Nonlinear interactions between ultrashort optical waveforms and solids can be used to induce and steer electric currents on femtosecond (fs) timescales, holding promise for electronic signal processing at PHz () frequencies [Nature 493, 70 (2013)]. So far, this approach has been limited to insulators, requiring extreme peak electric fields () and intensities (). Here, we show all-optical generation and control of electric currents in a semiconductor relevant for high-speed and high-power (opto)electronics, gallium nitride (GaN), within an optical cycle and on a timescale shorter than 2 fs, at intensities at least an order of magnitude lower than those required for dielectrics. Our approach opens the door to PHz electronics and metrology, applicable to low-power (non-amplified) laser pulses, and may lead to future applications in semiconductor and (photonic) integrated circuit technologies.
© 2016 Optical Society of America
Modern electronics relies on the control of electric current in solids . The faster currents can be switched on and off in a device, the higher its performance. High electron mobility transistors  operate at switching rates. Rates of can be attained in semiconductors exposed to ultrashort laser pulses via photoconductive switching  and coherent control [4–9]. Recent experiments showed that currents can be generated and controlled in dielectrics at near-PHz frequencies via interactions with intense few-cycle optical fields [10–12]. This effect—a result of highly nonlinear phenomena within the limit of interband tunneling [13,14]—requires very high fields (), limiting their potential applications.
Here, we demonstrate ultrafast, direct-field control of current at substantially lower fields in GaN, a material with a smaller bandgap (), relevant for high-frequency and high-power (opto)electronics due to its electron mobility, mechanical stability, and heat capacity . We show that charge displacement results from interference of multiphoton transitions  in the presence of field-induced intraband carrier motion and dynamic screening of the optical field. With increasing intensities, we observe a gradual transition from the multiphoton to the tunneling regime, supporting a unified quantum-mechanical picture valid in both limits.
We exposed the (0001) surface of wurtzite GaN to the waveform-controlled, linearly polarized visible/near-infrared (VIS/NIR) few-cycle laser pulses previously used in the prototypical study on silica  (see Supplement 1, Section 1). The instantaneous optical electric field, , was measured by attosecond streaking  in a parallel experiment [Figs. 1(a) and 4(b)]. The field was applied parallel to the surface, i.e., perpendicular to the permanent polarization of wurtzite GaN along its -axis . The stabilized carrier-envelope phase (CEP), , was adjusted by varying the propagation length inside a pair of fused silica wedges. We considered applied electric field peak amplitudes, , up to 0.9 V/Å (cycle-averaged peak intensity, ). Gold (Au) electrodes were patterned onto GaN, allowing for direct measurement of optically induced charge displacements (i.e., time-integrated electric currents) in the material [Fig. 1(a) and Supplement 1, Section 2].
Figure 1(b) shows the CEP-dependent fraction of the charge per pulse collected by the unbiased Au electrodes as a function of and . Here, was perpendicular to the electrodes along the -axis [Fig. 1(a)]. The signal reverses its sign periodically with CEP. Inverting the optical field reverses the direction of the charge displacement: the instantaneous electric field of the laser pulse is generated and controls , similar to the case of an insulator .
We measured for Au-GaN-Au junctions with inter-electrode distances of 100 nm, 5 and 10 μm at various field strengths. Within this electrode separation range, the maximum value of was given for 5 μm [ Coulomb at ; Fig. 1(b)]; for 100 nm and 10 μm, it was and , respectively (both at ). This hints at an optimal inter-electrode distance. A quantitative analysis of the maximum as a function of the junction size is beyond the scope of this study.
Figure 1(c) shows the CEP-optimized transferred charge, , as a function of and , for junctions with 100 nm and 10 μm inter-electrode spacing. For , the experimental data follow , independently of the junction size; this scaling law breaks down in larger fields. In comparison, data for from Ref.  shows a significantly higher order of nonlinearity and a breakdown of the power law scaling at a much stronger field (). Notably, for the same (e.g., ), signals for GaN are at least two orders of magnitude larger than those for .
When is varied, the transferred charge shifts with respect to [Figs. 2(b) and 2(c)], i.e., the charge-balancing CEP, , for which , increases monotonically [Fig. 2(a)]. Here, we focus (arbitrarily) on the charge-balancing CEP related to the rising edge of , i.e., . The dependence of on is not affected by the inter-electrode separation; it is an intrinsic characteristic of the material, as evidenced by the comparison with the case ; Fig. 2(a). The dependence allows for testing our theoretical model and aids the physical interpretation of our experiment.
Following the approach previously developed for , we decoupled injection (i) and driving (d) by exposing the junction to two synchronized, collinear VIS/NIR laser pulses with orthogonal electric fields (parallel to electrodes, along -axis; ) and (perpendicular, along the -axis, ); Fig. 3(a). The CEPs and of the respective fields were set according to the inset in Fig. 3(b), such that in single-pulse experiments (as in Figs. 1 and 2). Figure 4(b) shows as a function of the delay between the two pulses. For , oscillates with a period of , i.e., the period of the optical field [Fig. 1(a)]. In Fig. 3(c), was changed by ; was reversed. Here, oscillates with the same period but is reversed in comparison to Fig. 3(b).
To clarify the physics behind the generated current, we compared our experimental data with quantum-mechanical (QM) simulations based on the numerical solution of the time-dependent Schrödinger equation  (Supplement 1, Sections 3–5). We considered optical transitions between three valence (VB) and two conduction bands (CB) for crystal momenta along the direction in the Brillouin zone (BZ) [Figs. 4(a) and S1 in Supplement 1]. The electrodes’ orientations relative to the crystalline axes of the (0001) surface do not play an important role, since bands are isotropic in the vicinity of the -point  and our field amplitudes are too low for most charge carriers to reach the BZ boundaries.
The theoretical curves (Figs. 1–3) are in good agreement with the experiments within the range of the considered field strengths. We interpret our results as follows. The interaction between GaN and the laser pulse induces a nonequilibrium asymmetrical population distribution in the VBs and CBs [Fig. 4(a)], leading to a CEP-dependent current along the optical field [5,21]. This asymmetric population is due to quantum interference of excitation pathways [16,21], which can be constructive for and destructive for , or vice versa [see the calculated population distribution in Fig. S2c (Supplement 1), which is shifted from the BZ center and exhibits interference fringes]. The interference of the excitation pathways between electronic states in the initial and final bands with energies and is determined by the accumulation of dynamic phase 
In the multiphoton regime, this quantum interference scenario yields a power-law scaling of the transferred charge , where is the order of multiphoton interband transition and is the bandgap at a -point where the corresponding transition is allowed  (Supplement 1, Section 6). The scaling power law () observed in the experiment and in the QM model for [Fig. 1(c)] shows that, within this field range, the charge displacement is triggered by a multiphoton process, consistent with our estimation of the Keldysh  parameter (Supplement 1, Section 6).
For stronger fields, the slope of decreases and diverges from the scaling law. This is due to a combination of: (i) screening of the external field by the field-driven excited carrier displacement , and (ii) closing of the two-photon excitation channel  (Supplement 1, Section 6). The latter is a consequence of the ponderomotive energy becoming comparable to the photon energy, resulting in VB-to-CB transitions becoming nonresonant with the multiphoton process. This is indicative of nonperturbative dynamics and a gradual transition from the multiphoton to the tunneling regime.
The field amplitude dependence of the charge-balancing CEP, (Fig. 2), allows us to further test our QM model. The severe field-dependent shift of is accurately reproduced by the theoretical curve. It is a direct consequence of the field screening due to the motion of charge carriers (Fig. S4, Supplement 1).
The measured (Fig. 3) resolves the oscillations of the optical field. Thus, it can be used for the implementation of a solid-state attosecond streak camera (see Supplement 1, Section 7). The spectrum of extends to a maximal frequency , closely resembling the pulse spectrum [Fig. 3(d)]. According to the cross-correlation theorem, the carrier injection associated with each optical cycle cannot be confined to a time window significantly broader than , with significant contrast in the carrier excitation probability for adjacent optical cycles. The latter is ensured by the quasi-single-cycle character of the pulse and the nonlinearity of the process. Since the pulse duration is smaller than 4 fs, the current injection occurs within 2 fs. This is consistent with the recently observed nonlinear ultrafast carrier excitation in semiconductors [25,26].
In conclusion, we have demonstrated the injection and control of directly measurable currents in a semiconductor (GaN) on a timescale shorter than 2 fs. Our observations highlight the interplay between interfering multiphoton excitation channels and intraband carrier motion. As the latter becomes more significant, deviations from the perturbative scaling law become more severe. This indicates a continuous transition from the multiphoton to the tunneling regime and emphasizes the role of dynamic screening of the optical field inside the solid. Our findings pave the way for the development of ultrafast optically controlled solid-state electronics at intensities at least an order of magnitude smaller than those needed for an insulator. These intensities could further be decreased by optimizing junction geometries, opening the door to metrology for low-power (nonamplified) ultrashort laser pulse sources. Notably, this approach would leverage and further expand existing semiconductor and integrated circuit technologies.
Deutsche Forschungsgemeinschaft (DFG) Cluster of Excellence; Munich-Centre for Advanced Photonics (MAP); Max-Planck-Gesellschaft (MPG); Alexander von Humboldt Foundation; Swiss National Science Foundation (SNF); Marie Curie Fellowship (NANOULOP, 302157); European Research Council (ERC) (AEDMOS); Integrated Initiative LASERLAB-Europe; Australian Research Council (ARC) Future Fellowship; BaCaTeC; U.S. Department of Energy (DOE) (DE-AC02-05CH11231).
We thank Prof. F. Krausz for the helpful discussions, F. Scholz and K. Forghani for providing the GaN samples, and B. D. Harteneck for help in sample design and fabrication. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
See Supplement 1 for supporting content.
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