The speed limit of optoelectronics

The study investigates the ultimate speeds at which electronic signals can be processed by coupling semiconductor charge motion to optical fields with attosecond control. Prior strong-field excitation with ultrashort light pulses enabled sub-femtosecond wavepacket creation but typically populates multiple conduction bands with rapidly decreasing occupation versus energy. This imposes two key drawbacks for high-fidelity, high-speed signal processing: reduced effective bandwidth for short transients and ambiguous mapping of optical to electrical signals due to multi-band wavepackets. To overcome these issues, the authors create a one-femtosecond, single-band Bloch wavepacket via single-photon excitation and steer its motion with a few-cycle optical gate field, detecting the induced current in an external circuit. This linear petahertz photoconductive sampling (LPPS) approach aims to exploit the full bandwidth of a single conduction band while avoiding multi-band population. Using wide-bandgap LiF (Eg=13.6 eV, first conduction band width ΔECB1=6.2 eV), they probe fundamental limits to classical-field-driven electronics, focusing on how interband population transfer impacts fidelity and speed of optoelectronic signal control.

The work builds on developments in attosecond science and optical field control that opened exploration of petahertz-rate electronics. Earlier studies demonstrated strong-field excitation and sub-cycle control in dielectrics and semiconductors, enabling ultrafast carrier injection and high-harmonic generation in solids (e.g., Refs. 4–16). However, strong-field methods tend to populate multiple conduction bands, complicating high-fidelity signal mapping and reducing usable bandwidth. Conventional Auston switches achieve picosecond-scale photoconductive sampling by linear absorption (Refs. 17–18). Attosecond streaking is a standard for sampling optical fields via photoelectron momentum shifts (Refs. 30–34). The present study positions LPPS as a sub-femtosecond, linear-absorption analog to Auston switches, combining single-photon conduction band injection with field-driven wavepacket steering, and it benchmarks LPPS against attosecond streaking to validate linear field retrieval.

Experimental concept: Ultrafast vacuum-ultraviolet (VUV) source pulses (~1 fs) are generated via low-order harmonic generation in argon under high vacuum, driven by carrier-envelope-phase-stable, near-single-cycle visible few-cycle laser pulses. The VUV photon energy is tuned to inject electrons from the valence band into only the first conduction band (CB1) of LiF via single-photon absorption, creating a momentum-symmetric carrier distribution ρ0(n,k) with no initial current. A delayed visible-to-near-infrared gate field EGate(t) subsequently accelerates carriers. Two electrodes on the LiF surface detect the induced current through the external circuit, arising from gate-field-driven electron–hole separation (image charges in electrodes shield the dipole). The induced charge S(τ) versus source–gate delay τ maps the gate field’s vector potential A(τ). Microscopic picture: Following Bloch’s acceleration theorem, carriers injected at time τ with momentum k0 are shifted by the vector potential to kfinal(τ)=k0+A(τ)/ħ after the gate pulse. Without inter-conduction-band transitions, the final distribution is ρfinal(n,k,τ)=ρ0(n,k−A(τ)) and the current density j(τ)∝∫BZ ρfinal(n,k,τ) v(n,k) dk with group velocity v(n,k)=∇k ε(n,k). Near-parabolic dispersion in CB1 yields linear dependence of the current on A(τ), enabling direct mapping of the gate vector potential by LPPS. Gate field benchmarking: The gate vector potential A(τ) is measured in situ via attosecond streaking in neon, using a thin Al/Sc filter stack to generate a suitable high-energy cutoff and a time-of-flight spectrometer along the laser polarization. The LPPS S(τ) is compared to A(τ), confirming a linear relationship and validating LPPS as a high-fidelity optical-field sampling technique without photoelectron detection in vacuum. Linear operation is demonstrated up to ~1.7 V/nm peak gate field in LiF. VUV pulse duration retrieval: Since S(τ) represents a cross-correlation of the VUV-injection temporal profile with A(τ), deconvolution using the streaking-retrieved A(τ) yields an injection window duration ΔτFWHM≈1.4 fs, demonstrating femtosecond-scale conductivity switching by linear absorption. The injection duration imposes a cutoff frequency ~0.4 PHz (≈710 nm). Accurate phase retrieval beyond 0.5 PHz implies spectral correction can extend measurement bandwidth; photoinjected carrier lifetime in LiF (~0.5 ps) sets an upper bound to usable gate pulse durations. Intensity-dependent LPPS and control measurements: LPPS traces at increasing gate intensities are compared to a low-intensity reference to obtain deviations ΔS(τ). A neon control (gas target between electrodes) shows negligible ΔS(τ) even at highest amplitudes, confirming solid-state origins of nonlinearity in LiF. In LiF, ΔS(τ) becomes prominent prior to the gate field maximum, indicating processes occurring 1–2 fs after injection. Interpretation of deviations: Intraband effects (non-parabolicity near zone boundary) would yield symmetric leveling of extrema depending on A(τ) at injection. The observed time-advanced deviations indicate interband Landau–Zener transitions at avoided crossings (CB1→CB2 and higher), splitting the wavepacket into components with inverted group velocities, suppressing the net current before the gate maximum. Theoretical modeling: Time-dependent optical Bloch equations are solved in the basis of Houston orbitals using density-functional-theory-derived band structures and dipole matrix elements for LiF along the Γ–X direction. The LDA bandgap (8.9 eV) is corrected by adjusting source central frequency (11.5 eV). Simulations include four valence and eight conduction bands and are converged in k-point density and time step. The model reproduces linear behavior at moderate gate fields and increasing pre-maximum deviations at higher fields due to CB1→CB2 (and CB3) population transfer. Turning off inter-conduction-band couplings removes the time-advanced deviation, confirming its interband origin. Simulations also explore chirped VUV source pulses shifting injection to k-values near avoided crossings, advancing the deviation timing. A neon model with a parabolic single conduction band (ionization continuum) shows linear mapping at all intensities. Experimental details and controls: Strong suppression of residual driving radiation is achieved using apertures and divergence differences; tests with the harmonic source turned off confirm no spurious photocurrents. Filtering tests (indium and aluminum foils) and current attenuation factors verify that detected currents originate predominantly from VUV photons in the 11–17 eV range. Currents are recorded via lock-in detection by flipping the gate field CEP each pulse; transimpedance amplification is used. Two electrode/sample geometries rule out artifacts from electrode illumination. Propagation effects are negligible due to <15 nm VUV penetration depth and <70 as group-delay walk-off. Signal-to-noise ratio for gate intensity structure is ~26 dB in the linear regime when averaging ~10^8 VUV photons/s; field amplitude changes >15% exceed experimental SD.

• Demonstration of linear petahertz photoconductive sampling (LPPS): single-photon injection into LiF CB1 followed by field-driven separation yields a current that maps the gate vector potential A(τ) with high fidelity; linear operation up to ~1.7 V/nm gate field.
• One-femtosecond-scale conduction band population: deconvolution of LPPS with attosecond-streaking-retrieved A(τ) gives an injection window ΔτFWHM ≈ 1.4 fs, enabling near-petahertz bandwidth switching via linear absorption.
• Bandwidth and cutoff: Injection duration imposes a cutoff frequency ~0.4 PHz (≈710 nm). Phase retrieval remains accurate beyond 0.5 PHz, suggesting spectral correction can extend usable bandwidth.
• Identification of the speed-limiting mechanism: At higher gate intensities, LPPS deviates from linear mapping one optical half-cycle before the gate maximum, traced to Landau–Zener transitions from CB1 to higher conduction bands (notably CB2), which invert group velocities and suppress the net current. Simulations indicate that a 7.5% population transfer from CB1 to CB2 can reduce the LPPS signal by up to 17%.
• Material parameters underpinning performance: LiF’s wide bandgap (Eg=13.6 eV) and large CB1 bandwidth (ΔECB1=6.2 eV) support high-field, high-speed operation; photoinjected carrier lifetime ~0.5 ps sets upper limits on gate duration.
• Feasibility of petahertz optoelectronics: Results imply robust, high-fidelity field-to-current mapping up to the petahertz regime and identify interband population transfer as the fundamental limitation for classical signal processing speed in solids.

The research addresses whether and how optical fields can be mapped to electronic currents at petahertz rates with high fidelity. By preparing a single-band Bloch wavepacket via single-photon excitation and steering it with a few-cycle gate field, the authors achieve a direct, linear mapping between the gate vector potential and the measured current, validated against attosecond streaking. This shows that classical signal processing at petahertz frequencies is feasible in wide-bandgap dielectrics when multi-band occupation is avoided. The observed breakdown of linearity prior to the gate maximum at higher fields, together with modeling, reveals that interband Landau–Zener transitions (CB1→CB2 and beyond) split the wavepacket into components with opposite group velocities, suppressing net current and thus limiting control speed. Consequently, the ultimate speed of solid-state optoelectronics is governed not only by how fast carriers can be injected but critically by maintaining single-band occupancy during field-driven transport. These insights define a materials and waveform-engineering pathway—maximizing single-band bandwidth usage while minimizing interband coupling—to extend high-fidelity control toward 1 PHz.

This work introduces linear petahertz photoconductive sampling (LPPS), demonstrating sub-femtosecond single-photon conduction-band injection in LiF and faithful optical field sampling via induced current that maps the gate vector potential. The injection window of ~1.4 fs enables near-petahertz bandwidth operation, and linearity persists up to ~1.7 V/nm. Time-resolved deviations at higher fields expose interband Landau–Zener transitions and resultant group-velocity inversion as the fundamental mechanism limiting how fast electric currents can be steered in solids. The findings imply a fundamental limit to classical signal processing speed in solids while supporting the feasibility of solid-state optoelectronics approaching 1 PHz. Future research could explore materials with wider single-band bandwidths and reduced interband couplings, spectral and temporal shaping (including chirp control) to tailor injection k-distributions, and device architectures optimizing electrode coupling and signal extraction for petahertz electronics.

• Modeling simplifications: Simulations sample one-dimensional cuts (near Γ–X) rather than the full 3D Brillouin zone, limiting quantitative agreement with experiment.
• Source and detection constraints: The injection-duration-limited cutoff (~0.4 PHz) and current spectral roll-off constrain bandwidth; finite attosecond streaking delay range limits detailed spectral amplitude retrieval. Signal-to-noise is limited by VUV flux and electronic detection noise.
• Material and field limits: Linearity demonstrated up to ~1.7 V/nm; higher fields induce interband transitions that degrade fidelity. Photoinjected carrier lifetime (~0.5 ps) limits usable gate pulse durations.
• Sensitivity to VUV pulse characteristics: Central energy and chirp influence the extent and timing of interband transfer; while not altering qualitative conclusions, they affect quantitative deviations.