Information storage and retrieval in a single levitating colloidal particle

Transcription

1 Information storage and retrieval in a single levitating colloidal particle Christopher J. Myers, Michele Celebrano & Madhavi Krishnan Fig. 1. Laser scanningg miscroscope set-up too control and monitor the t state of optically and electrically actuated single nanorod switch. Electrical fields are applied to the chip using Tungsten microprobe electrodes. Abbreviations used: GM galvanometric mirrors; BS beam splitter; Pol. polarizer; Obj. O Objective; * computer controlled; / /2 /2 waveplate. NATURE NANOTECHNOLOGY 1

2 Fig. 2. Absorption spectrum of silver nanorods. The linearly polarized probe beam at 671 nm excites the broad longitudinal resonance off the rod. p Fig. 3. Measured electro-osmoticc flow velocity, veof as a function of 4 2 applied electric field, E. The proportionality constant k ( ) 10 μm /s V from the linear fit is used to relate the applied electric field too the force on the rod. 2 NATURE NANOTECHNOLOGY

3 SUPPLEMENTARY INFORMATION Fig. 4. Conductance measurement for a single nanoslit.. Current was measured on a stack of 75 parallel nanoslits as a function of applied a voltage. Displayed above is the measured current for a single nanoslit of length 5 mm, height, 2h 90nm 12 and width 20 m. The linear fit yields a conductance S, which translates to a resistance of 730 M for a pixel of nominal length and width 1 m. Since the conductance in silica nanoslits is surface-dominated, the quantity reaches a limiting value independent of slit height (e.g., for low bulk fluid conductivity 100 S/cm, the limiting conductance e is attained for 2h 200 nm) (19). Symbol colors indicate independent measurement series on the same device. NATURE NANOTECHNOLOGY 3

4 Fig. 5. Electrostatic rotational relaxation time. In order r to measure t, e re, the relaxation time of the rod due to the electrostatic field alone, we apply a periodic optical gate pulse whose polarization is orthogonal to the equilibrium orientation off a nanorod trapped in a well similar to minimum 1 of Fig. 5. Optical torquee causes the rod to orient along the gate beam electric field on a timescale of around a 28 s as displayed in Fig. 5d, and for parallel probe and gate beam polarizations, the rod scatters light strongly. When the gate beam is turnedd off ( t 0in the above plot), the rod returns to equilibrium under the influence of the underlying electrostatic torque and the signal decays to zero. Superimposing 200 ON-OFF transitions gives an average intensity trace t for a single rod depicted above. An exponential fit to the intensity decayy yields a timescale of t re, μs that represents electrostatic rotational relaxation of the nanorod. 4 NATURE NANOTECHNOLOGY

5 SUPPLEMENTARY INFORMATION Fig. 6. Potential energy landscape in the presence of optical torque. The plot displays the calculated electrostatic energy of a single nanorod as a function of spatial position, x and rod angle, in a T-shaped well consisting only off minima 1 and 2 of the quadrastable potential well as shown in Fig. 5. As presented in Fig. 5b, the energy landscape results in a much lower barrier for the forward transition (1 2) compared to the backward transition ( 2 1), when driven by b optical torque. For example, in order to follow rod motionn from well 1 to 2 driven by optical torque, we start at the rod s initial position at x = 0 and trace the energy profile along 0 (solid arrow) the rod s orientation in the presence of a horizontally polarizedd gate beam (G x, see Fig.1). Driving thee rod back from well 2 to t 1 using a vertically polarized gate beam (G y ) however, would encounter a higherr electrostatic barrier ( 5 kbt ), as revealed by the contour of energy corresponding to 2 (broken arrow). Thus when driven by a torque rather than a force, thee T-shaped potential well inherently imposes directionality on rod translation. Note that due to thee symmetry of the system, the barrier for the 2 1 transition is identical to that of the 1 4transition depicted in Fig. 5b. Line profiles for the two transitions are shown in Fig. 5b. An open- used in the experiment in Fig. 5 could be used to generate optically driven net directedd displacement of the loop arrangement of T-shaped wells as opposed to the closed loop configuration rod. NATURE NANOTECHNOLOGY 5

6 Section 1. Calculation of the 2D distributions of electrostatic energy and most probable angle shown in Figs. 1b and c & 2d. The calculated 2D electrostatic potential, shown in Fig. 1b is based on the solution of the Poisson-Boltzmann equation for the spatial electrostatic potential in the 3D nanostructure as described in previous work (Refs ). In this work we model the nanorod as a two dimensional rectangular box of dimensions 160nm 50nm, carrying a total charge q uniformly distributed over its area, and approximate its free energy by the electrostatic energy, We have verified using full 3D calculations of the free energy (Ref. 13) that this approximation is reasonable; it is also computationally much cheaper. The center of mass of the box is scanned over the landscape, and at each point the rod is rotated through an angle about the z-axis. The mean electrostatic energy for each is estimated by determining where A denotes the area of the box. Fig. 1b is a projection onto the xy plane of the overall minimum value of axial and angular energy, at each point in xy. Figs. 1c and 2d present plots of the most probable angle as a function of spatial position in xy and are derived from the distribution at z = h representing the mid-plane of the slit. The box representing the nanorod is rotated through 180 at each point in and the angular electrostatic energy determined as before. Due to the geometry of the trap the angular energy distribution at each locus goes through a minimum which corresponds to the most probable (most energetically favourable) orientation. We further point out that this most probable angle is associated with a stiffness that defines the magnitude of the local angular fluctuations of the rod, rms. For the case in Fig. 1c, we find rms =18 at the minima of the bistable well. Section 2. Variability and stability of single switch performance There is some variability in performance of individual switches in the three operation modes (Figs. 2, 4 and 5). We currently attribute this mainly to the dispersion in particle properties rather than the fabricated nanostructures. The tolerance achieved in trap fabrication ca. 5 nm, is much smaller than the relevant length scale for the electrostatics, the Debye length (ca. 40 nm). So the trap landscape itself is highly reproducible. The particles however are not monodisperse in terms of shape, size and charge (see figure below). Individual rods can vary in dimensions by more than 60% and their charge can also show substantial variation (gold nanospheres in a previous work of ours showed a factor 3-4 spread in charge 1 ). We therefore attribute the observed experimental variability mainly to that of individual nanorods. (1) Volatile electrical switching (Fig. 2) The data shown in Fig. 2 is representative of ~ 90% of switches. At high fields 10 mv/ m, however we find that about 50% of 6 NATURE NANOTECHNOLOGY

7 SUPPLEMENTARY INFORMATION the switches fail (particles are ejected from the trap upon prolonged switching, ca. 100 cycles). The plot above shows OFF-ON switching time, t s as a function of electric field, E for volatile operation of 6 switches in different devices. Transmission electron micrographs of representative nanorods (from a sample of 11) are depicted on the left. Thus for controlled comparisons with simulationss we switchh a single rod over the entire range of electric fields. The strongest influence we observe is at the level of the breakdown voltage for each pixel. In our model, the breakdown force (given by the gradient of the free energy at the edges of the pixel) is proportional to rod charge. As a result weakly charged particles are ejected from the trap as a we rampp up the external field in order to drive down switching times (in fact we note on the side that this approach could serve as a sensitive s route to measure single particle properties!). This issue becomes more pronounced in non-volatile operation, where in our current configuration the force f to overcome the barrier between statess is only about a factor 2 smaller than the breakdown force. (2) Non-volatile electrical switching (Fig. 4) Allowing for at most 50% error-rate in switching, we could get an estimated 20-25% working switches. In experiment (2) higher fields f are needed to overcome the high barrier between the states, which leads to more frequent ejection of weakly charged/small particles compared to (1). Further, the asymmetry of the potential landscape in forward and reverse motion (green curves in Fig. 4b) contributes to the failure f rate since we use the same magnitude of forward and reverse applied field in the switching process. Finally, the exponential dependence of switching time on applied field makes the stability of a pixel strongly dependent on the duration of the applied pulse, which wee kept constant in our experiments. NATURE NANOTECHNOLOGY 7

8 (3) Non-volatile optical switching (Fig. 5). Here, particle ejection from the trap is no longer an issue but radiation pressure from the optical torque beam can cause weakly charged particles to stick to the slit surface. This is the primary failure mode. In this experiment, we pre-screened switches based on on-off state lifetimes. Again allowing for at most 50% error rate over a few switching cycles, we find 25-50% working switches. Clearly design optimization of the barrier and edge-gradients will greatly improve the tolerance of the traps to dispersion in particle size and charge and improve the error-rate and endurance. We can currently achieve >8000 operations in volatile operation. This number is expected to increase dramatically upon further fine-tuning well design with pixel edge-gradients that support higher breakdown forces, in addition to the use of highly monodisperse particles from specialized colloidal syntheses. Finally, long term stability of charge both on the surfaces and in the fluid phase is critical to the lifespan of the colloidal switch. Surface charge-mediated electrostatic stabilization of colloids in suspension is a ubiquitous mechanism, both in nature and in the laboratory. It is common experience that particles in suspension retain their charge and remain stable for several years: suspensions of charged gold colloid have been known to be stable for several decades. The fluid phase on the other hand needs to be adequately isolated from changes in charge density (ionic strength) due to ions diffusing in from extraneous sources such as the silicon dioxide or glass substrates. It is worth adding that the concept is not limited to the use of water as the fluid phase; apolar and less polar fluid media may also be used. Nevertheless, for our proof-of-concept scientific demonstration we use off-the-shelf particles suspended in water, substrate materials without optimization, and have implemented no special measures to ensure stability beyond the experimental time scale of a few hours. In order to create a highly reliable commercially viable device, additional measures such as sealing and isolation of the fluid phase, as well as optimization of the surface chemistry of both the particle and wall surfaces would be essential. Section 3. Comparison with current electronic memory and storage technologies Below we provide a comparison of various figures of merit of our fluid-phase colloidal bit (FCB) with a selection of (solid-state) commercialized and prototype approaches. A more appropriate comparison might perhaps involve other approaches at the laboratory research stage, but the schemes under investigation cover gas-phase atoms to nanomechanics, a range that is too varied to facilitate a succinct comparison of performance metrics that is yet fair and meaningful. 8 NATURE NANOTECHNOLOGY

9 SUPPLEMENTARY INFORMATION Table 1. Comparison of electronic memory and storage technologies. This data was adapted from Yang et al. Nature Nanotechnology 8, (2013), originally sourced from ITRS International Technology Roadmap for Semiconductors, 2011 Ed. Abbreviations: PCM, phase change memory ; STTRAM, spin torque transfer random access memory ; SRAM, static RAM ; DRAM, dynamic RAM ; HDD, hard disk drive; FCB, fluid-phase colloidal bit; V volatile operation mode; NV non-volatile mode. Notes: *The electronic read-time quoted for our experiment is the read-out rate of the external CMOS camera that records the switched state. This value represents the energy loss purely due to viscous dissipation. In the current configuration the energy loss for high speed operation would be much higher (by 2 orders of magnitude), as for highly charged surfaces most of current arises from the surface conductance at the walls which does not contribute strongly to the bulk fluid velocity. Use of alternate surface materials could enable the attainment of the friction-limited regime. [1] As long as voltage is applied. There is substantial interest in the development of the universal memory which combines the speed of SRAM with the non-volatility of Flash. As can be seen from Table 1, speed and non-volatility generally do not go together. Our fluidic bit could in principle meet this requirement. References 1. Mojarad, N. & Krishnan, M. Measuring the size and charge of single nanoscale objects in solution using an electrostatic fluidic trap, Nature Nanotech. 7, (2012). NATURE NANOTECHNOLOGY 9