Dynamics of Single-Photon Emission from Electrically Pumped Color Centers

At a Glance

Metadata	Details
Publication Date	2017-08-31
Journal	Physical Review Applied
Authors	Igor A. Khramtsov, Mario Agio, Dmitry Yu. Fedyanin, Igor A. Khramtsov, Mario Agio
Institutions	University of Siegen, Quantum Science and Technology in Arcetri
Citations	30
Analysis	Full AI Review Included

Technical Analysis & Documentation: Electrically Pumped Single-Photon Emitters in Diamond

Reference: Khramtsov, I. A., Agio, M., & Fedyanin, D. Yu. (2017). Dynamics of single-photon emission from electrically pumped color centers.

Executive Summary

This research validates a critical theoretical framework for developing high-performance, electrically driven single-photon sources (SPS) utilizing Nitrogen-Vacancy (NV) centers in diamond p-i-n diodes. This work directly informs the material specifications required for scalable quantum optoelectronics.

Core Achievement: Established a physical model interpreting the single-photon emission dynamics (g⁽²⁾ function) of electrically pumped NV centers, reproducing complex experimental results.
Mechanism Identified: Single-photon emission dynamics are governed by the speed of electron and hole capture/release processes between the color center and the semiconductor bands, not the excited state lifetime (τ₀).
Speed Advantage: The fast hole capture rate determines the device response time, enabling the realization of true single-photon sources driven by short electrical pulses (on-demand operation).
Material Requirement: Successful device operation relies on precisely engineered diamond p-i-n structures with controlled doping concentrations (10¹⁸ to 10¹⁹ cm^-3) and high carrier mobility in the intrinsic layer.
Scalability: The theoretical approach is generalized and applicable to other wide-bandgap semiconductors (SiC, GaN, ZnO, hBN) and quantum dots, paving the way for integrated quantum circuits.
Performance Metric: The characteristic time (τ₂) of the g⁽²⁾ function monotonically decreases as pump current density increases, confirming faster antibunching at higher injection levels.

Technical Specifications

The following hard data points were extracted from the analysis of the diamond p-i-n diode structure and the NV center dynamics:

Parameter	Value	Unit	Context
Diode Diameter	220	µm	Physical dimension of the diamond disc.
N-Layer Thickness	500	nm	Phosphorus-doped layer thickness.
Intrinsic (i) Layer Thickness	10	µm	Undoped region containing the NV center.
P-Layer Doping (Boron)	10¹⁹	cm^-3	High concentration required for ohmic contact/injection.
N-Layer Doping (Phosphorus)	10¹⁸	cm^-3	Concentration in the n-type layer.
NV Center Depth	300	nm	Distance from the surface/contact.
Simulated Quantum Efficiency (η)	78	%	Efficiency used in numerical simulations.
NV⁰ Excited State Lifetime (τ₀)	5.1	ns	Lifetime at 30% quantum efficiency [25].
Hole Capture Cross-Section (NV^-)	3.2 x 10^-14	cm²	Calculated cross-section at room temperature.
Electron Capture Cross-Section (NV⁰)	~10^-15	cm²	Approximate cross-section.
Electron Mobility (n-layer)	150	cm²/Vs	Experimentally measured mobility.
Hole Mobility (p-layer)	10	cm²/Vs	Experimentally measured mobility.
Intrinsic Region Mobility (Electrons)	~2500	cm²/Vs	High mobility required for efficient transport.
Intrinsic Region Mobility (Holes)	~1200	cm²/Vs	High mobility required for efficient transport.

Key Methodologies

The research employed rigorous self-consistent numerical simulations to model the complex dynamics of the electrically pumped NV center.

Device Structure Modeling: Analysis focused on a diamond p-i-n diode structure, where the single NV center is strategically placed within the high-purity intrinsic (i) region to facilitate charge carrier delivery under forward bias.
Transport Simulation: Self-consistent numerical simulations of electron and hole transport were performed using the nextnano software [35], integrating:
- Poisson equation (for electrostatic potential).
- Drift-diffusion current equations.
- Electron and hole continuity equations.
Charge State Rate Equations: A system of rate equations was established to model the populations of the three relevant NV charge states: NV⁰ excited state (x), NV⁰ ground state (f), and NV^- ground state (1-x-f).
Dynamics Calculation: The second-order photon autocorrelation function, g⁽²⁾(τ), was derived analytically by solving the rate equations with initial conditions corresponding to the NV center being in the NV⁰ ground state immediately after photon emission (g⁽²⁾(0) = 0).
Key Physical Processes: The model explicitly included electron and hole capture rate constants (c_n, c_p) and thermal emission constants (e_n, e_p), demonstrating that carrier exchange dominates the emission dynamics over internal excited state transitions at room temperature.

6CCVD Solutions & Capabilities

6CCVD provides the specialized MPCVD diamond materials and precision engineering services necessary to replicate, optimize, and scale the electrically pumped single-photon sources described in this research.

Applicable Materials

Replicating the high-performance p-i-n diode requires diamond with exceptional purity, precise doping control, and high carrier mobility—all core strengths of 6CCVD’s MPCVD growth technology.

Component Requirement	6CCVD Material Solution	Technical Rationale
Intrinsic (i) Layer	Electronic Grade SCD (Single Crystal Diamond)	Required for the high carrier mobilities (~2500 cm²/Vs for electrons) essential for efficient charge delivery to the NV center [22]. Our SCD offers ultra-low nitrogen content for minimal background defects.
P-Layer (10¹⁹ cm^-3)	Custom Boron-Doped SCD (BDD)	We provide precise, heavy Boron doping (up to 10²¹ cm^-3) necessary to achieve the 10¹⁹ cm^-3 concentration and low compensation ratio required for the p-type injector layer.
N-Layer (10¹⁸ cm^-3)	Custom Phosphorus-Doped SCD	We offer controlled n-type doping to achieve the 10¹⁸ cm^-3 concentration, critical for balancing the p-i-n junction and ensuring efficient electron injection.
Alternative Platform	Optical Grade PCD (Polycrystalline Diamond)	For scaling up device arrays or integrating with larger substrates (up to 125mm diameter), our PCD offers excellent optical transparency and mechanical stability.

Customization Potential

The fabrication of quantum devices demands stringent control over geometry and interface engineering. 6CCVD’s custom capabilities directly address the specific dimensions and integration needs of this p-i-n structure:

Precision Thickness Control: The device requires an n-layer thickness of 500 nm and an i-layer thickness of 10 µm. 6CCVD specializes in growing and processing both SCD and PCD layers with thickness control ranging from 0.1 µm to 500 µm (for active layers) and substrates up to 10 mm.
Custom Dimensions and Geometry: While the paper used a 220 µm disc, 6CCVD can provide custom laser cutting and shaping services to produce wafers, plates, or discs up to 125mm in diameter (PCD) or custom-sized SCD plates for high-density array fabrication.
Metalization Services: Reliable ohmic contacts are crucial for electrical pumping. 6CCVD offers in-house metalization capabilities, including deposition of Ti, Pt, Au, Pd, W, and Cu, allowing researchers to define specific contact geometries for optimal current injection and heat dissipation.
Surface Finish: Achieving high-quality interfaces is essential for minimizing carrier scattering. Our polishing services guarantee surface roughness of Ra < 1 nm for SCD and Ra < 5 nm for inch-size PCD, ensuring optimal device performance and integration with immersion optics.

Engineering Support

6CCVD’s in-house PhD team specializes in defect engineering and material optimization for quantum applications. We can assist researchers in:

Material Selection: Consulting on the optimal doping profiles and compensation ratios required to achieve the high carrier densities (n, p > 10¹⁷ cm^-3) necessary for ultra-fast single-photon emission dynamics (τ₁, τ₂ < 1 ns).
Defect Creation: Advising on post-growth processing techniques to create high-quality, shallow NV centers (like the 300 nm depth used in this study) suitable for efficient electrical pumping and photon collection.
Scaling and Integration: Providing expertise on transitioning from single-device prototypes to scalable, integrated quantum photonic circuits using large-area PCD or customized SCD substrates.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. Global shipping is available (DDU default, DDP available).

View Original Abstract

Low-power, high-speed and bright electrically driven true single-photon sources, which are able to operate at room temperature, are vital for the practical realization of quantum communication networks and optical quantum computations. Color centers in semiconductors are currently the best candidates, however, in spite of their intensive study in the past decade, the behavior of color centers in electrically controlled systems is poorly understood. Here we present a physical model and establish a theoretical approach to address single-photon emission dynamics of electrically pumped color centers, which interprets experimental results. We support our analysis with self-consistent numerical simulations of a single-photon emitting diode based on a single nitrogen-vacancy center in diamond and predict the second-order autocorrelation function and other emission characteristics. Our theoretical findings demonstrate remarkable agreement with the experimental results and pave the way to the understanding of single-electron/single-photon processes in semiconductors.