1. INTRODUCTION

There has been steady progress in widening the scope of attosecond science since the first attosecond light pulses were measured in 2001 [1,2]. Using attosecond streaking, the motion of electrons in atoms can now be resolved with attosecond precision [3 –6]. Attosecond streaking has also been used to measure relative time delays in photoemission from different initial states on tungsten [7] and magnesium [8] surfaces. The attosecond time domain response of solid surfaces to light fields involves electron correlations that are yet to be fully understood, but which can in principle be studied using streaking. From a technological perspective, measuring the time evolution of electron–hole pair formation, charge density distributions, and electron propagation in wide-bandgap semiconductors during interaction with ultrashort laser pulses will aid the design of ultrafast optoelectronic circuits [9,10].

In a typical attosecond streaking experiment, a photoelectron wavepacket is emitted by an extreme ultraviolet (XUV) pulse in the presence of a strong near-infrared (NIR) laser field (the streaking field), and the electrons are subsequently accelerated in the field. This process can imprint timing information onto the photoelectron wavepacket due to the well-defined relationship [11] ${\mathit{v}}_f={\mathit{v}}_0+(e/m_e)\mathit{A}(t_i)$ between the final photoelectron velocity ${\mathit{v}}_f$ and the instantaneous vector potential $\mathit{A}(t_i)$ at the time of photoemission, where ${\mathit{v}}_0$ is the initial photoelectron velocity. The temporal structure of the photoemitted electron wavepacket can be extracted from experimental streaking traces [12]. For attosecond streaking measurements performed in gas phase atoms, the photoelectron wavepacket can generally be taken as a replica of the incident XUV pulse [2,13]. In contrast, there is additional information encoded into the temporal properties of a photoelectron wavepacket emitted from a solid about electron transport, for instance, transport distance and dispersion. Thus, the photoelectron wavepacket temporal profile is an important observable for studying dynamics following the photoexcitation of electrons in solids.

In this paper, we present attosecond streaking measurements on thin films of polycrystalline Au, a material widely used in plasmonics, and amorphous ${\mathrm{WO}}_3$, a wide-bandgap semiconductor (3.41 eV bandgap [14]). We show for the first time, to the best of our knowledge, that dynamics taking place within the surface of a solid can cause photoemitted wavepackets to be significantly longer than the incident excitation pulse. We measure photoelectron wavepacket durations consistent with a spread of electron transport times to the surface associated with a range of emission depths. From the streaking traces we also fully characterize the streaking field at the surface of each sample.

2. PHOTOELECTRON WAVEPACKET BROADENING MECHANISMS

A simple estimate of the duration of an electron wavepacket photoemitted from a solid can be made by considering the photoelectron mean free path, and the wavepacket dispersion. For incident photons with energies in the XUV, the maximum depth into the solid from which electrons can be photoemitted is limited by the photoelectron mean free path (typically $<1\mathrm{nm}$), rather than the photon penetration depth into the solid (typically on the order of 100 nm). The valence band photoemission from a solid can be either surface or bulk in origin, with the dominant mechanism being dependent on the bandstructure of the solid [15]. Electrons emitted from the bulk travel, on average, one mean free path to the surface. Assuming perfect screening of the streaking field at the surface, the photoelectrons are streaked with a time delay associated with the transport time to the surface [8,15].

For bulk photoelectrons there will be a range of emission depths, with the main contribution to the total photoelectron yield coming from within one mean free path of the surface. Thus, there is a spread of emission times, and the photoelectron wavepacket emerging from the bulk will be longer than the incident excitation pulse [15]. The temporal broadening of the photoelectron wavepacket compared to the incident XUV pulse is $\sim \lambda \sqrt{m_e/2\mathcal{E}}$, where $\lambda$ is the mean free path and $\mathcal{E}$ is the photoelectron energy. For a mean free path comparable to the XUV photon penetration depth, the streaking trace would become heavily smeared in the time direction [16]. For 84 eV photoelectrons (the typical photoelectron energy in our experiments) the mean free paths in gold and ${\mathrm{WO}}_3$ are $\sim 0.39\mathrm{nm}$ and $\sim 0.49\mathrm{nm}$, respectively, calculated using the Tanuma, Powell, and Penn (TPP-2M) formula [17], with parameters for the calculation taken from [14,18]. Over these mean free paths the expected temporal broadening is 72 as for gold and 90 as for ${\mathrm{WO}}_3$.

The dispersion of the final state will act to further broaden the photoelectron wavepacket in time. For high-energy photoelectrons ($\mathcal{E}\gg W_f$, where $\mathcal{E}$ is the photoelectron energy and $W_f$ is the work function of the solid) one can, to a first approximation, treat the final electron state as unbound. The free-electron group-velocity dispersion is given by

3. METHODS

We performed streaking measurements on two types of samples: an amorphous 20-nm-thick film of the semiconductor ${\mathrm{WO}}_3$ on a silicon (100) substrate, and a polycrystalline 52-nm-thick gold film on silicon (100). Further information about the samples is given in Supplement 1. Additional streaking measurements were performed on atomic gas samples using the same XUV pulses to provide a reference photoelectron wavepacket measurement free from surface effects.

A chirped pulse amplification laser system (Femtolasers GmbH, Femtopower HE CEP) was used to generate 28 fs pulses with up to 2.5 mJ energy, at a 1 kHz repetition rate. Pulses with 1 mJ energy were delivered to a differentially pumped hollow core fiber pulse compression system, which was used to produce 0.4 mJ, sub-4-fs carrier envelope phase stable few-cycle NIR pulses [19]. The few-cycle pulses were used for high-harmonic generation (HHG) in neon within the beamline described in [20].

The copropagating high harmonics and NIR pulses were spatially and spectrally filtered using a Kapton/Zr filter as shown in Fig. 1. The spatial filtering of the NIR, and additional attenuation using a motorized iris, provided sufficient attenuation to prevent sample damage; the peak intensity at the laser focus (110 μm measured spot size) was $1.3\times {10}^{10}\mathrm{W}{\mathrm{cm}}^{-2}$ for the ${\mathrm{WO}}_3$ measurement, and $6\times {10}^9\mathrm{W}{\mathrm{cm}}^{-2}$ for the Au measurement (determined from the streaking measurements). At these intensities, above threshold photoemission from the NIR in the valence band region was negligible compared to photoemission from the XUV pulse. The NIR and high harmonics entered an ultra-high vacuum (UHV) chamber with a base pressure of $3\times {10}^{-9}$ mbar. A two-part mirror setup, incorporating an 8 eV bandwidth multilayer MoSi mirror with a peak reflectivity at 93 eV, selected the cutoff harmonics to produce isolated $248\pm 15$ as XUV pulses. A piezo stage with 10 as resolution introduced a time delay between the XUV and NIR pulses. Photoelectrons emitted from the sample surface were detected using a time-of-flight (TOF) electron spectrometer with a collection angle of $\pm 2.4°$ and an energy resolution of $\mathrm{\Delta }\mathcal{E}/\mathcal{E}\approx 0.004$.

 

Fig. 1. Surface streaking experimental setup. NIR and XUV pulses are focused onto the sample with a variable time delay. Photoemitted electrons are detected with a time-of-flight (TOF) spectrometer. The inset shows the geometry of the incident beam with respect to the sample. The pulses are focused onto the sample with an incidence angle of $\sim 20°$. The laser polarization lies approximately along the TOF axis. The incident beam is also rotated in a horizontal plane by $\sim 6°$.

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4. RESULTS AND DISCUSSION

The valence band region of the experimental ${\mathrm{WO}}_3$ photoelectron spectrum is shown in Fig. 2(a), and displays a clear valence band peak at 84 eV. Experimental photoelectron spectra were Fourier filtered, and the secondary electron background from photoelectrons inelastically scattered on their way to the surface was subtracted using the Shirley method [8,21]. The filtered and background-subtracted attosecond streaking trace from ${\mathrm{WO}}_3$, acquired using 300 as time-delay steps and 120 s integration time ($1.2\times {10}^5$ laser shots) at each time-delay step, is shown in Fig. 2(b).

 

Fig. 2. (a) Unstreaked valence band photoelectron (PE) spectrum of ${\mathrm{WO}}_3$, showing raw data (solid black), Fourier filtered spectrum (red), secondary electron background (dashed black), and background-subtracted and filtered spectrum (blue). (b) Fourier filtered and background-subtracted streaking trace from ${\mathrm{WO}}_3$. The delay-dependent central energy of the valence band is shown by the black curve. (c) Retrieved photoelectron wavepacket intensity (red) and phase (black) from FROG-CRAB PCGPA algorithm. The shaded area shows the incident XUV pulse. The retrieved wavepacket has a duration of ${359}_{-25}^{+42}$ as. (d) Band-pass filtered electric field retrieved from ${\mathrm{WO}}_3$ streaking trace (black curve), and unfiltered data points. Retrieved fields from eight separate gas phase streaking measurements [23] are also shown (red curves). The peak electric field from each gas phase streak has been scaled to the peak field from ${\mathrm{WO}}_3$ to aid comparison.

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The photoelectron wavepacket was retrieved using a standard attosecond retrieval technique, frequency resolved optical gating for complete reconstruction of attosecond bursts [12] (FROG-CRAB) with a principal components generalized projections algorithm [22] (PCGPA). The low collection efficiency ($8.8\times {10}^{-4}$) of our TOF limited the signal-to-noise ratio of the streaking measurements. To allow an estimate of the error on the retrieved wavepacket duration associated with the noise in the streaking traces (which is predominantly from counting statistics), the FROG-CRAB retrieval was performed on the background-subtracted streaking trace without any Fourier filtering applied. The ${\mathrm{WO}}_3$ trace was interpolated onto a $134\times 134$ grid, and $2.5\times {10}^3$ iterations of the FROG-CRAB algorithm were performed. The FROG error of the retrieved streaking trace was 0.05.

The algorithm errors in the retrieved wavepacket temporal intensity, phase, and duration were calculated from the reconstructed FROG-CRAB traces following the approach in [13]. The features in the streaking trace with the lowest signal-to-noise ratio are those at the low-energy and high-energy extrema of the valence band. We estimated the error in the wavepacket duration resulting from these extrema by varying the spectral window size of the input experimental trace into the FROG-CRAB algorithm from 18 to 22 eV (centered around the valence band peak). The error associated with the uncertainty in the Shirley secondary electron background was estimated by using two independent approaches for its calculation. The overall wavepacket durations and experimental errors were taken as the median and range of retrieved pulse durations for all combinations of spectral windows and secondary electron backgrounds. For further discussion of the error analysis, see Supplement 1. The duration of the retrieved photoelectron wavepacket from the ${\mathrm{WO}}_3$ streaking trace was ${359}_{-25}^{+42}$ as, which is longer than the incident XUV pulse by ${111}_{-42}^{+57}$ as.

The central energy ${\mathcal{E}}_{\mathrm{COM}}$ of the valence band in the Fourier filtered and background-subtracted streaking trace, and the error in the central energy, were extracted using the center-of-mass procedure in [7]. The instantaneous vector potential $\mathit{A}$ of the streaking field at the time of XUV photoemission is then related to the energy shift $\mathrm{\Delta }\mathcal{E}={\mathcal{E}}_{\mathrm{COM}}-{\mathcal{E}}_{\mathrm{init}}$ of the photoelectron spectrum by [11]

A streaking measurement on the polycrystalline gold sample is presented in Fig. 3. The streaking trace was acquired using 300 as time-delay steps and 40 s integration time ($4\times {10}^4$ laser shots) at each step. The streaking trace was interpolated onto a $108\times 108$ grid, and $2.5\times {10}^3$ iterations of the FROG-CRAB algorithm were performed. The FROG error of the retrieved streaking trace was 0.10. The retrieved photoelectron wavepacket, shown in Fig. 3(c), has a duration of ${319}_{-37}^{+43}$ as. The electric field at the gold surface is shown in Fig. 3(d). The majority of the gold surface is plane with a roughness of 0.7 nm, and we do not therefore expect any substantial plasmonic effects. Indeed, the retrieved near field is in agreement with fields retrieved from our gas phase streaking measurements.

 

Fig. 3. (a) Unstreaked valence band PE spectrum of Au. (b) Fourier filtered and background-subtracted streaking trace from Au. (c) Photoelectron wavepacket from FROG-CRAB PCGPA algorithm and incident XUV pulse. The retrieved wavepacket has a duration of ${319}_{-37}^{+43}$ as. (d) Retrieved electric fields from Au, and from gas phase streaking measurements. The legends are the same as in Fig. 2.

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The photoelectron wavepackets emitted from both ${\mathrm{WO}}_3$ and gold surfaces have significantly longer durations than those emitted from atomic gas phase samples. The measured temporal broadening for ${\mathrm{WO}}_3$ is in agreement, within the experimental error, with the 90 as of broadening expected from the range of photoemission depths. Similarly for gold, the measured temporal broadening is close to the expected value of 72 as. These results are consistent with a spread of photoelectron transport times to the surface from depths of up to one mean free path. This spread of transport times gets encoded onto the duration of the final electron wavepacket emerging from the surface. Within our simple estimate of the wavepacket broadening, we made the assumption that the NIR field is screened perfectly at the sample surface. Very recent experiments on hybrid systems consisting of Mg adlayers on single-crystalline W indicate a screening depth in the range of 0–0.3 nm [24]. Longer screening depths would reduce the wavepacket broadening associated with the spread of emission depths. Additional sources of wavepacket broadening, caused, for instance, by interaction of the wavepacket with the crystal structure, and electron correlations, may also therefore play a role in the observed wavepacket durations. Nevertheless, temporal characterization of photoelectron wavepackets will provide an additional observable for disentangling the different physical mechanisms ensuing when light interacts with solids.

Our measurements were performed using XUV pulses with a photon energy much larger than the work function, leading to wavepackets with free-electron-like character. At lower photon energies, the effective mass can be significantly larger than 1, and the dispersion relation departs further from that of free electrons [25]. The dispersion relation can exhibit rapid variations in the group velocity with energy [25], which would increase the dispersion of the electron wavepacket during propagation through the solid, increasing the amount of temporal broadening. It would be interesting to investigate these effects by performing attosecond streaking measurements at lower photon energies.

Using the subcycle photoemitted wavepackets we made an attosecond-resolved measurement of the electric field at the surface of each sample, which has the same temporal structure as the incident NIR pulses. No sputtering or annealing of the sample surface was required prior to making the streaking measurements. The ability to perform streaking on samples without prior surface preparation is a prerequisite for streaking measurements on most types of plasmonic samples, since delicate nanostructures will generally be restructured or destroyed by UHV surface preparation techniques, which typically cause morphological changes on nanometer length scales. A number of theoretical studies have indicated that the temporal structure of near fields around plasmonic nanostructures [26 –28] could be measured using attosecond streaking, which would aid in tailoring the plasmonic response of a system for applications emerging in areas such as strong-field physics [29 –31] and ultrafast optoelectronics [32].

5. CONCLUSIONS

In conclusion, we have used attosecond streaking to temporally characterize photoemitted electron wavepackets from films of amorphous ${\mathrm{WO}}_3$ and polycrystalline Au. The wavepacket was temporally broadened compared to the incident $248\pm 15$ as XUV pulse by ${111}_{-42}^{+57}$ as for ${\mathrm{WO}}_3$ and ${71}_{-54}^{+58}$ as for Au. This broadening is consistent with electrons emitted at different depths in the solid taking different amounts of time to travel to the surface. The temporal structure of electron wavepackets photoemitted from condensed matter will yield additional information about the fundamental electronic response to an incident light field. For example, the temporal restructuring of an electron wavepacket as it travels through a solid, which might be influenced in a dynamical manner by electron correlations, could in principle be resolved.