Characterizing the Switching Thresholds of Magnetophoretic Transistors

Abstract

The switching thresholds of magnetophoretic transistors for sorting cells in microfluidic environments are characterized. The transistor operating conditions require short 20-30 mA pulses of electrical current. By demonstrating both attractive and repulsive transistor modes, a single transistor architecture is used to implement the full write cycle for importing and exporting single cells in specified array sites.

Keywords: magnetism; microfabrication; microfluidics; single cells; transistors.

Figure 1. Illustration of the transistor geometry and potential energy distribution

(a) Ni₈₁Fe₁₉ permalloy disks (gray circles) of radius, R, and thickness, τ_m are designed with a small gap of distance, d. A gate electrode (gold wire) is overlaid with its left edge shifted from the opposing gap side by a distance, λ. A magnetized cell (black circle) of radius, a, is shown moving along the magnetic track. The external field direction, H_ext, is aligned along the track axis, depicted as the black arrow. The potential energy line cross-section simulated at a vertical height of z = a is shown in (b) from finite element (FEM) analysis (black line), and from analytical charge model (red line) based on Eqs. 1–2. A photograph of the chip and 3D printed container used to test the transistors are shown in (c). The overall instrument apparatus is shown in (d).

Figure 2. Transistor operational modes and their energy landscapes

Magnetic potential energy landscapes are shown in (a–c) with corresponding experiments shown in (d–f). In (a–c), the line cross-sections are shown when no gate current is applied (a), in the attractive mode (b), and in the repulsive mode (c). In all cases, a constant uniform magnetic field is applied along the positive x-direction and denoted by the black arrow. In part (d), the bead remains on the same side of the gap due to the double well potential of part (a). In a clockwise rotating field (e), the bead moves across the gap towards the wire due to a gate current in the positive y-direction. In a counter-clockwise rotating field (f), the bead crosses the gap and moves away from the wire due to a gate current in the negative y-direction. Field rotation sense is denoted by the circular arrows, and gate currents are shown as red arrows.

Figure 3. Transistor switching thresholds are depicted for magnetic beads

The experimental switching efficiency in the dynamic transistor tests is shown for the repulsive mode (a) and attractive mode (b) for driving frequencies of 0.2 Hz (blue), 0.5 Hz (red), and 0.8 Hz (black). In these dynamic tests, the rotating field magnitude is H_ext=45Oe. The experimental switching thresholds in the static transistor tests for the repulsive mode (c) and attractive mode (d) are shown for device geometries of d=8μm and λ=6.5μm (green bars), d=10μm and λ=7μm (black bars), d=10μm and λ=8μm (red bars), d=10μm and λ=9μm (blue bars). Theoretical results presented in (e,f), correspond to the transistor mode types of (c,d) respectively.

Figure 4. Transistor switching efficiency for magnetically labeled T-cells

The experimental switching efficiency of magnetically labeled T-cells in the dynamic transistor tests is shown for the repulsive mode (a) and attractive mode (b) for driving frequencies of 0.2 Hz (blue), 0.5 Hz (red) in a constant 45Oe rotating magnetic field. The switching thresholds for cells in the static transistor tests for the repulsive mode (c) and attractive mode (d) are shown for device geometries of d=8μm and λ =6.5μm (green), d=10μm and λ=7μm (black), d=10μm and λ=8μm (red), d=10μm and λ=9μm (blue).

Figure 5. Multiplexed arrays

An 8×8 array was designed and built to import, store, and export magnetized objects. A small section of the array is shown here, in which 3 beads are temporarily stored in array sites 42, 53, and 64 with the import trajectories shown in red. At a later time, the beads are exported from these storage sites with the trajectoreis shown in green. The full trajectories can be found in Supplementary Movie S5.