The epitaxial growth of BaF2on (001)hyphen;oriented GaAs substrates as well as on thin intermediate (001)hyphen;oriented SrF2buffers has been studied byinsitureflection highhyphen;energy electron diffraction. Despite the huge lattice mismatch of 9.7percnt; between GaAs and BaF2, a perfect overgrowth, but in a threehyphen;dimensional manner, is observed at sufficiently high substrate temperatures (Ts=580thinsp;deg;C). With an intermediate SrF2buffer of about 500 Aring; thickness the growth mode for BaF2becomes quasi two dimensional. At room temperature, thermal misfit strains of about 5times;10minus;3are observed by xhyphen;ray diffractometry for both the SrF2and BaF2layers if their total thickness is lower then 1500 Aring;. For thicker BaF2layers strain relief is observed.
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