent with theory |
| Equilibrium Constant (Ath) | 4.5 Ă 1014 | cm-3 K-3/2 | Theoretical value based on effective masses |
| Exciton Internal Transition Frequency | ~15 | THz | 1s-2p transition |
| DUV Pump Wavelength | 267 | nm | Generated via Third Harmonic Generation (THG) |
| DUV Excitation Density | 2.5 | mJ/cm2 | Incident on sample |
| Initial Free-Carrier Density (neh) | ~4.9 Ă 1015 | cm-3 | Measured at 10 ps delay, 100 K |
| Exciton Density (nex) | 4.1 Ă 1015 | cm-3 | Measured at 550 ps delay, 100 K |
| Critical Mott Transition Density | 4 Ă 1018 | cm-3 | Thomas-Fermi screening approximation |
| THz Probe Spectral Range | 2-25 | THz | Broadband measurement range |
| Electron Density-of-State Mass (mde) | 0.39m0 | N/A | Used for theoretical A calculation |
| Hole Density-of-State Mass (mdh) | 0.94m0 | N/A | Used for theoretical A calculation |
| Reduced Mass (m**) | 0.19m0 | N/A | m** = (1/me + 1/mh)-1 |
| Lattice Temperatures (TL) | 100, 160 | K | Used for dynamics study |
Key Methodologies
Section titled âKey MethodologiesâThe detailed balance was studied using a custom-designed DUV pump-THz probe spectroscopy system, overcoming limitations of conventional THz-TDS systems.
- Sample Preparation: A 500 ”m thick, high-purity CVD diamond sample (N < 5 ppb, B ~ 1 ppb) was used.
- DUV Pump Generation: An 800 nm Ti:sapphire amplifier pulse was converted to 267 nm via third harmonic generation (THG). The DUV pulse was incident at 45° with an excitation density of 2.5 mJ/cm2.
- Carrier Generation: Transient free carriers (neh ~ 1015 cm-3) were homogeneously generated throughout the sample thickness via a two-photon absorption process, ensuring the density remained below the Mott transition critical density (4 Ă 1018 cm-3).
- Broadband THz Probe Generation and Detection:
- Generation: A broadband THz pulse (2-25 THz) was generated using a collinear air plasma method (mixing fundamental and second harmonic beams). This method was chosen to bypass the phonon absorption limits (2-5 THz) of conventional nonlinear crystal systems.
- Detection: The THz field was detected using the air-biased coherent detection (ABCD) method.
- Cryostat Customization: A custom cryostat was designed with three exchangeable windows (Ge, Si, and quartz) to ensure transparency in both the DUV pump region and the required THz frequency range (2-25 THz).
- Data Analysis (Dielectric Function): The photoinduced change in the complex dielectric function (ÎΔ) was measured at various time delays (Ît = -10 ps to 550 ps) and lattice temperatures (TL).
- Spectral Fitting:
- The measured ÎΔ was fitted using a combination of the Drude model (for free carriers, neh) and the Lorentz oscillator model (for excitons, nex).
- The Drude component decay (sub-nanosecond) was correlated with the calculated cooling dynamics of the carrier temperature (Tc), confirming exciton formation accompanied by thermalization.
- Saha Equation Application: At chemical equilibrium (Ît = 550 ps), the temperature dependence of the free-carrier density (neh) was fitted using the classical Saha equation (Equation 2) to determine the equilibrium constant A and the exciton binding energy Eex.
Commercial Applications
Section titled âCommercial ApplicationsâThe precise understanding of exciton and free-carrier dynamics in diamond is critical for optimizing devices that rely on high-purity diamondâs exceptional electronic and thermal properties.
- Deep-Ultraviolet (DUV) Optoelectronics:
- DUV Light-Emitting Diodes (LEDs): Diamond-based DUV LEDs utilize exciton luminescence (10). Accurate knowledge of Eex and the detailed balance equation is essential for maximizing exciton formation efficiency and device output power.
- DUV Detectors: High-efficiency detectors operating in harsh environments.
- High-Power Electronics and Devices:
- Power Devices: Diamondâs large band gap and high breakdown voltage make it ideal for high-voltage, high-frequency power switches and rectifiers, where minimizing carrier recombination losses is crucial.
- High Thermal Conductivity Substrates: Used in extreme environment applications where heat dissipation is paramount.
- High-Energy Particle Detection:
- Radiation Detectors: Diamond is used in high-energy particle and radiation detectors (3-7). Understanding carrier dynamics (trapping, recombination, and exciton formation) dictates detector speed and sensitivity.
- Fundamental Semiconductor Research:
- The methodology (broadband THz-TDS) provides a new, accurate technique for determining fundamental material constants (A, Eex, effective masses) in wide-bandgap semiconductors, facilitating the design of next-generation photonic and electronic devices.
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.
Tech Support
Section titled âTech SupportâOriginal Source
Section titled âOriginal SourceâReferences
Section titled âReferencesâ- 1994 - Properties and Growth of Diamond