^{1,2}, R. K. Rajkumar

^{3,4}, A. Manzin

^{1,a)}, O. Kazakova

^{3}and A. Tzalenchuk

^{3}

### Abstract

The present paper investigates the influence of localized magnetic and electric fields, produced by a magnetic scanning tip, on the response of high-mobility two-dimensional electron gas in a Hall bar geometry. We have developed a comprehensive numerical model, validated it by experiment and found the optimal design for magnetic sensing and limitation of perturbing effects due to electric field. This approach can be straightforwardly extended to the design of sensors for the detection of charged magnetic nanoparticles.

This work has been supported by the EMRP JRP IND 08 “Metrology for Advanced Industrial Magnetics (MetMags).” The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. The work has been also supported by Progetto Premiale MIUR-INRIM “Nanotecnologie per la metrologia elettromagnetica.”

I. INTRODUCTION

II. NUMERICAL MODEL

III. MODEL VALIDATION

A. Experimental results

B. Modeling results

IV. NUMERICAL ANALYSIS

A. Influence of bias current

B. Influence of geometry

V. CONCLUSIONS

### Key Topics

- Electric fields
- 35.0
- Magnetic fields
- 23.0
- Magnetic field sensors
- 12.0
- Numerical modeling
- 11.0
- Electric currents
- 10.0

## Figures

Schemes of the modeled devices: (a) the reference double-cross device with right corners; (b) the device with sharp slits at the junction corners; and (c) the device with rounded corners at the junction area.

Schemes of the modeled devices: (a) the reference double-cross device with right corners; (b) the device with sharp slits at the junction corners; and (c) the device with rounded corners at the junction area.

Measured maps of the transverse voltage *V* _{AB} of an InAs/GaSb-based device with geometry reported in Fig. 1(a) , width of the current arm *w* _{1} = 1 *μ*m and width of the voltage arm *w* _{2} = 1.5 *μ*m. The maps correspond to the cases of grounded tip, i.e., *V* _{tip} = 0 V, (a) and *V* _{tip} = 0.9 V (b), 2.57 V (c), and −2.57 V (d).

Measured maps of the transverse voltage *V* _{AB} of an InAs/GaSb-based device with geometry reported in Fig. 1(a) , width of the current arm *w* _{1} = 1 *μ*m and width of the voltage arm *w* _{2} = 1.5 *μ*m. The maps correspond to the cases of grounded tip, i.e., *V* _{tip} = 0 V, (a) and *V* _{tip} = 0.9 V (b), 2.57 V (c), and −2.57 V (d).

Computed maps of the transverse voltage *V* _{AB} of an InAs/GaSb-based device with geometry reported in Fig. 1(a) , width of the current arm *w* _{1} = 1 *μ*m and width of the voltage arm *w* _{2} = 1.5 *μ*m. (a) Map of the transverse voltage in the absence of capacitive coupling between the tip and the sample, i.e., assuming only the magnetic effect of the tip. (b)–(f) Maps computed for different values of parameter ψ*: (b) ψ* = −0.012, (c) ψ* = −0.004, (d) ψ* = −0.002, (e) ψ* = 0.001, and (f) ψ* = 0.016.

Computed maps of the transverse voltage *V* _{AB} of an InAs/GaSb-based device with geometry reported in Fig. 1(a) , width of the current arm *w* _{1} = 1 *μ*m and width of the voltage arm *w* _{2} = 1.5 *μ*m. (a) Map of the transverse voltage in the absence of capacitive coupling between the tip and the sample, i.e., assuming only the magnetic effect of the tip. (b)–(f) Maps computed for different values of parameter ψ*: (b) ψ* = −0.012, (c) ψ* = −0.004, (d) ψ* = −0.002, (e) ψ* = 0.001, and (f) ψ* = 0.016.

Case of reference cross geometry (symmetric cross structure with right corners and arm width *w* = 1.5 *μ*m). Computed maps of the transverse voltage *V* _{AB} (a) with and (b) without capacitive coupling between the tip and the sample, i.e., assuming only the magnetic effect of the tip, for *I* _{bias} = 50 *μ*A.

Case of reference cross geometry (symmetric cross structure with right corners and arm width *w* = 1.5 *μ*m). Computed maps of the transverse voltage *V* _{AB} (a) with and (b) without capacitive coupling between the tip and the sample, i.e., assuming only the magnetic effect of the tip, for *I* _{bias} = 50 *μ*A.

Case of symmetric cross structure with right corners. (a) Effect of bias current *I* _{bias} on the transverse voltage *V* _{AB} when the tip is over the cross centre and on the peak signals at the corners. Computed transverse voltage for different positions of the scanning tip along the (b) *u* _{1} and (c) *u* _{2} diagonal directions for two values of bias current *I* _{bias}. The dashed lines are obtained disregarding the electric field contribution.

Case of symmetric cross structure with right corners. (a) Effect of bias current *I* _{bias} on the transverse voltage *V* _{AB} when the tip is over the cross centre and on the peak signals at the corners. Computed transverse voltage for different positions of the scanning tip along the (b) *u* _{1} and (c) *u* _{2} diagonal directions for two values of bias current *I* _{bias}. The dashed lines are obtained disregarding the electric field contribution.

Case of symmetric cross structure with right corners. Computed transverse voltage (*V* _{AB}) for different positions of the scanning tip along the*u* _{1} diagonal direction versus the Hall bar width *w*. The dashed lines are obtained disregarding the electric field contribution. The inset shows the effect of *w* on the transverse voltage when the tip is over the cross centre and on the peak signals at the corners.

Case of symmetric cross structure with right corners. Computed transverse voltage (*V* _{AB}) for different positions of the scanning tip along the*u* _{1} diagonal direction versus the Hall bar width *w*. The dashed lines are obtained disregarding the electric field contribution. The inset shows the effect of *w* on the transverse voltage when the tip is over the cross centre and on the peak signals at the corners.

Case of asymmetric cross structure with right corners. (a) Computed transverse voltage (*V* _{AB}) for different positions of the scanning tip along the *u* _{1} diagonal direction versus the width of the voltage arm *w* _{2} (*w* _{1} = 1.5 *μ*m). The dashed lines are obtained disregarding the electric field contribution. The inset shows the effect of *w* _{2} on the transverse voltage when the tip is over the cross centre and on the peak signals at the corners. Computed maps of the transverse voltage (b) with and (c) without capacitive coupling between the tip and the sample, for *w* _{2} = 0.5 *μ*m.

Case of asymmetric cross structure with right corners. (a) Computed transverse voltage (*V* _{AB}) for different positions of the scanning tip along the *u* _{1} diagonal direction versus the width of the voltage arm *w* _{2} (*w* _{1} = 1.5 *μ*m). The dashed lines are obtained disregarding the electric field contribution. The inset shows the effect of *w* _{2} on the transverse voltage when the tip is over the cross centre and on the peak signals at the corners. Computed maps of the transverse voltage (b) with and (c) without capacitive coupling between the tip and the sample, for *w* _{2} = 0.5 *μ*m.

Case of Hall cross with slits at the corners (Fig. 1(b) ). Computed transverse voltage (*V* _{AB}) for different positions of the scanning tip along the *u* _{1} diagonal direction versus parameter *a* (*b =* 0.5 *μ*m). The dashed lines are obtained disregarding the electric field contribution. The inset shows the effect of *a* on the transverse voltage when the tip is over the cross centre and on the peak signals at the corners.

Case of Hall cross with slits at the corners (Fig. 1(b) ). Computed transverse voltage (*V* _{AB}) for different positions of the scanning tip along the *u* _{1} diagonal direction versus parameter *a* (*b =* 0.5 *μ*m). The dashed lines are obtained disregarding the electric field contribution. The inset shows the effect of *a* on the transverse voltage when the tip is over the cross centre and on the peak signals at the corners.

(a) Computed map of the transverse voltage *V* _{AB} for the Hall cross with slits at the corners when parameter *a* = 0.5 *μ*m. (b) Computed map of *V* _{AB} for the Hall cross with rounded corners when parameter *r* = 1 *μ*m.

(a) Computed map of the transverse voltage *V* _{AB} for the Hall cross with slits at the corners when parameter *a* = 0.5 *μ*m. (b) Computed map of *V* _{AB} for the Hall cross with rounded corners when parameter *r* = 1 *μ*m.

Case of Hall cross with rounded corners (Fig. 1(c) ). Computed transverse voltage (*V* _{AB}) for different positions of the scanning tip along the *u* _{1} diagonal direction versus parameter *r*. The dashed lines are obtained disregarding the electric field contribution. The inset shows the effect of *r* on the transverse voltage when the tip is over the cross centre and on the peak signals at the corners.

Case of Hall cross with rounded corners (Fig. 1(c) ). Computed transverse voltage (*V* _{AB}) for different positions of the scanning tip along the *u* _{1} diagonal direction versus parameter *r*. The dashed lines are obtained disregarding the electric field contribution. The inset shows the effect of *r* on the transverse voltage when the tip is over the cross centre and on the peak signals at the corners.

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