A dynamical study of electron-exciton collision process in pure germanium is made by means of millimeter-wave cyclotron resonance combined with a photopulse technique. It is found that carrier recombination occurs primarily via exciton formation and subsequent annihilation process. The exciton lifetime is determined as a function of temperature.Contribution of electron-exciton interaction to the linewidth of electron cyclotron resonance in pure germanium has been investigated by means of intense photopulses combined with a boxcarconnected delayed gate circuit. It is demonstrated that the cyclotron-resonance linewidth excluding the contribution of electron-phonon interaction consists of two parts, namely, electron-exciton and electron-hole (or carrier-carrier) interactions. Both electron and exciton lifetimes are determined by varying the delay time of the gate. Intensity versus linewidth measurement of the electron resonance signal also definitely supports the existence of exciton contributions to the linewidth.An ultrahigh-purity germanium crystal lying in a 35-GHz nonresonant waveguide is illuminated with an EG & G FX-108 xenon flash tube at the repetition rate of 25 Hz. Each photopulse has a width of 1 Msec. The opening of the gate is set at 2 Msec. The magnetic field is applied along the (111) direction in the (110) plane and the linewidth of the first electron cyclotron resonance which corresponds to the cyclotron mass of 0.08ra 0 is measured. As the delay time is increased, both intensity and linewidth decrease. Results obtained at 4.2°K are shown in Figs. 1(a) and 1 (b). The contribution of elect ron-phonon scattering to the linewidth is subtracted beforehand. 1 The intensity measurement can also be regarded as a relative carrier-density measurement, and hence the notation n is introduced. The open circles in Fig. 1 (a) give the relevant linewidth, or the inverse relaxation time l/r, due to other than elect ron-phonon collisions. The variation consists of two branches: The first branch decays fast while the second decays slowly. The closed circles give the intensities of the resonance signals. The slope of the line connecting these circles yields the free carrier lifetime. Figure 1(b) gives the inverse relaxation time as a function of carrier density. Naturally we see a kink again here corresponding to Fig. 1 (a). The first branch in Fig. 1(b) is proportional to n l/2 while the second is proportional to n 2 . The second branch is obtained for shorter delay times io M h 310' 40 60 80 DELAY TIME (^sec) _^ T o JH IME H-Z o §'0'°

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We have shown that modulation spectroscopy can be extended with the necessary high resolution up to at least 35 eV. Available band-structure calculations, based on Fermi-surface and ultraviolet-photoemission-spectroscopy measurements, give good results for the filled parts of the conduction bands and account for the lowerenergy interband absorption, but they do not explain satisfactorily all of our higher-energy data. The thermoreflectance spectrum presented in this Letter provides a great amount of new information, mostly concerning final states far above the Fermi level, information which is necessary for future improved calculations of highly excited states. We also suggest that evaluation of some dipole matrix elements would enable a better understanding of the optical and ultraviolet photoelectron spectra.