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Ultrafast Silicon Photonics with Visible to MidInfrared Pumping of Silicon Nanocrystals Benjamin T. Diroll, Katelyn S. Schramke, Peijun Guo, Uwe R. Kortshagen, and Richard D. Schaller Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b03393 • Publication Date (Web): 11 Sep 2017 Downloaded from http://pubs.acs.org on September 12, 2017

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Ultrafast Silicon Photonics with Visible to MidInfrared Pumping of Silicon Nanocrystals Benjamin T. Diroll,1 Katelyn S. Schramke,2 Peijun Guo,1 Uwe R. Kortshagen,2 and Richard D. Schaller1,3* 1

Center for Nanoscale Materials, Argonne National Laboratory, 9700 S. Cass Avenue,

Lemont, Illinois 60349, United States 2

Department of Mechanical Engineering, University of Minnesota, 111 Church Street SE,

Minneapolis, Minnesota 55455, United States 3

Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston,

Illinois 60208, United States

ABSTRACT. Dynamic optical control of infrared (IR) transparency and refractive index is achieved using boron-doped silicon nanocrystals excited with mid-IR optical pulses. Unlike previous silicon-based optical switches, large changes in transmittance are achieved without a fabricated structure by exploiting strong light coupling of the localized surface plasmon resonance (LSPR) produced from free holes of p-type silicon nanocrystals. The choice of optical excitation wavelength allows selectivity between hole heating and carrier generation through intraband or interband photoexcitation, respectively. Mid-IR optical pumping heats the free holes

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of p-Si nanocrystals to effective temperatures greater than 3500 K. Increases of the hole effective mass at high effective hole temperatures lead to a sub-picosecond change of the dielectric function resulting in a redshift of the LSPR, modulating mid-IR transmission by as much as 27% and increasing the index of refraction by more than 0.1 in the mid-IR. Low hole heat capacity dictates sub-picosecond hole cooling, substantially faster than carrier recombination, and negligible heating of the Si lattice, permitting mid-IR optical switching at terahertz repetition frequencies. Further, the energetic distribution of holes at high effective temperatures partially reverses the Burstein-Moss effect, permitting modulation of transmittance at telecommunications wavelengths. The results presented here show that doped silicon, particularly in micro- or nanostructures, is a promising dynamic metamaterial for ultrafast IR photonics. KEYWORDS. Silicon photonics, optical switching, infrared, plasmonics, doping Silicon-based all-optical devices, particularly at telecommunications wavelengths, are subject to intense interest for optical data processing on chip, because of silicon’s earth abundance, technological maturity, and commanding place in electrical processing.1 Many silicon photonic devices for near-infrared (IR) optical switching operate via third order nonlinear Kerr effects or two-photon absorption.2–4 Because of the relatively weak nonlinearity in silicon at relevant wavelengths,5 common device geometries for silicon all-optical devices include microfabricated (1-1000 µm scale) photonic crystals and ring resonators coupled to waveguides, which exhibit acute sensitivity to changes in refractive index and display high quality factors.2,3,6 The fluences required to induce appreciable Kerr effects at telecommunications wavelengths often also yield two-photon absorption, which generates carriers that must then recombine before the device is returned to its original state.


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Here we show that optically pumping the linear absorption of free carriers in doped silicon provides a distinct mechanism for all-optical control in silicon photonics. Rather than change the number of free carriers to induce Burstein-Moss effects,7–9 as occurs in interband excitation, intraband excitation in the mid-IR changes carrier effective temperature and avoids the challenges associated with the weak nonlinearity in silicon at telecommunications wavelengths. By selective intraband excitation of free holes in the mid-IR, this method manipulates the IR dielectric function of silicon through the heating of free holes to high effective electronic temperatures greater than 3500 K. Spectrally, the effects of high effective hole temperatures are broad, with appreciable changes from telecommunications wavelengths through the mid-IR. This intraband heating occurs in < 100 fs and the cooling of holes proceeds in < 1 ps, allowing optical switching at frequencies exceeding 1 terahertz. This is significantly faster than 10-100 picosecond optical switching in which carrier generation and recombination occur in silicon or even GaAs.10 This technique is demonstrated using boron-doped silicon nanocrystals synthesized via a gas-phase, nonthermal plasma process11 and inertially impacted as a porous film onto a BaF2 substrate to provide mid-IR transparency (a photograph of a sample is pictured in Figure 1). The nanocrystals studied in this work (Figure 1a) have a diameter of 7.2 ± 1.0 nm, which includes a thin oxide layer.11,12 After the formation of a silicon oxide layer, these materials show free hole concentrations on the order of 1020 cm-3 due, primarily, to ionization of surface-segregated dopants.11 The collective oscillation of these free holes on a confined nanoscopic particle results in a localized surface plasmon resonance (LSPR) which here is centered at 4.8 µm, as shown in the FTIR data in Figure 1b. LSPRs have long been known to arise from the collective oscillation of free electrons on the surface of nanoscale structures of noble metals.13 More recently, heavily-


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doped semiconductors of many compositions, including p-type and n-type silicon, have been exploited for the same property, but for doped semiconductors the LSPR is tuned from the nearto mid-IR spectral region depending on the doping level of the material.11,14–23 Because the free carries of the LSPR interact strongly with light, dynamic modulation of the LSPR is a promising method for optical switching and beam steering.24–28 The LSPR feature observed for the p-type silicon nanocrystals in the IR is readily modeled using a Drude (metallic) oscillator within an effective medium (air), using a MaxwellGarnett model. Generically, the Drude oscillator consists of a high-frequency dielectric (ε∞) and a damping parameter (γ) related to carrier mobility: = − ⁄ + . The plasma frequency ωp depends on the free carrier density (N), electron charge (e), carrier effective mass (m*), and permittivity of free space (ε0) as = ⁄ ∗ . The red line in Figure 1b shows the computed absorption for a Drude oscillator matching the properties of the silicon nanocrystals (7.2 nm, 15 vol%) in an air medium, with a hole effective mass of 0.45,29 hole mobility of 12.7 cm2V-1s-1, and free hole concentration of 3.3×1020 cm-3. Although more sophisticated models have been derived for other nanocrystal systems, the Drude model is sufficient to capture the physics of the doped silicon nanocrystals presented here without introducing additional complexity. The hole effective mass and the low hole mobility reflect the high doping concentration of the material,29 but it is also true that the mobility is a lower bound estimate as spectral broadening of the LSPR at least partially derives from inhomogeneities of doping, size, and shape of the nanocrystals.30,31


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Figure 1. (b) Transmission electron microscopy images of boron-doped silicon nanocrystals synthesized in nonthermal plasma. Inset shows the same particles at higher resolution. (a) Fourier-transform infrared absorption spectrum of boron-doped silicon nanocrystals deposited on to BaF2 windows (pictured inset). The dashed red line shows the simulated absorption of a Drude oscillator in an effective medium. Absorptions at 4.8 µm and 7.3 µm correspond to Si-H and SiO-Si bonds, respectively.

Figure 2. (a) Diagrams of the band structure of doped silicon and different optical pumping schemes. 2.5 µm excitation induces intraband heating of holes; 2.0 µm excitation induces both hole heating and two-photon absorption; and the response from 400 nm pumping is dominated by interband absorption. (b) Map of the change in transmission for a film of boron-doped silicon nanocrystals induced by a 2.0 µm pump beam (3.1 mJ/cm2) as a function of wavelength and


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delay time. Apparent discontinuities at 4.3 µm, 5.1 µm, and 5.8 µm reflect different banks within the array detector. (c-e) Quantitative change in transmitted signal for a film of boron-doped silicon nanocrystals (c) 2.5 µm pump, 4.5 µm probe, (d) 400 nm pump, 4.0 µm probe, and (e) 2.0 µm pump, 4.5 µm probe. The inset of (e) shows the signal from 2.0 µm pump (3100 µJ/cm2) and 400 nm pump (1400 µJ/cm2) normalized at 0.7 ps of delay time, showing the induced absorption signal at longer times under both pumping regimes. To perform transient extinction experiments, the samples were pumped either at 2.5 µm, 2.0 µm, or 400 nm using the output of an optical parametric amplifier (OPA, for 2.0 µm and 2.5 µm) or the frequency-doubled fundamental (400 nm) of a 35 fs Ti: sapphire laser. These different pump wavelengths were utilized to evaluate different regimes (intraband or interband) of excitation. Here, the red edge of the mid-IR pump wavelength and power used in these experiments were limited by the output of the OPA. The transmission of the films was probed using a separate beam (achieved from uncertainty broadening) from 4-6 µm output from a second OPA driven by the same amplified laser and spectra of each pulse were detected using a HgCdTe array and compared to produce transient extinction data. As shown in Figure 2a, 2.5 µm excitation, on resonance with the LSPR feature directly, excites free holes in the valence band of p-type silicon nanocrystals, heating them nearly instantaneously to high effective temperatures. Excitation at 2.0 µm can heat free holes through absorption into the LSPR, but at sufficient excitation fluence can also generate additional carriers through two-photon absorption. (Threephoton absorption of 2.5 µm excitation is not clearly observed here.) Finally, 400 nm pulses lack resonance with the LSPR, but provide interband absorption and concomitant generation of additional carriers. An example of the spectrally-resolved transient extinction data for doped silicon nanocrystals with intraband pumping at 2.0 µm is shown in the two-dimensional map in Figure 2b. The transient extinction data at the LSPR wavelength is dominated by a transient red-shift of the LSPR feature, characterized by a large bleach feature on the blue edge of the LSPR (3.8-5.2


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µm), leading to increased transmission, and an induced absorption on the red edge of the LSPR (5.2-6.1 µm), leading to decreased transmission. Similar results have been observed in pumpprobe experiments of noble metal nanomaterials32–35 and heavily-doped semiconductor nanomaterials with IR LSPR features.24,25,36–38 This transient red-shift results from heating and cooling of free holes in the non-parabolic valence band. As we will explore quantitatively later in this work, higher effective electronic temperatures for the excited holes changes their effective mass, which redshifts the plasma frequency of the doped silicon.24,25,39 Quantitative changes in transmission for the three pump configurations are plotted in Figures 2c-2e. Mid-IR pumping generates large increases in the IR transmittance of the B-doped Si nanocrystal film on the blue edge of the LSPR feature—up to 15 % with 2.5 µm and 27 % with 2.0 µm excitation probed at 4.5 µm —through a transient redshift. Further, the changes in optical density are linear over the range of fluence measured (See Supporting Information Figure S4), indicating that the maximal transmittance modulations observed in Figure 2 are constrained only by the pump fluence. As indicated in Figure 2a, 2.5 µm excitation heats free holes in the Bdoped Si nanocrystals nearly instantaneously. Rise times of the transient absorption signal are close to the instrument response function at ~60 fs. After heating, holes cool by dissipating energy to the silicon lattice through hole-phonon coupling, followed, at longer time scales not measured in this work, by phonon-phonon dissipation of heat from the nanocrystal lattice to the surrounding environment.35 The decay time to 1/e for the samples excited at 2.5 µm (Supporting Information Figure S5) is 255 ± 9 fs, very close to the 240 fs hole-phonon coupling time found in previous work.40 Compared to metallic systems, weak power dependence of the hole-phonon coupling and rapid cooling both reflect small heat capacity of holes in doped silicon due to the low free hole concentration.33,41,42


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In the data collected with 400 nm pumping (Figure 2d), a comparatively weaker, for the same input fluence, and longer-lived induced absorption on the blue edge of the LSPR feature occurs. This feature arises from additional carriers blue-shifting the LSPR feature due to absorption and generation of electron-hole pairs. The time-scale of recovery from the intraband and interband pumping regimes are dramatically different because of the distinct underlying physical processes: 2.5 µm pumping leads to a return of the signal from the peak to less than 1% ∆T/T in less than 1 ps (Supporting Information Figure S5), as hot holes cool with negligible lattice heating, which we model quantitatively below. The LSPR blue-shift induced by 400 nm pumping reaches 1% ∆T/T only after ~20 ps, rapid for typical recombination (carrier diffusion in nanocrystals is unlikely), but more than an order of magnitude longer than hole cooling. Intraband excitation can therefore offer significant increases both speed (up to terahertz switching frequencies) and signal level over optical switching in which carrier generation occurs. Excitation at 2.0 µm generates a more complicated optical response. Although the change in transmittance with 2.0 µm pumping is dominated by a redshift indicative of intraband heating, a weak induced absorption feature also occurs 2.0 µm pumping at delay times > 0.7 ps (Figure 2e), which is assigned to two-photon absorption, based upon four pieces of evidence. First, the induced absorption feature is observed with 2.0 µm pumping, for which two-photon absorption across the silicon band gap is possible, and not for 2.5 µm pumping, for which it is not. Second, the magnitude of the signal at ~2 ps increases superlinearly with fluence, although the signal still contains a large linear component (Supporting Information Figure S3). Third, the spectral signature is that of a small blue-shift of the LSPR consistent with additional carrier generation.24,28,38 That is, at longer delay times red of the LSPR center, transmission increases and blue of the LSPR center, transmission decreases exactly opposite what occurs at early delay


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times. Last, the time-scale of the decay of the bleach feature with 2.0 µm pumping is comparatively slow. This is consistent with the transient decays observed with 400 nm pumping, which is unambiguously related to carrier recombination (see inset to Figure 2e). Due to the large difference in time-scale and opposite sign of the optical switching signal achieved with intraband heating and interband excitation, selection of the excitation wavelength can dramatically change the properties of switching based upon manipulation of the LSPR feature of the doped silicon nanocrystals. Even further, selection of the excitation fluence at a single wavelength, rather than two-color pumping,43 can tune the relative weights of intraband heating and interband excitation. The absolute magnitude of the change in transmittance with optical pumping depends on the pump wavelength and pump fluence as well as the temperature-dependent specific heat capacity of holes in boron-doped silicon, which dictate the degree of effective hole temperature elevation under optical pumping. Quantitative information on the effective temperature of holes under intraband excitation can be obtained using a two-temperature model which accounts for the effects of valence band non-parabolicity and the changes of hole specific heat capacity at elevated temperatures.25 The two-temperature model of hole temperature Th and lattice temperature TL is described by two coupled differential equations:

= − −

= −

(1)

(2)

in which Ch(Th) is the temperature-dependent specific heat capacity of holes, CL is the specific heat capacity of the lattice, and G is the electron-phonon coupling parameter. Computed hole and lattice temperatures for the case of 2.5 µm pumping, in which no carrier generation occurs, are


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shown in Figure 3a with the corresponding optical data shown in Supporting Information Figure S6. Because the hole specific heat capacity of doped silicon is low (approximately 0.1% of the silicon lattice at 300 K), optical excitation heats free holes to high effective temperatures. As shown in Figure 3b, computed effective hole temperatures reach close to 1900 K for the highest fluence pumping at 2.5 µm and 3800 K with 2.0 µm pumping. At higher powers, increasing fluence leads to smaller increases in effective hole temperature due to the increasing specific heat capacity of holes at high temperature. Despite the high temperatures reached by free holes in the B-doped silicon nanocrystals, lattice heating is minimal due to the much larger lattice heat capacity,44 increasing less than 5 K for 990 µJ/cm2 fluence with 2.5 µm pumping.

Figure 3. (a) Computed change in temperature for holes (solid lines) and the silicon lattice (dashed lines) for the silicon nanocrystal sample pumped at the stated fluences at 2.5 µm, based upon a two-temperature model. (b) Computed peak effective hole temperatures derived from the temperature-dependent specific heat capacity of B-doped silicon nanocrystals. (c) Estimated IR change of index of refraction (n) for a Drude-like p-type silicon at different effective hole temperatures, compared to the index at 300 K. Transient changes in the optical density of the silicon LSPR detected in the mid-IR due to high effective hole temperatures indicate broadband changes in the refractive index of the material. Whereas interband absorption increases the free carrier density, leading to the blue-shift described above for 400 nm and 2.0 µm pumping, intraband excitation does not change the free carrier concentration. Indeed, in the parabolic approximation of bands, the plasma frequency of


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the silicon nanocrystals should remain fixed under intraband excitation and no change of the LSPR should occur.25 However, high effective hole temperatures red-shift the Drude function (i.e. ωp) that describes the indices of refraction for doped silicon in the IR by increasing hole occupation of lower-energy valence band states, which are not described by the parabolic approximation, and thereby increasing the average hole effective mass.24,25,38 The changes in the index of refraction of the doped silicon nanocrystals due to changes in the hole temperature is estimated at several effective hole temperatures in Figure 3c, using a Drude model with the mobility and the carrier concentration fixed. (Changes in k are plotted in Figure S8.) The change in the hole temperature induced by intraband excitation increases the index of refraction of doped silicon throughout the IR, with ∆n values larger than 0.1, limited in this case only by the pump fluence. This underlines the ability to use spectrally-remote intraband excitation for broadband manipulation of the index of refraction of photonic structures on ultrafast time-scale.45 Intraband excitation of free carriers offers a distinct mechanism for alloptical control of silicon-based photonic devices, separate from Kerr effects or interband excitation. To be sure, free carriers in silicon increase transmission losses in near-IR photonic devices.46,47 However, careful selection of the doping level or the use of doped material in proximity to a waveguide may sufficiently reduce absorption losses for certain applications.


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Figure 4. (a) Fractional change in transmission at 1.3 µm for a B-doped silicon nanocrystal film excited at 2.5 µm. (b) Absorption of same B-doped silicon nanocrystal film in the near-IR. The value of the bandgap (Eg) of undoped silicon is indicated with a dashed line. (c) Cartoons of hole occupation as a function of temperature. Higher hole temperatures relax the blue-shift of the band gap arising from the Burstein-Moss effect. Direct observation of the quantitative change in transmission for the doped silicon nanocrystal film pumped at 2.5 µm and probed at 1.3 µm is shown in Figure 4a. The response at this technologically relevant wavelength is more complex than the change in the LSPR in the mid-IR. Unlike the intraband heating data measured in the mid-IR, the transmission of the sample decreases with carrier heating, indicating that a red-shift of the LSPR feature, which dominates the mid-IR transient response, does not dominate in the near-IR. The time-scale of the response is nonetheless comparable to intraband cooling observed in the mid-IR: the signal is dominated by a ~350 fs decay, faster than interband recombination. The ∆T/T signal at 1.3 µm increases in a sublinear manner with fluence, indicating that carrier generation from three-photon absorption is not the likely cause for induced absorption. The steady-state absorption spectrum of the nanocrystal film, shown in Figure 4b, offers a potential explanation for this unexpected result. The doped samples show not only interband absorption for energies above the bulk band gap of silicon, and free carrier absorption increasing at longer wavelength, but also a density of optically-active shallow states in the vicinity of the bulk gap.


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As with any heavily-doped semiconductor, optical transitions near the band gap are bleached by electron or hole occupation, leading to the apparent widening of the optical bandgap, identified as the Burstein-Moss effect (See model in Figure 4c).7,8 With the intraband heating of free holes induced by the 2.5 µm pump, the fixed density of free holes is thermally distributed over a larger number of states in the valence band, partially reversing the BursteinMoss effect, resulting in transient induced absorption on the time-scale of hole cooling.45 This may be recognized as a change in ε∞, or high-frequency dielectric, which is used in the Drude model. Such changes in the band-edge states are negligible for the spectrally-remote mid-IR dynamics described above, but significant in the near-IR. Whereas in an ideal material, this effect would typically only be observed at energies at or slightly above the band-gap of the semiconductor, here we propose that it may be observed at 1.3 µm due to optically-active subgap states. The origin of the longer-lived transient signal at 1.3 µm is unclear, but it is observed to be roughly constant for hundreds of picoseconds, which suggests that the signal arises from lattice heating, with thermo-optical changes in the dielectric function of silicon largest near the band gap.48 In conclusion, we have shown that the use of doped silicon in photonic structures offers a mid-IR handle to adjust the transmittance and index of refraction throughout the IR. The use of intraband pumping to heat free holes allows a large transient red-shift of the LSPR feature as the effective mass of free carriers changes dramatically with their electronic temperature. Intraband heating and cooling is shown to exhibit a substantially larger change in transmission, for similar input fluence, and dramatically faster response on a sub-picosecond time-scale compared with interband excitation. Although the LSPR feature provides a strong, localized optical extinction


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feature, similar behavior may be obtained using thin films, photonic structures, or bulk doped material.49,50 ASSOCIATED CONTENT Details on methods and additional data are available in the supporting information file. The following files are available free of charge. Supporting methods and data.pdf AUTHOR INFORMATION Corresponding Author *[email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was performed, in part, at the Center for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility, and supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357. K.S.S. and U.R.K. were supported by the Army Office of Research under MURI Grant W911NF-12- 1-0407. Parts of this work were carried out in the Minnesota Nano Center which receives partial support from NSF through the NNIN program. Aspects of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program. REFERENCES (1)

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