Band Gap Renormalization, Carrier Multiplication, and Stark

Subscriber access provided by YORK UNIV

Communication

Bandgap Renormalization, Carrier Multiplication and Stark Broadening in Photoexcited Black Phosphorous Zhesheng Chen, Jingwei Dong, Evangelos Papalazarou, Marino Marsi, Christine Giorgetti, Zailan Zhang, Bingbing Tian, Jean-Pascal Rueff, Amina Taleb-Ibrahimi, and Luca Perfetti Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b04344 • Publication Date (Web): 10 Dec 2018 Downloaded from http://pubs.acs.org on December 12, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Bandgap Renormalization, Carrier Multiplication and Stark Broadening in Photoexcited Black Phosphorous

Zhesheng Chen,† Jingwei Dong,‡ Evangelos Papalazarou,¶ Marino Marsi,¶ Christine Giorgetti,‡ Zailan Zhang,§ Bingbing Tian,§ Jean-Pascal Rue,† k Amina ,

Taleb-Ibrahimi,† and Luca Perfetti∗ ‡ ,

†Société civile Synchrotron SOLEIL, L'Orme des Merisiers, Saint-Aubin - BP 48, 91192

GIF-sur-Yvette, France ‡Laboratoire des Solides Irradiés, Ecole polytechnique,e, CNRS, CEA, Université

Paris-Saclay, 91128 Palaiseau cedex, France ¶Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, Université

Paris-Sud, 91405 Orsay, France §SZU-NUS Collaborative Innovation Center for Optoelectronic Science and Technology,

International Collaborative Laboratory of 2D Materials for Optoelectronics Science and Technology of Ministry of Education, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China. kSorbonne Université, CNRS, Laboratoire de Chimie Physique - Matiere et Rayonnement,

LCPMR, F-75005 Paris, France E-mail: [email protected]

Abstract 1

ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

We investigate black phosphorous by time and angle resolved photoelectron spectroscopy. The electrons excited by 1.57 eV photons, relax down to conduction band minimum within 1 ps. Despite the low bandgap value, no relevant amount of carrier multiplication could be detected at excitation density 3 − 6 × 1019 cm−3 . In the thermalized state, the bandgap renormalization is negligible up to a photoexcitation density that lls the conduction band by 150 meV. Astonishingly, a Stark broadening of the valence band takes place at an early delay time. We argue that electrons and holes with high excess energy lead to inhomogeneous screening of near surface elds. As a consequence the chemical potential is no longer pinned in a narrow impurity band.

Keywords : Black Phosphorous, Ultrafast, ARPES, Stark, Band-Gap-Renormalization

Introduction The quest for two-dimensional materials with tunable bandgap and high carriers mobility brought into the spotlight several semiconductors with interesting optoelectronic properties. Within this family, the black phosphorous is one of most prominent examples. Its electronic gap depends on thickness, 1 attaining the value of 1.5-1.7 eV in the monolayer 2 and shrinking down to 0.3 eV in the bulk limit. 3,4 Photodetectors based on this material display high carriers mobilities, 5,6 broadband photoresponse 7 and intrinsic anisotropy. 4,8,9 Most interestingly, the band structure of black phosphorous is particularly sensitive to external electric elds 10,11 and surface dipoles. 12,13 Angle resolved photoelectron spectroscopy measurements have shown that adsorption of alkaline metals at the sample surface generates a two-dimensional electron gas that can be tuned across the band inversion point. 12 Alternatively, a depletion layer induced via electrostatic gating can shrink the bandgap by 35%. 10 Upon dual gating, 11 it is possible to further approach the transition from a semiconductor to a Dirac semimetal. Although the response to an electric eld has been extensively characterized, much less 2


Page 2 of 18

Page 3 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

is known about black phosphorous in the photoexcited state. In analogy to two dimensional semiconductors, a sizeable bandgap renormalization may be expected at moderate excitation uence. 14 Eventually, the low gap size may lead to a measurable amount of carriers multiplication. 1517 The time resolved experiments that have been performed so far 1820 could not answer these questions. In order to gain more insights, we investigate black phosphorous by means of time and angle resolved photoelectron spectroscopy (time resolved ARPES). The non-equilibrium electronic distribution discloses the dynamics of photoexicted carriers in reciprocal space. 2123 After photoexcitation centered at 1.57 eV, the electrons relax at the bottom of the conduction band by nearly conserving the initial density. No reduction of the bandgap could be detected in the explored regime of photon ux. To our big surprise, the photoexcited state is less homogeneous than the equilibrium one. Indeed, a Stark broadening smears the electronic states at an early delay time. This eect is ascribed to a spatially varying potential that builds up along the surface upon the sudden change of electronic screening. More insights on the reported phenomenon are obtained by a characterization of the photoelectron signal as function of pump uence.

Experimental details Time-resolved ARPES experiments are performed on the femto-ARPES setup, 24 using a Ti:sapphire laser system delivering 50 fs pulses at 1.57 eV (790 nm) with a 250 kHz repetition rate. Part of the laser beam is used to generate 6.3 eV photons through cascade frequency mixing in BaB2 O4 (BBO) crystals. The 1.57 and 6.3 eV beams are employed to photoexcite the sample and induce photoemission, respectively. The overall energy resolution of the experiment is ∼ = 30 meV whereas the cross correlation between pump and probe pulse has Full Width Half Maximum FWHM of 0.16 ps. All data have been acquired with p polarized probe at an incident angle of 45◦ . Single crystals of black phosphorous grown

from `HQgraphene' have been cleaved and measured at the base pressure of 7 × 10−11 mbar. 3


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Our samples have been oriented by low energy electron diraction and measured at the temperature of 135 K. The bulk material is naturally p-doped, 3 due to the presence of intrinsic vacancies that generate acceptor states near to the valence band maximum. 25 Apparently, the orbital momentum and the electronic occupation of these charged defects can be tuned via an external bias. 26

Results and discussion Figure 1a) shows the intensity maps t = 1 ps after the arrival of a pump pulse with incident pump uence of 230 µJ/cm2 . The wavevector asymmetry and drop of signal at the conduction band minimum are due to matrix elements of the photoemission process. We t the dispersion along the armchair direction by the pseudo-relativistic expression E = ±(δ +

p m2x vx4 + vx2 p2 ), where mx is the eective mass and vx is the band velocity in the

linear section. As shown by the dotted lines in Fig. 1a), the parameters mx = 0.07 ± 0.02me (where me is the free electron mass), vx = 0.61 ± 0.2 × 106 m/s and δ = 0.01 eV reproduce both the valence and conduction band with good accuracy. Along the zigzag direction (see Fig.1b)), the band structure has the parabolic shape E = ±(∆/2 + p2 /2my ) with eective mass my = mcy = 1.1±0.1me for electrons and my = mvy = 0.6±0.05me for holes. Within the experimental uncertainties, the derived values are consistent with Shubnikov-de Haas oscillations in high magnetic eld 3 and ab-initio calculations (see also SSupporting Information document). The extracted bandgap ∆ = 2(mx vx2 + δ) = 0.31 ± 0.02 eV is in agreement with the value reported by infrared spectroscopy 4 and scanning tunneling microscopy. 25 In order to verify that photoexcitation does not renormalize the bandgap, we repeated the measurements of Fig. 1a) after reducing the pump uence by a factor six. As shown by Fig. 1c), the eventual dierence of bandgap is smaller than the experimental uncertainties. The negligible bandgap renormalization is ascribed to the moderate photoexcitation density and to the 3D screening 4


Page 4 of 18

Page 5 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 1: Photoelectron intensity map acquired at pump probe delay time t = 1 ps in the following conditions: a) along the armchair direction with pump uence of 230 µJ/cm2 , b) along the zigzag direction with pump uence of 230 µJ/cm2 , c) along the armchair direction with pump uence of 40 µJ/cm2 . The zero of the energy axis has been dened as the center of the bandgap ∆ (the actual chemical potential being 80 meV above the valence band maximum). We multiplied the signal at positive energy by a factor between 50-300 in order to visualize conduction and valence band on the same colorscale. White and red dotted line stand for the modeled dispersion of electronic states. The blue solid line is the expected lling of the conduction band under the assumption of negligible carriers multiplication. Photoexcitation density ρ = 6, 3, 1 × 1019 cm−3 correspond to φ = 150, 110, 45 meV in panel a), b), c), respectively (see Supporting Information document).

5


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

of the Coulomb interaction. We stress that the dimensionality of the electronic bands is an essential aspect of the problem. It is established that a large redistribution of spectral weight takes place in the 2D chalcogenides. 14 Upon photoexcitation of such monolayer semiconductors, the correlated electron hole plasma generated by the dissociation of strongly bound excitons deeply reshapes the optical properties. However, the ecient screening of 3D black phosphorus restrains the binding of excitons below 20 meV. 3 Consistently with our experimental nding, these weakly bounds electron-hole pairs cannot have large impact on the size of the bandgap. Secondly, we consider the role that hot phonons may have on the band structure. At the moderate excitation uence of 230 µJ/cm2 the pump pulse injects roughly 2 meV for each atom of phosphorous. Under these conditions, the eective temperature of the transverse optical branch cannot increase more than 30 K. According to the data of Villegas et al., 27 the adiabatic electron-phonon coupling and anharmonic interactions may lead to a gap opening of few meV. Such small eect is also compatible with the uncertainties our measurement. Last but not least, our result points out that photoexcitation and surface doping have little in common. By doping the surface layer of black phosphorous with alkaline atoms, the local electronic screening lowers the binding energy of the conduction band down to an inversion point. 12 The bandgap shrinks by 25% when the electrons ll the conduction band up to 150 meV. 13 However, the surface dipole that induces the local band inversion upon alkaline atoms adsorption 12,13 or electrostatic gating 10,11 has no analogous in an optical absorption. Several scattering mechanisms contribute to the thermalized state in Fig. 1. The excited electrons dissipate energy via phonon emission, 21 generate new electron-hole pairs by impact ionization and interact with each other via Auger scattering. Only the rst mechanism conserves the carrier density, the second leads to carrier multiplication and the third favors recombination. A simple analysis establishes if the number of conducting charges is preserved. The pulse centered at 1.57 eV and polarized along the armchair direction has optical penetration depth 9 of 140 nm. By taking into account reection losses, an incidence uence 6


Page 6 of 18

Page 7 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

of 230 µJ/cm2 corresponds to photoexcitation density ρ = 6 × 1019 cm−3 . Being fermions, the electrons in the conduction band must obey to the Pauli exclusion principle. After 1 ps the electrons have suciently cooled down to approach a Fermi-Dirac distribution with eective lling level. Under the hypothesis that thermalization does not change the carrier density, the electron gas at 1 ps would display a lling level φ = 150 meV (see Supporting Information document). An equivalent analysis holds in the zigzag direction instead of the armchair one. However, the penetration depth of light polarized along the y axis 4,8,9 is twice longer. Since the polarization of the pump was always pointing along the slit of the analyzer, an intensity map acquired along the zigzag direction should display φ = 110 meV. The blue lines in Fig. 1(a,b) show that estimated and measured lling of the conduction band are in good agreement. It follows that 3 − 6 × 1019 cm−3 electrons excited by 1.57 eV photons roughly conserve the initial density during the thermalization process. Either the electron-phonon is the dominant scattering process or impact ionization is well balanced by Auger scattering. 15 This nding is in contrast with experimental results in graphene, where carrier multiplication has been detected at early delay time up to high photoexcitation density. 16,17 The dierence between semimetallic graphene and black phosphorous stems from the reduced phase space for electron-electron scattering in the presence of a bandgap. 28 Such a constrain becomes even stronger in few- or mono-layer phosphorene, where the larger gap size 2 increases the minimal photon energy for impact ionization. Eventually the carriers multiplication may become detectable in the limit of low photoexcitation density, when Auger recombination is surely negligible with respect to impact ionization. At ρ = 1 × 1019 cm−3 , the intensity map of Fig. 1c) suggests that the measured lling overcomes the estimated φ = 45 meV. Although the data of Fig. 1c) could be compatible with a multiplication factor appreciably larger than one, the false impression of a larger lling may also arise from φ becoming comparable to our energy resolution. The full temporal evolution of the transient signal is shown in Fig. 2a), where we plot the dierential intensity maps acquired for increasing pump probe delay. The signal at positive 7


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2: a) Dierence between an intensity map at delay time t = 0.1, 0.5, 1, 2, 5, 10, 25, 40 ps and an intensity map at delay time -0.2 ps. The data have been acquired along the armchair direction with pump uence of 230 µJ/cm2 . The photoelectron intensity at positive energy has been multiplied by a factor 30. Rectangles in the upper right panel indicate the area in the conduction and valence band where the dierential signal has been integrated. Temporal evolution of pump induced signal at the bottom of the conduction band (blue circles) and top of the valence band (red squares) for b) early and c) longer delay times. The contribution of Stark broadening has been removed from the integrated signal in the valence band (see Supporting Information document). Filled and open symbols stand for measurements performed on two dierent cleaves. Solid lines are ts of the experimental data with the test function (1 + t/τ )−1 .

8


Page 8 of 18

Page 9 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

energy has been multiplied by a factor 30 to equalize the contrast of valence and conduction band. At an early delay time, the electronic occupation of the conduction band still lingers below our detection limit. The carrier concentration at the bands edges gradually builds up, reaching its maximum at t = 1 ps. We show in Fig. 2b,c) the temporal evolution of the dierential signal integrated in a small area at the edge of the conduction band or valence band. In order to isolate the evolution of photoexcited hole density, the extra contribution of Stark broadening has been subtracted from the integrated signal in the valence band (see Supporting Information document). Figure 2b) conrms that also holes require 1 ps to thermalize. On the long timescale, diusion, drift and recombination rule the dynamics of excited carriers. A detailed modeling of such inter-twinned mechanisms is out of the scope of the present article. Nonetheless, we note that a phenomenological expression (1 + t/τ )−1 ts well the experimental data of Fig. 2c) if τ = τh = 10 ps for holes and τ = τe = 2.5 ps for electrons. The explanation of such asymmetry is very simple. Since black phosphorous is naturally p doped, the electrons in the conduction band are captured by acceptor states. Therefore the lifetime of minority carriers is shorter than the one of the majority one. 29 We also recall that built-in elds may restrain the diusion of holes in the bulk of the sample. 22 Next, we discuss the large impact that photoexcitation has on the spectral distribution of the valence band. Figure 3a-b) compare the photoelectron intensity maps acquired at t = −0.5 ps and 0.1 ps along the armchair direction. Note the blurry look of the valence

band at positive delay. The dierence intensity map reported in Fig. 3c) is consistent with a photoinduced broadening of ∼ = 80 meV, joint to a mean shift of 8 meV towards higher energy (see Supporting Information document). Figure 3d-f) show the analogous analysis along the zigzag direction. We ascribe the Stark broadening to the emergence of an inhomogeneous potential along the surface plane. In black phosphorous, the natural source of inhomogeneity is the formation of defects during the crystal growth. Scanning Tunneling Microscopy (STM) experiments on samples grown by `HQgraphene' have imaged single vacancies with atomic resolution. 25,26 The acceptors in the near surface region are negatively charged, therefore 9


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3: Photoelectron intensity map acquired along the armchair direction a) at t = −0.5 ps and b) at t = 0.1 ps. c) Dierence between the armchair maps at positive and negative delay. Photoelectron intensity map acquired along the zigzag direction d) at t = −0.5 ps and e) at t = 0.1 ps. f) Dierence between the zigzag maps at positive and negative delay. g) Intensity map of Momentum Distribution Curves (MDCs) extracted at -0.1 eV as a function of pump probe delay. h) Photoinduced variation of MCDs FWHM as a function of pump probe delay. All the data in this image have been acquired with pump uence of 230 µJ/cm2 .

10


Page 10 of 18

Page 11 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

generating local elds. 26 Electrons bounded to these sites have a localization length d ∼ =5 nm along the armchair direction and d ∼ = 2 nm along the zigzag one. According to STM data, 26 the density of the acceptors N ∼ = 1018 cm−3 veries 0.1 < dN 1/3 < 1. In this regime, impurities can be viewed as a diluted quantum system forming a narrow band. 30 Although the electronic occupation may change from site to site, charge uctuations with long wavelength are small enough to guaranty a good pinning of the chemical potential. 30 As a consequence, each plane parallel to the surface is nearly isopotential. Upon photoexcitation, the average excess energy of the excited carriers rises abruptly to 0.3-0.6 eV. In analogy to interference patterns generated by quasiparticles, 25 the injected carriers scatter strongly with localized states. Electrons around defects are ionized or strongly perturbed, so that an inhomogeneous screening of the local potential give rise to electric elds parallel to the surface plane. We cannot exclude that a Stark renormalization of the local band-gap takes place before that electrons and holes have thermalized. This interesting issue calls for transient absorption experiments in the mid-infrared region. Figure 3g) shows an intensity map of Momentum Distribution Curves (MDCs) extracted at energy of -0.1 eV and variable pump probe delay. The variation of the MDCs Full Width Half Maximum is plotted in Fig. 3h). As expected from a purely electronic process, the rise of Stark broadening takes place within the duration of the pump pulse and recovers during the thermalization time of ∼ = 1 ps. As shown by Fig. 3h), the remnant eect at longer delay decays with time constant of 20 ps. Based on these results, we identify three dierent intervals: i) In equilibrium conditions, the chemical potential is pinned in the impurity band via screened interactions. ii) Just after photoexcitation, the large excess energy of the electrons and holes give rise to a redistribution of the charge density and inhomogeneous elds. iii) At longer delay, the thermalized and hot plasma is again capable of pinning the chemical potential, although deviations from the equilibrium case can still be measured. Further insights of on the Stark broadening are provided by the acquisition of dierential intensity maps for dierent pumping uence. The scaling of the signal in Fig. 4a) strongly 11


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4: a) Dierential intensity maps along the armchair direction, acquired at t = 0.1 ps and dierent values of the pump uence. b) The FWHM variation of MDCs extracted at −0.1 eV and t = 0.1 ps (circles). Experimental data (black marks) have been t by the test function α ln(1 + ρ/ρ0 ) (solid red line). deviates from a linear progression. Figure 4b shows that the MDCs FWHM increases with photoexcitation density as the phenomenological expression α ln(1 + ρ/ρ0 ). The parameter, ρ0 = 5 × 1017 cm−3 is comparable to the nominal acceptor density of our sample, while α = 0.06 1/nm constrains the energy spread of inhomogeneous elds to one third of the gap

size. Such ndings pave the view for the development of a microscopic model that will be able to merge: diluted quantum systems, intrinsic disorder and an ultrafast quench.

Conclusions In conclusion, we explored the band structure and charge dynamics of black phosphorous by means of time resolved ARPES. At excitation density larger than 3 × 1019 cm−3 , the photoexcited electrons relax by leading to negligible amount of carrier multiplication. No signature of bandgap renormalization has been detected in the thermalized state of the electron-hole plasma. On the other hand, a Stark broadening of the valence band takes place just after the arrival of the pump pulse. We argue that carriers with high excess 12


Page 12 of 18

Page 13 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

energy ionize charged defects and induce the inhomogeneous screening of a local potential. As a consequence, the pinning of the valence band is perturbed by development of elds parallel to the surface plane.

Acknowledgement We acknowledge enlightening discussions with Sergio Ciuchi for the interpretation of the experimental results. The nancial support has been provided by the EU/FP7 under the contract Go Fast (Grant No. 280555), by "Investissement d'Avenir" Labex PALM (ANR-10LABX-0039-PALM), by the Equipex ATTOLAB (ANR11-EQPX0005-ATTOLAB) by the ANR Iridoti (Grant ANR-13-IS04-0001), by the Région Ile-de-France (DIM OxyMORE) and by the China Scholarship Council (CSC, Grant No. 201706170091).

Supporting Information Available • Supporting Information document containing the sections: X-ray Photoelectron Spec-

troscopy; structural and electronic properties of black phosphorous; estimate of the lling factor; time evolution of the photoexcited hole density; Stark broadening and Stark shift.

13


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5: Table Of Content

14


Page 14 of 18

Page 15 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

References (1) Tran, V.; Soklaski, R.; Liang, Y.; Yang, L. Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys. Rev. B 2014, 89, 235319. (2) Liu, H.; Neal, A. T.; Zhu, Z.; Luo, Z.; Xu, X.; Tomnek, D.; Ye, P. D. Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility. ACS Nano 2014, 8, 4033. (3) Morita, A. Semiconducting black phosphorus. Appl. Phys. A 1986, 39, 227. (4) Xia, F.; Wang, H.; Jia, Y. Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nature Comm. 2014, 5, 4458. (5) Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Hui, C. X.; Zhang, Y. Black phosphorus eld-eect transistors. Nature Nanotech. 2014, 9, 372. (6) Koenig, S. P.; Doganov, R. A.; Schmidt, H.; Castro Neto, A. H.; Özyilmaz, B. Electric eld eect in ultrathin black phosphorus. Appl. Phys. Lett. 2014, 104, 103106. (7) Buscema, M.; Groenendijk, D. J.; Blanter, S. I.; Steele, G. A.; van der Zant, H. S. J.; Castellanos-Gomez, A. Fast and Broadband Photoresponse of Few-Layer Black Phosphorus Field-Eect Transistors. Nano Lett. 2014, 14, 3347. (8) Yuan, H. et al. Polarization-sensitive broadband photodetector using a black phosphorus vertical p-n junction. Nature Nanotech. 2015, 10, 707. (9) Ling, X. et al. Anisotropic Electron-Photon and Electron-Phonon Interactions in Black Phosphorus. Nano Lett. 2016, 16, 2260. (10) Liu, Y.; Qiu, Z.; Carvalho, A.; Bao, Y.; Xu, H.; Tan, S. J. R.; Liu, W.; Castro Neto, A. H.; Loh, K. P.; Lu, J. Gate-Tunable Giant Stark Eect in Few-Layer Black Phosphorus. Nano Lett. 2017, 17, 1970.

15


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(11) Deng, B.; Tran, V.; Xie, Y.; Jiang, H.; Li, C.; Guo, Q.; Wang, X.; Tian, H.; Koester, S. J.; Wang, H.; Cha, J. J.; Xia, Q.; Yang, L.; Xia, F. Ecient electrical control of thin-lm black phosphorus bandgap. Nature Comm. 2017, 8, 14474. (12) Kim, J.; Baik, S. S.; Ryu, S. H.; Sohn, Y.; Park, S.; Park, B.-G.; Denlinger, J.; Yi, Y.; Choi, H. J.; Kim, K. S. Observation of tunable band gap and anisotropic Dirac semimetal state in black phosphorus. Science 2015, 723, 349. (13) Kim, S.-W.; Jung, H.; Kim, H.-J.; Choi, J.-H.; Wei, S.-H.; Cho, J.-H. Microscopic mechanism of the tunable band gap in potassium-doped few-layer black phosphorus. Phys. Rev. B 2017, 96, 075416.

(14) Pogna, E. A. A.; Marsili, M.; De Fazio, D.; Dal Conte, S.; Manzoni, C.; Sangalli, D.; Yoon, D.; Lombardo, A.; Ferrari, A. C.; Marini, A.; Cerullo, G.; Prezzi, D. PhotoInduced Bandgap Renormalization Governs the Ultrafast Response of Single-Layer MoS2. ACS Nano 2016, 10, 1188. (15) Winzer, T.; A., K.; Malic, E. Carrier multiplication in graphene. Nano Lett. 2010, 10, 4839. (16) Plotzing, T.; Winzer, T.; Malic, E.; Neumaier, D.; Knorr, A.; Kurz, H. Experimental Verication of Carrier Multiplication in Graphene. Nano Lett. 2014, 14, 5371. (17) Johannsen, J. C. et al. Tunable carrier multiplication and cooling in graphene. Nano Letters 2015, 15, 326.

(18) Ge, S.; Li, C.; Zhang, Z.; Zhang, C.; Zhang, Y.; Qiu, J.; Wang, Q.; Liu, J.; Jia, S.; Feng, J.; Sun, D. Dynamical Evolution of Anisotropic Response in Black Phosphorus under Ultrafast Photoexcitation. Nano Lett. 2015, 15, 4650. (19) Iyer, V.; Ye, P.; Xu, X. Mid-infrared ultrafast carrier dynamics in thin lm black phosphorus. 2D Materials 2017, 4, 021032. 16


Page 16 of 18

Page 17 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(20) Nurmamat, M.; Ishida, Y.; Yori, R.; Sumida, K.; Zhu, S.; Nakatake, M.; Ueda, Y.; Taniguchi, M.; Shin, S.; Akahama, Y.; Kimura, A. Prolonged photo-carriers generated in a massive-and anisotropic Dirac material. Scientic Reports 2018, 8, 9073. (21) Chen, Z.; Giorgetti, C.; Sjakste, J.; Cabouat, R.; Veniard, V.; Zhang, Z.; TalebIbrahimi, A.; Papalazarou, E.; Marsi, M.; Shukla, A.; J., P.; Perfetti, L. Ultrafast electron dynamics reveal the high potential of InSe for hot-carrier optoelectronics. Physical Review B 2018, 97, 241201.

(22) Papalazarou, E.; Khalil, L.; Caputo, M.; Perfetti, L.; Nilforoushan, N.; Deng, H.; Chen, Z.; Zhao, S.; Taleb-Ibrahimi, A.; Konczykowski, M.; Hruban, A.; Wolos, A.; Materna, A.; Krusin-Elbaum, L.; M., M. Unraveling the Dirac fermion dynamics of the bulk-insulating topological system Bi2 Te2 Se. Phys. Rev. Materials 2018, 2, 104202. (23) Chen, Z.; Lee, M.-i.; Zhang, Z.; Diab, H.; Garrot, D.; Lédée, F.; Fertey, P.; Papalazarou, E.; Marsi, M.; Ponseca, C.; Deleporte, E.; Tejeda, A.; Perfetti, L. Time-resolved photoemission spectroscopy of electronic cooling and localization in CH3 NH3 PbI3 crystals. Phys. Rev. Materials 2017, 1, 045402. (24) Faure, J.; Mauchain, J.; Papalazarou, E.; Yan, W.; Pinon, J.; Marsi, M.; Perfetti, L. Full characterization and optimization of a femtosecond ultraviolet laser source for time and angle-resolved photoemission on solid surfaces. Rev. Sci. Instrum. 2012, 83, 043109. (25) Kiraly, B.; Hauptmann, N.; Rudenko, A. N.; Katsnelson, M. I.; Khajetoorians, A. A. Probing Single Vacancies in Black Phosphorus at the Atomic Level. Nano Lett. 2017, 17, 3607.

(26) Qiu, Z.; Fang, H.; Carvalho, A.; Rodin, A. S.; Liu, Y.; Tan, S. J. R.; Telychko, M.; Lv, P.; Su, J.; Wang, Y.; Castro Neto, A. H.; Lu, J. Resolving the Spatial Structures of Bound Hole States in Black Phosphorus. Nano Lett. 2017, 17, 6935.

17


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(27) Villegas, C. E. P.; Rocha, A. R.; Marini, A. Anomalous Temperature Dependence of the Band Gap in Black Phosphorus. Nano Lett. 2016, 16, 5095. (28) Bernardi, M.; Vigil-Fowler, D.; Lischner, J.; Neaton, J. B.; Louie, S. G. Ab initio study of hot carriers in the rst picosecond after sunlight absorption in silicon. Phys. Rev. Lett. 2014, 112, 257402.

(29) Schultes, F. J.; Christian, T.; Jones-Albertus, R.; Pickett, E.; Alberi, K.; Fluegel, B.; Liu, T.; Misra, P.; Sukiasyan, A.; Yuen, H.; Haegel, N. M. Visualizing optical phase anisotropy in black phosphorus. Appl. Rev. Lett. 2013, 103, 242106. (30) Shklovskii, B.; Efros, A. L. Electronic Properties of Doped Semiconductors. Springer, Heidelberg 1984,

18


Page 18 of 18

Band Gap Renormalization, Carrier Multiplication, and Stark

Recommend Documents