Optical transitions between entangled electron–phonon states in silicon

At a Glance

Metadata	Details
Publication Date	2025-10-06
Journal	Applied Physics Letters
Authors	Yael Gutiérrez, Mateusz Rębarz, Christoph Cobet, Josef Resl, Saúl Vázquez-Miranda
Institutions	Extreme Light Infrastructure Beamlines, Bioanalytica (Switzerland)
Analysis	Full AI Review Included

Technical Documentation & Analysis: Ultrafast Electron-Phonon Dynamics in Diamond-Structure Materials

This documentation analyzes the research paper “Optical transitions between entangled electron-phonon states in silicon” (Appl. Phys. Lett. 127, 141102, 2025). The findings regarding Time-Resolved Spectroscopic Ellipsometry (TRSE) in centrosymmetric lattices are highly relevant to 6CCVD’s Single Crystal Diamond (SCD) and Polycrystalline Diamond (PCD) products, offering a pathway to characterize fundamental quantum dynamics in diamond.

Executive Summary

The research successfully employs Time-Resolved Pump-Probe Spectroscopic Ellipsometry (TRSE) to investigate ultrafast electron-phonon coupling in silicon, a material sharing the centrosymmetric diamond lattice structure with CVD diamond.

Novel Probing Technique: TRSE is demonstrated as a viable method to probe optical phonons in centrosymmetric materials, which are traditionally inaccessible via conventional IR absorption or Raman spectroscopy.
Sub-Bandgap Excitation: The use of 50 fs pump pulses below the indirect bandgap (1.08 eV) via Two-Photon Absorption (TPA) minimizes thermalization effects, allowing for the observation of subtle, coherent quantum dynamics.
Coherent State Observation: The study successfully detected entangled electron-phonon states (Longitudinal Optical Phonon Sidebands, LOPSs) that persist for a coherent time window of up to ≈300 fs.
Quantized Energy Levels: Observed LOPSs exhibit a periodic energy spacing of 57 ± 9 meV, consistent with the LO phonon energy near the L-point of the Brillouin zone.
Multi-Phonon Processes: Further sidebands (TPSs) were detected with an 81 ± 7 meV spacing, attributed to two-phonon-assisted electronic transitions (LO + TA phonon combinations).
Direct Relevance to Diamond: This methodology is critical for studying electron-phonon scattering and coherence times in wide-bandgap SCD, essential for quantum computing and high-power electronics applications.

Technical Specifications

The following hard data points were extracted from the experimental results, focusing on the parameters defining the ultrafast dynamics and excitation conditions.

Parameter	Value	Unit	Context
Pump Pulse Duration	50	fs	Temporal resolution of the pump pulse used for TPA excitation.
Coherent State Lifetime	≈300	fs	Dephasing time of the entangled electron-phonon state (LOPSs).
LOPS Energy Spacing (ΔE)	57 ± 9	meV	Periodicity of Longitudinal Optical Phonon Sidebands (LOPSs).
TPS Energy Spacing (ΔE)	81 ± 7	meV	Periodicity of Two-Phonon Sidebands (TPSs).
Primary Pump Photon Energy (PP)	1.08	eV	Sub-bandgap excitation energy (1150 nm).
Pump Fluence (at 1.08 eV)	1.75	mJ/cm²	Fluence used for the primary TRSE measurements.
Probe Spectral Range	1.9 - 3.8	eV	Energy range for measuring the transient pseudo-dielectric function.
LO Phonon Energy (Γ-point)	63	meV	Longitudinal Optical (LO) phonon energy in Si (15.3 THz).
LO Phonon Energy (L-point)	52.1	meV	Longitudinal Optical (LO) phonon energy in Si (12.4 THz).

Key Methodologies

The experiment relied on Time-Resolved Pump-Probe Spectroscopic Ellipsometry (TRSE) combined with carefully selected sub-bandgap excitation to isolate coherent electron-phonon interactions.

TRSE Setup: The experiment measured the time-dependent complex pseudo-dielectric function (€) = (€₁) + i(€₂) across a broad spectral range (1.9-3.8 eV) using femtosecond temporal resolution.
Sub-Bandgap Excitation: Pump pulses (PPs) of 50 fs duration were utilized with photon energies (e.g., 1.08 eV) below the indirect bandgap of Si (1.24 eV at room temperature).
Two-Photon Absorption (TPA): Excitation was achieved via TPA, which provides a non-resonant pathway, significantly reducing lattice perturbation and mitigating thermalization effects common in above-bandgap excitation.
Coherence Measurement: The spectral oscillations (sidebands) in the pseudo-dielectric function were tracked over time delays ranging from -0.05 ps to 4.5 ns to determine the lifetime of the coherent electron-phonon coupled states (≈300 fs).
Spectral Analysis: Periodic modulations in the energy domain were analyzed to determine the energy spacing (ΔE), which directly corresponds to the quantized phonon contributions (LOPSs and TPSs).

6CCVD Solutions & Capabilities

The fundamental physics explored in this paper—ultrafast electron-phonon coupling in a centrosymmetric lattice—is directly transferable to CVD diamond (SCD/PCD). Diamond, with its superior bandgap and thermal properties, is the ideal material for extending this research into high-performance quantum and electronic applications. 6CCVD provides the specialized materials and customization required to replicate and advance these TRSE experiments.

Applicable Materials

To replicate or extend this research into the wide-bandgap regime, 6CCVD recommends the following materials:

Optical Grade Single Crystal Diamond (SCD): Essential for studying intrinsic electron-phonon dynamics without interference from grain boundaries. High-purity SCD is critical for maximizing the coherence time of quantum states (e.g., NV centers) where phonon scattering is the limiting factor.
High-Purity Polycrystalline Diamond (PCD): Suitable for high-fluence experiments or large-area applications requiring mechanical robustness, with custom dimensions available up to 125mm.
Boron-Doped Diamond (BDD): For experiments requiring tunable conductivity or the study of plasmon-phonon coupling, BDD offers a robust, conductive platform.

Customization Potential

6CCVD’s in-house capabilities ensure that researchers can obtain materials perfectly tailored to their advanced optical setups:

Research Requirement	6CCVD Capability	Technical Specification
Material Geometry	Custom Dimensions & Thickness Control	Plates/wafers up to 125mm (PCD). SCD/PCD thickness from 0.1 µm to 500 µm. Substrates up to 10mm.
Surface Quality	Ultra-Precision Polishing	SCD: Ra < 1 nm. Inch-size PCD: Ra < 5 nm. Critical for high-accuracy ellipsometry measurements.
Device Integration	Custom Metalization Services	Internal capability for depositing Au, Pt, Pd, Ti, W, and Cu contacts, enabling integrated electrical biasing for future TRSE experiments.
Orientation Specificity	Custom Crystal Orientation	SCD wafers available in specific orientations (e.g., [100], [111]) necessary for probing directional phonon modes (like the X- and A-directions mentioned in the paper).

Engineering Support

The complexity of ultrafast pump-probe experiments demands precise material selection. 6CCVD’s in-house PhD team specializes in the growth and characterization of CVD diamond and can assist researchers in:

Material Selection: Optimizing diamond purity and defect density (e.g., controlling nitrogen incorporation) to maximize the coherence time (T₂) for similar electron-phonon coupling projects.
Recipe Development: Consulting on the optimal thickness and surface preparation necessary for high-energy, sub-bandgap TPA experiments in diamond.

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

View Original Abstract

Silicon crystallizes in the diamond structure with two atoms per unit cell and supports three optical phonon modes. However, due to the centrosymmetric nature of the lattice, these modes do not induce a net dipole moment and are therefore inactive in infrared absorption. Even in polar semiconductors, where optical phonons can be IR-active, conventional techniques such as infrared absorption and Raman spectroscopy are restricted to probing phonons at the Brillouin zone center (Γ-point). In this work, we demonstrate that time- and spectrally resolved pump-probe ellipsometry enables access to the coherent response of electron-phonon coupled states involving both valence and conduction bands. Following two-photon absorption induced by the femtosecond pump pulse, the electronic excitation relaxes and drives the generation of coherent longitudinal optical phonons along the X-direction of the Brillouin zone, followed by optical transitions of entangled electron-phonon states along the Λ-direction. This process results in a transient, strongly correlated electron-phonon state that persists for up to ≈ 300 fs. Within this coherent time window, the silicon crystal exhibits optical resonances at electronic transition energies modulated by quantized phonon contributions. Finally, we detect further sidebands in the ellipsometric spectrum, which are 81 meV apart and assign these to two-phonon-assisted electronic transitions.

Tech Support

Original Source

DOI: https://doi.org/10.1063/5.0288893

References

1999 - Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures