How useful is Hooge's empirical relation

Abstract

Merits of Hooge's empirical relation for 1/f noise are investigated: S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> /R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = α/Nf with N the number of free charge carriers and α a parameter with a range: 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> <; α <; 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , depending on temperature, lattice quality and mobility μ. Parameters affecting the α-value are discussed. We propose a model explaining: α ~ μ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-m</sup> with m ≈ 3 as observed in undoped quantum wells (QW) and m ≈ 1 attributed to screening as observed in 2DEG's of gated QW. Hooge's relation implies that 1/f noise is a bulk effect. The normalized noise in films for bias, frequency and unit area as C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">us</sub> [cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ] is proportional to the sheet resistance R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sh</sub> [Ω]. The proportionality factor K [cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /Ω] = C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">us</sub> /R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sh</sub> is also a figure of merit, applicable for materials even if N is unknown. The K- and α-values are a useful metrics.