Photoluminescence ͑PL͒ decay dynamics of Ge nanocrystals (nc-Ge) 1.2-3.2 nm in average diameter embedded in SiO 2 matrices was studied. The samples showed a PL peak in the near-infrared region with strong size dependence. A very fast component ͑Ӷ1 s͒ was found in decay curves for all the samples. For the samples containing relatively large nc-Ge, a slow component of the order of microseconds was also observed. With decreasing the size, the slow component gradually faded out, and the PL

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... increased significantly. The transition from indirect to direct recombination of carriers with decreasing the size is considered to be responsible for the observed PL decay dynamics. Optical properties of nanometer size Si and Ge crystals have been investigated in recent years. 1 The band gap widening and the increase in the oscillator strength caused by the quantum size effects would appear in such nanocrystals. In particular, for Si nanocrystals (nc-Si), the relationship between the size and the photoluminescence ͑PL͒ properties has been revealed. [2] [3] [4] With decreasing the size, the PL peak shifts from the band gap of bulk Si to the visible region 2-5 and the decay time becomes shorter from milliseconds to microseconds. [5] [6] [7] [8] In contrast to nc-Si, little is known on the PL properties of Ge nanocrystals (nc-Ge). Since the exciton Bohr radius of bulk Ge crystal ͑17.7 nm͒ is much larger than that of bulk Si crystal ͑4.9 nm͒, 1 quantum size effects will appear more conspicuously for nc-Ge than nc-Si. Recently, we have succeeded in observing size dependent PL from nc-Ge in the near-infrared ͑NIR͒ region. 9 A PL peak was observed at about 0.88 eV for nc-Ge 5.3 nm in average diameter (d ave ). With decreasing the size, the PL peak shifted to higher energies and reached 1.54 eV for d ave ϭ0.9 nm. The PL intensity increased about two orders of magnitude as the size decreased. From these results, we concluded that the observed PL comes from the radiative recombination of electron-hole pairs confined in nc-Ge. In this work, in order to clarify the recombination process of electron-hole pairs confined in nc-Ge, PL decay measurements were performed for the same samples as those studied in our previous work. 9 It will be demonstrated that the PL decay time is much shorter than that reported for nc-Si. The transition of carrierrecombination process from indirect to direct one will be discussed. Ge nanocrystals embedded in SiO 2 matrices were prepared by a radio frequency cosputtering method similar to those used in our previous studies on nc-Ge embedded in SiO 2 matrices. 9-11 Small pieces of Ge chips ͑2ϫ2 ϫ0.5 mm 3 , purity 99.999 9%͒ were placed on a SiO 2 target ͑10 cm in diameter, purity 99.99%͒ and they were cosputtered in Ar gas of 2.7 Pa. Substrates were fused quartz plates. After cosputtering, the films were thermally annealed in N 2 gas ambient for 30 min at 800°C to grow nc-Ge in SiO 2 matrices. In the present preparation method, the size of nc-Ge can be controlled by changing the volume fraction of Ge in films ( f Ge ). 9-11 In our previous work, we prepared nc-Ge with d ave ϭ0.9-5.3 nm by changing f Ge from 0.2-7.2 vol %. 9 The size of nc-Ge was determined by cross-sectional highresolution transmission electron microscopic ͑HRTEM͒ observation ͓JEM-2010 ͑JEOL͔͒. For the samples with d ave р2.3 nm, nc-Ge were not observed in HRTEM images due probably to the intense background image of SiO 2 matrices. The size of nc-Ge for these samples was estimated by the relationship between the size of nc-Ge and f Ge . 9 In this work, we used the same samples as those studied in our previous work. The PL spectra were measured at room temperature using a HR-320 monochromator ͑Jobin Yvon͒, a R5509-72 photomultiplier ͑Hamamatsu Photonics͒ and a SR830 lock-in amplifier ͑Stanford Research͒. The excitation source was the 457.9 nm line of an Ar-ion laser. The beam power density was about 1 W/cm 2 . The spectral response of the detection system was calibrated with the aid of a reference spectrum of a standard tungsten lamp. For the PL decay measurements, a SR430 multichannel scaler ͑Stanford Research͒ was used. Excitation pulses were obtained from the 488.0 nm line of an Ar-ion laser by using an acoustic-optic modulator. The pulse width and repetition frequency were 400 ns and 11 kHz, respectively. The time resolution of the system is about 40 ns. Figure 1 shows the PL spectra for the samples with various d ave . The PL spectra are normalized at their maximum intensities and the scaling factors for the normalization are a͒