Magnetic field dependence of the acoustic two‐pulse echo envelope modulation in Si:B at very low temperatures

Abstract

At temperatures below about 30 mK in Si:B the phase relaxation time T 2 of the two-level systems associated with the acceptor ground state can be determined from the decay of the two-pulse echo. It has been shown to depend on the concentration of interacting resonant states if the latter is high enough. This concentration is not only given by the boron concentration but depends also on internal and external stress, and the magnetic field. Under conditions of low concentration T 2 becomes long and we observe a modulation of the echo decay. From its dependence on magnetic field strength we can associate this modulation with the interaction of the acceptor hole with the 29 Si nuclei (I = 1/2) present within the extended acceptor wave function. The interaction with the central boron nucleus does not seem to contribute to the observed modulation. IntroductionThe fourfold degenerate Γ 8 ground state of acceptors such as boron in silicon becomes a two-level system (TLS) of two two-fold degenerate Kramers-levels by the application of stress. Random internal strains originating from crystal defects will thus lead to distributions of the separations of these TLS. The dependence of the width and form of such distributions on the concentration of point defects has been investigated previously [1] at temperatures above 1 K. Relaxation times T 1 and T 2 have been obtained in this temperature range from relaxation attenuation, saturation, and hole burning [2].At much lower temperatures we have found [3] that the relaxation times are long enough to observe phonon echoes, acoustic solitons and sound amplification as was previously observed for the TLS of glasses (see e.g. [4]). The phase relaxation time T 2 was determined from the decay of the acoustic two-pulse echo amplitude. ¿From its dependence on boron concentration, internal and external stress, and magnetic field we concluded that the spin-spin interaction is determined by the concentration of TLS on speaking terms if this concentration is high enough. In these experiments the magnetic field was the only parameter that could be used to change the concentration of resonant interacting TLS during a low-temperature run. This change is effected by the additional splitting of the two Kramers doublets so that one gets a changed distribution of level separations due to the mixed effect of stress and magnetic field.Here we show that in the case of low boron doping and broader distribution of TLS T 2 becomes longer and does not depend significantly on the magnetic field, i.e. resonant spin-spin interaction is not any more predominant. In addition we find that the echo amplitude does not decay monotonously with time but is modulated in some analogy to a recent observation for polarization echoes in glasses [5]. In the following we will concentrate on this latter observation.