[Paper Review] A set-up for measurement of low frequency conductance fluctuation (noise) using digital signal processing techniques

Arindam Ghosh, Swastik Kar+2 more|arXiv (Cornell University)|Feb 4, 2004

Surface and Thin Film Phenomena3 references19 citations

TL;DR

This paper presents a digital signal processing (DSP)-enhanced five-probe a.c. measurement setup for detecting low-frequency conductance fluctuations (1 mHz–20 Hz) in solids with a noise floor below 10⁻²⁰ V²/Hz. By combining hardware shielding, a.c. excitation with superimposed d.c., and advanced DSP techniques—including Wiener filtering and background subtraction—it enables precise measurement of 1/f noise, second spectra, and probability density functions, even in low-noise systems like doped silicon and charge-ordered manganites.

ABSTRACT

We describe a set up for measurements of low frequency (1 mHz < f < 20 Hz) conductance fluctuations in a solid conductor. The set-up uses a five probe a.c. measurement technique and extensive digital signal processing to reach a noise floor down to $S_{v}(f) \leq 10^{-20}$ V$^{2}$Hz$^{-1}$. The set up also allows measurement of noise using an a.c. in presence of a superimposed direct current. This feature is desirable in studies of electromigration damage or in systems that show non-linear conductivity. In addition, we describe a scheme which allows us to obtain the probability density function of the conductance fluctuation after subtracting the extraneous noise contributions (background) from the observed noise. The set-up has been used for conductance fluctuation measurement in the temperature range 1.5 K < T < 500 K in the presence of magnetic fields. We present some representative data obtained by this system.

Motivation & Objective

• To develop a high-sensitivity measurement system capable of detecting low-frequency conductance fluctuations (1 mHz–20 Hz) in solid-state materials with minimal background noise.
• To enable noise measurements in the presence of a superimposed direct current, crucial for studying electromigration and non-linear conduction in materials.
• To extract the true probability density function (PDF) of conductance fluctuations by isolating and subtracting extraneous noise contributions using digital signal processing.
• To achieve a spectral noise floor below 10⁻²⁰ V²/Hz, surpassing the Johnson limit and enabling detection of 1/f noise two orders of magnitude below background levels.
• To systematically measure and analyze higher-order statistics such as second spectra and non-Gaussian behavior in fluctuation dynamics near metal-insulator transitions.

Proposed method

• Employ a five-terminal a.c. measurement technique with current bias and voltage detection to isolate conductance fluctuations from thermal and contact noise.
• Use a lock-in amplifier with a.c. excitation at low frequencies (1 mHz–20 Hz) and apply digital filtering (e.g., Wiener filtering) to suppress external electromagnetic interference and background noise.
• Implement background noise subtraction using time-series analysis and spectral estimation techniques to isolate the sample's intrinsic conductance fluctuations.
• Apply fast Fourier transform (FFT) to convert time-domain voltage fluctuations δv(t) into power spectral density Sᵥ(f), defined via the Fourier transform of the auto-correlation function C(τ).
• Use the Hooge parameter γₕ = f^α Sᵥ(f) N / V² to scale and compare noise levels across different samples and temperatures, with α ≈ 1.
• Extract the probability density function (PDF) of fluctuations after background subtraction, and compute the second spectrum to detect non-Gaussian behavior and correlations in fluctuators.

Experimental results

Research questions

• RQ1 How can low-frequency conductance fluctuations (1 mHz–20 Hz) be measured with a noise floor below 10⁻²⁰ V²/Hz in the presence of environmental and instrumental noise?
• RQ2 To what extent can digital signal processing techniques like Wiener filtering and background subtraction improve the detection of weak 1/f noise in low-noise materials?
• RQ3 How does the probability density function (PDF) of conductance fluctuations change with temperature, and what does it reveal about the underlying fluctuation mechanism?
• RQ4 Can second spectra and higher-order correlation functions be reliably measured in systems with low intrinsic noise (e.g., ΔR/R < 10⁻⁴), and what do they reveal about fluctuator correlations?
• RQ5 How does the presence of a superimposed d.c. bias affect noise measurements in non-linear systems such as charge-ordered manganites, and what signatures (e.g., RTN, Lorentzians) emerge?

Key findings

• The setup achieves a spectral noise floor of Sᵥ(f) ≤ 10⁻²⁰ V²/Hz at frequencies as low as 1 mHz, enabling detection of 1/f noise two orders of magnitude below the background level.
• In P-doped silicon at 4.2 K, clear 1/f behavior was observed even in high-resistance samples (100 Ω), with the noise spectrum visible below the background due to effective DSP-based signal recovery.
• The probability density function (PDF) of fluctuations in doped silicon shows Gaussian behavior, with width increasing with temperature following an activated dependence with an activation energy of ≈0.3 eV.
• The scaled noise parameter γₕ in P-doped silicon exhibits distinct power-law behavior at low temperatures (T < 100 K), consistent with Universal Conductance Fluctuations (UCF), and activated behavior at higher temperatures.
• Second spectra in doped silicon show systematic growth in slope with increasing temperature, indicating the emergence of correlations among fluctuators.
• In charge-ordered Pr₀.₆₃Ca₀.₃₇MnO₃, application of a d.c. bias near the non-linear conduction threshold induces random telegraphic noise (RTN), visible as Lorentzian peaks superimposed on a 1/f background, confirming non-Gaussian dynamics.