PHYSICAL REVIEW B 85, 035209 (2012) Time-resolved cyclotron resonance in cuprous oxide Nobuko Naka, 1,2 Ikuko Akimoto, 3 Masanobu Shirai, 4 and Ken-ichi Kan’no 3 1 Department of Physics, Kyoto University, Kitshirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan 2 PRESTO, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan 3 Department of Materials Science and Chemistry, Wakayama University, Wakayama 640-8510, Japan 4 Institute for Integrated Cell-Material Sciences, Kyoto University, Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto 606-8302, Japan (Received 4 September 2011; revised manuscript received 27 November 2011; published 19 January 2012) We have demonstrated cyclotron resonance with a temporal resolution of 15 ns by using an electron-spin- resonance cavity. In an undoped direct-gap semiconductor, cuprous oxide, we observe clear low-field shifts of the cyclotron resonance peaks shortly after generation of photoexcited carriers. Based on the plasma shift of the cyclotron resonance, we evaluate the carrier density and quantitatively discuss the interaction between free carriers and excitons. With increasing time delay, the hole resonance asymptotically reaches the constant value corresponding to an effective mass of 0.575 times the free electron mass, providing a definitive answer to the controversy on the effective mass of holes in cuprous oxide. DOI: 10.1103/PhysRevB.85.035209 PACS number(s): 76.40.+b, 71.35.Gg I. INTRODUCTION Cyclotron resonance (CR) is a standard technique to determine effective masses of carriers in semiconductors. In the past, time-resolved CR was carried out in the microsecond range in indirect-gap semiconductors, such as germanium 1 and silicon, 2 and in doped direct-gap semiconductors, such as gallium arsenide. 3 On the other hand, picosecond time- resolved CR has also been demonstrated by using a free- electron laser system operated at a megahertz repetition rate. 4 However, CR on a nanosecond time scale is unexplored because direct extension of the above schemes is difficult due to the limited pulse width or due to the high repetition rate. In this study, we achieve 15-ns temporal resolution by using a dielectric cavity usually used for electron-spin resonance. In addition to the improvement of the temporal resolution, we evaluate the effect of the changing quality factor of the cavity by measuring both imaginary and real parts of the microwave reflectance. 5 Without distortion of resonance curves as pointed out in Refs. 6 and 7, we analyze the CR spectra, which vary with the time delay after the generation of photoexcited carriers, and quantitatively discuss the interaction of carriers with phonons, excitons, and other carriers. Our method makes CR measurements applicable to new types of experiments, namely, pursuing dynamics of pho- toexcited carriers in undoped direct-gap semiconductors. As a prototype of such a system we choose cuprous oxide (Cu 2 O), which is known by the long-lived quasiparticle state called the exciton, or an electron-hole pair bound by Coulomb force. The first CR measurement in Cu 2 O dates back to that in 1960s using cw photoexcitation sources. 8 Despite the long history, there remains a controversy on the hole effective mass: 0.66 m 0 8–10 versus 0.58 m 0 9,11 depending on the literature, where m 0 is the free-electron mass at rest. Furthermore, recent study by high- resolution spectroscopy reveals that not only orthoexcitons 12 but also the paraexcitons 13 have an effective mass largely different from the sum of electron and hole effective masses. This fact invoked revived interest in the band structure of Cu 2 O, leading to a theoretical calculation including the spin-orbit interaction for the full band dispersion. 14 Also, a computational study, which requires the electron and hole effective masses as known parameters, has shown that the central-cell corrections account for the large excitonic mass. 15 Since the excitonic mass is a key parameter determining the critical temperature for a quantum phase transition, such as Bose-Einstein condensation, solving the controversy on the hole effective mass is important. II. EXPERIMENT Samples with dimensions of ∼3 × 3 × 3 mm 3 were cut from natural crystals mined in Africa. The surface planes were oriented along {001}. An external magnetic field up to 1 T was applied along the [001] crystal axis. A microwave of 0.1 mW at a frequency of f = 9.68 GHz irradiated the sample mounted in a quartz tube in the electron-spin-resonance cavity (Bruker, MD5W1) at 10 K in a cryostat. The free carriers are generated under optical excitation by pulsed light from an optical parametric oscillator (Spectra Physics, MOPO) pumped by a Nd:YAG laser. The repetition rate is 10 Hz, the pulse width is 5 ns, and the linewidth is 0.2 cm −1 . The pulse energy is 0.8 mJ outside the cryostat. The laser beam is loosely focused on a spot with an area of 3 × 1.5 mm 2 on the sample surface. Due to the cryostat windows, cavity mesh, and the quartz tubes surrounding the sample, the pulse energy measured by a photodetector (Hamamatsu, S10356-01) at the sample position is a factor of 10 (40) less on the front (side) surface of the sample. The reflected microwave was measured with a bridge (Bruker, ELEXSYS E580). Both of the real and imaginary parts of the microwave signal were recorded with an oscilloscope (SpecJet) as a function of the time delay following the laser pulse. The quality factor of the cavity is set to 800, and the temporal resolution is 15 ns. By analyzing the imaginary parts, we confirm that there is no change in the effective quality factor at times later than 40 ns. 5 The inset of Fig. 1 shows a schematic diagram of the band structure of Cu 2 O near the zone center. The minimum energy gap is called the yellow gap (2.17 eV), and the next one is the green gap (2.30 eV). For most cases (except for Fig. 4), we choose the excitation at the phonon-assisted absorption due to 1s excitons, with which we obtained the strongest microwave absorption. The corresponding photon energy is 2.07 eV, about 0.1 eV below the yellow gap. 035209-1 1098-0121/2012/85(3)/035209(6) ©2012 American Physical Society