Low-frequency noise in nanowires

Abstract

40 years of research on low-frequency (LF) noise and random-telegraph noise (RTN) in metallic and semiconducting nanowires (NWs) demonstrate the importance of defects and impurities to each system. The fluctuating...

Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations

“…where τ ↓ and τ ↑ are, respectively, the minimum and maximum pulse durations. Equation ( 3) is mentioned in [25] and [26] as a substantiation of 1/f noise originating from P τ ∼ 1/τ . We remark that integrating equation (3) with P τ = 1/τ yields a logarithmic expression, ln[τ 2 ↑ (1 + τ 2 ↓ ω 2 )/(τ 2 ↓ (1 + τ 2 ↑ ω 2 ))] ≁ 1/ω, which does not display the 1/ω signature even in the limit of an infinitely wide distribution.…”

“…Its definition follows in section 3.2, while the upper-truncated and the lower-truncated Pareto distributions are defined in appendices B.1 and B.2, respectively. The unbounded Pareto distribution is not well defined and cannot be normalized to comply with equation (26). Instead, an inverse Gamma distribution is considered, as it is well defined for an unbounded support τ ∈ (0, ∞) due to a smooth exponential cutoff for small values of τ .…”

“…The inverse Gamma distribution has the same support span τ ∈ (0, ∞) as the ill-defined unbounded Pareto distribution. However, due to the smooth cutoff at low values of τ resulting from the exponential term, it is both well-defined according to equation (26), and it has a finite, non-diverging mean satisfying the normalization condition (27).…”

Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations

“…where τ ↓ and τ ↑ are, respectively, the minimum and maximum pulse durations. Equation ( 3) is mentioned in [25] and [26] as a substantiation of 1/f noise originating from P τ ∼ 1/τ . We remark that integrating equation (3) with P τ = 1/τ yields a logarithmic expression, ln[τ 2 ↑ (1 + τ 2 ↓ ω 2 )/(τ 2 ↓ (1 + τ 2 ↑ ω 2 ))] ≁ 1/ω, which does not display the 1/ω signature even in the limit of an infinitely wide distribution.…”

“…Its definition follows in section 3.2, while the upper-truncated and the lower-truncated Pareto distributions are defined in appendices B.1 and B.2, respectively. The unbounded Pareto distribution is not well defined and cannot be normalized to comply with equation (26). Instead, an inverse Gamma distribution is considered, as it is well defined for an unbounded support τ ∈ (0, ∞) due to a smooth exponential cutoff for small values of τ .…”

“…The inverse Gamma distribution has the same support span τ ∈ (0, ∞) as the ill-defined unbounded Pareto distribution. However, due to the smooth cutoff at low values of τ resulting from the exponential term, it is both well-defined according to equation (26), and it has a finite, non-diverging mean satisfying the normalization condition (27).…”

Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations

“…where τ ↓ and τ ↑ are, respectively, the minimum and maximum pulse durations. Equation ( 3) is mentioned in [25] and [26] as a substantiation of 1/f noise originating from P τ ∼ 1/τ . We remark that integrating equation (3) with P τ = 1/τ yields a logarithmic expression, ln[τ 2 ↑ (1 + τ 2 ↓ ω 2 )/(τ 2 ↓ (1 + τ 2 ↑ ω 2 ))] ≁ 1/ω, which does not display the 1/ω signature even in the limit of an infinitely wide distribution.…”

“…Its definition follows in section 3.2, while the upper-truncated and the lower-truncated Pareto distributions are defined in appendices B.1 and B.2, respectively. The unbounded Pareto distribution is not well defined and cannot be normalized to comply with equation (26). Instead, an inverse Gamma distribution is considered, as it is well defined for an unbounded support τ ∈ (0, ∞) due to a smooth exponential cutoff for small values of τ .…”

“…The inverse Gamma distribution has the same support span τ ∈ (0, ∞) as the ill-defined unbounded Pareto distribution. However, due to the smooth cutoff at low values of τ resulting from the exponential term, it is both well-defined according to equation (26), and it has a finite, non-diverging mean satisfying the normalization condition (27).…”

Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations

“…where τ ↓ and τ ↑ are, respectively, the minimum and maximum pulse durations. Equation ( 3) is mentioned in [25] and [26] as a substantiation of 1/f noise originating from P τ ∼ 1/τ . We remark that integrating equation (3) with P τ = 1/τ yields a logarithmic expression, ln[τ 2 ↑ (1 + τ 2 ↓ ω 2 )/(τ 2 ↓ (1 + τ 2 ↑ ω 2 ))] ≁ 1/ω, which does not display the 1/ω signature even in the limit of an infinitely wide distribution.…”

“…Its definition follows in section 3.2, while the upper-truncated and the lower-truncated Pareto distributions are defined in appendices B.1 and B.2, respectively. The unbounded Pareto distribution is not well defined and cannot be normalized to comply with equation (26). Instead, an inverse Gamma distribution is considered, as it is well defined for an unbounded support τ ∈ (0, ∞) due to a smooth exponential cutoff for small values of τ .…”

“…The inverse Gamma distribution has the same support span τ ∈ (0, ∞) as the ill-defined unbounded Pareto distribution. However, due to the smooth cutoff at low values of τ resulting from the exponential term, it is both well-defined according to equation (26), and it has a finite, non-diverging mean satisfying the normalization condition (27).…”