Resolution improvement of optoelectronic tweezers using patterned electrodes

Abstract

An optoelectronic tweezer (OET) device is presented that exhibits improved trapping resolution for a given optical spot size. The scheme utilizes a pair of patterned physical electrodes to produce an asymmetric electric field gradient. This, in turn, generates an azimuthal force component in addition to the conventional radial gradient force. Stable force equilibrium is achieved along a pair of antipodal points around the optical beam. Unlike conventional OETs where trapping can occur at any point around the beam perimeter, the proposed scheme improves the resolution by limiting trapping to two points. The working principle is analyzed by performing numerical analysis of the electromagnetic fields and corresponding forces. Experimental results are presented that show the trapping and manipulation of micro-particles using the proposed device.

Nondestructive trapping and manipulation of micro-/nano-sized objects are of great interest in biotechnology, lab-on-a-chip, and various other applications.^1–4 Conventional optical tweezers,^5,6 plasmonic tweezers,^7,8 and dielectrophoresis (DEP)^9,10 based techniques have widely been used for such applications.¹¹ However, optoelectronic tweezers (OETs)¹² have become increasingly popular as they require less optical power than conventional optical trapping and can be more versatile than dielectrophoretic devices.^4,13–15 Hence, improving the performance of OETs can be of significant interest.

Trapping techniques for micro-/nano-particles usually involve polarizing the particle in a nonuniform electric field. The interaction between the polarized charges on the particle surface and the applied electric field produces a gradient force¹⁶ that either attracts the particle towards high-field regions, or repels it away from such regions. Trapping and manipulation are achieved by controlling the spatial distribution of the electric field. Optical trapping uses focused light beams to create the non-uniform field, whereas DEP uses DC or AC voltage at RF frequencies (kHz–MHz) to achieve the same.^17,18 OETs employ optically induced dielectrophoresis,¹⁹ where an AC voltage is used to create the electric field (as in DEP) but the field non-uniformity is generated through an optical beam. This is done by using a photoconductor layer, which is excited by the optical beam. By spatially translating the light pattern, OETs become a dynamic particle manipulation platform. As it does not take much optical power to excite a photoconductor, OETs can operate with very low powered optics. Thus, they are highly suitable for manipulating sensitive bio-samples, which may not survive the high-powered focused lasers used in conventional optical tweezers.¹²

Much like the physical micro-electrodes used in DEP systems, OETs employ virtual electrodes^12,20 to create the field gradients. Virtual electrodes are illuminated photoconductor regions that have higher electrical conductivity than their surroundings. They behave similarly to physically fabricated electrodes while having the added benefit of being movable through the steerable light pattern. For a Gaussian optical beam, the virtual electrode is also Gaussian shaped²¹ and the resulting field gradient is usually rotationally symmetric. The corresponding gradient force has identical equilibrium points around the rim of the virtual electrode where a particle can be trapped. In general, it is not possible to trap the particle at a specific point on the rim. Thus, the trapping resolution is limited by the size of the optical spot and the corresponding virtual electrode size. While projecting multiple beams or complex light patterns using spatial light modulators can improve the issue, the trapping resolution is still fundamentally limited by the smallest optical feature that can be faithfully projected on the photoconductor. As stringent optical requirements introduce complexities and cost, a resolution improvement scheme that is independent of the optics is desirable.

In this work, we propose an approach of obtaining high spatial trapping resolution without requiring a small optical illumination spot. This is achieved by creating an asymmetric field gradient around the virtual electrode by using patterned physical electrodes below the photoconductor layer. This configuration generates a force with an azimuthal component in addition to the usual radial forces. Once the radial force traps a particle around the rim of the virtual electrode, this azimuthal force pushes it toward two distinct regions around the rim. The trapped particles end up being localized near two antipodal points instead of being arbitrary distributed around the entirety of the beam perimeter. Thus, the resolution is enhanced.

The schematic of the proposed OET device is shown in Fig. 1. Plasma enhanced chemical vapor deposition (PECVD) is used to deposit hydrogenated amorphous silicon (a-Si:H) on top of a patterned quartz substrate to fabricate the OET. The a-Si:H acts like a photoconductor for visible wavelengths.^22–24 Optical excitation to the a-Si:H is provided through the transparent substrate using a 638 nm diode laser. During experiment, a colloidal solution of particles is sandwiched between the photoconductor and the top indium tin oxide (ITO) coated conductive coverslip. A spacer forms a well to seal in the liquid. The key difference between the proposed device and conventional OETs is the absence of a planar ITO electrode beneath the photoconductor. Instead of that, two parallel rectangular (electrically shorted to each other externally) gold electrodes sit beneath the photoconductor. AC electric voltage is applied between these electrodes and the top ITO coverslip. It should be noted that patterned OETs have been reported.²⁵ However, they usually involve patterning the photoconductor and not the planar electrode below. Such designs are excellent in performing complex manipulations. However, they do not focus on resolution improvement. We had previously investigated the addition of physical electrodes on top of a planar ITO layer with promising results.²⁶ However, removing the planar electrode and relying completely on the rectangular electrodes produces a vastly different field distribution and force profile, which has not been reported. The rectangular electrodes produce more field gradients along the x direction than y direction that results in an asymmetric field distribution in the xy plane. This configuration produces an azimuthal force component that is comparable in magnitude to the radial component. Thus, it substantially affects the trapping dynamics.

FIG. 1.

Geometry of the proposed OET trapping scheme. (a) xy plane view and (b) xz plane view. Figures are not drawn to scale.

It should be noted that this design requires additional lithography steps to pattern the electrodes. This makes the fabrication process slightly more complicated than that of standard OETs. However, this added complexity can be justified by the improved performance.

To investigate the operation of the proposed OET, an electromagnetic simulation of the system is performed. Due to computational constraints, a scaled version of the fabricated device is considered for simulation. All relevant geometrical and electrical parameters are scaled down by a factor of 20. It should be noted that the uniform scaling of the voltage and device dimensions preserves the electric field distribution. The parameters are listed in Table I. The material properties (i.e., permittivity and conductivity) are also necessary for the electromagnetic field calculations. They are obtained from the literature^22–24,27 and are listed in Table II. This leaves out only the electrical conductivity near the virtual electrode. Optical excitation generates electron–hole pairs in the photoconductor, resulting in an increased conductivity. Ignoring diffusion lengths of the photocarriers (which are much smaller than the beam dimensions considered here²⁸), the high-conductive region is expected to follow the optical beam profile. For a Gaussian-shaped beam centered on the xy plane and incident on the bottom of the photoconductor ( $z=-t_{\text{pc}}$), the conductivity profile is modeled as

$${\sigma }_{\text{pc}}(r)={\sigma }_{\text{amb}}+({\sigma }_{\text{illum}}-{\sigma }_{\text{amb}})e^{\left[-r^2/w^2-\alpha (z+t_{\text{pc}})\right]}.$$ (1)

Here, $r=\sqrt{x^2+y^2}$ is the polar radial coordinate, (x, y) are the Cartesian coordinates, ${\sigma }_{\text{pc}}(r)$ is the conductivity profile of the a-Si:H photoconductor, ${\sigma }_{\text{amb}}$ and ${\sigma }_{\text{illum}}$ are the conductivity of the a-Si:H under ambient light and under optical excitation, respectively, $t_{\text{pc}}$ is the height of the photoconductor, w is the $1/e$ radius of the Gaussian beam, and α is the absorption coefficient of a-Si:H. The values of these parameters are listed in Tables II and III. Using these values and Eq. (1), the electrical conductivity of all the relevant regions can be calculated. The conductivity profile near the virtual electrode is shown in Fig. 2. We define the effective radius of the virtual electrode, $r_{\text{ve}}$, as the radial distance satisfying ${\sigma }_{\text{pc}}(r_{\text{ve}})=2{\sigma }_{\text{amb}}$. It is a good estimate for the extent of the high conductive region. For the current set of parameter values, the calculation yields $r_{\text{ve}}\approx 4.2\hspace{0.17em}\mu \mathrm{m}$.

TABLE I.

Geometrical and electrical parameters.

Parameter	Actual value	Scaled value
Spacer height, $h_{\text{sp}}$	100 μm	5 μm
Electrode separation, $w_{\text{sep}}$	700 μm	35 μm
Width of the electrodes, $w_{\mathrm{e}}$	20 μm	1 μm
Applied AC voltage, VAC	60 V (20 kHz)	3 V (20 kHz)

TABLE II.

Material parameters.

Parameter	Relative permittivity, ϵr	Conductivity, σ (S/m)
Polystyrene beads, ϵr	2.55	$1\times {10}^{-4}$
Liquid medium (water)	80	$1\times {10}^{-2}$
a-Si:H (ambient light)	11.7	$3\times {10}^{-2}$
a-Si:H (illuminated)	11.7	$2\times {10}^2$

TABLE III.

Optical and photoconductor parameters.

Parameter	Value
Absorption coefficient,29 α	${10}^4\hspace{0.17em}{\text{cm}}^{-1}$
Gaussian beam $1/e$ radius, w	1.4 μm
Virtual electrode effective radius, $r_{\text{ve}}$	4.2 μm
Photoconductor height, $t_{\text{pc}}$	0.8 μm

FIG. 2.

Conductivity profile near the virtual electrode when it is optically excited. Conductivity along (a) the xz plane and (b) the xy plane. Both plots share the same colorbar and x axis.

With all the parameters defined, the electromagnetic field distribution near the virtual electrode is simulated using a full-wave numerical electromagnetic solver. The obtained electric field distribution can be used to find the trapping/manipulation force near the virtual electrode. For a given spherical particle size, the generated gradient force, ${\mathbf{F}}_{\text{grad}}$, is approximately related to the field intensity gradient and material properties as follows:

$${\mathbf{F}}_{\text{grad}}\propto \Re \left[{\tilde{C}}_M\right]\nabla \left(|\mathbf{E}(x,y){|}^2\right).$$ (2)

Here, $\mathbf{E}(x,y)$ is the electric field distribution, ${\tilde{C}}_M$ is a complex number called the Clausius–Mossotti factor, and $\Re [·]$ is the real operator. ${\tilde{C}}_M$ represents the contrast between the material properties of the particle and the medium. ${\tilde{C}}_M$ and the electric field distribution are discussed in more detail in the supplementary material. From the obtained field data, the spatial gradient of the electric field intensity is calculated. The x and y gradients of the field intensity scaled by $\Re [{\tilde{C}}_M]$ are plotted in Fig. 3. Based on Eq. (2), the generated gradient force is expected to follow a similar spatial distribution.

FIG. 3.

Scaled electric field intensity gradients near the virtual electrode (i.e., illuminated photoconductor region) at the $z=0.1\hspace{0.17em}\mu \mathrm{m}$ plane. (a) x gradient and (b) y gradient. Here, $C_M=\Re [{\tilde{C}}_M]=-0.43$ and $E_0=0.6\hspace{0.17em}\mathrm{V}/\mu \mathrm{m}$. The figures share the same y axis.

The location of the zeros in Fig. 3 indicates the approximate equilibrium positions of a trapped particle. From Fig. 3(a), the x force component is found to have stable equilibrium at the points around the rim of the virtual electrode defined by the set $\left\{(x,y)\in {ℝ}^2|\sqrt{x^2+y^2}\approx r_{\text{ve}}\right\}$. The forces are larger along the y = 0 axis. The y component of the force, as suggested by Fig. 3(b), has a more complex nature with both stable and unstable equilibrium points around the perimeter of the virtual electrode. Unstable equilibrium in the context of trapping refers to the case when a small perturbation in the particle position would dislodge it from the trap³⁰ and can be determined by noting the directions of the force near an equilibrium point. In Fig. 3(b), the points along the y = 0 line provide stable equilibrium, while the others are unstable. This indicates that particles would preferentially be trapped along the two antipodal points along the y = 0 line.

The field gradient distribution depends not only on the optical beam but also on the electrode geometry. The rectangular electrodes running parallel to the y axis produces field gradients along the x direction. It is this gradient that limits the equilibrium trapping position to the two antipodal points. Other electrode configurations can be explored that can produce similarly advantageous field gradient profiles. The effective manipulation area can be increased by creating multiple electrode pairs. Interdigitated electrodes can be investigated for this purpose.

To investigate the force profile further, the Maxwell stress tensor (MST) method^1,31 is used to compute the force for various particle positions near the virtual electrode. The Cartesian force components (F_x and F_y) are then converted to polar components (radial, F_r, and azimuthal, $F_{\theta }$) for analysis. The details are provided in the supplementary material. Figure 4 shows the computed force profile as functions of polar coordinates in the $z=r_o+0.2\hspace{0.17em}\mu \mathrm{m}=0.7\hspace{0.17em}\mu \mathrm{m}$ plane. This plane is selected as particle trapping, and manipulation occurs very close to the photoconductor top surface. Figure 4(a) shows a schematic representation of the force components around the virtual electrode. From Fig. 4(b), the equilibrium position for the radial force is noted to be at $r\approx r_{\text{ve}}=4.2\hspace{0.17em}\mu \mathrm{m}$. Thus, a particle will be trapped around the rim of the virtual electrode, which is consistent with the field intensity analysis. It should be noted that the radial equilibrium position slightly varies with the azimuthal angle. To find the true equilibrium point, a two-dimensional analysis of both the radial and the azimuthal forces needs to be performed. According to Fig. 4(c), the $F_{\theta }$ component has equilibrium at $\theta =0°$, and by symmetry at $\theta =180°$. For $-90°<\theta <0°,\hspace{0.17em}{F}_{\theta }$ is positive and the particle is pushed toward the $\theta =0°$ axis. For $0°<\theta <90°,\hspace{0.17em}{F}_{\theta }$ is negative and the particle is again pushed toward the $\theta =0°$ axis. Similar phenomenon happens near points around $\theta =180°$. The combined effect of F_r and $F_{\theta }$ creates two antipodal points at $(r,\theta )=(r_{\text{ve}},0°)$ and $(r_{\text{ve}},180°)$ where particles can be stably trapped. For smaller/larger virtual electrode size, the general trend of the force remains the same. Thus, trapped particles can be confined at two points around the rim of the virtual electrode without imposing any strict constraints on the size of the optical spot.

FIG. 4.

Force profile near the virtual electrode. (a) Schematic of the radial (F_r) and azimuthal ( $F_{\theta }$) force components, (b) F_r distribution for various angular positions, and (c) $F_{\theta }$ distribution for various radial positions. z position of the particle is taken as $z_o=r_o+0.2\hspace{0.17em}\mu \mathrm{m}=0.7\hspace{0.17em}\mu \mathrm{m}$.

Along with the xy plane force profile, the z component of the force also plays an important role in the trapping dynamics. The MST analysis of the z directional force shows that the force is attractive toward the photoconductor surface. Thus, the equilibrium trapping position would be near the virtual electrode and close to the photoconductor surface. The supplementary material contains detailed analysis of the z directional force.

The OET device is experimentally tested to verify the trapping dynamics. Polystyrene microbeads of radius $r_o=0.5\hspace{0.17em}\mu \mathrm{m}$ suspended in water are used in the experiment to demonstrate trapping and manipulation. The sample preparation process is discussed in the supplementary material. A video of the experiment is recorded using a CMOS camera and is included with the paper as multimedia file 1. A few frames of the experimental video are shown in Fig. 5. The two trapping regions around the virtual electrode rim are clearly visible. The two regions remain fairly constant as the optical spot size is gradually increased as shown in Figs. 5(a)–5(e). The resolution improvement is substantial for the large beam in Fig. 5(e) that would usually trap particles all around its perimeter for a conventional OET device. Control over the optical spot size is achieved by moving a pair of beam expansion lenses located at the path of the laser beam. The schematic of the complete optical setup is shown in Fig. 6. Separate optical paths for the laser excitation and the imaging are used here. However, the device operation would remain identical if a standard upright microscope is used where the excitation and the imaging is done through the same objective lens.

FIG. 5.

Frames from experimental video of particle trapping. (a)–(e) Varying optical beam size while maintaining trapping resolution. The rectangular electrodes run parallel to the y axis and are outside the field of view. Multimedia available online Download video file ^{(13.6MB, avi)} DOI: 10.1063/5.0160939.1.

FIG. 6.

Schematic of the experimental setup.

In conclusion, an OET device that improves the trapping resolution without needing to reduce the optical spot size is demonstrated. Electromagnetic analysis shows that the use of patterned rectangular bottom electrodes creates asymmetric field and force profiles. This reduces the stable trapping region to two antipodal points instead of spanning across the entire perimeter of the optical beam. Experimental results verified the prediction of the electromagnetic model. The resolution improvement mechanism lies within the geometry of the device rather than the external optical components. Such devices are highly suitable for lab-on-a-chip applications where complex optical setups are not desirable.

See the supplementary material for details about the numerical simulations and sample preparation.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Mohammad Asif Zaman: Conceptualization (equal); Data curation (equal); Formal analysis (lead); Investigation (equal); Writing – original draft (lead). Mo Wu: Conceptualization (supporting); Data curation (equal); Writing – review & editing (equal). Wei Ren: Investigation (supporting); Resources (supporting); Writing – review & editing (supporting). Michael Anthony Jensen: Investigation (supporting); Resources (equal); Writing – review & editing (equal). Ronald Davis: Funding acquisition (equal); Resources (supporting); Supervision (supporting). Lambertus Hesselink: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Supervision (lead); Writing – review & editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available within the article and its supplementary material.