1. INTRODUCTION

To understand condensed materials as demonstrated by band theory, one could imagine that electrons behave as an extended plane wave. This theory derives an energy band structure for electrons in a periodic lattice of atoms, and electrons in the material may be described as having or not having a bandgap [1,2]. In this description, electrons in the material can be considered as being in a “sea” of the averaged motion of the other quasi-particles. This approach of nearly free particles is valid in some well-understood materials, such as most metals, as the interaction strength between quasi-particles is negligible compared with their kinetic energy. However, strong correlation between the quasi-particles leads to a new type of behavior in some important materials. Such materials are difficult to describe theoretically because strong interactions between quasi-particles cause phenomena that cannot be predicted by studying the behavior of individual particles alone, and these interactions play a major role in determining the properties of such systems. The seemingly simple material NiO, as the typical example of metal–insulator transitions, would be expected to be a good conductor with a partially filled 3D band [3]. However, the strong Coulomb repulsion between electrons makes NiO an insulator. Therefore, this type of strongly correlated material cannot be understood using a free-electron-like scenario. In addition to the metal–insulator transitions just mentioned [3,4], there are numerous physical properties arising from the effects of strong correlations, e.g., high-$T_c$ superconductivity [5], colossal magnetoresistance [6], heavy fermions [7], multiferroics [8], and low-dimensional phenomena [9]. Accordingly, the crucial correlations between quasi-particles can be responsible for significant characteristics of some materials and so it is extremely important to discover the underlying interactions among quasi-particles in these materials.

Because interactions among quasi-particles are known to play an important role in understanding condensed matter, experimental techniques that can unambiguously clarify these interactions are needed. Studies have demonstrated the ability of numerous methods to indirectly estimate correlation among quasi-particles by measuring certain related physical characteristics, such as the carrier mobility [10], Shubnikov–de Haas oscillations [11], the thermoelectric power [12], the Burstein–Moss shift [13], the Raman shift [14], and Faraday rotation [15]. As an example, electron–electron interaction is usually studied by transport measurements. However, the contribution of electron–electron interaction to the resistivity can be observed only at low temperatures because the electrical resistance is primarily dominated by electron–phonon scattering above the Debye temperature. On the other hand, the electron–phonon interaction strength can be determined from the phonon linewidths obtained through Raman or neutron scattering, which are easily influenced by selection rules and inhomogeneous broadening. Moreover, the quasi-particle interactions obtained by the techniques just mentioned are derived mainly from stationary experiments.

Ultrafast spectroscopy is one of the desired techniques that enable direct observation of transient interactions among quasi-particles. With transient spectroscopy, the so-called pump–probe measurement, we can monitor energy transfer among quasi-particles and even specify the interaction strength, as shown in Fig. 1. Taking advantage of developments in the area of ultrashort pulses in recent decades [16–20], ultrafast optical spectroscopy can provide the required time resolution for studying ultrafast primary phenomena on the characteristic time scales of electron, phonon, and spin dynamics [21–33], that is, in the range of femtoseconds (${10}^{-15}\mathrm{s}$), picoseconds (${10}^{-12}\mathrm{s}$), and nanoseconds (${10}^{-9}\mathrm{s}$). Advanced progress in pulsed lasers has also extended ultrafast spectroscopy from the visible region to the mid-infrared (MIR) and ultraviolet (UV) regions using nonlinear techniques such as optical parametric amplification, sum and difference frequency generation, and four-wave mixing [34–36].

 

Fig. 1. Schematic representation of a system including electron, phonon, and spin degrees of freedom.

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2. BROADBAND TIME-RESOLVED SPECTROSCOPY

A. Development

Compared with monochromatic detection, the use of spectral broadband probes for optical measurements provides the ability to record responses at various wavelengths simultaneously and obtain much broader insight into the underlying physics. In 1964, optical broadband detection was first used by Jones and Stoicheff [37]. In that influential work, a continuum light source was generated by incident maser radiation on liquid toluene to study the induced Raman absorption of liquid benzene. The sample was irradiated simultaneously with a monochromatic excitation light of frequency ${\nu }_0$ and a continuum probe light. The excited atoms and molecules change their energy states by $\pm h{\nu }_M$ and absorb frequencies at the Stokes frequency, ${\nu }_0-{\nu }_M$, and anti-Stokes frequency, ${\nu }_0+{\nu }_M$, from the continuum probe light. This breakthrough in broad spectrum generation enabled the first Raman absorption spectrum measurement.

Seven years later, a broadband pulsed light source was applied to transient absorption spectroscopy for studying nonradiative relaxation processes in excited molecules [38,39]. Photoisomerization on a time scale of picoseconds was observed in 3-3′diethyloxadicarbocyanine iodide by broadband detection in the visible region [39]. In 1979, pioneering work by Shank et al., who used a time-resolved white-light continuum pulse probe to study GaAs thin films, opened a new era for dynamic studies in solid-state physics [40]. In this period, broadband probe pulses were generated by focusing the 750 nm pulses from a Nd:YAG amplifier into a cell containing water. The spectral range of interest, 785–835 nm, was selected using filters. By taking advantage of broadband detection, the entire relaxation process of band filling and bandgap renormalization was clearly observed within 0.5 ps. In addition, the relaxation processes of excited carriers in the heavy, light, and split-off hole bands were simultaneously observed by broadband detection [41,42]. Furthermore, the dynamics of magnetoexcitons in GaAs quantum wells were studied using a spin-resolved broadband probe [43]. Circularly polarized pump and probe beams were used to resolve excitonic interactions with regard to angular momentum states. By using the broadband probe, interactions between magnetoexcitons generated by the pump pulses at various angular states were unambiguously revealed. Magnetoexcitons with identical spins repel each other and cause a blueshift, whereas those with opposite spins attract each other, causing a redshift.

This brief review shows how the evolution of broadband time-resolved spectroscopy was driven by the development of light sources. In the 1970s, most continuum light sources were generated by self-phase modulation (SPM) and stimulated Raman scattering by focusing a colliding pulse mode-locked dye laser on a medium [44–46] or fiber [47], or generated by the fluorescence from a scintillator dye [48]. In the 1990s, femtosecond light sources were significantly improved with the development of solid-state laser materials [49], e.g., a sapphire crystal (${\mathrm{Al}}_2{\mathrm{O}}_3$) doped with titanium ions (Ti:sapphire) and the chirp-pulse amplification technique [50]. Solid-state lasers have allowed optical parametric conversion to extend the spectral range of femtosecond pulses to the UV [35], visible [34], and IR [51,52] regions. A novel method, the noncollinear optical parametric amplifier (NOPA), was proposed to provide a broad spectrum with a sub-10-fs pulse width [53,54] or even a sub-5-fs pulse width [19,20,55], and the pulse width has recently even reached 2.4 fs [56].

These advanced broadband light sources with ultrashort pulse duration have been applied to various research areas, including ultrafast chemical reactions, photoisomerization, biophysics, and solid-state materials. By using their extremely high time resolution, the relaxation processes during trans–cis isomerization in the retinal chromophore of bacteriorhodopsin have been revealed by studying the real-time vibrational dynamics [57]. The environmentally affected vibrational photoisomerization processes of push–pull substituted azobenzene dye have been disclosed [58]. Broadband detection has enabled demonstration of the energy transfer channels and efficiencies in photosynthetic light harvesting [59]. The pathways for exciton fine structure relaxation in CdSe nanorods have also been revealed [60]. Furthermore, the electron–phonon interaction strength in high-$T_c$ superconductors was unambiguously determined recently [61].

Time-resolved spectroscopy provides a versatile and effective tool for studying the dynamics of photoexcited carriers in real time. Moreover, light sources with a broad spectrum and high time resolution enable the unambiguous discovery of the dynamics of energy transfer among quasi-particles both extensively and correctly. According to the measured energy transfer rate, the interplay among electron, phonon, spin, and orbital measurements in various materials or at the interfaces between dissimilar functional materials can be clearly revealed. Therefore, we can further understand some previously baffling issues in crystalline and dissimilar functional materials.

B. Femtosecond Light Sources

1. Narrowband Optical Parametric Amplifier

A regenerative amplifier (RGA) seeded with a Ti:sapphire laser oscillator served as a light source for a homemade optical parametric amplifier (OPA). The type-I ($e\to o+o$) $\beta \text{-}\mathrm{BBO}$ (barium borate, ${\mathrm{BaB}}_2{\mathrm{O}}_4$)-based OPA was pumped by the second harmonic of the RGA (wavelength, 400 nm; repetition rate, 5 kHz) to obtain output pulses in the visible range of 500–700 nm.

The second harmonic of the RGA was generated by 800 nm pulses focused on a BBO crystal. The 400 nm beam was separated into two copies; one served as the pump beam of the parametric interaction process and the other was used to obtain a white-light continuum as the signal beam. The white-light continuum was produced by focusing the 400 nm pulses on a sapphire disk to induce SPM. Then the white-light continuum passed through a prism pair to remove the fundamental light (400 nm). Both the signal (the white-light continuum) and pump (400 nm) beams were focused on a BBO crystal to realize a NOPA. The phase-matching condition is satisfied in the visible broadband region from 500 to 700 nm, so the wavelength of the amplified signal beam can be selected by adjusting the delay between the pump pulse and the linearly chirped visible seed pulse. As a result, the output wavelength of the signal beam can be tuned from 500 to 700 nm continuously (Fig. 2).

 

Fig. 2. Schematic diagram of BBO-based OPA. The OPA was pumped by 400 nm pulses, and its tunable range is 480–700 nm with a pulse duration of 35 fs. Inset: normalized output spectra of the wavelength-tunable OPA, ranging from 500 to 700 nm.

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It is noteworthy that the constructed narrowband OPA system is based on information on the carrier envelope phase structure in the NOPA. The noncollinear geometry in the OPA process is used to amplify the broad visible tuning range. For the present purposes of the narrowband OPA, the seed pulse is positively chirped with further insertion of the prism. Therefore, the OPA spectrum can be linearly adjusted to have a single color by changing the delay between the pump pulse and seed pulse. Additionally, the gain of the OPA was saturated to avoid variation in its output caused by the fluence of the RGA pulses.

2. Broadband Optical Parametric Amplifier

For the broadband OPA, we also used the noncollinear configuration, which is the same as that used in the narrowband OPA. However, the signal beam, namely, the femtosecond continuum, is generated by the SPM of an 800 nm pulse focused on a 2 mm sapphire plate. To amplify the femtosecond visible broadband continuum in the full bandwidth, the signal pulses are precompressed using a pair of ultrabroadband chirped mirrors. The signal beam is then noncollinearly overlapped with the pump pulse and focused on a BBO crystal with the noncollinear angle of $\alpha =3.7°$ to fulfill the broadband phase-matching condition [19,55].

Finally, both the pulse front-tilted pump beam and the noncollinearly incident signal beam are focused on a BBO crystal. The signal beam is then amplified through the OPA process. The pulse energy is 86 nJ after the first-stage amplification. Both pump and signal beams are reflected back to the BBO crystal by concave mirrors in the confocal configuration for the second-stage amplification. The resulting amplified output pulse energy is 144 nJ, which is not affected by the fluence of the RGA pulses owing to the gain saturation of the OPA.

By using a total pulse compressor, the pulse width was compressed to $\sim 9\mathrm{fs}$. The output pulse energy after compression is 40 nJ. Amplitude and phase characterization of the compressed broadband OPA pulses was verified by a second-harmonic generation frequency-resolved optical gating (SHG FROG) in a very thin BBO crystal (5 μm). The corresponding spectrum and the measured SHG FROG are shown in Fig. 3; it exhibits a wide visible spectrum with a nearly constant phase.

 

Fig. 3. (a) Broadband OPA output spectrum, which covers almost the entire visible range. (b) Measured second-harmonic generation frequency-resolved optical gating (SHG FROG) trace of the output broadband OPA pulses.

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C. Pump–Probe Spectroscopy

As shown in Fig. 4, the general idea of the pump–probe technique is that responses from a sample induced by a pump pulse are investigated by detecting the changes in the reflectivity ($\mathrm{\Delta }R$) or transmissivity ($\mathrm{\Delta }T$) of probe pulses as a function of the delay time between pump and probe pulses. However, the difference in absorbance should be obtained indirectly from $\mathrm{\Delta }R$ and $\mathrm{\Delta }T$. The absorbance of the target material without excitation, i.e., before a pump pulse arrives, is

 

Fig. 4. (a) Schematic diagram of the pump–probe technique. Time delay ($\mathrm{\Delta }t$) between pump and probe pulses can be controlled by a mechanical delay line. (b) Fundamental principle of pump–probe spectroscopy. Time-dependent refractive index changes $n(t)$ of the sample induced by pump pulses can be observed by detecting the intensity variations of probe pulses.

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On the other hand, the absorbance after excitation is

The femtosecond time evolutions are derived by delaying the relative arrival times of the pump and probe pulses using a mechanical delay line. The fluence of the probe beam is usually much weaker than that of the pump beam to avoid a second excitation in the samples. Further, the polarizations of the pump and probe pulses are set perpendicular to each other to avoid interference between the pump and probe beams [62].

1. Fast-Scan Techniques

In pump–probe measurements, traditional scanning methods collect data step by step, which is time consuming and easily influenced by the ultrashort pulse laser’s instability. The instability of the light sources thus hinders precise determination of electronic decay dynamics and may introduce systematic errors. This makes it difficult to obtain reproducible and reliable experimental data. However, a fast-scan pump–probe spectroscopic system that can complete a single scan in 5 s has been developed [63]. The rapid scan system is described in detail in [63].

In the fast-scan method, the signal ($\mathrm{\Delta }R$ or $\mathrm{\Delta }T$) is collected while the delay time is scanned rapidly in 500 steps across the scanning range. A fast-scan stage with a total accessible pulse delay range of 15 ps is controlled by an external voltage generated by a digital/analog converter. At each delay point, the signal is obtained in 10 ms and stored in the memory of the lock-in amplifier. Averaged values of the data are collected for several hundred scans. This method provides a good signal-to-noise ratio and avoids the effects of laser fluctuations, including instability of the laser output power and pulse width.

2. Broadband Detection Techniques

To detect the relatively weak signal (on the order of ${10}^{-4}$ or less) in pump–probe measurements at multiple probe wavelengths, a multichannel lock-in amplifier developed by our group was used for time-resolved spectroscopy. The avalanche photodiodes (APDs) were commercial products optimized for UV to visible light detection.

As shown in Fig. 5, the probe pulse was dispersed by a polychromator into a 96-branch fiber bundle whose other end was separated into 96 fiber branches and connected to APDs. Therefore, the time-resolved absorption differences at 96 probe wavelengths were simultaneously detected at the photodiodes. The detected signals were sent to a multichannel lock-in amplifier to be spectrally resolved for simultaneous detection of tiny changes in the probe intensity over the entire spectral region.

 

Fig. 5. Schematic diagram of the multichannel lock-in amplifier for the broadband pump–probe measurement system. APDs, avalanche photodiodes.

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3. ULTRAFAST DYNAMICS IN NOVEL CONDENSED MATTER

A. Spin-Valley Coupled Polarization in Monolayer ${\mathsf{MoS}}_{\mathsf{2}}$

The discovery of graphene initiated a new era for two-dimensional (2D) materials in condensed matter physics. In particular, much attention has been focused on single-layer semiconducting materials. For example, the transition metal dichalcogenide ${\mathrm{MoS}}_2$ exhibits unique physical, optical, and electrical properties correlated with its atomic layered structure. ${\mathrm{MoS}}_2$ is a 2D material consisting of a horizontal single layer of molybdenum stacked vertically between two single layers of sulfur, as shown in the inset of Fig. 6. The sulfur layers are held together by weak van der Waals forces, allowing ${\mathrm{MoS}}_2$ sheets to be easily separated. Unlike pristine graphene, which does not have a bandgap for applications, ${\mathrm{MoS}}_2$ possesses an indirect bandgap of 1.2 eV in bulk form, similar to that of silicon, and a direct bandgap of 1.8 eV as an atomically thin monolayer [64,65]. Moreover, the inherent coupling between the valley and spin in monolayer ${\mathrm{MoS}}_2$ provides a noteworthy characteristic for spintronics [66], valleytronics [67], and semiconductor devices [9,68]. For example, monolayer ${\mathrm{MoS}}_2$ exhibits a high channel mobility ($200{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$) and current ON/OFF ratio ($1\times {10}^8$) when it is used as the channel material in a field-effect transistor [68].

 

Fig. 6. Spectra of 1.89 eV pump pulse (red), 2.01 eV pump pulse (orange), broadband visible probe pulse (gray), and the stationary absorption of monolayer ${\mathrm{MoS}}_2$ at room temperature (blue). Inset: lattice structure of ${\mathrm{MoS}}_2$ in out-of-plane direction. Adapted from [72].

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Highly polarized luminescence in monolayer ${\mathrm{MoS}}_2$ has been observed with resonant excitation. Furthermore, the valley–spin lifetime was previously predicted to be larger than 1 ns [69]. However, a time-resolved study of the polarized photoluminescence (PL) demonstrated that the carrier spin flip has a time scale of several picoseconds, which is limited by the time resolution of the time-resolved PL measurement system [70]. Mai et al. further observed that the polarized exciton A decays within only several hundred femtoseconds according to optical pump–probe measurements [71]. This controversial situation was resolved by a conclusive study of the full dynamics and physical nature of polarized excitons in monolayer ${\mathrm{MoS}}_2$, including the spin–valley coupling [72].

The absorption spectrum of monolayer ${\mathrm{MoS}}_2$ in Fig. 6 clearly shows A (1.89 eV) and B (2.04 eV) excitonic transitions, which indicate the splitting of the valence band at the $\text{K}$ valley due to spin–orbit coupling [64,65]. The pump pulse was generated by an OPA (as demonstrated in Section 2.B.1), and the excitation energy was set to be resonant with either exciton A or B. A probe pulse with a visible broadband spectrum was produced by SPM of an RGA pulse in a sapphire plate. To distinguish the nonequivalent $\text{K}$ and ${\text{K}}^{\prime }$ valleys, the polarizations of the pump and probe beams were adjusted to be circular by broadband quarter-wave plates. The pump (probe) beam was focused on the sample in a spot with an area of $1.3\times {10}^{-4}{\mathrm{cm}}^2$ ($0.7\times {10}^{-4}{\mathrm{cm}}^2$) and a pulse energy of 40 μJ (3 μJ). The time resolution of the measuring system was estimated to be 30 fs. The transient absorbance changes of the probe pulses induced by the pump pulses were detected by a CCD camera at all probe wavelengths simultaneously. The sample was mounted inside a cryostat to control the environmental temperature of the samples.

Figure 7 shows a 2D display of the photon-energy and time-resolved transient absorbance difference $\mathrm{\Delta }A(\omega ,t)$ at 78 K. For the measurements, the polarizations of the broadband probe pulses were adjusted to be ${\sigma }^{+}$ and ${\sigma }^{-}$, whereas the pump pulses were set to ${\sigma }^{+}$ circular polarization and 1.89 eV to resonate with exciton A. For both the ${\sigma }^{+}$ and ${\sigma }^{-}$ probes, the time-resolved spectra exhibited negative $\mathrm{\Delta }A$ in the spectral band of excitons A and B. The negative $\mathrm{\Delta }A$ signal could be caused by stimulated emission from the excited state and/or photobleaching due to depletion of the ground state and population of the excited state. The lifetime of photobleaching is usually much longer than that of stimulated emission because stimulated emission occurs only within the lifetime of the excited state whereas photobleaching remains until the ground state is fully repopulated.

 

Fig. 7. (a) Transient absorbance difference ($\mathrm{\Delta }A$) induced by excitation using ${\sigma }^{+}$ circularly polarized pump pulses with a photon energy of 1.89 eV and probed by ${\sigma }^{+}$ circularly polarized pulses at 78 K. Black curves are contours for $\mathrm{\Delta }A=\text{zero}$. Red line indicates expected values of transition $A$ as a function of the time delays and probe photon energies. (b) Probe delay time traces of $\mathrm{\Delta }A$ at various probe photon energies. Red and blue lines represent ${\sigma }^{+}$ and ${\sigma }^{-}$ probes, respectively, and horizontal green lines show $\mathrm{\Delta }A=0$. Adapted from [72].

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Obviously, $\mathrm{\Delta }A$ is significantly probe polarization dependent within 100 fs, as shown in Fig. 7(b). The nonlinear optical response after 100 fs is independent of the angular momentum of the initially excited distribution, which indicates that the initial polarization distribution relaxes to some quasi-equilibrium states in 100 fs. Following fast spin-polarization relaxation, the peaks in the $\mathrm{\Delta }A$ spectrum show a blueshift before 10 ps and a redshift after 10 ps, as shown by the red line in Fig. 7(a). We note that the pump-induced response at the ${\text{K}}^{\prime }$ valley is observed even when exciton A at the $\text{K}$ valley is excited by the ${\sigma }^{+}$ pump in contrast to cases of excitons coupled to pump and probe pulses, which do not share common states. This unexpected phenomenon could be explained by various possible mechanisms, e.g., dark excitons generated by pump pulses [71], weakening of the excitonic binding energy [43], or dielectric screening from the excited excitons [43] (see Supplement 1).

The measured time-resolved traces of $\mathrm{\Delta }A(\omega ,t)$ were fitted using the sum of three exponential functions and a constant term, as follows:

 

Fig. 8. Triple exponential fitting results of time-resolved $\mathrm{\Delta }A$ data excited by 2.01 eV and ${\sigma }^{+}$ pump pulse at 78 K. Left column, ${\sigma }^{+}$ probe; right column, ${\sigma }^{-}$ probe. (a) $\mathrm{\Delta }A$ spectra, (b) time constant of each component. Dotted lines indicate estimated values. Adapted from [72].

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After the excitons are dissociated to become free carriers in highly excited states, the exciton peak exhibits a redshift, as shown by the red line in Fig. 7(a). This shift is attributed to intravalley scattering of free carriers, in which electrons relax to the bottom of the conduction band and holes relax to the top of the valence band. The $\mathrm{\Delta }{A}_{\text{carrier}}$ spectra show the sum of bleaching at the transition energy peaks and the induced absorption of a broad conduction band. Thus, the intermediate relaxation time ${\tau }_{\text{carrier}}\sim 25\mathrm{ps}$ was assigned to the intraband transition of free carriers. The decay time of $\mathrm{\Delta }{A}_{e-h}$ is found to be too long to be determined in the present work. The constant term $\mathrm{\Delta }{A}_{e-h}$ represents only bleaching behavior, which can be attributed to electron–hole recombination in the direct band. The recombination time was estimated to be $\sim 300\mathrm{ps}$ in a previous study [75].

The present study completely elucidates the fairly comprehensive ultrafast dynamics of spin-polarized excitons in monolayer ${\text{MoS}}_2$, as schematically shown in Fig. 9. Owing to the high temporal resolution and visible broadband detection, the time constants for the 60 fs spin-polarized exciton decay, 1 ps exciton dissociation (intervalley scattering), and 25 ps hot carrier relaxation (intravalley scattering) are clearly identified. Moreover, substantial intervalley scattering strongly diminished the spin–valley coupled polarization under off-resonant excitation. These results provide a complete understanding of spin–valley coupled polarization anisotropy and carrier dynamics of atomic-layer ${\text{MoS}}_2$, which can further help us to develop ultrafast multilevel logic gates.

 

Fig. 9. Schematic diagram of the relaxation processes in monolayer ${\mathrm{MoS}}_2$. Adapted from [72].

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B. Effect of Annealing on the Performance of P3HT:PCBM Solar Cells

The demand for renewable energy sources has stimulated progress in the development of efficient photovoltaic devices, and organic solar cell research has achieved several critical milestones in recent decades. Replacing traditional inorganic semiconductor-based solar cells, organic solar cells have become established as a future photovoltaic technology because of their advantages of cost-effective production, large area, light weight, and flexibility [76,77]. The highest reported power-conversion efficiency to date is 10.8% [78], whereas it barely reached 1% in the first reported polymer solar cell [79]. In the past couple of years, the polymer–fullerene heterojunction has dominated organic solar cell research [80,81]. For standard bulk polymer–fullerene heterojunction systems, the polymer poly(3-hexylthiophene) (P3HT) as the electron donor and the fullerene [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) as the electron acceptor are typically blended to create a composite material that has been demonstrated to exhibit effective device performance [81].

In solar cell devices, an anode and cathode are necessary to collect separated charges. The anode is made of tin-doped indium oxide (ITO) coated with a layer of poly-ethylene-dioxythiophene:polystyrene-sulfonic acid (PEDOT:PSS). ITO is one of the most extensively used electrode materials because of its high electrical conductivity and optical transparency. The transparent, water-soluble PEDOT:PSS is used to smooth the rough ITO surface and further effectively collect the separated holes into the electrode because it has a higher work function. A metal layer (e.g., aluminum) serves as the cathode.

For a P3HT:PCBM device, as shown in the inset of Fig. 10, ITO-coated glass substrates were used as the anode; they were modified by spin-coating with $\sim 40\mathrm{nm}$ thick conductive PEDOT:PSS followed by baking at 150°C for 30 min. P3HT was blended with PCBM at a weight ratio of 2.5% and dissolved in 1,2-dichlorobenzene. The active layer was thermally annealed at 190°C for 10 min in a nitrogen-filled glove box before (preannealing) or after (post-annealing) deposition of the aluminum. The cathode, which had a 100 nm Al layer, was thermally evaporated onto the polymer film at a base pressure of $7.5\times {10}^{-9}$ Pa to form an active area of $0.06{\mathrm{cm}}^2$. The current density–voltage ($J\text{-}V$) characteristics for the devices were recorded under light illumination using standard solar irradiation of $100\mathrm{mW}/{\mathrm{cm}}^2$ with a xenon lamp as the light source and a computer-controlled voltage–current source meter.

 

Fig. 10. Current density–voltage ($J\text{-}V$) characteristics of solar cells of ITO/PEDOT:PSS/P3HT:PCBM/Al with pre- and post-annealing processes. Inset: device architecture of a bulk heterojunction solar cell device. The Al layer is the cathode. The active layer is a semiconducting polymer/fullerene blend. ITO coated with PEDOT:PSS serves as the anode. These layers are deposited on a glass substrate. Adapted with permission from [86]. Copyright (2015) American Chemical Society.

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Figure 10 shows the current density–voltage ($J\text{-}V$) characteristics of a device with the structure ITO/PEDOT:PSS/P3HT:PCBM/Al and different thermal annealing processes. As expected, the device fabricated using a preannealing process exhibits poor performance characteristics and its power conversion efficiency is only 1.63%. The other device, prepared with a post-annealing process, demonstrates better performance and its power conversion efficiency is 2.88%. In terms of device performance, both the open-circuit voltage ($V_{\mathrm{OC}}$) and short-circuit current ($J_{\mathrm{SC}}$) are improved by the post-annealing process. Some crucial studies [82–85] have pointed out the reasons for the higher performance in post-annealed devices. However, the microscopic viewpoint of high-performance devices has yet to be considered. Here, the fundamental carrier dynamics directly correlated to the efficiency of charge transport in solar cell devices are studied by ultrafast spectroscopy [86]. The stationary absorbance spectra of pre- and post-annealed devices in the visible range show that the absorbance increases rapidly at photon energies greater than $\sim 1.9\mathrm{eV}$ (see Supplement 1), which demonstrates that the polymer has a wide absorption band [80]. The spectra of both pre- and post-annealed devices exhibit the $\pi -{\pi }^{*}$ transition of P3HT at 2.05 and 2.23 eV [87,88].

Time-resolved spectroscopy using sub-10-fs visible pulses from a broadband OPA (as demonstrated in Section 2.B.2) was performed at room temperature. The output pulses of a broadband OPA were separated into pump and probe pulses. The fluences of the pump and probe pulses at the sample were $2.7\mathrm{mJ}/{\mathrm{cm}}^2$ and $0.3\mathrm{mJ}/{\mathrm{cm}}^2$, respectively. The changes in the sample induced by a pump pulse were obtained by detecting the change in absorption ($\mathrm{\Delta }A$) of probe pulses as a function of probe delay time. The femtosecond time evolutions were derived by delaying the relative arrival times of the pump and probe pulses rapidly by a fast-scan stage (Section 2.C.1). The probe pulse was dispersed using a polychromator into a 96 branch fiber bundle, the other end of which was separated into 96 fiber branches and connected to APDs with a spectral resolution of 2.56 nm, i.e., $\sim 10\mathrm{meV}$ (Section 2.C.2). Therefore, the time-resolved absorption differences at 96 probe wavelengths were simultaneously detected at the photodiodes. The detected signals were sent to a multichannel lock-in amplifier to be spectrally resolved for simultaneous detection of low-intensity signals over the entire spectral region.

The time- and photon-energy-resolved transient absorption difference, $\mathrm{\Delta }A(\omega ,t)$, of the pre- and post-annealed devices was measured using the pump–probe technique. Figures 11(a) and 11(c) show 2D plots of the $\mathrm{\Delta }A$ spectra as functions of time and photon energy. The $\mathrm{\Delta }A$ spectrum is positive at photon energies of less than $\sim 1.98\mathrm{eV}$, which is attributed to the induced absorption for transitions from the first excited state to higher states. The negative $\mathrm{\Delta }A$ at photon energies greater than $\sim 1.98\mathrm{eV}$ is due to stimulated emission from the excited state and photobleaching due to ground state depletion. The two peaks at 2.05 and 2.23 eV represent the $\pi -{\pi }^{*}$ transition in P3HT. Figure 12 illustrates the relaxation processes of the P3HT:PCBM blend, which are excited by pump pulses with a photon energy of $>1.9\mathrm{eV}$ (the absorption gap energy) [89,90]. In the composite samples, it is estimated that more than 60% of the incident photons are absorbed by the polymer [91]. Therefore, the sample excited by the pump pulses generates excited electron–hole pairs, primarily in P3HT molecules. The excited electrons at the lowest unoccupied molecular orbital (LUMO) of P3HT are transferred to the LUMO of PCBM, and the holes remain in the P3HT to form a bounded polaron pair (BPP) with the excited electrons. The time constant for this interfacial charge transfer is measured as $\sim 90\mathrm{fs}$ [90,92]. The generated BPP then relaxes to the ground state via the parallel processes of dissociation into separated polarons, trapping by defect states, and recombination. The time constants for dissociation into the separated polarons and defect trapping are reported to be $\sim 0.95$ and $\sim 2.8\mathrm{ps}$ [90], respectively.

 

Fig. 11. (a), (c) Two-dimensional plots of transient absorption difference $\mathrm{\Delta }A(\omega ,t)$. (b), (d) $\mathrm{\Delta }A(\omega )$ spectra at various time delays for preannealed and post-annealed P3HT:PCBM devices in (a) and (c), respectively. Adapted with permission from [86]. Copyright (2015) American Chemical Society.

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Fig. 12. Schematic representation of ultrafast carrier dynamics after photoexcitation. $E_{\mathrm{LUMO}}^D$, the LUMO of the electron donor; $E_{\mathrm{HOMO}}^D$, the highest occupied molecular orbital (HOMO) of the electron donor; $E_{\mathrm{LUMO}}^A$, the LUMO of the electron acceptor; $E_{\mathrm{HOMO}}^A$, the HOMO of the electron acceptor. In this study, the electron donor and electron acceptor are P3HT and PCBM, respectively. $\tau$ is the time constant for the relaxation processes. Adapted with permission from [86]. Copyright (2015) American Chemical Society.

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According to the scenario just described, the real-time traces for $\mathrm{\Delta }A(\omega ,t)$ are expressed by the equation

It should be emphasized that pump–probe spectroscopy with high time and photon energy resolution can be further used to show the relative amount of photoexcited carriers relaxed through each of the relaxation processes in the $E_{\mathrm{LUMO}}^D$ state (see Fig. 12), which is the key to understanding any improvement in device performance. The percentage of carriers relaxed through every channel is calculated using the coefficients $A_{\mathrm{CT}}$, $A_{\mathrm{SP}}$, $A_{\text{trap}}$, and $A_{\text{Recomb}}$. In addition, the percentage of each component in the region of 1.98–2.13 eV for stimulated emission can be further estimated (Fig. 13). The percentage of charge transfer increases by 4.5% for the post-annealed devices. This demonstrates that interfacial charge transfer from an electron donor (P3HT) to an electron acceptor (PCBM) in the post-annealed devices is more efficient than that in the preannealed devices. There are 1.8% more separated polarons in the post-annealed devices than in the preannealed devices, but there is 6.4% less recombination in the post-annealed devices. Consequently, more charges are transferred from the electron donor (P3HT) to the electron acceptor (PCBM). More separated polarons and less recombination mean that there are more effective free carriers, which produces a larger short-circuit current ($J_{\mathrm{SC}}$) in the post-annealed devices, as shown in Fig. 10.

 

Fig. 13. Average percentages of each of the relaxation processes shown in Fig. 12 at 1.98–2.13 eV. Adapted with permission from [86]. Copyright (2015) American Chemical Society.

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4. CONCLUSION AND PERSPECTIVES

In conclusion, in this short review article we describe the fascinating relationships between the energy, spin, and valley in monolayer ${\mathrm{MoS}}_2$. By using these degrees of freedom, optically driven logic gates can be realized. A two-level logic gate can be operated by sequential excitation with circularly polarized 2.01 eV (resonant with exciton B) and 1.98 eV (resonant with exciton A) pulses at room temperature. According to our time-resolved studies, the nonequilibrium population between the K and ${\text{K}}^{\prime }$ valley lasts for $\sim 1\mathrm{ps}$ in monolayer ${\mathrm{MoS}}_2$, making it an excellent candidate material for ultrafast optical control. For application to high-rate optical pulse control, the problem of accumulation of the remnant coherence after the control pulse always exists. Thus, the following pulse to control the succeeding step must wait for decoherence of the target, which limits the bandwidth of optical spin control devices. Additionally, analyses of each relaxation process in P3HT:PCBM solar cells show that there are increases in the charge transfer and the number of separated polarons and a decrease in the amount of recombination between excited carriers, which is one of the physical mechanisms responsible for enhanced performance after a post-annealing process. These findings are consistent with observations of the annealing-dependent surface morphology and vertical distribution of P3HT:PCBM blends, which provides key information for the design of high-performance solar cells.

These important results and conclusions indicate that ultrabroadband time-resolved spectroscopy provides a powerful means of studying the interactions between quasi-particles, which are the basis for composing a material. Using broadband OPA, we can observe several energy levels simultaneously with extremely high time resolution and study the correlations among them. This provides much clearer physical insight into the interactions of quasi-particles in several novel types of condensed matter. The development of ultrabroadband light sources continues. For example, the generation of ultrabroadband MIR coherent light using four-wave difference-frequency generation from two-color femtosecond pulses in gases has been demonstrated [93]. This type of ultrabroadband light source extending to the MIR region as well as the terahertz region is desirable and extremely important for investigating the detailed ultrafast dynamics in solids, as the bandgap energy or number of optical transitions have resonance energies in this frequency region.