Critical Behavior of the Low Temperature Dielectric Constant of Si:As

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Abstract

<jats:p> Capacitance measurements on insulating uncompensated Si:As have been made to temperatures as low as 10mK from 10Hz to 1MHz. As T→0 C(ω,T) shows very little dispersion from hopping and one obtains the dielectric response <jats:italic>ε</jats:italic>'(N)-<jats:italic>ε</jats:italic> <jats:sub>h</jats:sub>=4π<jats:sub>χ</jats:sub>'(N). As N→N<jats:sub>c</jats:sub>-χ'(N)∝(N<jats:sub>c</jats:sub>/N-1)<jats:sup>-ζ</jats:sup> and we obtain ζ=1.18±.08 for N<jats:sub>c</jats:sub>=8.55±.05×10<jats:sup>18</jats:sup>/cm<jats:sup>3</jats:sup>, thus finding ζ=2µ where µ is the DC conductivity exponent. These agree with Si:P results and confirm universality of the exponents and the Mott criterion for n=type Si. </jats:p>

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