Abstract

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 (1015Hz) frequencies [Nature 493, 70 (2013)]. So far, this approach has been limited to insulators, requiring extreme peak electric fields (>1V/Å) and intensities (>1013W/cm2). 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 [1]. The faster currents can be switched on and off in a device, the higher its performance. High electron mobility transistors [2] operate at 1THz switching rates. Rates of 100THz can be attained in semiconductors exposed to ultrashort laser pulses via photoconductive switching [3] and ω2ω coherent control [49]. Recent experiments showed that currents can be generated and controlled in dielectrics at near-PHz frequencies via interactions with intense few-cycle optical fields [1012]. This effect—a result of highly nonlinear phenomena within the limit of interband tunneling [13,14]—requires very high fields (>1V/Å), 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 (Eg3.4eV), relevant for high-frequency and high-power (opto)electronics due to its electron mobility, mechanical stability, and heat capacity [15]. We show that charge displacement results from interference of multiphoton transitions [16] 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 [10] (see Supplement 1, Section 1). The instantaneous optical electric field, FL(t), was measured by attosecond streaking [17] 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 c-axis [18]. The stabilized carrier-envelope phase (CEP), ϕCE, was adjusted by varying the propagation length Δl inside a pair of fused silica wedges. We considered applied electric field peak amplitudes, F0, up to 0.9 V/Å (cycle-averaged peak intensity, I01013W/cm2). 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: Fig. 1.

Fig. 1. (a) GaN surface patterned with gold electrodes (inset: SEM image) exposed to a CEP-controlled few-cycle VIS/NIR pulse with an instantaneous electric field, FL(t). Electrodes are unbiased. (b) CEP-dependent component QP of the collected charge per pulse as a function of propagation length Δl in the fused silica wedges and of the CEP change, ΔϕCE. Applied peak field amplitude, F0=0.4V/Å. Inter-electrode spacing: 5 μm. (c) Maximum QP (amplitude of sine fit of QP(ΔϕCE)) as a function of F0 and I0 for 100 nm and 10 μm junctions. Data normalized with respect to values for maximum F0. Data for SiO2 [10] are shown for comparison. Arrows indicate breaking of the scaling power law. Solid curves: quantum-mechanical simulation.

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Figure 1(b) shows the CEP-dependent fraction QP of the charge per pulse collected by the unbiased Au electrodes as a function of Δl and ΔϕCE. Here, FL(t) was perpendicular to the electrodes along the x-axis [Fig. 1(a)]. The signal QP reverses its sign periodically with CEP. Inverting the optical field (ΔϕCE=π) reverses the direction of the charge displacement: the instantaneous electric field of the laser pulse is generated and controls QP, similar to the case of an insulator [10].

We measured QP(Δl) 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 QP was given for 5 μm [4±0.1A fs=(4±0.1)×1015 Coulomb at F00.4V/Å; Fig. 1(b)]; for 100 nm and 10 μm, it was 1±0.1 and 2.8±0.1Afs, respectively (both at F00.8V/Å). This hints at an optimal inter-electrode distance. A quantitative analysis of the maximum QP as a function of the junction size is beyond the scope of this study.

Figure 1(c) shows the CEP-optimized transferred charge, QP(max), as a function of F0 and I0, for junctions with 100 nm and 10 μm inter-electrode spacing. For F00.45V/Å, the experimental data follow QP(max)F05, independently of the junction size; this scaling law breaks down in larger fields. In comparison, data for SiO2 from Ref. [10] shows a significantly higher order of nonlinearity and a breakdown of the power law scaling at a much stronger field (F01.7V/Å). Notably, for the same F0 (e.g., 0.9V/Å), signals for GaN are at least two orders of magnitude larger than those for SiO2.

When F0 is varied, the transferred charge shifts with respect to ΔϕCE [Figs. 2(b) and 2(c)], i.e., the charge-balancing CEP, ϕCE(+0), for which QP(ϕCE(+0))=0, increases monotonically [Fig. 2(a)]. Here, we focus (arbitrarily) on the charge-balancing CEP related to the rising edge of QP(ΔϕCE), i.e., QP(ϕCE(+0))/ϕCE>0. The dependence of ϕCE(+0) on F0 is not affected by the inter-electrode separation; it is an intrinsic characteristic of the material, as evidenced by the comparison with the SiO2 case [12]; Fig. 2(a). The dependence ϕCE(+0)(F0) allows for testing our theoretical model and aids the physical interpretation of our experiment.

 figure: Fig. 2.

Fig. 2. (a) Charge-balancing CEP, ϕCE(+0), as a function of F0 and I0. Zero reference for ϕCE(+0) is set at F0=0.8V/Å. Data for SiO2 are shown for comparison [12]. Solid curves: quantum mechanical simulation. (b), (c) QP(ΔϕCE) for F0=0.79 [B in (a)] and 0.47 V/Å (C). Vertical dashed lines indicate the shift of ϕCE(+0) with F0. Solid curves: smoothed experimental data.

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Following the approach previously developed for SiO2 [10], we decoupled injection (i) and driving (d) by exposing the junction to two synchronized, collinear VIS/NIR laser pulses with orthogonal electric fields FL(i)(t) (parallel to electrodes, along y-axis; F0(i)0.4V/Å) and FL(d)(t) (perpendicular, along the x-axis, F0(d)0.06V/Å); Fig. 3(a). The CEPs ϕCE(i) and ϕCE(d) of the respective fields were set according to the inset in Fig. 3(b), such that QP(ΔϕCE)=0 in single-pulse experiments (as in Figs. 1 and 2). Figure 4(b) shows QP as a function of the delay Δt between the two pulses. For Δt0fs, QP(Δt) oscillates with a period of 2.5fs, i.e., the period of the optical field [Fig. 1(a)]. In Fig. 3(c), ϕCE(d) was changed by π; FL(d) was reversed. Here, QP(Δt) oscillates with the same period but is reversed in comparison to Fig. 3(b).

 figure: Fig. 3.

Fig. 3. (a) Injection-drive experiment. Two orthogonally polarized VIS/NIR laser pulses, delayed by Δt, irradiate a 5 μm Au-GaN-Au junction (F0(i)0.4V/Å;F0(d)0.06V/Å). ϕCE(i) and ϕCE(d) are set such that QP(ΔϕCE)=0 when FL(i)(t) and FL(d)(t) are applied independently. (b) CEP-dependent component QP as a function of Δt. (c) Same as (b), with ΔϕCE(d)=π. (d) Normalized modulus squared (solid) and phase (dashed) of the Fourier transform of QP(Δt), Q˜P=F[QP(Δt)], in (b) (blue) and (c) (cyan). Red: VIS/NIR pulse spectrum.

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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 [19] (Supplement 1, Sections 3–5). We considered optical transitions between three valence (VB) and two conduction bands (CB) for crystal momenta kx along the ΓM 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 Γ-point [20] and our field amplitudes are too low for most charge carriers to reach the BZ boundaries.

The theoretical curves (Figs. 13) 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 kx and destructive for kx, 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 Ei(k) and Ef(k) is determined by the accumulation of dynamic phase [22]

Δφfi(kx,t1,t2)=1t1t2ΔEfi[Kx(t)]dt,
due to the intraband motion of electron-hole pairs between times t1 and t2 during exposure to the optical field. Here, ΔEfi(k)=Ef(k)Ei(k), Kx(t)=kx+eA(t)/ is the semiclassical equation of intraband motion, e>0 is the electron charge, and A(t)=tF(t)dt is the vector potential of the total electric field F(t) in the Au-GaN-Au junction. For example, if, over an optical cycle, Δφfi(kx,t1,t1+2π/ωL)=2πN (N=1,2,), then contributions from different cycles interfere constructively and electron–hole pairs are efficiently excited. In the weak field limit, intraband motion can be neglected, Kx(t)kx, and Δφfi=2πN yields the condition for absorbing N photons: ΔEfi(kx)=NωL. Resonances of different orders N can exist within an intense broadband pulse; their interference determines the asymmetry of k-space population distributions.

 figure: Fig. 4.

Fig. 4. (a) Current injection mechanism in GaN. Charge carriers are created via interfering two- and three-photon transitions between valence (VB) and conduction (CB) bands (blue circles: occupied states; white: unoccupied). Heavy hole, light hole, and crystal-field split-off VBs are shown. Background: laser pulse spectrum. Dynamic phase shifts (dashed black arrows) Δφfi(±)Δφfi(±kx,t1,t2) resulting from field-induced intraband carrier motion (solid black arrows) determine whether interferences are constructive or destructive. (b) Applied optical electric field FL(t), induced polarization field FP(t) calculated with quantum mechanical dynamic screening model and total field F(t)=FL(t)+FP(t). (c), Time-dependent current density J(t) and electron population in the two lowest CBs calculated with quantum mechanical dynamic screening model.

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In the multiphoton regime, this quantum interference scenario yields a power-law scaling of the transferred charge QP(max)F02N+1, where N=E˜g/ωL is the order of multiphoton interband transition and E˜g is the bandgap at a k-point where the corresponding transition is allowed [16] (Supplement 1, Section 6). The scaling power law QP(max)F05 (N=2) observed in the experiment and in the QM model for F00.45V/Å [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 [14] parameter γK2 (Supplement 1, Section 6).

For stronger fields, the slope of QP(max)(F0) decreases and diverges from the F02N+1 scaling law. This is due to a combination of: (i) screening of the external field by the field-driven excited carrier displacement [23], and (ii) closing of the two-photon excitation channel [24] (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, ϕCE(+0) (Fig. 2), allows us to further test our QM model. The severe field-dependent shift of ϕCE(+0) 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 QP(Δt) (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 QP(Δt) extends to a maximal frequency fmax0.5PHz, 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 1/(2fmax)1fs, 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.

Funding

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).

Acknowledgment

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.

REFERENCES

1. Y. Taur and T. H. Ning, Fundamentals of Modern VLSI Devices (Cambridge University, 1998).

2. R. Lai, X. B. Mei, W. R. Deal, W. Yoshida, Y. M. Kim, P. H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska, and A. Fung, “Sub 50 nm InP HEMT device with Fmax greater than 1 THz,” in IEEE International Electron Devices Meeting (IEDM 2007) (IEEE, 2007), pp. 609–611.

3. H. Shimosato, M. Ashida, T. Itoh, S. Saito, and K. Sakai, “Ultrabroadband detection of terahertz radiation from 0.1 to 100 THz with photoconductive antenna,” in Ultrafast Optics V (Springer, 2007), pp. 317–323.

4. G. Kurizki, M. Shapiro, and P. Brumer, Phys. Rev. B 39, 3435 (1989). [CrossRef]  

5. A. Hache, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. Van Driel, Phys. Rev. Lett. 78, 306 (1997). [CrossRef]  

6. L. Costa, M. Betz, M. Spasenovic, A. D. Bristow, and H. M. Van Driel, Nat. Phys. 3, 632 (2007). [CrossRef]  

7. I. Franco, M. Shapiro, and P. Brumer, Phys. Rev. Lett. 99, 126802 (2007). [CrossRef]  

8. I. Franco and P. Brumer, J. Phys. B 41, 074003 (2008). [CrossRef]  

9. C. Ruppert, S. Thunich, G. Abstreiter, A. F. I. Morral, A. W. Holleitner, and M. Betz, Nano Lett. 10, 1799 (2010). [CrossRef]  

10. A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013). [CrossRef]  

11. O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016). [CrossRef]  

12. T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014). [CrossRef]  

13. C. Zener, Proc. R. Soc. London Ser. A 145, 523 (1936). [CrossRef]  

14. L. V. Keldysh, Sov. Phys. J. Exp. Theor. Phys. 20, 1307 (1965).

15. S. Nakamura, S. Pearton, and G. Fasol, The Blue Laser Diode: The Complete Story (Springer, 2000).

16. S. Y. Kruchinin, M. Korbman, and V. S. Yakovlev, Phys. Rev. B 87, 115201 (2013). [CrossRef]  

17. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004). [CrossRef]  

18. H. Morkoc, R. Cingolani, and B. Gil, Solid State Electron. 43, 1909 (1999). [CrossRef]  

19. J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986). [CrossRef]  

20. M. Suzuki, T. Uenoyama, and A. Yanase, Phys. Rev. B 52, 8132 (1995). [CrossRef]  

21. T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004). [CrossRef]  

22. M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, Phys. Rev. Lett. 116, 197401 (2016). [CrossRef]  

23. F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J.-M. Jancu, Appl. Phys. Lett. 74, 2002 (1999). [CrossRef]  

24. J. G. Story, D. I. Duncan, and T. F. Gallagher, Phys. Rev. A 49, 3875 (1994). [CrossRef]  

25. H. Mashiko, K. Oguri, T. Yamaguchi, A. Suda, and H. Gotoh, Nat. Phys. 12, 741 (2016). [CrossRef]  

26. M. Schultze, K. Ramasesha, C. D. Pemmaraju, S. A. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, Science 346, 1348 (2014). [CrossRef]  

References

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  1. Y. Taur and T. H. Ning, Fundamentals of Modern VLSI Devices (Cambridge University, 1998).
  2. R. Lai, X. B. Mei, W. R. Deal, W. Yoshida, Y. M. Kim, P. H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska, and A. Fung, “Sub 50  nm InP HEMT device with Fmax greater than 1  THz,” in IEEE International Electron Devices Meeting (IEDM 2007) (IEEE, 2007), pp. 609–611.
  3. H. Shimosato, M. Ashida, T. Itoh, S. Saito, and K. Sakai, “Ultrabroadband detection of terahertz radiation from 0.1 to 100  THz with photoconductive antenna,” in Ultrafast Optics V (Springer, 2007), pp. 317–323.
  4. G. Kurizki, M. Shapiro, and P. Brumer, Phys. Rev. B 39, 3435 (1989).
    [Crossref]
  5. A. Hache, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. Van Driel, Phys. Rev. Lett. 78, 306 (1997).
    [Crossref]
  6. L. Costa, M. Betz, M. Spasenovic, A. D. Bristow, and H. M. Van Driel, Nat. Phys. 3, 632 (2007).
    [Crossref]
  7. I. Franco, M. Shapiro, and P. Brumer, Phys. Rev. Lett. 99, 126802 (2007).
    [Crossref]
  8. I. Franco and P. Brumer, J. Phys. B 41, 074003 (2008).
    [Crossref]
  9. C. Ruppert, S. Thunich, G. Abstreiter, A. F. I. Morral, A. W. Holleitner, and M. Betz, Nano Lett. 10, 1799 (2010).
    [Crossref]
  10. A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
    [Crossref]
  11. O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016).
    [Crossref]
  12. T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
    [Crossref]
  13. C. Zener, Proc. R. Soc. London Ser. A 145, 523 (1936).
    [Crossref]
  14. L. V. Keldysh, Sov. Phys. J. Exp. Theor. Phys. 20, 1307 (1965).
  15. S. Nakamura, S. Pearton, and G. Fasol, The Blue Laser Diode: The Complete Story (Springer, 2000).
  16. S. Y. Kruchinin, M. Korbman, and V. S. Yakovlev, Phys. Rev. B 87, 115201 (2013).
    [Crossref]
  17. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
    [Crossref]
  18. H. Morkoc, R. Cingolani, and B. Gil, Solid State Electron. 43, 1909 (1999).
    [Crossref]
  19. J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986).
    [Crossref]
  20. M. Suzuki, T. Uenoyama, and A. Yanase, Phys. Rev. B 52, 8132 (1995).
    [Crossref]
  21. T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
    [Crossref]
  22. M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, Phys. Rev. Lett. 116, 197401 (2016).
    [Crossref]
  23. F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J.-M. Jancu, Appl. Phys. Lett. 74, 2002 (1999).
    [Crossref]
  24. J. G. Story, D. I. Duncan, and T. F. Gallagher, Phys. Rev. A 49, 3875 (1994).
    [Crossref]
  25. H. Mashiko, K. Oguri, T. Yamaguchi, A. Suda, and H. Gotoh, Nat. Phys. 12, 741 (2016).
    [Crossref]
  26. M. Schultze, K. Ramasesha, C. D. Pemmaraju, S. A. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, Science 346, 1348 (2014).
    [Crossref]

2016 (3)

O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016).
[Crossref]

M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, Phys. Rev. Lett. 116, 197401 (2016).
[Crossref]

H. Mashiko, K. Oguri, T. Yamaguchi, A. Suda, and H. Gotoh, Nat. Phys. 12, 741 (2016).
[Crossref]

2014 (2)

M. Schultze, K. Ramasesha, C. D. Pemmaraju, S. A. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, Science 346, 1348 (2014).
[Crossref]

T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
[Crossref]

2013 (2)

S. Y. Kruchinin, M. Korbman, and V. S. Yakovlev, Phys. Rev. B 87, 115201 (2013).
[Crossref]

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
[Crossref]

2010 (1)

C. Ruppert, S. Thunich, G. Abstreiter, A. F. I. Morral, A. W. Holleitner, and M. Betz, Nano Lett. 10, 1799 (2010).
[Crossref]

2008 (1)

I. Franco and P. Brumer, J. Phys. B 41, 074003 (2008).
[Crossref]

2007 (2)

L. Costa, M. Betz, M. Spasenovic, A. D. Bristow, and H. M. Van Driel, Nat. Phys. 3, 632 (2007).
[Crossref]

I. Franco, M. Shapiro, and P. Brumer, Phys. Rev. Lett. 99, 126802 (2007).
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2004 (2)

T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
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O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016).
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T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
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L. Costa, M. Betz, M. Spasenovic, A. D. Bristow, and H. M. Van Driel, Nat. Phys. 3, 632 (2007).
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L. Costa, M. Betz, M. Spasenovic, A. D. Bristow, and H. M. Van Driel, Nat. Phys. 3, 632 (2007).
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T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
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J. G. Story, D. I. Duncan, and T. F. Gallagher, Phys. Rev. A 49, 3875 (1994).
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T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
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T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
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I. Franco and P. Brumer, J. Phys. B 41, 074003 (2008).
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I. Franco, M. Shapiro, and P. Brumer, Phys. Rev. Lett. 99, 126802 (2007).
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R. Lai, X. B. Mei, W. R. Deal, W. Yoshida, Y. M. Kim, P. H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska, and A. Fung, “Sub 50  nm InP HEMT device with Fmax greater than 1  THz,” in IEEE International Electron Devices Meeting (IEDM 2007) (IEEE, 2007), pp. 609–611.

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R. Lai, X. B. Mei, W. R. Deal, W. Yoshida, Y. M. Kim, P. H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska, and A. Fung, “Sub 50  nm InP HEMT device with Fmax greater than 1  THz,” in IEEE International Electron Devices Meeting (IEDM 2007) (IEEE, 2007), pp. 609–611.

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J. G. Story, D. I. Duncan, and T. F. Gallagher, Phys. Rev. A 49, 3875 (1994).
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M. Schultze, K. Ramasesha, C. D. Pemmaraju, S. A. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, Science 346, 1348 (2014).
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T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
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H. Morkoc, R. Cingolani, and B. Gil, Solid State Electron. 43, 1909 (1999).
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A. Hache, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. Van Driel, Phys. Rev. Lett. 78, 306 (1997).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
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C. Ruppert, S. Thunich, G. Abstreiter, A. F. I. Morral, A. W. Holleitner, and M. Betz, Nano Lett. 10, 1799 (2010).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
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A. Hache, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. Van Driel, Phys. Rev. Lett. 78, 306 (1997).
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J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986).
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H. Shimosato, M. Ashida, T. Itoh, S. Saito, and K. Sakai, “Ultrabroadband detection of terahertz radiation from 0.1 to 100  THz with photoconductive antenna,” in Ultrafast Optics V (Springer, 2007), pp. 317–323.

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T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, Phys. Rev. Lett. 92, 147403 (2004).
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T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
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T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
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O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016).
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O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016).
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Kim, J. J.

O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016).
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R. Lai, X. B. Mei, W. R. Deal, W. Yoshida, Y. M. Kim, P. H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska, and A. Fung, “Sub 50  nm InP HEMT device with Fmax greater than 1  THz,” in IEEE International Electron Devices Meeting (IEDM 2007) (IEEE, 2007), pp. 609–611.

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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
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S. Y. Kruchinin, M. Korbman, and V. S. Yakovlev, Phys. Rev. B 87, 115201 (2013).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
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A. Hache, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. Van Driel, Phys. Rev. Lett. 78, 306 (1997).
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Krausz, F.

T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, Nature 493, 70 (2013).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
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J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986).
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T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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M. S. Wismer, S. Y. Kruchinin, M. Ciappina, M. I. Stockman, and V. S. Yakovlev, Phys. Rev. Lett. 116, 197401 (2016).
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S. Y. Kruchinin, M. Korbman, and V. S. Yakovlev, Phys. Rev. B 87, 115201 (2013).
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T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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G. Kurizki, M. Shapiro, and P. Brumer, Phys. Rev. B 39, 3435 (1989).
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O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016).
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R. Lai, X. B. Mei, W. R. Deal, W. Yoshida, Y. M. Kim, P. H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska, and A. Fung, “Sub 50  nm InP HEMT device with Fmax greater than 1  THz,” in IEEE International Electron Devices Meeting (IEDM 2007) (IEEE, 2007), pp. 609–611.

Lange, M.

R. Lai, X. B. Mei, W. R. Deal, W. Yoshida, Y. M. Kim, P. H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska, and A. Fung, “Sub 50  nm InP HEMT device with Fmax greater than 1  THz,” in IEEE International Electron Devices Meeting (IEDM 2007) (IEEE, 2007), pp. 609–611.

Lee, J.

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M. Schultze, K. Ramasesha, C. D. Pemmaraju, S. A. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, Science 346, 1348 (2014).
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O. Kwon, T. Paasch-Colberg, V. Apalkov, B. K. Kim, J. J. Kim, M. I. Stockman, and D. Kim, Sci. Rep. 6, 21272 (2016).
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T. Paasch-Colberg, A. Schiffrin, N. Karpowicz, S. Kruchinin, O. Saglam, S. Keiber, O. Razskazovskaya, S. Muhlbrandt, A. Alnaser, M. Kubel, V. Apalkov, D. Gerster, J. Reichert, T. Wittmann, J. V. Barth, M. I. Stockman, R. Ernstorfer, V. S. Yakovlev, R. Kienberger, and F. Krausz, Nat. Photonics 8, 214 (2014).
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M. Schultze, K. Ramasesha, C. D. Pemmaraju, S. A. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, Science 346, 1348 (2014).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
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Supplementary Material (1)

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» Supplement 1: PDF (1832 KB)      This document provides supplementary information on our experimental methods and theoretical formalism.

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Figures (4)

Fig. 1.
Fig. 1. (a) GaN surface patterned with gold electrodes (inset: SEM image) exposed to a CEP-controlled few-cycle VIS/NIR pulse with an instantaneous electric field, F L ( t ) . Electrodes are unbiased. (b) CEP-dependent component Q P of the collected charge per pulse as a function of propagation length Δ l in the fused silica wedges and of the CEP change, Δ ϕ CE . Applied peak field amplitude, F 0 = 0.4 V / Å . Inter-electrode spacing: 5 μm. (c) Maximum Q P (amplitude of sine fit of Q P ( Δ ϕ CE ) ) as a function of F 0 and I 0 for 100 nm and 10 μm junctions. Data normalized with respect to values for maximum F 0 . Data for SiO 2 [10] are shown for comparison. Arrows indicate breaking of the scaling power law. Solid curves: quantum-mechanical simulation.
Fig. 2.
Fig. 2. (a) Charge-balancing CEP, ϕ CE ( + 0 ) , as a function of F 0 and I 0 . Zero reference for ϕ CE ( + 0 ) is set at F 0 = 0.8 V / Å . Data for SiO 2 are shown for comparison [12]. Solid curves: quantum mechanical simulation. (b), (c)  Q P ( Δ ϕ CE ) for F 0 = 0.79 [B in (a)] and 0.47 V/Å (C). Vertical dashed lines indicate the shift of ϕ CE ( + 0 ) with F 0 . Solid curves: smoothed experimental data.
Fig. 3.
Fig. 3. (a) Injection-drive experiment. Two orthogonally polarized VIS/NIR laser pulses, delayed by Δ t , irradiate a 5 μm Au-GaN-Au junction ( F 0 ( i ) 0.4 V / Å ; F 0 ( d ) 0.06 V / Å ). ϕ CE ( i ) and ϕ CE ( d ) are set such that Q P ( Δ ϕ CE ) = 0 when F L ( i ) ( t ) and F L ( d ) ( t ) are applied independently. (b) CEP-dependent component Q P as a function of Δ t . (c) Same as (b), with Δ ϕ CE ( d ) = π . (d) Normalized modulus squared (solid) and phase (dashed) of the Fourier transform of Q P ( Δ t ) , Q ˜ P = F [ Q P ( Δ t ) ] , in (b) (blue) and (c) (cyan). Red: VIS/NIR pulse spectrum.
Fig. 4.
Fig. 4. (a) Current injection mechanism in GaN. Charge carriers are created via interfering two- and three-photon transitions between valence (VB) and conduction (CB) bands (blue circles: occupied states; white: unoccupied). Heavy hole, light hole, and crystal-field split-off VBs are shown. Background: laser pulse spectrum. Dynamic phase shifts (dashed black arrows) Δ φ f i ( ± ) Δ φ f i ( ± k x , t 1 , t 2 ) resulting from field-induced intraband carrier motion (solid black arrows) determine whether interferences are constructive or destructive. (b) Applied optical electric field F L ( t ) , induced polarization field F P ( t ) calculated with quantum mechanical dynamic screening model and total field F ( t ) = F L ( t ) + F P ( t ) . (c), Time-dependent current density J ( t ) and electron population in the two lowest CBs calculated with quantum mechanical dynamic screening model.

Equations (1)

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Δ φ f i ( k x , t 1 , t 2 ) = 1 t 1 t 2 Δ E f i [ K x ( t ) ] d t ,

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