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Abstract
We are proposing next-generation lab-on-a-chip plasmonic tweezers with a built-in optical source that can be activated electrically. The building block of these tweezers is composed of an Au/p+-InAs/p+-AlAs0.16Sb0.84 Schottky diode, with a circular air-hole opened in the Au layer. Under an appropriate forward bias, the interband optical transitions in InAs, acting as a built-in optical source that can excite the localized surface plasmons (LSPs) around the edge of the hole. Numerical simulations show that the LSPs mode penetrates a chamber that is filled with water and electrically isolated from the top gold layer, providing the gradient force components desired for trapping the target nanoparticles suspended in the water. Moreover, we show that tweezers with air-holes of radius 90 nm under an applied bias of −1.6 V, can trap polystyrene nanoparticles of radius as small as 93 nm. The proposed structure provides a new platform for developing the next-generation compact on-chip plasmonic tweezers with no need for any external optical pump.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Dimensions of the particles that can be trapped by conventional optical tweezers are diffraction-limited [1,2]. This limitation can be surmounted by the optical near field of surface-plasmons at a metal/dielectric interface, enabling plasmonic tweezers [3–4]. Unlike conventional optical tweezers, plasmonic tweezers can overcome this limitation and trap sub-wavelength particles [5–12]. However, the significant plasmonic loss in metals seems to be a major obstacle to the development of efficient metal plasmonic tweezers [13]. To overcome this impediment, some researchers have replaced the metal with graphene [14–17], others have suggested using an active gain medium adjacent to the metal [18,19]. In the latter configuration, the metal loss can be compensated by the optical gain of the active medium, when appropriately pumped by an external optical source [20–24] or electric power supply [25–27]. In other words, the gain medium can amplify the surface plasmons polaritons (SPPs) at its interface with the metal.
In our most recent work [28], taking advantage of electrically activated graphene-based spasers [29,30], we have developed the first ultralow-power electrically activated lab-on-a-chip plasmonic tweezers with a built-in light source. There, we have demonstrated that such plasmonic tweezers, needless to a bulky and expensive laser as the external optical source, are capable of trapping polystyrene (PS) nanoparticles of diameters as small as 9 nm, under applied voltages of less than 200 mV. The building block of those tweezers consisted of (Al, In)As/(Ga, In)As/(Al, In)As/(Ga, In)As/(Al, In)As quantum cascaded heterostructures, topped with a graphene nanodisk of fixed chemical potential (0.5-0.7 eV).
Seeking a more feasible and simpler built-in optical source that can be achieved via much less expensive fabrication processes, we have employed the idea first used in [26] and designed a new built-in light source for plasmonic tweezers that consists of a metal-semiconductor Schottky contact with an appropriate hole ion-milled into the metal. Unlike our previous work [28], this new design does not require the fabrication of delicate and complex spasers, involving nano-pillars of quantum cascaded heterostructures each covered by a graphene nanodisk.
2. Proposed device and operating principles
Seeking a metal-based built-in source with a simpler structure we have employed the idea first used in [26], with a geometry similar to that shown in Fig. 1, except for the hole of radius R patterned into the Au thin layer. The original structure consisted of an electrically pumped active plasmonic waveguide made of an Au/p+-InAs/p+-AlAs0.16Sb0.84 Schottky diode. The low refractive index SiO2 layers, surrounding the waveguide core act as the claddings.
Fig. 1. A 3D schematic view of the built-in light source, as the building block for the proposed on-chip tweezers.
Applying an appropriate forward bias to the Schottky diode (i.e. a negative voltage, V < 0, to the top electrode) inverts the surface of the p+-InAs. The carriers’ recombination within the inversion layer results in the interband optical transitions of frequency 85.4 THz (i.e., equivalent to the InAs bandgap ∼354 meV). These optical transitions excite the surface plasmons at the Au/InAs interface while providing the desired gain within the region. In this plasmonic tweezers, the near-field coupling [31,32] plays the role of the phase-matching mechanism between the interband optical transitions and the surface plasmons. The near-field coupling highly depends on the distance between the built-in light source and the metal surface, with an optimum value of ∼10–20 nm [31]. On the other hand, the population inversion responsible for the optical interband transition forms within an ultrathin inversion layer of the same order that is limited by the Debby length. Moreover, the strength of the coupling between the matter and light can be generally increased either by increasing the oscillator strength (i.e., the dipole moment) associated with the matter or by decreasing the mode volume. Furthermore, a plasmonic mode volume is extremely small, confined within a nanoscale region at the semiconductor/metal interface. Besides, the coupling strength depends on the strength of the confined optical field (i.e., the number of photons), which can be enhanced by the gain medium in the proposed structure. Hence, the use of an appropriate active material, like p+-InAs and a right applied voltage that can facilitate the desired population inversion confined within a nanoscale region at the Au/InAs interface can cause interband optical transitions with an oscillator strength that can provide a large number of photons in that nanoscale volume. The near-field coupling of these highly confined photons with the surface plasmons, the Purcell effect [31,32], and the circular nanohole in the Au all together satisfy the required phase-matching condition.
3. Simulation results and discussion
Using the same procedure as reported in [25,26], and using the finite-difference method to solve the Poisson’s, the thermionic emission, and the continuity equations, self-consistently, we have obtained the gain−voltage characteristics of the active medium in the steady-state (Fig. 2). As can be observed from this figure, for V <−0.6 V, the gain increases almost linearly with the applied bias, compensating the metal loss. This can be attributed to the fact that the Schottky barrier height is greater than the InAs bandgap [26].
All the physical and geometrical parameters used in simulations, except otherwise stated, are given in Table 1.
Table 1. The Geometrical and physical parameters used in simulations
To obtain the distribution of the plasmonic mode intensity(|E|2), resulted from the band-to-band optical transition within the waveguide, we have solved the full-wave Maxwell’s equations numerically, using the 3D finite-difference time-domain method. Depending on its lateral dimension (W), the waveguide can support different plasmonic modes. Figure 3 depicts the mode intensity distribution in the x-z plane at y = 0, for V = −1.6 V, below the Au surface, with no hole. The horizontal white dots represent the InAs/AlAsSb interface and the vertical dots show the core/claddings interfaces.
Fig. 3. Profile of SPPs mode intensity (|E|2) below the Au surface, with no hole, in the x-z plane at y = 0, for V = −1.6 V. The horizontal white dots represent the InAs/AlAsSb interface and the vertical dots show the core/claddings interfaces.
As can be observed from this figure, the designed plasmonic waveguide with the given dimensions and boundaries can only guide the fundamental plasmonic TM00 mode with a single maximum, similar to that in [26]. The relatively large plasmonic gain, observed in Fig. 3, can be attributed to the peculiar feature of the semiconductor confinement factor (ΓS) in the plasmonic waveguide near the surface plasmons resonance [34–36]. In other words, in a metal-semiconductor plasmonic waveguide, the slowing-down average energy propagation near the surface plasmons resonance causes the ΓS to exceed the metal confinement factor (ΓM), resulting in a large net modal gain that is the difference between the semiconductor modal gain (Gm= G0 ΓS) and the metal modal loss (αM = α0ΓM), wherein G0 and α0 being the semiconductor material gain and the metallic loss [35].
Figure 3 also shows that the initial plasmonic waveguide (i.e., Fig. 1 with no hole in the Au) layer is not suitable for particle trapping. Because the SPPs mode intensity starts decaying just before the Au/InAs interface and vanishes in the gold layer at one Au skin-depth away from the interface. Hence, to be suitable as the building block of plasmonic tweezers, it should be modified. In this modification, we have opened a periodic array of circular air-holes of radii R along the waveguide length (i.e., y-direction), with a unit cell as depicted in Fig. 1.
The amplified SPPs at the Au-InAs interface penetrating the outside world via each circular hole, exciting the desired localized surface plasmons polaritons (LSPs) around the edge of that particular hole and beyond. This makes each unit cell suitable for use in on-chip plasmonic tweezers with a built-in optical source. Before going any further, we show the effect of the radii of the holes on the penetration of the LSPPs mode intensity. Figure 4 shows the profiles of mode intensity penetration in the x-z plane at y = 0, above the circular holes of radii R = 60 (a), 70 (b), 80 (c), and 90 nm (d). The vertical white dots show the x-positions of the left and right edges of the hole and the white lines indicate the x-position of the left and right core/cladding boundaries. As can be observed in Fig. 4, the plasmonic mode intensity (|E|2) above the surface of the circular nanohole in each unit cell peaks near the hole perimeter. Moreover, the color contours in each illustration disclose that as the filed penetrates in the z-direction, the corresponding maxima converge to form a monopole in a focal plane at a specific z-position for each unit cell. As an example, Fig. 5 illustrates the bell-shaped profile of the plasmonic mode intensity in the x-y-plane at z = 10 nm above the unit cell with R = 60 nm (i.e. near its focal plane).
Fig. 4. Penetration of LSPs mode intensity (|E|2) in the x-z plane at y = 0, above the circular hole of R = (a) 60, (b) 70, (c) 80, and (d) 90 nm.
Fig. 5. The plasmonic mode intensity profile in the x-y-plane at z = 10 nm above the unit cell with R = 60 nm.
Utilizing the proposed unit cell in on-chip tweezers, we may employ the 3D FDTD method to solve the well-known Maxwell stress tensor (T (r, t)) [37–39] numerically and evaluate the components of the average plasmonic force exerted on a particle, positioned above the circular hole,
Now consider an on-chip trapping system, in which the unit cell of Fig. 1, is covered with an appropriate chamber filled with water as a typical fluid used in optophoresis systems [8,13] that is electrically isolated from the Au layer with a 5-nm thick SiO2, similar to that in [28]. Figure 6(a) shows a schematic top view of the chamber Then, we consider four individual unit cells that only differ in their circular holes radii (i.e., 60, 70, 80, and 90 nm). The calculated components of the average gradient force excreted on a PS nanoparticle of radius r=95 nm at various x-positions, 10 nm above the Au top surface, and y = 0 are respectively depicted in Fig. 6(b)−6(e). As can be seen from each of the four cases, the y-component of the gradient force is zero (i.e., Fy (x, y=0, z=10 nm) = 0), and the z-component Fz is negative. The latter component can be balanced by various opposing forces, originating from thermophoresis, fluidic lift, gravity, and electrostatic mechanisms, keeping the particle above the surface [10], presumably trapped vertically at 10 nm above the top Au surface. Due to the circular symmetry of the LSPs profile in the x-y plane at any given z-position, the y-dependence of Fy and Fz at the fixed position of (x=0, z=10 nm) is the same as the x-dependence of Fx and Fz at the fixed position of (y=0, z=10 nm), while Fx(x=0, y, z=10 nm) = 0.
Fig. 6. Schematic top view of the water chamber (a). Components of the plasmonic force exerted on a PS particle of r=95 nm along the x-axis of the x-y plane at 10 nm above the Au top surface with the circular hole of the radius (b) 60, (c) 70, (d) 80, or (e) 90 nm. The corresponding potential energies along the x-axis (f).
Using the x-component of the gradient force, Fx, one can obtain the distribution of the potential energy along the x-direction that determines the trapping capability of the tweezers [39]:
This equation, for a dielectric particle of radius r and dielectric constant εP that is surrounded by water with dielectric constant εW, at a point where the LSPs mode intensity is I $\propto$ |E |2 (2) can be written as [28,40],Two critical parameters of these tweezers are their trapping sensitivities in response to the minute changes in the particle refractive index and radius. Figure 7(a) depicts the variation of U(x) versus the refractive index of a dielectric nanoparticle of radius r = 95 in the tweezers with R = 70 nm. The slope of the linear fit —i.e., Sn ≡ dU/dn ≈ −17 (kBT·RIU−1) — shows that a ±0.01 change in the particle’s refractive index results in a change of ∼∓4.4 meV in the potential energy at room temperature. Figure 7(b) shows a similar plot for U(x) versus r. As can be deduced from this figure, the sensitivity Sr = dU/dr≈−1.4 (kBT·nm−1), showing that a ±0.1 nm change in r changes U by ∼∓3.6 meV.
Fig. 7. Potential energy experienced by a particle versus its (a) refractive index (n), and (b) radius (r).
4. Conclusion
In conclusion, we have designed a new generation of lab-on-a-chip plasmonic tweezers that does not need any external optical source. These compact plasmonic tweezers rather have a built-in optical source that can be pumped electrically. The built-in optical source is composed of a Schottky barrier made of Au/p+-InAs/p+-AlAs0.16Sb0.84. When this diode is under an appropriate forward applied bias, the InAs top surface becomes inverted with electrons coming from the Au layer, recombining with the background holes and resulting in the light emission that can excite the LSPs around the edge of the circular air-hole patterned in the top Au layer and beyond. The gradient force components due to the penetrated LSPs within the microfluidic chamber, covering the Au layer, are strong enough to trap PS nanoparticles. Using 3D finite-difference time-domain method and performing multi-physics numerical simulations, we have shown that the proposed on-chip tweezers with air-holes of radii 60, 70, 80, and 90 nm, under the applied bias of −1.6 V, can trap PS particles of radii as small as 96.5, 94.6, 94, and 93 nm, respectively. Investigating the sensitivity of the tweezer to a minute change in the particle size (refractive index), we have shown that a change of Δr ∼ ±0.1 nm (Δn ∼ ±0.01) changes the trapping potential by ΔU ∼ ∓3.6 (∓4.4) meV, at room temperature. These electrically activated on-chip plasmonic tweezers pave the way for the development of the next-generation optophoresis systems for manipulating biomolecules.
Funding
Tarbiat Modares University (IG-39703).
Disclosures
The authors declare no conflicts of interest.
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