^{1,a)}, Peng Xiong

^{1}, Stephan von Molnár

^{1}, Mark Field

^{2}and Gerard J. Sullivan

^{2}

### Abstract

Hall sensors with cross width of were fabricated from quantum well semiconductor heterostructures containing two-dimensional electron gas. The room-temperature device characteristics were examined by Hall effect and electronic noise measurements along with analytical calculations. In the low-frequency range, from , the noise-equivalent magnetic field resolution was found to be limited by and generation-recombination noise from . The corresponding noise-equivalent magnetic moment resolution reached at and was even lower at higher frequencies. Using a phase-sensitive measurement technique, detection of a single diameter bead, suitable for biological applications, was achieved with a signal to noise ratio of , as well as detection of six beads with a signal to noise of per bead. The work demonstrates the efficacy of InAs quantum well Hall devices for application in high sensitivity detection of single magnetic biomolecular labels.

The authors gratefully acknowledge Dr. Keita Ohtani and Professor Dr. Hideo Ohno from Tohoku University, Japan, for supplying InAs QWSHs in the initial stages of this work. They are also grateful to Martech engineers Jim Valentine and Ian Winger for their technical assistance at several stages of the work. The work was supported by NSF-NIRT Grant No. ECS-0210332. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357.

I. INTRODUCTION

II. BACKGROUND

A. Magnetic field resolution and electronic noise

B. Magnetic moment resolution

III. EXPERIMENTAL PROCEDURES

IV. RESULTS AND DISCUSSION

A. Room-temperature device characterization

B. Noise analysis

C. Detection of superparamagnetic beads

V. CONCLUSIONS AND OUTLOOK

### Key Topics

- 1/f noise
- 44.0
- Magnetic fields
- 28.0
- Magnetic field sensors
- 26.0
- Thermal noise
- 26.0
- Machinery noise
- 22.0

## Figures

(Color online) The noise-equivalent magnetic moment resolution of a 2DEG Hall sensor as a function of the Hall cross width and the distance from the magnetic dipole. The curves are calculated according to Eq. (12). Upper inset: Schematic diagram of the configuration used in the derivation of Eq. (9). Lower inset: An example of a magnetic field distribution within the Hall cross area in a 2DEG plane calculated according to Eq. (9).

(Color online) The noise-equivalent magnetic moment resolution of a 2DEG Hall sensor as a function of the Hall cross width and the distance from the magnetic dipole. The curves are calculated according to Eq. (12). Upper inset: Schematic diagram of the configuration used in the derivation of Eq. (9). Lower inset: An example of a magnetic field distribution within the Hall cross area in a 2DEG plane calculated according to Eq. (9).

(Color online) A typical Langevin response of a superparamagnetic bead to an applied magnetic field and a sketch of the physical principle underlying the detection method. , , and represent rms values of the corresponding ac quantities. Inset shows the expected Hall voltage signal upon applying the dc field when the bead is (red) and is not (black) present on the Hall cross.

(Color online) A typical Langevin response of a superparamagnetic bead to an applied magnetic field and a sketch of the physical principle underlying the detection method. , , and represent rms values of the corresponding ac quantities. Inset shows the expected Hall voltage signal upon applying the dc field when the bead is (red) and is not (black) present on the Hall cross.

(Color online) Hall voltage output of the micro-Hall sensor as a function of externally applied perpendicular magnetic field for several dc bias currents. Upper inset: The Hall resistance as a function of the magnetic field for different dc bias currents. Lower inset: SEM image of the Hall cross used in the measurements, adapted to show the actual measurement configuration.

(Color online) Hall voltage output of the micro-Hall sensor as a function of externally applied perpendicular magnetic field for several dc bias currents. Upper inset: The Hall resistance as a function of the magnetic field for different dc bias currents. Lower inset: SEM image of the Hall cross used in the measurements, adapted to show the actual measurement configuration.

(Color online) (a) Noise voltage spectral density as a function of frequency measured at Hall voltage contacts for several different dc bias currents. Inset shows a SEM image of the Hall cross used in the measurements, adapted to show the actual measurement configuration. (b) Noise-equivalent magnetic field resolution of the sensor as a function of frequency for several different dc bias currents and zero external magnetic field.

(Color online) (a) Noise voltage spectral density as a function of frequency measured at Hall voltage contacts for several different dc bias currents. Inset shows a SEM image of the Hall cross used in the measurements, adapted to show the actual measurement configuration. (b) Noise-equivalent magnetic field resolution of the sensor as a function of frequency for several different dc bias currents and zero external magnetic field.

Noise-equivalent magnetic moment resolution of the sensor as a function of frequency.

Noise-equivalent magnetic moment resolution of the sensor as a function of frequency.

(Color online) (a) Conductivity noise voltage PSD for several different bias currents measured at Hall voltage contacts in zero magnetic field. (b) Conductivity noise voltage PSD measured at Hall voltage contacts as a function of bias current squared for several different frequencies. The lines are linear fits to the data. (c) Product of frequency and conductivity noise voltage PSD normalized to the bias current squared as a function of frequency for a bias current of . The red line is a fit according to Eq. (14).

(Color online) (a) Conductivity noise voltage PSD for several different bias currents measured at Hall voltage contacts in zero magnetic field. (b) Conductivity noise voltage PSD measured at Hall voltage contacts as a function of bias current squared for several different frequencies. The lines are linear fits to the data. (c) Product of frequency and conductivity noise voltage PSD normalized to the bias current squared as a function of frequency for a bias current of . The red line is a fit according to Eq. (14).

(Color online) The longitudinal conductivity noise voltage PSD for several different bias currents obtained from the measurements along the longitudinal direction of the Hall bar structure. A SEM image is shown in the inset. The data are obtained in zero external magnetic field.

(Color online) The longitudinal conductivity noise voltage PSD for several different bias currents obtained from the measurements along the longitudinal direction of the Hall bar structure. A SEM image is shown in the inset. The data are obtained in zero external magnetic field.

(Color online) (a) A SEM image of two adjacent Hall crosses with a diameter superparamagnetic bead positioned on one of them. The image was adapted to show the actual detection measurement configuration. (b) ac Hall voltage as a function of time for the two crosses shown in part (a) of the figure. The drop in the signal from one cross upon applying the static field is due to the presence of the bead. The blue arrows indicate the moments of time when was applied (↓) and removed (↑), respectively.

(Color online) (a) A SEM image of two adjacent Hall crosses with a diameter superparamagnetic bead positioned on one of them. The image was adapted to show the actual detection measurement configuration. (b) ac Hall voltage as a function of time for the two crosses shown in part (a) of the figure. The drop in the signal from one cross upon applying the static field is due to the presence of the bead. The blue arrows indicate the moments of time when was applied (↓) and removed (↑), respectively.

(Color online) (a) A SEM image of the Hall cross with Nanomag D-250 superparamagnetic beads. Six beads are located in the Hall cross area (marked as a red square for clarity). (b) Hall voltage signal as a function of time from the Hall cross shown in part (a) of the figure. The drop in the signal upon applying the static field is due to the presence of the beads.

(Color online) (a) A SEM image of the Hall cross with Nanomag D-250 superparamagnetic beads. Six beads are located in the Hall cross area (marked as a red square for clarity). (b) Hall voltage signal as a function of time from the Hall cross shown in part (a) of the figure. The drop in the signal upon applying the static field is due to the presence of the beads.

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