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OPTICS LETTERS / Vol. 40, No. 1 / January 1, 2015
Ultrafast carrier dynamics and coherent acoustic phonons in bulk CdSe Wenzhi Wu1,2 and Yaguo Wang1,* 1
Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA 2 School of Electronic Engineering, Heilongjiang University, Harbin 150080, China *Corresponding author: [email protected] Received October 16, 2014; revised November 17, 2014; accepted November 18, 2014; posted November 20, 2014 (Doc. ID 224835); published December 19, 2014
The femtosecond pump-probe technique is used to study the dynamics of photoexcited carriers and coherent acoustic phonons in bulk CdSe semiconductor. A turning point from fast to slow decay is observed, whose amplitude decreases with pump fluences and eventually flips the sign of differential reflectivity. The maximum change of differential reflectivity shows a saturation at high pump fluences, which is attributed to the optical energy gap dependent on carrier density. Long-lasting coherent oscillations of acoustic phonons have also been detected, and their amplitude and lifetime have a strong dependence on pump fluences. Our results can facilitate the understanding of ultrafast carrier and phonon dynamics in CdSe nanocrystals. © 2014 Optical Society of America OCIS codes: (160.6000) Semiconductor materials; (260.7120) Ultrafast phenomena; (300.6240) Spectroscopy, coherent transient; (320.7100) Ultrafast measurements. http://dx.doi.org/10.1364/OL.40.000064
The interaction of femtosecond laser pulses with solid state matters has generated many interesting ultrafast phenomena expanding from femtosecond to picosecond time scales, such as inter/intra-band carrier excitation/ relaxation, electron-phonon coupling, coherent phonon generation/dephasing, and ballistic carrier/heat diffusion. Careful studies of these phenomena will elucidate the fundamental physics of electron/phonon dynamics in the materials, which are not accessible with traditional transport measurements. Femtosecond pump-probe spectroscopy is a powerful technique that has been utilized to investigate ultrafast carrier/phonon dynamics in semiconductors [1], semi-metals [2], and metal thin films [3]. CdSe, especially nanocrystalline CdSe, is a semiconducting material with important technological applications. Interesting ultrafast phenomena have been observed in CdSe nanocrystals (NCs), including blinking [4], multiexciton generation [5], and phonon bottle effect [6]. Coherent acoustic phonons (CAPs) have also been extensively studied [7,8]. The most distinct feature of NCs is the discretized electronic band structure, opposed to the continuum in bulk, which is believed to slow down the electronic relaxation due to phonon emission. However, almost all the studies about the ultrafast dynamics in CdSe NCs focused only on the influence of particle sizes of several microns to several nanometers, without any information about the differences of observed phenomena in bulk and in NCs. The few studies of ultrafast dynamics in bulk CdSe have emphases different from interests of nowadays, and the results cannot be directly compared with that in NCs [9–11]. In this work, we investigated the carrier and phonon dynamics in bulk CdSe, with two-color femtosecond pump-probe experiments. The results can be compared with those in NCs and facilitate the understanding of carrier/phonon dynamics in CdSe NCs. All the experiments were performed in standard collinear two-color pump–probe (3.10 and 1.55 eV) scheme. Laser pulses with 35-fs FWHM are generated by a mode-locked Ti:sapphire regenerative amplifier (Spectra Physics, Spit fire ACE) with the center wavelength at 0146-9592/15/010064-04$15.00/0
1.55 eV, repetition rate of 5 kHz, and maximum pulse energy about 1.2 mJ. A second harmonic generation crystal is used to double the photon energy to 3.10 eV, after which a band-pass filter is used to block the residual laser beam at 1.55 eV. The pump and probe beams are focused onto the sample at normal incidence with diameters of 80 and 20 μm, respectively. The pump beam is modulated by an optical chopper at 500 Hz, which works with a lock-in amplifier to obtain the signal. The sample under investigation is bulk CdSe (5 × 5 × 2 mm) polycrystal with wurtzite structure, and the cleaved surface is perpendicular to the laser incident direction. At room temperature the band gap of CdSe is 1.74 eV [12]. In the two-color scheme, photon energy of pump pulse is 3.10 eV, well above the band gap and is able to excite free electrons and holes at the surface of bulk CdSe crystal. The probe energy is fixed at 0.2 pJ/pulse for all our measurements. In the two-color pump-probe experiments, the pump pulse firstly excites electrons from valence band to the bottom of conduction band, since the next smallest vertical transition in bulk CdSe is 7.6 eV [13]. Then electrons thermalize quickly to the Fermi-Dirac distribution through electron-electron scattering. Because the temperature of excited electrons is much higher than of the cold lattice, electrons then transfer energy to phonons through electron-phonon coupling. Coherent phonons can also be generated due to the thermal and electronic stress created by pump pulse. The observed reflectivity change −ΔR∕R consists of the effects from all the processes mentioned above, and can be expressed with a convolution of a response function Rtotal with the crosscorrelation function Gcross-correlation : −ΔR∕R Rtotal ⊗ Gcross-correlation ;
(1)
where Gcross-correlation is a Gaussian function and usually determined with measurements. Rtotal can be expressed as the summation over three parts: electron Re , lattice RL , and coherent acoustic phonon RCAP : © 2015 Optical Society of America
January 1, 2015 / Vol. 40, No. 1 / OPTICS LETTERS
Ae;i e−t∕τe;i
i
AL 1 − e−t∕τL Aph e−t∕τph cosΩ βtt φ. (2) The electron contribution can be described with a set of decaying exponential functions, representing different electron relaxation mechanisms, vary in specific samples and under different pump-probe conditions. Ae;i and τe;i represent the amplitude and life time of the ith component in electron relaxation processes. RL takes account of the reflectivity change due to the increase of lattice temperature. AL and Aph denote the amplitudes of lattice response and coherent oscillations, Ω stands for the CAP oscillation frequency, β is the chirping coefficient, and φ is the initial phase. The finite time expansion of pump and probe pulses are taken into account via the convolution in Eq. (1). Figure 1(a) shows the −ΔR∕R at three pump fluences. The sharp increase of −ΔR∕R around zero time delay comes from the free-carrier absorption of probe photons, because two-photon absorption of bulk CdSe at 800 nm is negligible [14]. At 0.15 mJ∕cm2 , no coherent oscillations occur and the decay is slow. At higher fluences, coherent oscillations start to appear and become stronger. A fast decay component after electron excitation adds upon the slow decay, with a turning point around 5 ps. As seen in Fig. 1(b), the normalized −ΔR∕R can be fitted very well with Eqs. (1) and (2) across a broad range of pump fluences, using the lattice response RL and two exponential functions for the electron term Re , representing the fast and slow carrier relaxations, respectively. The response of CAP is not included in the fitting and will be discussed separately later. The fast electronic decay could be attributed to the momentum relaxation and thermalization among excited carriers, which takes shorter time at higher fluences because of stronger carrier-carrier scattering with increasing carrier density. The slow electronic decay could be associated with the carrier-phonon coupling and electron-hole recombination. Lattice responses dominate at much longer time delays, expanding from about 500 ps to nanoseconds, which is common for semiconductors. One striking feature observed in Fig. 1(b) is the evolution of the turning point with pump fluence. The amplitude of the turning point (−ΔR∕R) continuously decreases with pump fluence, resulting in a change of sign at high pump fluences. The turning point for all the pump fluences happen around 5 ps, comparable to the time of carrier-phonon scattering, at which most energy of
excited carriers has been transferred to the lattice. The evolution and change of sign of the turning point might be related to the increase of lattice temperature. At room temperature, E g of bulk CdSe is 1.74 eV, smaller than the pump photon energy but larger than the probe photon energy. Only the pump photons can excite electrons from valence band to the conduction band, and the probe photon can only be absorbed by free carriers, causing the positive value of −ΔR∕R. However, the band gap near sample surface can become narrower due to the transient increase of local lattice temperature at high pump fluences [15]. When E g becomes smaller than 1.55 eV, the sign of −ΔR∕R can flip because of the stimulated emission of photons with the same frequency as the probe. This effect is transient and disappears when heat is conducted out of the excited area. The turning point around 5 ps has also been observed in CdSe NCs when the probe energy is below the bandgap [8]. When probing with photon energy above band gap, the turning points shift to earlier delay times. However, the reason of this shift is not known. The peak intensities of −ΔR∕R at different pump fluences are plotted in Fig. 2 as black dots. −ΔR∕Rmax increases linearly with pump fluence until about 1.17 mJ∕cm2 , after which the increase rate becomes slower and eventually saturates at high fluences. The peak intensities are usually associated with the maximum electron temperature, T e;max . Because the thermalization of photoexcited electrons occurs much faster than electron-phonon coupling, the hot electrons can be described by a separate temperature much higher than that of phonon. The T e;max in CdSe can be estimated as follows. The energy density absorbed by electrons is RT αF∕δs T 0e;max cv dt , where α is the absorptivity (0.6 at 3.10 eV), δs is the penetration depth of pump (about 50 nm) beam, T 0 is the initial electron temperature (room temperature in our case). The specific heat capacity of the excited electrons cν is calculated by cν απ 2 k2B T e ne ∕2εF , where kB is the Boltzmann constant, T e is the electron temperature, and εF is the Fermi energy. The hot electron density ne is estimated as, ne α∕δs FS∕νE g , where F is the pump fluence, and S is pump spot size S πd∕22 . d 80 μm is the diameter of pump beam. ν represents the repetition rate of laser system, 5 kHz in our case. Here avalanche excitation of electrons is assumed since the photon energy (3.10 eV) is much larger than the band gap. The obtained 18
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Fig. 1. (a) Differential reflectivity −ΔR∕R signal of bulk CdSe obtained using a two-color pump-probe setup at low pump fluences. (b) Four transient reflectivity −ΔR∕R signals of bulk CdSe obtained at different pump fluences.
0.00 0.00
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Fig. 2. Peaks of −ΔR∕R at different pump fluences (black dot) and the estimated maximum electron temperatures (blue triangle).
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OPTICS LETTERS / Vol. 40, No. 1 / January 1, 2015
ACAP(a.u.)
electron density is then used to evaluate the renormalized Fermi energy due to the excited electrons, εF ℏ2 3π 2 ne 2∕3 ∕2 m, where m is the mass of electrons and ħ is the reduced Planck constant. Therefore, ΔT e;max T e;max − T 0 can be estimated as: ΔT e;max 4εF αF∕π 2 ne δs 1∕2 ∕kB . The estimated ΔT e;max against pump fluences is plotted in Fig. 2 as blue triangles. It can be seen that even though the trend of ΔT e;max agrees relatively well with that of −ΔR∕Rmax at low fluences, it increases as a power function at higher pump fluences, and no saturation appears. This discrepancy is worthy of further discussion. Because the polycrystalline CdSe sample we use is very thick (>10 cm), and the absorption depth at 400 nm pump is only about 50 nm, the sample is opaque for pump pulse, and the observed trend can also be understood from the aspect of absorption of pump photons. Since the lighthole and heavy-hole levels of the valence band degenerate at the Γ point in CdSe, the electrons from both the light-hole and heavy-hole levels can be excited to conduction band. Optical absorption involves transition from the highest filled level in valence band to the lowest unfilled level in conduction band. The optical band gap E OG is given by the difference between these two levels, rather than simply by E g , the minimum separation between the valence and conduction bands [16]. E OG can be approximated to Eg at low pump fluences and small carrier concentrations, but will increase rapidly at higher pump fluences. Saturation of absorption may happen when E OG is larger than the photon energy. This picture qualitatively agrees with our experimental observation. When estimating ΔT e;max , a static optical band gap, E g is assumed, which can cause the discrepancy of its trend with −ΔR∕Rmax at high pump fluences. The saturation of peak intensity has also been observed in CdTe NCs in a time-resolved second-harmonic generation experiment when the pump pulse energy at 400 nm is above 20 μJ [8]. The signal of CAP can be separated from the electronic and thermal background with a digital FFT filter. The CAP oscillations can be fitted with a damping harmonic oscillator described as RCAP in Eq. (2). Both the extracted CAP signal and its fitting are plotted in Fig. 3(a) at pump fluence of 17.49 mJ∕cm2 . The fitted frequency of CAP oscillation is about 23.6 GHz. The CAPs observed in CdSe are very different from those detected in semi-metal thin films [17]. There are two mechanisms to generate CAPs with ultrafast laser pulses. When the ultrafast pump pulses are absorbed at sample surface, the absorbed 2
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Fig. 3. (a) Extracted CAP of bulk CdSe and its fitting with RCAP at the pump fluence of 17.49 mJ∕cm2 . (b) The Fast Fourier Transform (FFT) of CAP oscillation of bulk CdSe at different pump fluences.
photon energy induces rises in the electron and phonon temperatures within a thin layer beneath the surface. A strain wave due to electronic and thermal stresses is generated and propagates into the sample. This strain wave can modify the local dielectric constants and create a discontinuity in reflectance or transmittance. If the probe photon energy is larger than the band-gap of measured material, it will only probe a thin layer beneath the surface. Acoustic echoes can be observed when the strain waves are reflected at some interfaces and travel back to surface region, which is the case for the observed acoustic phonons in thin films [18]. In bulk materials, where the samples are usually very thick, the reflected strain wave cannot be observed, either because of strong scattering after long travel, or because the time required to observe them is longer than what pump-probe experiment can provide. In our two-color experiments, the probe photon energy (1.55 eV) is well below the band gap of CdSe, and it can penetrate deeply into the sample (absorption depth for polycrystalline CdSe at 1.55 eV is larger than 200 μm [19]. When the probe pulse is incident onto the sample, part of the light is reflected by the top surface. When the transmitted light reaches the CAP wave propagating inside the sample, part of the light will be reflected due to the discontinuity in the dielectric constants. When the reflected light travels back to the surface and gets transmitted into the air, it will interfere with the light initially reflected at the surface, then oscillations will be observed in the reflectivity change. As the CAP wave travels, the top sample surface and the strain wave act as an interferometer. The reflected light will interfere constructively or destructively depending on the position of electronic and thermal stress, leading to the oscillation shown in Fig. 3(a). The frequency of this oscillation is related to the material properties and probe pulse wavelength, expressed as [20]: Ω 2π2n∕λpr υs 2nυs kpr ;
(3)
where n is the refractive index, which is 2.5 in bulk CdSe, λpr is the wavelength of the probe light, and υs is the longitudinal sound velocity. kpr is the probe-light wave number. The period of the CAP oscillation in Fig. 3(a) is 42.3 ps. With Eq. (3), the sound velocity for CdSe, υs , is estimated as 3783 m/s. This value is in good agreement with the longitudinal speed of sound in CdSe [21]. The FFTs of CAPs at various pump fluences are plotted in Fig. 3(b). It can be seen that CAPs in bulk CdSe have peak frequencies around 23.6 GHz at all pump fluences, unlike the coherent optical phonons (COP), which have a strong dependence on pump fluences (phonon softening effect) [22]. COPs in opaque materials are generated via displacive excitation of coherent phonons (DECP [2]). COPs are usually standing waves due to the small group velocity, hence the COP oscillations are strongly influenced by the concentration of photoexcited carriers near the surface, which has a strong dependence on pump fluences. Even though the CAPs are generated by the transient electronic/thermal stresses near the surface, they propagate out of the region of excited carriers very quickly. The absorption depth at 3.10 eV in CdSe is only about 50 nm, and it only takes 13 ps for the CAP to travel through this thickness, much shorter than a single
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January 1, 2015 / Vol. 40, No. 1 / OPTICS LETTERS
1.8 5
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20 2
Pump Fluence (mJ/cm )
Fig. 4. CAP properties at different pump fluences: (a) amplitude Aph , (b) decay time τph , and (c) chirp coefficient β.
oscillation period. As a result, the effect of pump fluences on CAP frequencies is negligible. The amplitude of CAPs increases linearly at low pump fluences and saturates at high pump fluences, as seen in Fig. 4(a). This trend is similar to that of −ΔR∕Rmax shown in Fig. 2. The transient stress that generates CAPs includes contributions from both electrons and phonons. After the electrons absorb photons, they become much “hotter” than the cold lattice. In semiconductors, hot electrons decay to the bottom of band valleys and emit phonons. If only single-photon absorption happens, each hot electron will emit a phonon with energy E − E g . The contributions of electrons and phonons to the stress can be written as [23]: σ zz σ ezz σ ph zz −BdE g ∕dPne −3Bα∕CE−E g ne ; (4) where B is bulk modulus, α is the linear thermal expansion coefficient, and C is the specific heat. Even though the CAPs can propagate out of the region of photoexcited carriers quickly, Eq. (4) shows that their initial amplitudes are closely associated with the carrier density, hence increases linearly at low pump fluences. The saturation at high fluencies may be a result of two competing effects: the increasing optical band gap E OG at high carrier densities, and the decreasing band gap E g at elevated lattice temperatures. Similar phenomenon have been reported in CdSe NCs, and the reason was attributed to the saturation of lattice displacement [8]. The lifetime of the oscillations shown in Fig. 3(a) is determined by both the propagating CAP and the probe beam, which can be estimated as [24]: 1 1 1 ; τ τph ξpr ∕υs
(5)
where ξpr is the absorption depth of probe beam. Since the photon energy of probe is well below the band gap of CdSe and δpr is extremely long, it is reasonable to assume τ ∼ τph . (ξpr∕ νs ≫ 50 ns). The lifetimes of CAPs, plotted in Fig. 4(b), only decrease slightly with pump fluences, because the photoexcited carriers can only scatter the CAPs for a very short period of time. As shown in Fig. 4(c), comparing with coherent optical phonons [2], chirping coefficients of CAPs are two orders smaller at all the pump fluences. Small chirping coefficient means the deformation of coherent phonons is negligible as they propagate into the sample, which is reasonable because the polycrystalline CdSe sample is isotropic in all directions. In summary, dynamics of photoexcited carriers and coherent acoustic phonons in polycrystalline CdSe are investigated by use of two-color pump-probe technique
67
based on femtosecond laser at 5 kHz repetition rate. A turning point from fast to slow decay is observed, whose amplitude decreases with pump fluences and eventually flips the sign of differential reflectivity. The maximum change of differential reflectivity shows a saturation at high pump fluences, which is attributed to the optical energy gap dependent on carrier density. Long-lasting coherent oscillations of acoustic phonons have also been detected, and their amplitude and lifetime have a strong dependence on pump fluences. Our results can facilitate the understanding of ultrafast carrier and phonon dynamics in CdSe NCs. The authors are grateful for the support from National Science Foundation (Grant No. CBET-1351881). Wu also acknowledges the support from National Science Foundation of China (Nos. 61204007, 61275117, 51372072), Heilongjiang Province (No. QC2011C008), Chinese Postdoctoral Foundation (Nos. LBH-Z10047, 2011049123, and 2013T60394), and Creative Team Project of Heilongjiang Province (2012TD007). References 1. P. E. Hopkins, E. V. Barnat, J. L. Cruz-Campa, R. K. Grubbs, M. Okandan, and G. N. Nielson, J. Appl. Phys. 107, 053713 (2010). 2. A. Q. Wu and X. Xu, Appl. Phys. Lett. 90, 251111 (2007). 3. L. Guo, S. L. Hodson, T. S. Fisher, and X. F. Xu, J. Heat Trans. 134, 042402 (2012). 4. O. Chen, J. Zhao, V. P. Chauhan, J. Cui, C. Wong, and M. G. Bawendi, Nat. Mater. 12, 445 (2013). 5. A. Franceschetti and Y. Zhang, Phys. Rev. Lett. 100, 136805 (2008). 6. S. V. Kilina, D. S. Kilin, and O. V. Prezhdo, ACS Nano 3, 93 (2009). 7. D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, Phys. Rev. B 77, 235321 (2008). 8. D. H. Son, J. S. Wittenberg, U. Banin, and A. P. Alivisatos, J. Phys. Chem. B 110, 19884 (2006). 9. G. R. Olbright, N. Peyghambarian, S. W. Koch, and L. Banyai, Opt. Lett. 12, 413 (1987). 10. S. S. Prabhu, A. S. Vengurlekar, and J. Shah, Phys. Rev. B 53, R10465 (1996). 11. G. M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, IEEE J. Quantum Electron. 34, 1374 (1998). 12. T. Trindade and P. Brien, Chem. Mater. 9, 523 (1997). 13. S. Reyes and J. Carlos, Universitas Scientiarum 13, 198 (2008). 14. G. L. Dakovski and S. Jie, J. Appl. Phys. 114, 014301 (2013). 15. G. Perna, V. Capozzi, and M. Ambrico, J. Appl. Phys. 83, 3337 (1998). 16. B. Elias, Phys. Rev. 93, 632 (1954). 17. Y. Wang, X. Xu, and R. Venkatasubramanian, Appl. Phys. Lett. 93, 113114 (2008). 18. H. T. Grahn, J. M. Humphrey, and T. Jan, IEEE J. Quantum Electron. 25, 2562 (1989). 19. T. K. Gupta and J. Doh, J. Mater. Res. 7, 1243 (1992). 20. S. Wu, P. Geiser, and J. Jun, Appl. Phys. Lett. 88, 041917 (2006). 21. http://cofrest.info/md20.htm 22. A. V. Bragas, C. Aku-Leh, and R. Merlin, Phys. Rev. B 73, 125305 (2006). 23. C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986). 24. D. Wang, A. Cross, G. Guarino, S. Wu, R. Sobolewski, and A. Mycielski, Appl. Phys. Lett. 90, 211905 (2007).
OPTICS LETTERS / Vol. 40, No. 1 / January 1, 2015
Ultrafast carrier dynamics and coherent acoustic phonons in bulk CdSe Wenzhi Wu1,2 and Yaguo Wang1,* 1
Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA 2 School of Electronic Engineering, Heilongjiang University, Harbin 150080, China *Corresponding author: [email protected] Received October 16, 2014; revised November 17, 2014; accepted November 18, 2014; posted November 20, 2014 (Doc. ID 224835); published December 19, 2014
The femtosecond pump-probe technique is used to study the dynamics of photoexcited carriers and coherent acoustic phonons in bulk CdSe semiconductor. A turning point from fast to slow decay is observed, whose amplitude decreases with pump fluences and eventually flips the sign of differential reflectivity. The maximum change of differential reflectivity shows a saturation at high pump fluences, which is attributed to the optical energy gap dependent on carrier density. Long-lasting coherent oscillations of acoustic phonons have also been detected, and their amplitude and lifetime have a strong dependence on pump fluences. Our results can facilitate the understanding of ultrafast carrier and phonon dynamics in CdSe nanocrystals. © 2014 Optical Society of America OCIS codes: (160.6000) Semiconductor materials; (260.7120) Ultrafast phenomena; (300.6240) Spectroscopy, coherent transient; (320.7100) Ultrafast measurements. http://dx.doi.org/10.1364/OL.40.000064
The interaction of femtosecond laser pulses with solid state matters has generated many interesting ultrafast phenomena expanding from femtosecond to picosecond time scales, such as inter/intra-band carrier excitation/ relaxation, electron-phonon coupling, coherent phonon generation/dephasing, and ballistic carrier/heat diffusion. Careful studies of these phenomena will elucidate the fundamental physics of electron/phonon dynamics in the materials, which are not accessible with traditional transport measurements. Femtosecond pump-probe spectroscopy is a powerful technique that has been utilized to investigate ultrafast carrier/phonon dynamics in semiconductors [1], semi-metals [2], and metal thin films [3]. CdSe, especially nanocrystalline CdSe, is a semiconducting material with important technological applications. Interesting ultrafast phenomena have been observed in CdSe nanocrystals (NCs), including blinking [4], multiexciton generation [5], and phonon bottle effect [6]. Coherent acoustic phonons (CAPs) have also been extensively studied [7,8]. The most distinct feature of NCs is the discretized electronic band structure, opposed to the continuum in bulk, which is believed to slow down the electronic relaxation due to phonon emission. However, almost all the studies about the ultrafast dynamics in CdSe NCs focused only on the influence of particle sizes of several microns to several nanometers, without any information about the differences of observed phenomena in bulk and in NCs. The few studies of ultrafast dynamics in bulk CdSe have emphases different from interests of nowadays, and the results cannot be directly compared with that in NCs [9–11]. In this work, we investigated the carrier and phonon dynamics in bulk CdSe, with two-color femtosecond pump-probe experiments. The results can be compared with those in NCs and facilitate the understanding of carrier/phonon dynamics in CdSe NCs. All the experiments were performed in standard collinear two-color pump–probe (3.10 and 1.55 eV) scheme. Laser pulses with 35-fs FWHM are generated by a mode-locked Ti:sapphire regenerative amplifier (Spectra Physics, Spit fire ACE) with the center wavelength at 0146-9592/15/010064-04$15.00/0
1.55 eV, repetition rate of 5 kHz, and maximum pulse energy about 1.2 mJ. A second harmonic generation crystal is used to double the photon energy to 3.10 eV, after which a band-pass filter is used to block the residual laser beam at 1.55 eV. The pump and probe beams are focused onto the sample at normal incidence with diameters of 80 and 20 μm, respectively. The pump beam is modulated by an optical chopper at 500 Hz, which works with a lock-in amplifier to obtain the signal. The sample under investigation is bulk CdSe (5 × 5 × 2 mm) polycrystal with wurtzite structure, and the cleaved surface is perpendicular to the laser incident direction. At room temperature the band gap of CdSe is 1.74 eV [12]. In the two-color scheme, photon energy of pump pulse is 3.10 eV, well above the band gap and is able to excite free electrons and holes at the surface of bulk CdSe crystal. The probe energy is fixed at 0.2 pJ/pulse for all our measurements. In the two-color pump-probe experiments, the pump pulse firstly excites electrons from valence band to the bottom of conduction band, since the next smallest vertical transition in bulk CdSe is 7.6 eV [13]. Then electrons thermalize quickly to the Fermi-Dirac distribution through electron-electron scattering. Because the temperature of excited electrons is much higher than of the cold lattice, electrons then transfer energy to phonons through electron-phonon coupling. Coherent phonons can also be generated due to the thermal and electronic stress created by pump pulse. The observed reflectivity change −ΔR∕R consists of the effects from all the processes mentioned above, and can be expressed with a convolution of a response function Rtotal with the crosscorrelation function Gcross-correlation : −ΔR∕R Rtotal ⊗ Gcross-correlation ;
(1)
where Gcross-correlation is a Gaussian function and usually determined with measurements. Rtotal can be expressed as the summation over three parts: electron Re , lattice RL , and coherent acoustic phonon RCAP : © 2015 Optical Society of America
January 1, 2015 / Vol. 40, No. 1 / OPTICS LETTERS
Ae;i e−t∕τe;i
i
AL 1 − e−t∕τL Aph e−t∕τph cosΩ βtt φ. (2) The electron contribution can be described with a set of decaying exponential functions, representing different electron relaxation mechanisms, vary in specific samples and under different pump-probe conditions. Ae;i and τe;i represent the amplitude and life time of the ith component in electron relaxation processes. RL takes account of the reflectivity change due to the increase of lattice temperature. AL and Aph denote the amplitudes of lattice response and coherent oscillations, Ω stands for the CAP oscillation frequency, β is the chirping coefficient, and φ is the initial phase. The finite time expansion of pump and probe pulses are taken into account via the convolution in Eq. (1). Figure 1(a) shows the −ΔR∕R at three pump fluences. The sharp increase of −ΔR∕R around zero time delay comes from the free-carrier absorption of probe photons, because two-photon absorption of bulk CdSe at 800 nm is negligible [14]. At 0.15 mJ∕cm2 , no coherent oscillations occur and the decay is slow. At higher fluences, coherent oscillations start to appear and become stronger. A fast decay component after electron excitation adds upon the slow decay, with a turning point around 5 ps. As seen in Fig. 1(b), the normalized −ΔR∕R can be fitted very well with Eqs. (1) and (2) across a broad range of pump fluences, using the lattice response RL and two exponential functions for the electron term Re , representing the fast and slow carrier relaxations, respectively. The response of CAP is not included in the fitting and will be discussed separately later. The fast electronic decay could be attributed to the momentum relaxation and thermalization among excited carriers, which takes shorter time at higher fluences because of stronger carrier-carrier scattering with increasing carrier density. The slow electronic decay could be associated with the carrier-phonon coupling and electron-hole recombination. Lattice responses dominate at much longer time delays, expanding from about 500 ps to nanoseconds, which is common for semiconductors. One striking feature observed in Fig. 1(b) is the evolution of the turning point with pump fluence. The amplitude of the turning point (−ΔR∕R) continuously decreases with pump fluence, resulting in a change of sign at high pump fluences. The turning point for all the pump fluences happen around 5 ps, comparable to the time of carrier-phonon scattering, at which most energy of
excited carriers has been transferred to the lattice. The evolution and change of sign of the turning point might be related to the increase of lattice temperature. At room temperature, E g of bulk CdSe is 1.74 eV, smaller than the pump photon energy but larger than the probe photon energy. Only the pump photons can excite electrons from valence band to the conduction band, and the probe photon can only be absorbed by free carriers, causing the positive value of −ΔR∕R. However, the band gap near sample surface can become narrower due to the transient increase of local lattice temperature at high pump fluences [15]. When E g becomes smaller than 1.55 eV, the sign of −ΔR∕R can flip because of the stimulated emission of photons with the same frequency as the probe. This effect is transient and disappears when heat is conducted out of the excited area. The turning point around 5 ps has also been observed in CdSe NCs when the probe energy is below the bandgap [8]. When probing with photon energy above band gap, the turning points shift to earlier delay times. However, the reason of this shift is not known. The peak intensities of −ΔR∕R at different pump fluences are plotted in Fig. 2 as black dots. −ΔR∕Rmax increases linearly with pump fluence until about 1.17 mJ∕cm2 , after which the increase rate becomes slower and eventually saturates at high fluences. The peak intensities are usually associated with the maximum electron temperature, T e;max . Because the thermalization of photoexcited electrons occurs much faster than electron-phonon coupling, the hot electrons can be described by a separate temperature much higher than that of phonon. The T e;max in CdSe can be estimated as follows. The energy density absorbed by electrons is RT αF∕δs T 0e;max cv dt , where α is the absorptivity (0.6 at 3.10 eV), δs is the penetration depth of pump (about 50 nm) beam, T 0 is the initial electron temperature (room temperature in our case). The specific heat capacity of the excited electrons cν is calculated by cν απ 2 k2B T e ne ∕2εF , where kB is the Boltzmann constant, T e is the electron temperature, and εF is the Fermi energy. The hot electron density ne is estimated as, ne α∕δs FS∕νE g , where F is the pump fluence, and S is pump spot size S πd∕22 . d 80 μm is the diameter of pump beam. ν represents the repetition rate of laser system, 5 kHz in our case. Here avalanche excitation of electrons is assumed since the photon energy (3.10 eV) is much larger than the band gap. The obtained 18
0.0 0.10 0.0
0.020
-ΔR/R
0.020
-ΔR/R
0.015
0.010 0.005
0.010
0.000 0
0.005
7
14
21
28
Delay time (ps) 0
200
400
Delay Time (ps)
600
0.0 1.0 0.5
0.0 1.2
0.0
0.8
1.0
0
2
14.71 mJ/cm
τe1=1.4 ps, τe2=18.5ps, τL=1408.9ps
0.53 mJ/cm
τe1=5.1 ps, τe2=18.1 ps, τL=537.2 ps
0.05 mJ/cm
100
200
12 10
0.08 τe1=1.1 ps, τe2=21.8 ps, τL=1308.9ps
0.6
0.6
0.000
0.6
2
-0.8
2
0.15mJ/cm 2 0.53mJ/cm 2 0.88mJ/cm
0.015
3
ne (X10 /cm )
0.4
19.29 mJ/cm
2
300
Delay time (ps)
(-ΔR/R)max
0.025
τe1=0.3 ps, τe2=25.2 ps, τL=1718.8ps
(b) 0.8
0.025
-ΔR/R (Normalized)
(a)
0.2
8 0.06 6 (-ΔR/R)max
0.04
ΔΤe,max
4
2
400
0.02
3
X
ΔΤe,max(X10 K)
Rtotal Re RL RCAP
65
2
500
Fig. 1. (a) Differential reflectivity −ΔR∕R signal of bulk CdSe obtained using a two-color pump-probe setup at low pump fluences. (b) Four transient reflectivity −ΔR∕R signals of bulk CdSe obtained at different pump fluences.
0.00 0.00
3.46
6.92
10.38
13.84
2
17.30
0
Pump fluence F( mJ/cm )
Fig. 2. Peaks of −ΔR∕R at different pump fluences (black dot) and the estimated maximum electron temperatures (blue triangle).
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OPTICS LETTERS / Vol. 40, No. 1 / January 1, 2015
ACAP(a.u.)
electron density is then used to evaluate the renormalized Fermi energy due to the excited electrons, εF ℏ2 3π 2 ne 2∕3 ∕2 m, where m is the mass of electrons and ħ is the reduced Planck constant. Therefore, ΔT e;max T e;max − T 0 can be estimated as: ΔT e;max 4εF αF∕π 2 ne δs 1∕2 ∕kB . The estimated ΔT e;max against pump fluences is plotted in Fig. 2 as blue triangles. It can be seen that even though the trend of ΔT e;max agrees relatively well with that of −ΔR∕Rmax at low fluences, it increases as a power function at higher pump fluences, and no saturation appears. This discrepancy is worthy of further discussion. Because the polycrystalline CdSe sample we use is very thick (>10 cm), and the absorption depth at 400 nm pump is only about 50 nm, the sample is opaque for pump pulse, and the observed trend can also be understood from the aspect of absorption of pump photons. Since the lighthole and heavy-hole levels of the valence band degenerate at the Γ point in CdSe, the electrons from both the light-hole and heavy-hole levels can be excited to conduction band. Optical absorption involves transition from the highest filled level in valence band to the lowest unfilled level in conduction band. The optical band gap E OG is given by the difference between these two levels, rather than simply by E g , the minimum separation between the valence and conduction bands [16]. E OG can be approximated to Eg at low pump fluences and small carrier concentrations, but will increase rapidly at higher pump fluences. Saturation of absorption may happen when E OG is larger than the photon energy. This picture qualitatively agrees with our experimental observation. When estimating ΔT e;max , a static optical band gap, E g is assumed, which can cause the discrepancy of its trend with −ΔR∕Rmax at high pump fluences. The saturation of peak intensity has also been observed in CdTe NCs in a time-resolved second-harmonic generation experiment when the pump pulse energy at 400 nm is above 20 μJ [8]. The signal of CAP can be separated from the electronic and thermal background with a digital FFT filter. The CAP oscillations can be fitted with a damping harmonic oscillator described as RCAP in Eq. (2). Both the extracted CAP signal and its fitting are plotted in Fig. 3(a) at pump fluence of 17.49 mJ∕cm2 . The fitted frequency of CAP oscillation is about 23.6 GHz. The CAPs observed in CdSe are very different from those detected in semi-metal thin films [17]. There are two mechanisms to generate CAPs with ultrafast laser pulses. When the ultrafast pump pulses are absorbed at sample surface, the absorbed 2
1.2
17.49mJ/cm
(a)
0.6 0.0
-0.6 -1.2
FFT intensity (a.u.)
200
400
600
800
Delay time (ps)
Pump Fluence: 19.29 mJ/cm^2 14.71 mJ/cm^2 1.0 6.55 mJ/cm^2 3.79 mJ/cm^2 0.5 1.98 mJ/cm^2 1.5
1000
(b)
0.0
14
21
28
Frequency (GHz)
35
Fig. 3. (a) Extracted CAP of bulk CdSe and its fitting with RCAP at the pump fluence of 17.49 mJ∕cm2 . (b) The Fast Fourier Transform (FFT) of CAP oscillation of bulk CdSe at different pump fluences.
photon energy induces rises in the electron and phonon temperatures within a thin layer beneath the surface. A strain wave due to electronic and thermal stresses is generated and propagates into the sample. This strain wave can modify the local dielectric constants and create a discontinuity in reflectance or transmittance. If the probe photon energy is larger than the band-gap of measured material, it will only probe a thin layer beneath the surface. Acoustic echoes can be observed when the strain waves are reflected at some interfaces and travel back to surface region, which is the case for the observed acoustic phonons in thin films [18]. In bulk materials, where the samples are usually very thick, the reflected strain wave cannot be observed, either because of strong scattering after long travel, or because the time required to observe them is longer than what pump-probe experiment can provide. In our two-color experiments, the probe photon energy (1.55 eV) is well below the band gap of CdSe, and it can penetrate deeply into the sample (absorption depth for polycrystalline CdSe at 1.55 eV is larger than 200 μm [19]. When the probe pulse is incident onto the sample, part of the light is reflected by the top surface. When the transmitted light reaches the CAP wave propagating inside the sample, part of the light will be reflected due to the discontinuity in the dielectric constants. When the reflected light travels back to the surface and gets transmitted into the air, it will interfere with the light initially reflected at the surface, then oscillations will be observed in the reflectivity change. As the CAP wave travels, the top sample surface and the strain wave act as an interferometer. The reflected light will interfere constructively or destructively depending on the position of electronic and thermal stress, leading to the oscillation shown in Fig. 3(a). The frequency of this oscillation is related to the material properties and probe pulse wavelength, expressed as [20]: Ω 2π2n∕λpr υs 2nυs kpr ;
(3)
where n is the refractive index, which is 2.5 in bulk CdSe, λpr is the wavelength of the probe light, and υs is the longitudinal sound velocity. kpr is the probe-light wave number. The period of the CAP oscillation in Fig. 3(a) is 42.3 ps. With Eq. (3), the sound velocity for CdSe, υs , is estimated as 3783 m/s. This value is in good agreement with the longitudinal speed of sound in CdSe [21]. The FFTs of CAPs at various pump fluences are plotted in Fig. 3(b). It can be seen that CAPs in bulk CdSe have peak frequencies around 23.6 GHz at all pump fluences, unlike the coherent optical phonons (COP), which have a strong dependence on pump fluences (phonon softening effect) [22]. COPs in opaque materials are generated via displacive excitation of coherent phonons (DECP [2]). COPs are usually standing waves due to the small group velocity, hence the COP oscillations are strongly influenced by the concentration of photoexcited carriers near the surface, which has a strong dependence on pump fluences. Even though the CAPs are generated by the transient electronic/thermal stresses near the surface, they propagate out of the region of excited carriers very quickly. The absorption depth at 3.10 eV in CdSe is only about 50 nm, and it only takes 13 ps for the CAP to travel through this thickness, much shorter than a single
2
0
2
360 320 2.0
(b)
(c)
β (x10
-3
rad/ps
(a)
1
) τph(ps)
Aph (a.u.)
January 1, 2015 / Vol. 40, No. 1 / OPTICS LETTERS
1.8 5
10
15
20 2
Pump Fluence (mJ/cm )
Fig. 4. CAP properties at different pump fluences: (a) amplitude Aph , (b) decay time τph , and (c) chirp coefficient β.
oscillation period. As a result, the effect of pump fluences on CAP frequencies is negligible. The amplitude of CAPs increases linearly at low pump fluences and saturates at high pump fluences, as seen in Fig. 4(a). This trend is similar to that of −ΔR∕Rmax shown in Fig. 2. The transient stress that generates CAPs includes contributions from both electrons and phonons. After the electrons absorb photons, they become much “hotter” than the cold lattice. In semiconductors, hot electrons decay to the bottom of band valleys and emit phonons. If only single-photon absorption happens, each hot electron will emit a phonon with energy E − E g . The contributions of electrons and phonons to the stress can be written as [23]: σ zz σ ezz σ ph zz −BdE g ∕dPne −3Bα∕CE−E g ne ; (4) where B is bulk modulus, α is the linear thermal expansion coefficient, and C is the specific heat. Even though the CAPs can propagate out of the region of photoexcited carriers quickly, Eq. (4) shows that their initial amplitudes are closely associated with the carrier density, hence increases linearly at low pump fluences. The saturation at high fluencies may be a result of two competing effects: the increasing optical band gap E OG at high carrier densities, and the decreasing band gap E g at elevated lattice temperatures. Similar phenomenon have been reported in CdSe NCs, and the reason was attributed to the saturation of lattice displacement [8]. The lifetime of the oscillations shown in Fig. 3(a) is determined by both the propagating CAP and the probe beam, which can be estimated as [24]: 1 1 1 ; τ τph ξpr ∕υs
(5)
where ξpr is the absorption depth of probe beam. Since the photon energy of probe is well below the band gap of CdSe and δpr is extremely long, it is reasonable to assume τ ∼ τph . (ξpr∕ νs ≫ 50 ns). The lifetimes of CAPs, plotted in Fig. 4(b), only decrease slightly with pump fluences, because the photoexcited carriers can only scatter the CAPs for a very short period of time. As shown in Fig. 4(c), comparing with coherent optical phonons [2], chirping coefficients of CAPs are two orders smaller at all the pump fluences. Small chirping coefficient means the deformation of coherent phonons is negligible as they propagate into the sample, which is reasonable because the polycrystalline CdSe sample is isotropic in all directions. In summary, dynamics of photoexcited carriers and coherent acoustic phonons in polycrystalline CdSe are investigated by use of two-color pump-probe technique
67
based on femtosecond laser at 5 kHz repetition rate. A turning point from fast to slow decay is observed, whose amplitude decreases with pump fluences and eventually flips the sign of differential reflectivity. The maximum change of differential reflectivity shows a saturation at high pump fluences, which is attributed to the optical energy gap dependent on carrier density. Long-lasting coherent oscillations of acoustic phonons have also been detected, and their amplitude and lifetime have a strong dependence on pump fluences. Our results can facilitate the understanding of ultrafast carrier and phonon dynamics in CdSe NCs. The authors are grateful for the support from National Science Foundation (Grant No. CBET-1351881). Wu also acknowledges the support from National Science Foundation of China (Nos. 61204007, 61275117, 51372072), Heilongjiang Province (No. QC2011C008), Chinese Postdoctoral Foundation (Nos. LBH-Z10047, 2011049123, and 2013T60394), and Creative Team Project of Heilongjiang Province (2012TD007). References 1. P. E. Hopkins, E. V. Barnat, J. L. Cruz-Campa, R. K. Grubbs, M. Okandan, and G. N. Nielson, J. Appl. Phys. 107, 053713 (2010). 2. A. Q. Wu and X. Xu, Appl. Phys. Lett. 90, 251111 (2007). 3. L. Guo, S. L. Hodson, T. S. Fisher, and X. F. Xu, J. Heat Trans. 134, 042402 (2012). 4. O. Chen, J. Zhao, V. P. Chauhan, J. Cui, C. Wong, and M. G. Bawendi, Nat. Mater. 12, 445 (2013). 5. A. Franceschetti and Y. Zhang, Phys. Rev. Lett. 100, 136805 (2008). 6. S. V. Kilina, D. S. Kilin, and O. V. Prezhdo, ACS Nano 3, 93 (2009). 7. D. M. Sagar, R. R. Cooney, S. L. Sewall, E. A. Dias, M. M. Barsan, I. S. Butler, and P. Kambhampati, Phys. Rev. B 77, 235321 (2008). 8. D. H. Son, J. S. Wittenberg, U. Banin, and A. P. Alivisatos, J. Phys. Chem. B 110, 19884 (2006). 9. G. R. Olbright, N. Peyghambarian, S. W. Koch, and L. Banyai, Opt. Lett. 12, 413 (1987). 10. S. S. Prabhu, A. S. Vengurlekar, and J. Shah, Phys. Rev. B 53, R10465 (1996). 11. G. M. Schucan, R. G. Ispasoiu, A. M. Fox, and J. F. Ryan, IEEE J. Quantum Electron. 34, 1374 (1998). 12. T. Trindade and P. Brien, Chem. Mater. 9, 523 (1997). 13. S. Reyes and J. Carlos, Universitas Scientiarum 13, 198 (2008). 14. G. L. Dakovski and S. Jie, J. Appl. Phys. 114, 014301 (2013). 15. G. Perna, V. Capozzi, and M. Ambrico, J. Appl. Phys. 83, 3337 (1998). 16. B. Elias, Phys. Rev. 93, 632 (1954). 17. Y. Wang, X. Xu, and R. Venkatasubramanian, Appl. Phys. Lett. 93, 113114 (2008). 18. H. T. Grahn, J. M. Humphrey, and T. Jan, IEEE J. Quantum Electron. 25, 2562 (1989). 19. T. K. Gupta and J. Doh, J. Mater. Res. 7, 1243 (1992). 20. S. Wu, P. Geiser, and J. Jun, Appl. Phys. Lett. 88, 041917 (2006). 21. http://cofrest.info/md20.htm 22. A. V. Bragas, C. Aku-Leh, and R. Merlin, Phys. Rev. B 73, 125305 (2006). 23. C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986). 24. D. Wang, A. Cross, G. Guarino, S. Wu, R. Sobolewski, and A. Mycielski, Appl. Phys. Lett. 90, 211905 (2007).
