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Hot-Electron Dynamics in a Semiconductor Nanowire under Intense THz Excitation
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  • Andrei Luferau*
    Andrei Luferau
    Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany
    Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
    *Email: [email protected]
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    Orcidhttps://orcid.org/0009-0009-1876-2592
  • Maximilian Obst
    Maximilian Obst
    Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
    Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany
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    Orcidhttps://orcid.org/0000-0003-0370-425X
  • Stephan Winnerl
    Stephan Winnerl
    Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany
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  • Alexej Pashkin*
    Alexej Pashkin
    Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany
    *Email: [email protected]
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    Orcidhttps://orcid.org/0000-0003-1309-6171
  • Susanne C. Kehr
    Susanne C. Kehr
    Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
    Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany
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    Orcidhttps://orcid.org/0000-0002-3857-673X
  • Emmanouil Dimakis
    Emmanouil Dimakis
    Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany
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    Orcidhttps://orcid.org/0000-0002-7546-0621
  • Felix G. Kaps
    Felix G. Kaps
    Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
    Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany
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  • Osama Hatem
    Osama Hatem
    Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
    Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany
    Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta 31511, Egypt
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    Orcidhttps://orcid.org/0000-0003-4746-0963
  • Kalliopi Mavridou
    Kalliopi Mavridou
    Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany
    Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
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  • Lukas M. Eng
    Lukas M. Eng
    Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
    Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany
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    Orcidhttps://orcid.org/0000-0002-2484-4158
  • Manfred Helm
    Manfred Helm
    Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany
    Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
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ACS Photonics

Cite this: ACS Photonics 2024, 11, 8, 3123–3130
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https://doi.org/10.1021/acsphotonics.4c00433
Published August 9, 2024

Copyright © 2024 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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We report terahertz (THz)-pump/mid-infrared probe near-field studies on Si-doped GaAs–InGaAs core–shell nanowires utilizing THz radiation from the free-electron laser FELBE. Upon THz excitation of free carriers, we observe a red shift of the plasma resonance in both amplitude and phase spectra, which we attribute to the heating of electrons in the conduction band. The simulation of heated electron distributions anticipates a significant electron population in both the L- and X-valleys. The two-temperature model is utilized for quantitative analysis of the dynamics of the electron gas temperature under THz pumping at various power levels.

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Introduction

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High-quality epitaxial nanowires (NWs) based on III–V semiconductors offer the possibility to fabricate ultrafast optical devices. In particular, single NWs can serve as sensitive elements of terahertz (THz) radiation detectors that operate at room temperature. (1,2) Contactless investigation of the average charge carrier concentration and mobility in large ensembles of NWs is possible using THz time-domain spectroscopy. (3) The local investigation of these properties on individual NWs can be carried out by scattering-type scanning near-field optical microscopy (s-SNOM). (4) This technique offers a spatial resolution far beyond the diffraction limit, and in the case of far-infrared studies, it can be extended beyond λ/4600. (5,6) Utilizing near-infrared (NIR) excitation on (typically intrinsic) NWs, charge-carrier lifetimes in NW ensembles become accessible in far-field NIR-pump/THz-probe experiments. (7,8) Several studies demonstrated the feasibility of integrating the NIR-pump/THz-probe technique with near-field microscopy for the examination of III–V semiconductors. (9−12) The NIR pump served as interband excitation and enabled investigating the local recombination dynamics of photogenerated carriers in individual NWs. However, for some important applications of NWs such as field-effect transistors (13−15) or THz detectors, (1,2) it is important to study the response of doped NWs to intense THz radiation that does not change the carrier density but rather heats up the carrier system via intraband absorption.
Here, we report on THz-pump/mid-infrared (MIR) probe s-SNOM studies on highly doped GaAs/InGaAs core–shell NWs utilizing the intense narrowband THz radiation from the free-electron laser (FEL) FELBE (16) at the Helmholtz-Zentrum Dresden-Rossendorf. The analysis of the near-field spectra enables us to obtain the electron temperature as a function of the pump–probe delay time. Our results quantify the dynamics of hot electrons in the conduction band of the InGaAs shell and enable us to quantify the electron–phonon coupling. Furthermore, we gain insights into the electron heating and cooling dynamics by simulating it with the two-temperature model.

Results and Discussion

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Near-Field MIR Spectroscopy of the Nanowires

The samples under study are Si-doped GaAs/InGaAs core–shell NWs grown by molecular beam epitaxy. They consist of a 25 nm-thick GaAs core and an 80 nm-thick In0.44Ga0.56As shell that is homogeneously n-doped with a nominal Si-concentration of about 9 × 1018 cm–3. (17,18) For s-SNOM studies, these NWs are transferred onto a (100)Si substrate and dispersed randomly across it.
Our experiments are carried out with an s-SNOM setup from Neaspec GmbH equipped with a nanoscale Fourier transform infrared (nanoFTIR) module, including a broadband MIR difference-frequency generation (DFG) source (5–15 μm; 20–60 THz; Pavg ∼0.2 mW; 78 MHz; t < 100 fs) used as a probe. (19) Radiation is focused by an off-axis parabolic mirror (numerical aperture: 0.46, focal length: 11 mm) onto a metallized atomic force microscopy (AFM) tip that operates in tapping mode with an oscillation amplitude of about 100 nm. Tip–sample near-field interaction modifies the backscattered radiation, which is detected by a photoconductive mercury cadmium telluride (MCT) detector. To separate the near-field signal from the far-field signal, the detector signal is demodulated by a lock-in amplifier at the second harmonic of the AFM cantilever tapping frequency Ω ≈ 250 kHz. (20) The tip and the sample are located in one of the arms of an asymmetric Michelson interferometer of the nanoFTIR module (Figure 1a). Here, the tip-scattered near-field light optically interferes with the split MIR beam from the reference arm, and the detector signal is recorded as a function of the reference mirror position. (21) Finally, the obtained interferograms are Fourier transformed to obtain spectra of the near-field scattering amplitude s(ω) and phase ϕ(ω).

Figure 1

Figure 1. (a) Sketch of a time-resolved near-field spectroscopy setup based on s-SNOM. A Michelson interferometer enables MIR near-field spectroscopy (nanoFTIR) during THz pumping of the sample. (b) Topography of the GaAs/InGaAs core–shell NW recorded by AFM. The tip position chosen for spectrally resolved scans is highlighted with a red triangle. (c) Near-field amplitude s(ω) and phase ϕ(ω) spectra of the doped GaAs/InGaAs core–shell NW normalized to the response of Si along with the results of two-parameter fit based on the point–dipole and the Drude models.

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In Figure 1b, the AFM topography image of such a NW under study is shown, highlighting the chosen tip position for spectrally resolved scans with a red triangle. The orientation of NWs with respect to the incident angle of the laser shows no significant impact on the spectral response, while positioning the tip at the center of the NW prevents geometry-related artifacts like interference or shadowing.
A point–dipole model incorporating the frequency-dependent infrared permittivity ε(ω) of the NWs is used to estimate the near-field response of the samples. (22,23) In this model, the field Escat scattered by the tip is approximated by a dipolar near-field interaction between the tip apex and the sample surface, resulting in
Escat∝α0(1+rp)21−α0β16π(a+h)3Einc
(1)
where α0 = 4πa3 is the polarizability of the tip with a radius a induced by the incident field Einc, rp is the Fresnel reflection coefficient for p-polarized light, h is the tip apex–sample separation, and β = (ε – 1)/(ε + 1). Consideration of higher harmonic demodulation involves incorporating a sinusoidal tip oscillation h(t). The subsequent Fourier transformation of Escat[h(t)] results in En∝sneiϕn, where sn and ϕn represent the amplitude and phase of the scattered electric field at demodulation order n, respectively.
The frequency dependence of the permittivity ε(ω) in a doped semiconductor can be described by the Drude model as follows
εNW(ω)=εoptic−ωpl2εopticω2+iωγel
(2)
where εoptic is the high-frequency permittivity, and the second term in the equation describes the response of free charge carriers with the plasma frequency ωpl2 = ne2/(m*ε0εoptic) and the plasmonic damping γel = e/(μm*), where e is the elementary charge, n is the concentration of the charge carriers, and m* and μ are their effective mass and mobility, respectively. Here, we neglect the contribution from the polar phonon resonance since it is located well below the frequency range addressed in this study. Since the InGaAs shell is much thicker than the GaAs core, we neglect the core–shell structure and estimate the NW response as the plasmonic response of the heavily doped shell alone.
The unpumped near-field MIR response of the NW acquired in the standard nanoFTIR mode at demodulation order n = 2 is shown in Figure 1c. Both the amplitude spectrum s(ω) = sNW(ω)/sSi(ω) and the phase spectrum ϕ(ω) = ϕNW(ω) – ϕSi(ω) are normalized to the response of the Si substrate, assuming its permittivity to be constant for the photon energy range of the MIR probe. (24) Due to the interference between the tip-scattered radiation Escat and the reference beam, which is approximately identical to the incident on the tip field Einc, the MCT detector measures the homodyne detection intensity I∝|Escat||Einc|ei(ϕscat−ϕinc) rather than just the intensity of the scattered probe I∝|Escat|2. (25) Thus, normalizing the NW spectra to the Si reference eliminates the unknown parameters of the amplitude and phase of incident field Einc. In accordance with eq 1, this simplifies modeling the plasmonic response to just two physical parameters. The fitting of the experimental data provides us with the plasma frequency ωpl0 = (1050 ± 10) cm–1 and the damping γel0= (260 ± 20) cm–1. As seen from Figure 1c, the model can reliably reproduce the experimental amplitude and phase spectra.
Samples under study are grown in such a way that Si dopants are incorporated into InGaAs as a donor. (17) Due to the heavy n-doping of the sample, the observed plasmonic resonance is attributed to the response of electrons in the conduction band. The InGaAs Γ-valley conduction band is nonparabolic and can be approximately described by the equation εk (1 + αεk) = ℏ2k2/(2mΓ), (26) with the Γ-point effective mass mΓ and the nonparabolicity parameter α = 1/Eg, (27) where Eg is the band gap. The nonparabolicity leads to a variation of the effective mass with electron density m*(n). By solving the equation ne2/[ε0εopticm*(n)] = ωpl02, we obtain the unpumped electron density n0 = (8.5 ± 0.2) × 1018 cm–3 and the distribution function of electrons with a chemical potential of εF = 265 meV at 300 K. The value of the average effective mass m0* corresponding to the electron density n0 equates to 0.06me. Knowing the effective mass m0* also allows us to convert the fitted value of damping γel0 to the mobility μ0= (600 ± 50) cm2 V–1 s–1.

THz-Pump/MIR-Probe Experiment

For THz-pump/MIR-probe s-SNOM studies, we utilize the intense narrowband THz radiation from FELBE (16) as an intraband pump. Its pulses have a repetition rate of 13 MHz and a duration at full width at half-maximum (fwhm) of 2.85 ps at the chosen wavelength of λ = 25 μm (12 THz). This is the shortest wavelength that can be efficiently suppressed by a ZnSe high-pass filter placed before the detection scheme to avoid saturation of the detector. The temporal profile of the pulse and the duration were obtained from the measured FEL spectrum using the model in ref (28). Unless otherwise mentioned, the data shown in the paper are obtained with an average excitation power of Pavg = 6 mW (fluence of ≈12 μJ/cm2). The FEL pump beam is guided to the parabolic mirror with a focal length of 11 mm that focuses the beam, having a diameter of ≈4 mm, onto the tip apex into a diffraction-limited spot of ≈70 μm, resulting in an applied electric field of ≈80 kV/cm. The DFG probe source is locked to the sixth harmonic of the FEL repetition rate and synchronized with the FEL pulse train. The time delay between pump and probe pulses is varied by an optical delay line.
The 6-fold difference in the repetition rates of the FEL and the DFG source leads to an undesirable situation when the pump pulse excites the sample, and only every sixth probe pulse measures the real response of the sample to this excitation. This can be overcome technically during the measurement process via the sideband demodulation technique by introducing an additional modulation of the pump beam to directly detect the photoinduced change in the interferogram. (29) Since the FEL operates in a pulsed mode, our pump is originally modulated at the FEL repetition rate of 13 MHz, which we use as a carrier frequency, while the second harmonic of the AFM cantilever tapping frequency 2Ω ≈ 500 kHz is utilized as a sideband (see Supporting Information). Nonetheless, the 2 MHz cutoff frequency of the employed MCT detector diminishes the efficiency of the double demodulation technique. Substituting the employed detector with a faster one, however, results in compromised sensitivity within the probed range. To overcome this issue, we further suggest a data processing approach that enables the extraction of the relevant excited probe pulses from data acquired without additional modulation.
As previously mentioned, when the pump pulse excites the sample, only every sixth probe pulse measures the actual response of the sample to this excitation. The five following probe pulses are idle and measured the response of the sample in an unpumped state until the next pump pulse arrives. Assuming that the detector equally averages intensities of all the received probe pulses, we can define an average-measured intensity Imix as follows
Imix=Ipumped+5×Iunpumped6
(3)
where Ipumped and Iunpumped are the intensities of the probe pulses scattered from the sample in the excited and unexcited states, respectively. In the case of interferometric studies, eq 3 is also valid for each point of the interferogram and, therefore, is applicable to describe the mixing of the pumped and unpumped interference patterns as a whole. Thus, given the interferogram of the sample in the unexcited state, we can extract the pumped interferogram from the measured mixed interference pattern Imix. Considering the linearity of the Fourier transform, the same procedure can be applied to extract complex pumped scattering spectra from the measured mixed spectra. The extracted pumped spectra exhibit a superior signal-to-noise ratio (SNR) compared to the results obtained via side-demodulation detection (see Supporting Information) and are used for the presentation of the results in the following.
Figure 2a,b shows the near-field amplitude s(ω) and phase ϕ(ω) spectra of the InGaAs NW obtained with and without THz pumping, extracted according to eq 3, and normalized to the response of Si. Despite the increased noise in the extracted spectra, the implemented fitting model works well and additionally serves as a guide for the eye to observe a red shift of the NW plasma resonance upon the excitation. To trace the full dynamics of the resonance shift, we perform a series of spectroscopic scans with a 2 ps step of the optical delay line. Figure 2c,d depicts the results in the form of a color map, where every line represents extracted and normalized to Si near-field spectra obtained for different time delays between the THz-pump and broadband MIR-probe counted from an arbitrary time zero. We acknowledge that the time zero is set to the maximum of the FEL pulse (Figure 4b) as we do not have a direct method to determine it due to the noninstantaneous nature and relatively long rise time of our pump pulse. One can see a red shift in both the amplitude and phase of the near-field plasmonic response and recovery on the same time scale. To quantify the observed shift of the plasma resonance, all the spectra are fitted with the point–dipole model, and the fitted values of the plasma frequency ωpl for different time delays are plotted in Figure 2e. Since the intraband pump does not excite new electrons into the conduction band, the carrier density n0=(8.5±0.2)×1018cm−3 should remain constant. Thus, the time evolution of the plasma frequency ωpl can be converted to the time evolution of the effective mass m* (Figure 2f), which quantitatively illustrates the dynamics of the electron gas heating, reaching values of up to 0.09me for the 6 mW THz pump.

Figure 2

Figure 2. (a,b) Near-field amplitude s(ω) and phase ϕ(ω) spectra of the doped GaAs/InGaAs core–shell NW obtained with (red) and without (blue) THz pumping (6 mW) and normalized to the response of Si. The spectra are extracted from experimental data according to eq 3 and plotted along with the results of the two-parameter fit based on the point–dipole and the Drude models. (c,d) Color maps illustrating the evolution of the near-field amplitude s(ω) and the phase ϕ(ω) spectra of the doped InGaAs NW upon THz photoexcitation (6 mW), normalized to the response of Si. Every line represents normalized near-field spectra obtained for different time delays between the THz-pump and broadband MIR probe. (e) Fitting parameter of the plasma frequency ωpl as a function of pump–probe delay time. (f) Time evolution of the effective mass m* of electron gas upon intraband THz pumping.

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Figure 3

Figure 3. Simulation results: (a) In0.44Ga0.56As band structure scheme depicting the conduction band valleys relevant to the experiment [ (34). The blue dashed line is a parabolic approximation of the nonparabolic Γ-valley. (b,c) Normalized electron distributions for 300 and 1500 K. (d) Calculated fractions of electrons of each conduction band valley versus temperature. (e) Dependence of the total effective mass on temperature. The dashed line represents the simulation neglecting the impact of side valley transfer.

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Figure 4

Figure 4. (a) Temporal evolution of the electron-gas temperature upon THz-pumping of various powers. (b) Simulation of the temporal evolution of the electron temperature [the same axis as part (a)] based on the two-temperature model for three peak electric-field amplitudes of the FEL radiation inside the NW. The gray dashed line represents the normalized intensity profile of the FEL pulse.

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Dynamics of Electron Temperature

Several theoretical (30,31) and experimental (32,33) studies are dedicated to the heating of free electrons by MIR radiation. They associate the increase in effective mass of highly doped n-GaAs both with the nonparabolicity of the Γ-valley and, at high temperatures, with the transfer of electrons to the heavier mass l-valley, while the small contribution of X-valley electrons is typically neglected. In the case of the In0.44Ga0.56As alloy, a schematic band diagram of which is depicted in Figure 3a, the energy separation between the L- and X-minima almost disappears. (34) Therefore, in addition to the nonparabolicity (the parabolic approximation of the Γ-valley is shown in Figure 3a as a dashed line), we have to consider the redistribution of heated electrons between the three conduction valleys. By taking into account the boundary condition of carrier density conservation, we calculate electron distributions for various temperatures of the heated electron gas. Figure 3b,c depicts the calculated electron distributions for 300 and 1500 K, respectively, showing the change of the valley populations and the Fermi–Dirac distribution.
To quantify the repopulation of hot electrons and its effect on the effective mass, we introduce the value of the fraction of electrons in the ith valley, fi, normalized to the total density of electrons n0. Figure 3d shows the calculated temperature dependence of the fraction of electrons in each valley. Initially, all the electrons stay within the Γ-valley, and in order to transfer just 1% of them to the side valleys, the electron gas must be heated above 500 K. As the heating increases, the tail of the distribution widens enough for faster repopulation of electrons, which are evenly distributed over two side valleys up to 1000 K. At higher temperatures, the fraction of electrons settled in the X-valley becomes greater than that for the l-valley due to the fact that the density-of-states effective mass of X-valley electrons is somewhat larger than that of l-valley electrons. (34) The contribution of electrons from each valley to the total effective mass is estimated as for conductivity problems
1m*=fXmX*+fLmL*+fΓmΓ*(nΓ)
(4)
where fi is the fraction of electrons in the corresponding valley, mΓ*(nΓ) is the effective mass in the Γ-valley considering the nonparabolicity, and mX* and mL* are optical effective masses for anisotropic X- and L-minima, respectively, characterized by longitudinal ml and transverse mt effective masses and defined as (m)−1=(ml–1+2mt–1)/3. As a result, we obtain a simulated dependence of the total effective mass m*(T) on the temperature shown in Figure 3e. To emphasize the influence of side-valley electrons, we additionally simulated the temperature dependence of the total effective mass m* considering that all electrons stay within the nonparabolic Γ-valley (Figure 3e, dashed line). At temperatures below 500 K, both curves are equal, and the effective mass rises because of the Γ-valley nonparabolicity, while further heating leads to a significant increase of the total effective mass due to the transfer of electrons to the side valleys.
Knowing the temperature dependence of the total effective mass m*(T) enables us to extract the time evolution of the electron temperature T(t) from the experimental results on the temporal changes in the effective mass m*(t). Figure 4a presents the dynamics of electron temperature T(t) upon THz-pumping of various powers. The data points related to the excitation power of 6 mW are extracted directly from the data set depicted in Figure 2f, replacing each mass value m* with the associated temperature T according to the simulated m*(T) dependence. The data points corresponding to other power excitations are acquired in the same manner, and detailed outcomes of the related pump–probe experiments are available in the Supporting Information. In Figure 4a, all data points within the temperature range below 500 K exhibit significant error bars, attributed to error propagation resulting from the relatively flat segment of the simulated m*(T) dependence. At higher temperatures, the slope of the m*(T) is larger, which makes it possible to track temperature changes more precisely. However, excessively high temperatures are also challenging to track. Exciting the sample with a power of 27 mW enables us to discern temperatures up to approximately 2000 K as the upper detection limit. Excessive heating causes the plasma resonance to be shifted beyond our MIR probing range, and the exact temperature of the electron gas remains unknown.

Two-Temperature Modeling

For interpretation of the temporal response shown in Figure 4a, we performed a modeling of the electron temperature dynamics using the two-temperature model (35)
Ce(Te)dTedt=PFEL(t)−g(Te−Tl)
(5)
CldTldt=g(Te−Tl)
(6)
where Te and Tl are the temperatures of the electrons and the lattice, respectively; Ce and Cl are the specific heats of the electron and the lattice subsystems, respectively; g is the electron–phonon coupling constant; and PFEL(t) is the FEL power density absorbed by the electrons. The latter function can be written as
PFEL(t)=σ1(ωFEL,Te(t))EFEL2(t)
(7)
where σ1(ωFEL,Te) = ωFELIm[εNW(ωFEL,Te)]ε0 is the optical conductivity of the NW at the FEL frequency ωFEL estimated from the Drude model parameters in eq 2, and EFEL is the local electric field in the NW under the AFM tip induced by the FEL pumping. Since the effective mass depends on the transient electronic temperature Te(t), as depicted in Figure 3e, the plasma frequency ωpl and the optical conductivity in the Drude model also vary with time in our simulation. In contrast to metals, where the Fermi energy is large, the condition kBT ≪ εF is not fulfilled in our case of a doped semiconductor. Therefore, the usual assumption that the electronic specific heat Ce is proportional to Te does not hold. In our modeling, we used the Ce(Te) dependence calculated for the actual band structure of In0.44Ga0.56As (see Supporting Information for details).
Figure 4b shows the simulation results for three peak electric-field amplitudes of the FEL radiation inside the NW that properly scale with the FEL powers used in the experiment. We obtain reasonably good agreement with the experimentally measured temperature dynamics by varying only two parameters: the electron–phonon coupling g and the conversion factor between the FEL power and the local electric field EFEL2. The simulation confirms the quicker rise and slower decay of the electron temperature and accurately reproduces the substantial power-dependent extension in the duration the system stays in a heated state compared with the FEL pulse duration. This observation allows us to exclude the effect of band dispersion modification, which would cause a nearly instantaneous response lasting for just over the duration of the FEL pulse.
The two-temperature model captures the peak temperature levels for two lower excitation fields, but the simulated temperature for the highest field of 75 kV/cm seems to be overestimated. Although the experimental data also reveal that the electron temperature exceeds 2000 K around the peak for an FEL power of 27 mW, the simulation shows even more extreme heating with a maximal Te of 3700 K for a maximum field strength of 170 kV/cm that is reachable in our experiments. According to our calculations, the heating should transfer up to 87% of electrons to the side valleys.
First, let us discuss electron–phonon coupling. The coupling coefficient used in the simulation is independent of Te and equals g ≈ 1014 J/(m3 K s). It results in temperature relaxation times of 2–5 ps for the electronic temperature between 500 and 2000 K. This agrees with theoretical results predicting a nearly temperature-independent electron cooling time around 1 ps for electronic temperatures up to 500 K. (36) We would like to point out that our assumption of the temperature-independent electron–phonon coupling does not take into account that the LO phonon emission rate for the valley electrons is much higher than that for the Γ-valley. (37) This would lead to an increase in the electron–phonon coupling g at high electronic temperatures, consequently accelerating the cooling dynamics. However, this effect should not drastically affect the temperature dynamics in the range of electronic temperatures detected in our experiment.
Second, we compare the estimated peak FEL field in the focus of the parabolic mirror with the simulation results. Knowing the FEL pulse parameters and considering the Fresnel transmission coefficient of ≈25% for the p-polarized pump, we can estimate the peak FEL field inside the NW samples to be ≈15 kV/cm for an FEL power of 3 mW. Taking into account uncertainties in the experimental and modeling parameters, this value nearly matches the local electric field EFEL used in the simulations. This fact demonstrates that the pump-induced THz near-field under the SNOM tip does not have a superior effect on the sample heating compared to the focused far-field. At first glance, this result contradicts the near-field modeling predicting a few orders of magnitude enhancement of the near-field at the sample surface. (38,39) However, the normal electric field component inside the sample is reduced by a factor |ε| with respect to the field outside. In our case, the permittivity of the doped NW at the FEL frequency can be estimated from eq 2, giving |εNW| ≈ 60. Thus, it is possible that the tip enhancement of the near-field is compensated by the plasma screening inside the NW, resulting in a comparable effect on the sample heating from both near- and far-field.

Conclusions

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Our investigation of heavily doped GaAs/InGaAs core–shell NWs via THz-pump/MIR-probe s-SNOM provides valuable insights into the heating and cooling dynamics of electron gas in an individual NW. The localized plasmon resonance experiences a strong red shift under THz-FEL excitation. We have demonstrated that this behavior can be explained by the increase in the averaged effective electron mass caused by the hot-electron distribution that populates side valleys of the conduction band in InGaAs. Additionally, the simulation of heated electron distributions has allowed estimation of the temporal evolution of electron-gas temperatures under THz pumping. The observed features of the temporal response were accurately reproduced by the two-temperature model, yielding estimated values for both electron–phonon coupling and the local pump field. The results provide relaxation times that are consistent with theoretical predictions and suggest that the pump-induced THz near-field under the SNOM tip has a minimal impact on sample heating when compared to that of the focused far-field. Importantly, the THz-pump/MIR-probe s-SNOM has proven itself as a powerful tool for quantitatively exploring the nonlinear interaction of nanostructures with THz radiation, further broadening its applicability in the field of nanoscale science and technology.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.4c00433.

  • Results of the sideband modulation technique along with the point–dipole model-based simulations, extended power-dependent results, and calculation of the specific heat of the electron gas (PDF)

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  • Corresponding Authors
  • Authors
    • Maximilian Obst - Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany;  Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany;  Orcidhttps://orcid.org/0000-0003-0370-425X
    • Stephan Winnerl - Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany
    • Susanne C. Kehr - Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany;  Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany;  Orcidhttps://orcid.org/0000-0002-3857-673X
    • Emmanouil Dimakis - Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany;  Orcidhttps://orcid.org/0000-0002-7546-0621
    • Felix G. Kaps - Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany;  Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany
    • Osama Hatem - Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany;  Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany;  Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta 31511, Egypt;  Orcidhttps://orcid.org/0000-0003-4746-0963
    • Kalliopi Mavridou - Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany;  Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
    • Lukas M. Eng - Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany;  Würzburg-Dresden Cluster of Excellence, EXC 2147 (ct.qmat), Dresden 01062, Germany;  Orcidhttps://orcid.org/0000-0002-2484-4158
    • Manfred Helm - Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany;  Institut für Angewandte Physik, Technische Universität Dresden, Dresden 01062, Germany
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The authors are grateful to J. Michael Klopf and the ELBE team for the operation of the FEL FELBE and for their dedicated support and to Thales de Oliveira and Xiaoxiao Sun for their experimental assistance at the Helmholtz-Zentrum Dresden-Rossendorf. A.L. expresses gratitude to Markus B. Raschke for insightful discussions on sideband demodulation technique conveyed through private communications. M.O., S.C.K., F.G.K., O.H., and L.M.E. acknowledge funding by the Bundesministerium für Bildung und Forschung (BMBF, Federal Ministry of Education and Research, Germany) grant nos. 05K19ODA, 05K19ODB, and 05K22ODA as well as the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through project CRC1415 (ID: 417590517) and the Würzburg-Dresden Cluster of Excellence “ct.qmat” (EXC 2147, ID: 390858490).

References

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This article references 39 other publications.

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  1. Rainer Hillenbrand, Yohannes Abate, Mengkun Liu, Xinzhong Chen, D. N. Basov. Visible-to-THz near-field nanoscopy. Nature Reviews Materials 2025, 10 (4) , 285-310. https://doi.org/10.1038/s41578-024-00761-3
  2. Andrei Luferau, Alexej Pashkin, Stephan Winnerl, Maximilian Obst, Susanne C. Kehr, Emmanouil Dimakis, Thales V. A. G. de Oliveira, Lukas M. Eng, Manfred Helm. Time-resolved nanospectroscopy of III–V semiconductor nanowires. Nanoscale Advances 2025, 7 https://doi.org/10.1039/D5NA00307E
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  • Abstract

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    Figure 1

    Figure 1. (a) Sketch of a time-resolved near-field spectroscopy setup based on s-SNOM. A Michelson interferometer enables MIR near-field spectroscopy (nanoFTIR) during THz pumping of the sample. (b) Topography of the GaAs/InGaAs core–shell NW recorded by AFM. The tip position chosen for spectrally resolved scans is highlighted with a red triangle. (c) Near-field amplitude s(ω) and phase ϕ(ω) spectra of the doped GaAs/InGaAs core–shell NW normalized to the response of Si along with the results of two-parameter fit based on the point–dipole and the Drude models.

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    Figure 2

    Figure 2. (a,b) Near-field amplitude s(ω) and phase ϕ(ω) spectra of the doped GaAs/InGaAs core–shell NW obtained with (red) and without (blue) THz pumping (6 mW) and normalized to the response of Si. The spectra are extracted from experimental data according to eq 3 and plotted along with the results of the two-parameter fit based on the point–dipole and the Drude models. (c,d) Color maps illustrating the evolution of the near-field amplitude s(ω) and the phase ϕ(ω) spectra of the doped InGaAs NW upon THz photoexcitation (6 mW), normalized to the response of Si. Every line represents normalized near-field spectra obtained for different time delays between the THz-pump and broadband MIR probe. (e) Fitting parameter of the plasma frequency ωpl as a function of pump–probe delay time. (f) Time evolution of the effective mass m* of electron gas upon intraband THz pumping.

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    Figure 3

    Figure 3. Simulation results: (a) In0.44Ga0.56As band structure scheme depicting the conduction band valleys relevant to the experiment [ (34). The blue dashed line is a parabolic approximation of the nonparabolic Γ-valley. (b,c) Normalized electron distributions for 300 and 1500 K. (d) Calculated fractions of electrons of each conduction band valley versus temperature. (e) Dependence of the total effective mass on temperature. The dashed line represents the simulation neglecting the impact of side valley transfer.

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    Figure 4

    Figure 4. (a) Temporal evolution of the electron-gas temperature upon THz-pumping of various powers. (b) Simulation of the temporal evolution of the electron temperature [the same axis as part (a)] based on the two-temperature model for three peak electric-field amplitudes of the FEL radiation inside the NW. The gray dashed line represents the normalized intensity profile of the FEL pulse.

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      Eisele, M.; Cocker, T. L.; Huber, M. A.; Plankl, M.; Viti, L.; Ercolani, D.; Sorba, L.; Vitiello, M. S.; Huber, R.
      Nature Photonics (2014), 8 (11), 841-845CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
      A review. Phase-locked ultrashort pulses in the rich terahertz spectral range have provided key insights into phenomena as diverse as quantum confinement, first-order phase transitions, high-temp. supercond. and carrier transport in nanomaterials. Ultrabroadband electro-optic sampling of few-cycle field transients can even reveal novel dynamics that occur faster than a single oscillation cycle of light. However, conventional terahertz spectroscopy is intrinsically restricted to ensemble measurements by the diffraction limit. As a result, it measures dielec. functions averaged over the size, structure, orientation and d. of nanoparticles, nanocrystals or nanodomains. Here, we extend ultrabroadband time-resolved terahertz spectroscopy to the sub-nanoparticle scale (10 nm) by combining sub-cycle, field-resolved detection (10 fs) with scattering-type near-field scanning optical microscopy (s-NSOM). We trace the time-dependent dielec. function at the surface of a single photoexcited InAs nanowire in all three spatial dimensions and reveal the ultrafast (<50 fs) formation of a local carrier depletion layer.
    10. 10
      Wagner, M.; McLeod, A. S.; Maddox, S. J.; Fei, Z.; Liu, M.; Averitt, R. D.; Fogler, M. M.; Bank, S. R.; Keilmann, F.; Basov, D. N. Ultrafast dynamics of surface plasmons in InAs by time-resolved infrared nanospectroscopy. Nano Lett. 2014, 14 (8), 4529– 4534,  DOI: 10.1021/nl501558t
      10
      Ultrafast Dynamics of Surface Plasmons in InAs by Time-Resolved Infrared Nanospectroscopy
      Wagner, Martin; McLeod, Alexander S.; Maddox, Scott J.; Fei, Zhe; Liu, Mengkun; Averitt, Richard D.; Fogler, Michael M.; Bank, Seth R.; Keilmann, Fritz; Basov, D. N.
      Nano Letters (2014), 14 (8), 4529-4534CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      We report on time-resolved mid-IR (mid-IR) near-field spectroscopy of the narrow bandgap semiconductor InAs. The dominant effect we obsd. pertains to the dynamics of photoexcited carriers and assocd. surface plasmons. A novel combination of pump-probe techniques and near-field nanospectroscopy accesses high momentum plasmons and demonstrates efficient, subpicosecond photomodulation of the surface plasmon dispersion with subsequent tens of picoseconds decay under ambient conditions. The photoinduced change of the probe intensity due to plasmons in InAs is found to exceed that of other mid-IR or near-IR media by 1-2 orders of magnitude. Remarkably, the required control pulse fluence is as low as 60 μJ/cm2, much smaller than fluences of ∼1-10 mJ/cm2 previously utilized in ultrafast control of near-IR plasmonics. These low excitation densities are easily attained with a std. 1.56 μm fiber laser. Thus, InAs-a common semiconductor with favorable plasmonic properties such as a low effective mass-has the potential to become an important building block of optically controlled plasmonic devices operating at IR frequencies.
    11. 11
      Pizzuto, A.; Castro-Camus, E.; Wilson, W.; Choi, W.; Li, X.; Mittleman, D. M. Nonlocal time-resolved terahertz spectroscopy in the near field. ACS Photonics 2021, 8 (10), 2904– 2911,  DOI: 10.1021/acsphotonics.1c01367
      There is no corresponding record for this reference.
    12. 12
      Pushkarev, V.; Němec, H.; Paingad, V. C.; Maňák, J.; Jurka, V.; Novák, V.; Ostatnický, T.; Kužel, P. Charge Transport in Single-Crystalline GaAs Nanobars: Impact of Band Bending Revealed by Terahertz Spectroscopy. Adv. Funct. Mater. 2022, 32 (5), 2107403,  DOI: 10.1002/adfm.202107403
      There is no corresponding record for this reference.
    13. 13
      Egard, M.; Johansson, S.; Johansson, A.-C.; Persson, K.-M.; Dey, A. W.; Borg, B. M.; Thelander, C.; Wernersson, L.-E.; Lind, E. Vertical InAs nanowire wrap gate transistors with ft > 7 GHz and fmax > 20 GHz. Nano Lett. 2010, 10 (3), 809– 812,  DOI: 10.1021/nl903125m
      13
      Vertical InAs nanowire wrap gate transistors with ft > 7 GHz and fmax > 20 GHz
      Egard, M.; Johansson, S.; Johansson, A.-C.; Persson, K.-M.; Dey, A. W.; Borg, B. M.; Thelander, C.; Wernersson, L.-E.; Lind, E.
      Nano Letters (2010), 10 (3), 809-812CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      We report on high-frequency measurements on vertically standing III-V nanowire wrap-gate MOSFETs (metal-oxide-semiconductor field-effect transistors). The nanowire transistors are fabricated from InAs nanowires that are epitaxially grown on a semi-insulating InP substrate. All 3 terminals of the MOSFETs are defined by wrap around contacts. This makes it possible to perform high-frequency measurements on the vertical InAs MOSFETs. We present S-parameter measurements performed on a matrix consisting of 70 InAs nanowire MOSFETs, which have a gate length of about 100 nm. The highest unity current gain cutoff frequency, ft, extd. from these measurements is 7.4 GHz and the max. frequency of oscillation, fmax, is higher than 20 GHz. This is a viable technique for fabricating high-frequency integrated circuits consisting of vertical nanowires.
    14. 14
      Colinge, J.-P.; Lee, C.-W.; Afzalian, A.; Akhavan, N. D.; Yan, R.; Ferain, I.; Razavi, P.; O’Neill, B.; Blake, A.; White, M.; Kelleher, A.-M.; McCarthy, B.; Murphy, R. Nanowire transistors without junctions. Nat. Nanotechnol. 2010, 5 (3), 225– 229,  DOI: 10.1038/nnano.2010.15
      14
      Nanowire transistors without junctions
      Colinge, Jean-Pierre; Lee, Chi-Woo; Afzalian, Aryan; Akhavan, Nima Dehdashti; Yan, Ran; Ferain, Isabelle; Razavi, Pedram; O'Neill, Brendan; Blake, Alan; White, Mary; Kelleher, Anne-Marie; McCarthy, Brendan; Murphy, Richard
      Nature Nanotechnology (2010), 5 (3), 225-229CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
      All existing transistors are based on the use of semiconductor junctions formed by introducing dopant atoms into the semiconductor material. As the distance between junctions in modern devices drops below 10 nm, extraordinarily high doping concn. gradients become necessary. Because of the laws of diffusion and the statistical nature of the distribution of the doping atoms, such junctions represent an increasingly difficult fabrication challenge for the semiconductor industry. Here, we propose and demonstrate a new type of transistor in which there are no junctions and no doping concn. gradients. These devices have full CMOS functionality and are made using Si nanowires. They have near-ideal subthreshold slope, extremely low leakage currents, and less degrdn. of mobility with gate voltage and temp. than classical transistors.
    15. 15
      Morkötter, S.; Jeon, N.; Rudolph, D.; Loitsch, B.; Spirkoska, D.; Hoffmann, E.; Döblinger, M.; Matich, S.; Finley, J. J.; Lauhon, L. J.; Abstreiter, G.; Koblmüller, G. Demonstration of confined electron gas and steep-slope behavior in delta-doped GaAs-AlGaAs core--shell nanowire transistors. Nano Lett. 2015, 15 (5), 3295– 3302,  DOI: 10.1021/acs.nanolett.5b00518
      15
      Demonstration of Confined Electron Gas and Steep-Slope Behavior in Delta-Doped GaAs-AlGaAs Core-Shell Nanowire Transistors
      Morkotter S; Rudolph D; Loitsch B; Spirkoska D; Hoffmann E; Matich S; Finley J J; Abstreiter G; Koblmuller G; Jeon N; Lauhon L J; Hoffmann E; Abstreiter G; Doblinger M
      Nano letters (2015), 15 (5), 3295-302 ISSN:.
      Strong surface and impurity scattering in III-V semiconductor-based nanowires (NW) degrade the performance of electronic devices, requiring refined concepts for controlling charge carrier conductivity. Here, we demonstrate remote Si delta (δ)-doping of radial GaAs-AlGaAs core-shell NWs that unambiguously exhibit a strongly confined electron gas with enhanced low-temperature field-effect mobilities up to 5 × 10(3) cm(2) V(-1) s(-1). The spatial separation between the high-mobility free electron gas at the NW core-shell interface and the Si dopants in the shell is directly verified by atom probe tomographic (APT) analysis, band-profile calculations, and transport characterization in advanced field-effect transistor (FET) geometries, demonstrating powerful control over the free electron gas density and conductivity. Multigated NW-FETs allow us to spatially resolve channel width- and crystal phase-dependent variations in electron gas density and mobility along single NW-FETs. Notably, dc output and transfer characteristics of these n-type depletion mode NW-FETs reveal excellent drain current saturation and record low subthreshold slopes of 70 mV/dec at on/off ratios >10(4)-10(5) at room temperature.
    16. 16
      Helm, M.; Winnerl, S.; Pashkin, A.; Klopf, J. M.; Deinert, J.-C.; Kovalev, S.; Evtushenko, P.; Lehnert, U.; Xiang, R.; Arnold, A.; Wagner, A.; Schmidt, S. M.; Schramm, U.; Cowan, T.; Michel, P. The ELBE infrared and THz facility at Helmholtz-Zentrum Dresden-Rossendorf. Eur. Phys. J. Plus 2023, 138 (2), 158,  DOI: 10.1140/epjp/s13360-023-03720-z
      There is no corresponding record for this reference.
    17. 17
      Dimakis, E.; Ramsteiner, M.; Tahraoui, A.; Riechert, H.; Geelhaar, L. Shell-doping of GaAs nanowires with Si for n-type conductivity. Nano Res. 2012, 5, 796– 804,  DOI: 10.1007/s12274-012-0263-9
      17
      Shell-doping of GaAs nanowires with Si for n-type conductivity
      Dimakis, Emmanouil; Ramsteiner, Manfred; Tahraoui, Abbes; Riechert, Henning; Geelhaar, Lutz
      Nano Research (2012), 5 (11), 796-804CODEN: NRAEB5; ISSN:1998-0000. (Springer GmbH)
      A shell-doping scheme demonstrate the potential of using Si to achieve controlled n-type cond. for GaAs nanowires (NWs). In this approach, mol. beam epitaxy is used to grow first the undoped GaAs nanowire core in the Ga-assisted vapor-liq.-solid mode, and then the Si-doped GaAs shell layer conformally around the core in the vapor-solid mode. The incorporation site of Si was evaluated by Raman spectroscopy, and correlated with the growth conditions of the doped shell. In that way, a growth window that ensures the incorporation of Si as donor, and obtained donor concns. up to 1 x 1019/cm3, with the compensation level by Si acceptors remaining below 10%. Finally, resistivity measurements on planarized shell-doped nanowire ensembles were employed to probe the doping efficiency and the surface depletion of free-carriers. The achievement of n-type cond. for nanowires is essential for the realization of functional devices, and is particularly significant when a dopant as well understood and advantageous as Si is employed.
    18. 18
      Balaghi, L.; Bussone, G.; Grifone, R.; Hübner, R.; Grenzer, J.; Ghorbani-Asl, M.; Krasheninnikov, A. V.; Schneider, H.; Helm, M.; Dimakis, E. Widely tunable GaAs bandgap via strain engineering in core/shell nanowires with large lattice mismatch. Nat. Commun. 2019, 10 (1), 2793,  DOI: 10.1038/s41467-019-10654-7
      18
      Widely tunable GaAs bandgap via strain engineering in core/shell nanowires with large lattice mismatch
      Balaghi Leila; Hubner Rene; Grenzer Jorg; Ghorbani-Asl Mahdi; Krasheninnikov Arkady V; Schneider Harald; Helm Manfred; Dimakis Emmanouil; Balaghi Leila; Helm Manfred; Bussone Genziana; Grifone Raphael
      Nature communications (2019), 10 (1), 2793 ISSN:.
      The realisation of photonic devices for different energy ranges demands materials with different bandgaps, sometimes even within the same device. The optimal solution in terms of integration, device performance and device economics would be a simple material system with widely tunable bandgap and compatible with the mainstream silicon technology. Here, we show that gallium arsenide nanowires grown epitaxially on silicon substrates exhibit a sizeable reduction of their bandgap by up to 40% when overgrown with lattice-mismatched indium gallium arsenide or indium aluminium arsenide shells. Specifically, we demonstrate that the gallium arsenide core sustains unusually large tensile strain with hydrostatic character and its magnitude can be engineered via the composition and the thickness of the shell. The resulted bandgap reduction renders gallium arsenide nanowires suitable for photonic devices across the near-infrared range, including telecom photonics at 1.3 and potentially 1.55 μm, with the additional possibility of monolithic integration in silicon-CMOS chips.
    19. 19
      Huth, F.; Govyadinov, A.; Amarie, S.; Nuansing, W.; Keilmann, F.; Hillenbrand, R. Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution. Nano Lett. 2012, 12 (8), 3973– 3978,  DOI: 10.1021/nl301159v
      19
      Nano-FTIR Absorption Spectroscopy of Molecular Fingerprints at 20 nm Spatial Resolution
      Huth, Florian; Govyadinov, Alexander; Amarie, Sergiu; Nuansing, Wiwat; Keilmann, Fritz; Hillenbrand, Rainer
      Nano Letters (2012), 12 (8), 3973-3978CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      We demonstrate Fourier transform IR nanospectroscopy (nano-FTIR) based on a scattering-type scanning near-field optical microscope (s-SNOM) equipped with a coherent-continuum IR light source. We show that the method can straightforwardly det. the IR absorption spectrum of org. samples with a spatial resoln. of 20 nm, corresponding to a probed vol. as small as 10 zeptoliter (10-20 L). Corroborated by theory, the nano-FTIR absorption spectra correlate well with conventional FTIR absorption spectra, as exptl. demonstrated with poly(Me methacrylate) (PMMA) samples. Nano-FTIR can thus make use of std. IR databases of mol. vibrations to identify org. materials in ultrasmall quantities and at ultrahigh spatial resoln. As an application example we demonstrate the identification of a nanoscale PDMS contamination on a PMMA sample.
    20. 20
      Hillenbrand, R.; Knoll, B.; Keilmann, F. Pure optical contrast in scattering-type scanning near-field microscopy. J. Microsc. 2001, 202 (1), 77– 83,  DOI: 10.1046/j.1365-2818.2001.00794.x
      20
      Pure optical contrast in scattering-type scanning near-field microscopy
      Hillenbrand, R.; Knoll, B.; Keilmann, F.
      Journal of Microscopy (Oxford, United Kingdom) (2001), 202 (1), 77-83CODEN: JMICAR; ISSN:0022-2720. (Blackwell Science Ltd.)
      The authors have enhanced the aperture-less scattering-type scanning near-field optical microscope by 2 improvements which together achieve a recording of the true near field without any height-induced artifact. These are the use of interferometric detection of the scattered light on 1 hand, and the use of higher-harmonic dither demodulation of the scattered signal on the other. Here the authors present the basic rationale for these techniques, and give examples measured with 2 different expts., one in the IR (10 μm wavelength), the other in the visible (633 nm). The latter operates in a fully heterodyne mode and displays simultaneous images of optical near-field phase and amplitude, at <10 nm resoln.
    21. 21
      Huth, F.; Schnell, M.; Wittborn, J.; Ocelic, N.; Hillenbrand, R. Infrared-spectroscopic nanoimaging with a thermal source. Nat. Mater. 2011, 10 (5), 352– 356,  DOI: 10.1038/nmat3006
      21
      Infrared-spectroscopic nanoimaging with a thermal source
      Huth, F.; Schnell, M.; Wittborn, J.; Ocelic, N.; Hillenbrand, R.
      Nature Materials (2011), 10 (5), 352-356CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      Fourier-transform IR (FTIR) spectroscopy is a widely used anal. tool for chem. identification of inorg., org. and biomedical materials, as well as for exploring conduction phenomena. Because of the diffraction limit, however, conventional FTIR cannot be applied for nanoscale imaging. Here the authors demonstrate a novel FTIR system that allows for IR-spectroscopic nanoimaging of dielec. properties (nano-FTIR). Based on superfocusing of thermal radiation with an IR antenna, detection of the scattered light, and strong signal enhancement employing an asym. FTIR spectrometer, the authors improve the spatial resoln. of conventional IR spectroscopy by more than two orders of magnitude. By mapping a semiconductor device, the authors demonstrate spectroscopic identification of silicon oxides and quantification of the free-carrier concn. in doped regions with a spatial resoln. better than 100 nm. The authors envisage nano-FTIR becoming a powerful tool for chem. identification of nanomaterials, as well as for quant. and contact-free measurement of the local free-carrier concn. and mobility in doped nanostructures.
    22. 22
      Knoll, B.; Keilmann, F. Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy. Opt. Commun. 2000, 182 (4–6), 321– 328,  DOI: 10.1016/S0030-4018(00)00826-9
      22
      Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy
      Knoll, B.; Keilmann, F.
      Optics Communications (2000), 182 (4,5,6), 321-328CODEN: OPCOB8; ISSN:0030-4018. (Elsevier Science B.V.)
      'Apertureless' probe tips have a much higher resoln. potential compared to the traditional aperture tips of scanning near-field optical microscopes (SNOM), yet when illuminated by a laser focus a large amt. of unwanted background scattering occurs both at the probe shaft and at the sample. Here we study in detail how this background can be suppressed by dithering the probe-sample distance, and thereby demonstrate how to enhance the optical near-field contrasts. We find from theory that the coupling of probe dipole and its image in the sample causes a steep increase of scattering cross-sections at small probe-sample distances. This strongly non-linear behavior produces higher harmonics when modulating the distance. Demodulation at higher harmonics, therefore, enables an effective probe tip 'sharpening' and improves both resoln. and image contrast. This effect is exptl. confirmed by imaging purely dielec. contrast of a topog. flat pn+-nanostructured semiconductor, realizing λ/100 resoln. at 10 μm IR wavelength.
    23. 23
      Cvitkovic, A.; Ocelic, N.; Hillenbrand, R. Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy. Opt. Express 2007, 15 (14), 8550– 8565,  DOI: 10.1364/OE.15.008550
      23
      Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy
      Cvitkovic, A.; Ocelic, N.; Hillenbrand, R.
      Optics Express (2007), 15 (14), 8550-8565CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
      Nanometer-scale mapping of complex optical consts. by scattering-type near-field microscopy has been suffering from quant. discrepancies between the theory and expts. To resolve this problem, a novel anal. model is presented here. The comparison with exptl. data demonstrates that the model quant. reproduces approach curves on a Au surface and yields an unprecedented agreement with amplitude and phase spectra recorded on a phonon-polariton resonant SiC sample. The simple closed-form soln. derived here should enable the detn. of the local complex dielec. function on an unknown sample, thereby identifying its nanoscale chem. compn., crystal structure and cond.
    24. 24
      Chandler-Horowitz, D.; Amirtharaj, P. M. High-accuracy, midinfrared (450 cm–1⩽ ω⩽ 4000 cm–1) refractive index values of silicon. J. Appl. Phys. 2005, 97 (12), 123526,  DOI: 10.1063/1.1923612
      There is no corresponding record for this reference.
    25. 25
      Eisele, M. Ultrafast Multi-Terahertz Nano-Spectroscopy with Sub-cycle Temporal Resolution, Doctoral Dissertation, University of Regensburg, 2015. .
      There is no corresponding record for this reference.
    26. 26
      Lundstrom, M. Fundamentals of Carrier Transport; Cambridge University Press: Cambridge, 2000.
      There is no corresponding record for this reference.
    27. 27
      Nag, B. R. Electron Transport in Compound Semiconductors; Springer-Verlag: Berlin, 1980.
      There is no corresponding record for this reference.
    28. 28
      Regensburger, S.; Winnerl, S.; Klopf, J. M.; Lu, H.; Gossard, A. C.; Preu, S. Picosecond-scale terahertz pulse characterization with field-effect transistors. IEEE Trans. Terahertz Sci. Technol. 2019, 9 (3), 262– 271,  DOI: 10.1109/TTHZ.2019.2903630
      There is no corresponding record for this reference.
    29. 29
      Nishida, J.; Johnson, S. C.; Chang, P. T. S.; Wharton, D. M.; Dönges, S. A.; Khatib, O.; Raschke, M. B. Ultrafast infrared nano-imaging of far-from-equilibrium carrier and vibrational dynamics. Nat. Commun. 2022, 13 (1), 1083,  DOI: 10.1038/s41467-022-28224-9
      29
      Ultrafast infrared nano-imaging of far-from-equilibrium carrier and vibrational dynamics
      Nishida, Jun; Johnson, Samuel C.; Chang, Peter T. S.; Wharton, Dylan M.; Donges, Sven A.; Khatib, Omar; Raschke, Markus B.
      Nature Communications (2022), 13 (1), 1083CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
      Ultrafast IR nano-imaging has demonstrated access to ultrafast carrier dynamics on the nanoscale in semiconductor, correlated-electron, or polaritonic materials. However, mostly limited to short-lived transient states, the contrast obtained has remained insufficient to probe important long-lived excitations, which arise from many-body interactions induced by strong perturbation among carriers, lattice phonons, or mol. vibrations. Here, we demonstrate ultrafast IR nano-imaging based on excitation modulation and sideband detection to characterize electron and vibration dynamics with nano- to micro-second lifetimes. As an exemplary application to quantum materials, in phase-resolved ultrafast nano-imaging of the photoinduced insulator-to-metal transition in vanadium dioxide, a distinct transient nano-domain behavior is quantified. In another application to lead halide perovskites, transient vibrational nano-FTIR spatially resolves the excited-state polaron-cation coupling underlying the photovoltaic response. These examples show how heterodyne pump-probe nano-spectroscopy with low-repetition excitation extends ultrafast IR nano-imaging to probe elementary processes in quantum and mol. materials in space and time.
    30. 30
      Shkerdin, G.; Stiens, J.; Vounckx, R. Comparative study of the intra- and intervalley contributions to the free-carrier induced optical nonlinearity in n-GaAs. J. Appl. Phys. 1999, 85 (7), 3807– 3818,  DOI: 10.1063/1.369751
      There is no corresponding record for this reference.
    31. 31
      Shkerdin, G.; Stiens, J.; Vounckx, R. A multi-valley model for hot free-electron nonlinearities at 10.6 μm in highly doped n-GaAs. Eur. Phys. J. Appl. Phys. 2000, 12 (3), 169– 180,  DOI: 10.1051/epjap:2000185
      There is no corresponding record for this reference.
    32. 32
      Kash, K.; Wolff, P. A.; Bonner, W. A. Nonlinear optical studies of picosecond relaxation times of electrons in n-GaAs and n-GaSb. Appl. Phys. Lett. 1983, 42 (2), 173– 175,  DOI: 10.1063/1.93864
      There is no corresponding record for this reference.
    33. 33
      Auyang, S. Y.; Wolff, P. A. Free-carrier-induced third-order optical nonlinearities in semiconductors. JOSA B 1989, 6 (4), 595– 605,  DOI: 10.1364/JOSAB.6.000595
      There is no corresponding record for this reference.
    34. 34
      Vurgaftman, I.; Meyer, J. R.; Ram-Mohan, L. R. Band parameters for III--V compound semiconductors and their alloys. J. Appl. Phys. 2001, 89 (11), 5815– 5875,  DOI: 10.1063/1.1368156
      34
      Band parameters for III-V compound semiconductors and their alloys
      Vurgaftman, I.; Meyer, J. R.; Ram-Mohan, L. R.
      Journal of Applied Physics (2001), 89 (11, Pt. 1), 5815-5875CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
      A review with 1001 refs. We present a comprehensive, up-to-date compilation of band parameters for the technol. important III-V zinc blende and wurtzite compd. semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calcns., we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temp. and alloy-compn. dependences where available. Heterostructure band offsets are also given, on an abs. scale that allows any material to be aligned relative to any other.
    35. 35
      Anisimov, S. I.; Kapeliovich, B. L.; Perelman, T. L. Electron emission from metal surfaces exposed to ultrashort laser pulses. Zh. Eksp. Teor. Fiz. 1974, 66 (2), 375– 377
      There is no corresponding record for this reference.
    36. 36
      Lee, S.-C.; Galbraith, I.; Pidgeon, C. R. Influence of electron temperature and carrier concentration on electron-LO-phonon intersubband scattering in wide GaAs/AlxGa1-xAs quantum wells. Phys. Rev. B 1995, 52 (3), 1874– 1881,  DOI: 10.1103/PhysRevB.52.1874
      There is no corresponding record for this reference.
    37. 37
      Zhou, J.-J.; Bernardi, M. Ab initio electron mobility and polar phonon scattering in GaAs. Phys. Rev. B 2016, 94, 201201,  DOI: 10.1103/PhysRevB.94.201201
      37
      Ab initio electron mobility and polar phonon scattering in GaAs
      Zhou, Jin-Dian; Bernardi, Marco
      Physical Review B (2016), 94 (20), 201201/1-201201/6CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)
      In polar semiconductors and oxides, the long-range nature of the electron-phonon (e-ph) interaction is a bottleneck to compute charge transport from first principles. Here, we develop an efficient ab initio scheme to compute and converge the e -ph relaxation times (RTs) and electron mobility in polar materials. We apply our approach to GaAs, where by using the Boltzmann equation with state-dependent RTs, we compute mobilities in excellent agreement with expt. at 250-500 K. The e-ph RTs and the phonon contributions to intravalley and intervalley e-ph scattering are also analyzed. Our work enables efficient ab initio computations of transport and carrier dynamics in polar materials.
    38. 38
      Mooshammer, F.; Huber, M. A.; Sandner, F.; Plankl, M.; Zizlsperger, M.; Huber, R. Quantifying nanoscale electromagnetic fields in near-field microscopy by Fourier demodulation analysis. ACS Photonics 2020, 7 (2), 344– 351,  DOI: 10.1021/acsphotonics.9b01533
      38
      Quantifying Nanoscale Electromagnetic Fields in Near-Field Microscopy by Fourier Demodulation Analysis
      Mooshammer, Fabian; Huber, Markus A.; Sandner, Fabian; Plankl, Markus; Zizlsperger, Martin; Huber, Rupert
      ACS Photonics (2020), 7 (2), 344-351CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Confining light to sharp metal tips has become a versatile technique to study optical and electronic properties far below the diffraction limit. Particularly near-field microscopy in the mid-IR spectral range has found a variety of applications in probing nanostructures and their dynamics. Yet, the ongoing quest for ultimately high spatial resoln. down to the single-nanometer regime and quant. three-dimensional nano-tomog. depends vitally on a precise knowledge of the spatial distribution of the near fields emerging from the probe. Here, we perform finite element simulations of a tip with realistic geometry oscillating above a dielec. sample. By introducing a novel Fourier demodulation anal. of the elec. field at each point in space, we reliably quantify the distribution of the near fields above and within the sample. Besides inferring the lateral field extension, which can be smaller than the tip radius of curvature, we also quantify the probing vol. within the sample. Finally, we visualize the scattering process into the far field at a given demodulation order, for the first time, and shed light onto the nanoscale distribution of the near fields, and its evolution as the tip-sample distance is varied. Our work represents a crucial step in understanding and tailoring the spatial distribution of evanescent fields in optical nanoscopy.
    39. 39
      Huth, F.; Chuvilin, A.; Schnell, M.; Amenabar, I.; Krutokhvostov, R.; Lopatin, S.; Hillenbrand, R. Resonant antenna probes for tip-enhanced infrared near-field microscopy. Nano Lett. 2013, 13 (3), 1065– 1072,  DOI: 10.1021/nl304289g
      39
      Resonant Antenna Probes for Tip-Enhanced Infrared Near-Field Microscopy
      Huth, Florian; Chuvilin, Andrey; Schnell, Martin; Amenabar, Iban; Krutokhvostov, Roman; Lopatin, Sergei; Hillenbrand, Rainer
      Nano Letters (2013), 13 (3), 1065-1072CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      The authors report the development of IR-resonant antenna probes for tip-enhanced optical microscopy. Focused-ion-beam machining was used to fabricate high-aspect ratio Au cones, which replace the std. tip of a com. Si-based at. force microscopy cantilever. Calcns. show large field enhancements at the tip apex due to geometrical antenna resonances in the cones, which can be precisely tuned throughout a broad spectral range from visible to terahertz frequencies by adjusting the cone length. Spectroscopic anal. of these probes by EELS, FTIR spectroscopy, and FTIR near-field spectroscopy corroborates their functionality as resonant antennas and verifies the broad tunability. By using the novel probes in a scattering-type near-field microscope and imaging a single tobacco mosaic virus (TMV), high-performance mid-IR nanoimaging of mol. absorption was exptl. demonstrated. The probes offer excellent perspectives for optical nanoimaging and nanospectroscopy, pushing the detection and resoln. limits in many applications, including nanoscale IR mapping of org., mol., and biol. materials, nanocomposites, or nanodevices.

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    • Results of the sideband modulation technique along with the point–dipole model-based simulations, extended power-dependent results, and calculation of the specific heat of the electron gas (PDF)


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