Massively Parallel Nanorobotics for
Lithography and Data Storage
Aristides A. G. Requicha
Laboratory for Molecular Robotics
University of Southern California
Abstract
Nanometer-scale structures and devices can be constructed by using the tip of a Scanning Probe Microscope (SPM) as a robot. The tip manipulates nanocomponents to build assemblies, or induces material deposition to form patterns on a substrate. Fabrication by SPM methods has severe throughput problems, which can be solved by using arrays of tips built by MEMS (MicroElectroMechanical Systems) technology, in conjunction with the strategies and algorithms presented in this paper. Massively parallel methods are described here for writing and reading nanometer-scale patterns of lines or dots, or for manipulating nanoparticles with arrays of SPM tips. The tip array moves as a whole in the xy plane of the substrate, and does not require individual xy drives and controllers for the individual tips. Applications to nanolithography are discussed, as well as a microelectromechanical storage device, analogous to a compact disk (CD) on a chip, and called an editable nanoCD. NanoCDs can be read and edited by the tip array methods presented here, and have bit densities and reading speeds that are several orders of magnitude higher than current CDs.
Introduction
The SPM is only two decades old but it has had a major impact on science and technology [Wiesendanger 1994]. SPMs are typically used for imaging surfaces, often with atomic resolution. But a growing body of research shows that SPMs can function both as sensors and as actuators. They can modify surfaces and structures at the nanometer scale. For example, a Scanning Tunneling Microscope (STM) can draw lines on a hydrogen-passivated silicon surface by hydrogen removal, and can deposit gold dots or lines on a surface – see e.g. [Wiesendanger 1994, Salling 1996] for reviews of some of this work, which has been able to produce features that range from a few to hundreds of nm. And recently a “desktop factory” has been proposed for producing integrated circuits by STM-induced material deposition [Tabib-Azar & Litt 1997]. This application is roughly analogous to robotic spray-painting or welding in the macro-world. In our own lab we have built patterns of nanoparticles with diameters of 5-30 nm by using an Atomic Force Microscope (AFM) [Baur et al. 1997, Requicha et al. 1998], and others have also tackled challenging nanomanipulation tasks. These are examples of robotic manipulation and assembly at the nanoscale. Despite their remarkable achievements, SPM methods for fabrication or manipulation suffer from a major drawback: they are inherently serial, and therefore have low throughputs.
Recent developments in MEMS technology address this throughput problem by introducing parallelism through SPM tip replication. Massively parallel arrays of tips are currently being developed at several laboratories [Minne et al. 1996, Miller et al. 1997]. However, algorithms and strategies for exploiting such parallelism have not been published, to the best of our knowledge.
SPMs are conceptually simple instruments. To first approximation, the distance between an SPM tip and the sample underneath it is kept constant by a z-feedback loop. The tunneling current (in an STM) or the force (in an AFM) or some other quantity that depends on the tip/sample distance (in less common SPMs) is measured, and used by the feedback control to maintain the distance at a specified setpoint for imaging. Because a surface cannot be perfecly flat, each tip in an array must have its individual z-feedback loop to ensure that the tip floats above the surface at an appropriate distance. This implies that the chip that contains a tip array must have integrated actuators and circuitry for individual tip control in the z direction. Conventional, single-tip SPMs also have xy drives that move the tip over the sample in a scanning motion. For maximum flexibility, a tip array would need separate xy drives for each tip, but this would greatly increase the complexity of the chip, and of the algorithms that coordinate the motions of the individual tips to execute an overall task. Therefore, it is highly desirable to have a single xy drive pair for the entire tip array (or, equivalently, for the sample), although this implies that some tasks may be unachievable.
This paper shows that a massively parallel tip array without individual xy drives for each tip can accomplish important tasks efficiently. It describes methods for controlling tip motion for lithography in a Manhattan geometry suitable for integrated circuit fabrication, and for reading and editing digital data in a novel device, which we call an editable nanoCD and is a nanoscale analog of current compact discs or read-only memory cards.
Nanolithography
We first present our basic method for writing line patterns on an orthogonal grid, and then discuss some of the many possible extensions. Consider an array of N regularly spaced tips extending out of a plane. For concreteness, we assume that the plane is the xy horizontal plane, the tips are oriented downwards, in the —z direction, and the tips are arranged in a square grid, with a size d. We further assume that the tips can write on a substrate that is an approximately planar surface, parallel to the xy plane of the tip assembly, and lying under the tips. Writing by each individual tip is controlled by a signal supplied to the tip. For example, the signal might be a voltage pulse that causes an STM tip to start and stop writing by material deposition.
The patterns of lines to be written lie on the grid itself, although the length of a line is not required to be a multiple of the grid size d. Figure 1 shows a very simple line pattern that satisfies our assumptions. (We will see below that the lines may lie in a grid of size d’<d.)
All xy motion in our method is carried out by the substrate (or, equivalently, by the tip array as a whole) without individual xy control for each tip. Our scheme provides a specific algorithm for distributing work to each of the tips so that parallelism may be exploited. Although, in principle, N tips working in parallel should do a job N times faster than only one tip, in practice it is difficult to distribute the task so that the tips do not interfere with one another, and are kept sufficiently busy for significant time savings to occur.
The basic idea is to draw all the horizontal, or x, lines in a single, parallel operation involving a large number of tips, sometimes collaborating with one another to draw a long line. Then draw all the vertical lines in a similar operation. To draw the horizontal lines we move the substrate by a distance d in the —x direction (which is equivalent to moving all the tips together by d in x). To draw a horizontal line that fits entirely in one linear grid cell we need only tell the probe that “sweeps” through that cell to turn writing on and off at the appropriate times. If a line crosses cells’ boundaries, we tell several probes to each draw the portion of the line that falls within the cell swept by the probe. Then we do the same for vertical lines, and the line pattern is finished! The time taken by each of these operations is bounded by the time T needed to write one line of length d. The total time for writing the entire pattern is bounded by 2T.
Figure 1 – A simple line pattern lying on a grid of size d.
The algorithm for assigning tasks to tips and determining when to switch the tips on or off is very simple and thus suitable for hardware implementation. It may be summarized as follows. Choose the coordinate system so that the origin is at the lower, left corner of the tip array. Tip coordinates are x=id, i=0,1,…,m-1 and y=jd, j=0,1,…,m-1. The total number of tips is N=m2. A tip is represented by the corresponding indices (i,j). Lines in the pattern are represented by the coordinates of their endpoints. The algorithm is written in a self-explanatory pseudo-code, inspired by the Pascal or C family of languages. Double slashes indicate comments. We denote by v the uniform velocity at which the array moves.
for j = 0 to m-1 do // Horizontal line processing
{
for each horizontal line at y=jd with endpoints at x1,x2 do
{
p = Integer part of x1/d;
q = Integer part of x2/d;
if p = q then // Line falls in one cell only
{
// Assign to Tip (p,j):
TimeOn(p,j) = (x1 - p*d)/v; // v is the velocity
TimeOff(p,j) = (x2 - p*d)/v;
}
else // Line covers several cells
{
r = q - p;
// Assign to Tip (p,j):
TimeOn(p,j) = (x1 - p*d)/v;
TimeOff(p,j) = d/v;
for k=1 to r-1 do
{
// Assign to Tip (p+k,j):
TimeOn(p+k,j) = 0;
TimeOff(p+k,j) = d/v;
}
// Assign to Tip (p+r,j):
TimeOn(p+r,j) = 0;
TimeOff(p+r,j) = (x2 - q*d)/v;
}
}
}
for i = 1 to m-1 do // Vertical line processing
// Analogous to the horizontal line processing loop
The basic method described above can be extended in several directions, discussed below. The first is especially important.
- The line pattern to be drawn may have a resolution much smaller than the size of the tip array grid. Suppose that the lines are on a grid of smaller size d’=d/n, as shown in Figure 2. We draw first the horizontal lines that correspond to y=0, d, 2d, … as before. Then, we move the tip assembly in y to y=d’, and draw all the horizontal lines for y=d’, d’+d, d’+2d,… Next, move to y=2d’, and so on, until all horizontal lines are drawn. Since d = nd’, this takes n times longer than the earlier procedure for the larger grid. We do the analogous construction for vertical lines. The total construction time is upper bounded now by 2nT. This is a conservative estimate because it assumes that a line of a maximum length d is always written. Optimization techniques can reduce this time considerably. The time bound is independent of pattern complexity, and depends only on the minimum separation between lines.
- The method can also be used to write point patterns. It suffices to approximate the points with small horizontal (or vertical) lines with length equal to the line width. The tips are switched on for a constant amount of time, and the algorithm given above can be simplified in the obvious manner.
- The method can be used for reading, instead of writing. This requires tips capable of reading some relevant characteristic of the substrate, for example, capacitance probes that sense charges on the substrate, or more standard probes that read topographical data. Instead of applying a write signal as described earlier, one simply records the signals read by each tip in the horizontal or/and in the vertical motions.
Figure 2 – A line pattern on a grid of size d’ with a tip array on a grid of size d.
- A regular grid is essential, but it need not be a square grid. Any regular tiling of the plane will do. For example, Figure 3 shows a triangular grid, which permits writing (or reading) line (or point) patterns along 3 directions, instead of the horizontal and vertical directions of the basic method. Note that a square grid can also be considered a triangular tiling, in the two manners shown in Figure 4, and therefore used to draw lines along directions at +45 and -45 degrees.
- Time can be quantized in D t steps, resulting in lines with lengths which are multiples of a minimum value vDt.
Figure 3 – A grid of isoscelles triangles
Figure 4 – A square grid can also be viewed as a triangular grid
Editable NanoCDs
An editable nanoCD is a novel device that serves to store digital information, and is analogous to existing CDs (compact disks). The nanoCD encodes digital information into the positions of nanoparticles on a flat surface. Writing is done by nanomanipulation of the particles so as to position them appropriately, by using the tip of an SPM. Reading is done by scanning the nanoCD with the SPM. The nanoCD has bit densities several orders of magnitude higher than current devices, and it is rewritable, or editable. Other approaches to high-density storage are being studied at IBM, Hitachi, and elsewhere – see [Ried et al. 1997] and references therein.
Here we describe a concrete example of the nanoCD. There are many variations and extensions of the basic technology, as noted below. Imagine yourself in the early 1970s when minicomputers such as the HP 2116 first appeared. Program input was accomplished by reading perforated paper tape. Perforations corresponded to bits, and rows of bits defined text characters. In our nanoCD the perforations are replaced by nanoparticles.
Consider a rectangular grid on a flat surface, with distance between grid nodes equal to d. Each row of the grid has 8 nodes, and the number of rows is governed only by the available real estate. The existence of a nanoparticle at a node encodes a binary ‘1’; a ‘0’ corresponds to the lack of a nanoparticle. Therefore, a row corresponds to 8 bits or 1 byte. Figure 5 shows 3 rows that encode the characters ‘LMR’ (the initials of our lab) written in the binary ASCII code that is used in much of computing.
Figure 5 — Three rows of nanoparticles encoding ‘LMR’ in ASCII.
(The small dots represent grid points and the large dots nanoparticles.
For simplicity, assume d = 100 nm. This corresponds to 100 bits in an area of 1 square micrometer, or to a bit density of 10 Gb/cm2, which is approximately 100 times better than current CDs. We have demonstrated in our lab that gold particles can be placed at smaller distances, and therefore we can expect at least another order of magnitude improvement in density by using existing techniques.
Reading a row is done by a single line scan of the pattern with an AFM in non-contact mode. (Non-contact AFM operation uses a tip mounted on a vibrating cantilever and detects tip/sample force variations through the frequency shifts they cause [Wiesendanger 1994].) The result of reading a row of “nanobits” is a trace from which it is easy to decode the pattern by simple thresholding or more sophisticated filtering. Figure 6 illustrates the process by using actual images of a pattern of 15 nm gold balls constructed in our lab by pushing the nanoparticles with an AFM. It shows three rows of balls that encode “LMR”, the initials of our lab, and the trace obtained by reading the second row. Note the very high signal to noise ratio.
Writing can be done by a 2-step procedure as follows. In the first step, fill every other row with balls. In the second, or editing, step, for each full row, move down, to the next empty row, the balls necessary to leave the desired pattern in the original row. This procedure is illustrated in Figure 7, where the first row has been written with the character ‘L’ but the others are still awaiting the second step of the writing procedure.
To move a nanoparticle we use the pushing technique developed in our lab [Baur et al. 1997, Requicha et al. 1998], which may be summarized as follows. First we image the sample with the AFM in non-contact mode. Then we place the tip near a particle to be moved, turn off the z feedback and move the tip in a straight line by the desired amount, thereby pushing the particle. This procedure can be considered as a special case of the line writing operations discussed earlier, since it amounts to moving a tip in a straight line and turning a signal on and off. Pushing operations are conducted in ambient air at room temperature.
The two-step writing procedure wastes half of the real estate, but it makes the second step easy to accomplish, since particles have to be moved in a fixed direction and by a fixed, small amount d. It also provides redundancy for error detection and correction, since pairs of rows have complementary patterns. Since the balls lie on a regular pattern, and particle pushing is essentially a line writing operation, the second step can be done with a tip array by using the methods described earlier. Therefore, a nanoCD can be easily and efficiently edited.
Figure 6 — An encoded “LMR” pattern and the output signal corresponding to “M”.
Figure 7 — A 2-step writing procedure
The first writing step might also be performed by means of pushing operations starting from a random distribution of nanoparticles, but efficient strategies and algorithms for using a tip array for such a complex manipulation task are yet to be developed. Alternatively, the initial, regular configuration might be achieved by self-assembly or by deposition.
An estimate of the reading and editing speed may be obtained as follows. Assume that the tip array has 106 tips, on a square grid with distance d = 10 mm, which corresponds to a chip with 1,000 tips per side and 1 cm2 area. Assume also that the tips move at 2 mm/s. This is the speed that is used routinely in our lab for nanomanipulation experiments with a commercially-available AFM. Suppose further that the dots are located on a grid with d’ = 100 nm. Then each tip will traverse a 100 nm distance in 0.05 s and read or edit 1 bit. The entire array, therefore, will read or edit 106 bits in 0.05 s, which corresponds to a speed of 20 Mb/s. This is more than one order of magnitude better than standard CD speeds. Furthermore, scanning speeds on the order of 3 mm/s [Minne et al. 1966] or even higher [Ried et al. 1997] have been achieved by using specially-designed cantilevers and scanners. These correspond to reading speeds three orders of magnitude better than those we routinely use in our lab. Therefore, we can expect nanoCD reading speeds to exceed current CD speeds by several orders of magnitude.
Since reading is done in non-contact mode, the nanoCD and the AFM tip will not wear out significantly. Patterns seem to be very stable in ambient conditions. In our lab we have patterns that have been generated a year ago and show no signs of deterioration. Long term stability is yet to be investigated systematically.
There are many possible variations and extensions of the basic technology outlined above. A few follow:
- Most of our experimental work in nanomanipulation has been done with gold colloidal balls on a mica substrate. But many other nanoparticles/substrates should behave similarly. Many types of colloidal nanoparticles (e.g., metalic, semiconducting, magnetic) are available today.
- Encoding is not restricted to the ASCII code, and the current CD codes can be used as well. Successive bits or bytes in a file need not be stored sequentially. For example, successive bytes might be stored in rows d apart, to ensure that they are read in one single x motion of the tip array.
- Grids need not be rectangular, and rows need not contain only one byte of data. One can even make nanoCDs with circular nanoparticle patterns that are suitable for rotary devices, although not with the tip arrays discussed here.
- Smaller particles and shorter spacings can be used, with corresponding increases in bit density.
- Nanoparticle patterns may be used to create templates (masks, stamps or molds [Chou et al. 1996, Xia & Whitesides 1997] ) and these used for nanoCD reproduction in large quantities.
Summary and Conclusions
Recent developments in MEMS technology have produced integrated arrays of SPM (Scanning Probe Microscope) tips, motors and circuits for controlling the tip/sample distance, z. It has also been demonstrated that conventional, single-tip SPMs can be used to write and read patterns of features with dimensions in the order of a few nanometers. This paper shows that tip arrays with a single pair of drives that move the array as a whole in the xy plane of the sample can be used for important applications. Building suitable tip arrays by using MEMS technology is much easier and cheaper if only one set of xy motors and controllers is needed, instead of individual motors and controllers for each tip. For large arrays, the savings can be very large.
We describe massively parallel methods for writing and reading line or dot patterns on a substrate, and for manipulating arrays of nanoparticles by using all the tips of an array simultaneously. Fabrication of integrated circuits (ICs) by nanolithography, and testing of ICs with capacitance probes are examples of potential applications of these methods that have a large practical impact. More mundane applications, such as ink-jet printing might also benefit from our methods.
We also discuss a novel device, which we call an editable nanoCD, in which digital data is encoded in the positions of nanoparticles on a grid. Bit sizes and shapes are very uniform because monodisperse colloidal particles are readily available. NanoCDs are read and edited by using SPM tip arrays, with the methods described here. They may lead to a new class of storage devices with very high densities and reading speeds, and very small sizes. They may be used as stand-alone systems like conventional CDs, but, perhaps more interestingly, they may also serve as (editable) ROMs imbedded in miniaturized systems for a variety of applications. For example, a chip-sized memory card with an area of 1 cm2 would contain in the order of 10 GB of data, which would suffice for storing a high-resolution navigation map of a large region, or a CAD model of a large portion of a vehicle.
The concepts described here are promising, but much work is needed before they can be transmuted into practical devices and systems. Some of the issues to be investigated are the following.
- The effect of spatial uncertainties. For example, what is the effect of errors in the positions of the individual tips on the system’s behavior?
- Fault tolerance or compensation. A (hopefully small) number of tips is likely to fail. Strategies are needed for coping with such failures. A naïve approach consists of first determining which tips are not operational (by testing the array), and then assigning their tasks to neighboring tips. This, however, requires additional motion of the array and is costly in terms of speed.
- Operation over large areas. The maximal area that can be processed directly by the techniques described above is on the order of the array size. To cover larger areas, it may be possible to rely simply on the accuracy of the xyactuators. Alternatively, aligning marks may be made on the substrate by using micrometer-scale technology.
- Techniques for generating regular arrays, to be used as a first step in nanoCD writing or other applications. Self-assembly techniques for generating regular arrays are promising, and our preliminary investigations indicate that efficient algorithms for converting random patterns into regular ones also show promise.
- Environmental stability. Are the patterns affected by temperature, mechanical shock, and so on? What is their useful life?
- System engineering. The physical construction of an integrated system that demonstrates the principles described in this paper, and operates reliably at high speed and with high line or bit density, is a non-trivial engineering task.
Acknowledgements
The research reported here was partially supported by the Z. A. Kaprielian Technology Innovation Fund and the NSF under grant IIS-98-13563. I thank all of my colleagues at USC’s Laboratory for Molecular Robotics, who taught me much of what I know about SPM technology, and were instrumental in the development of the nanomanipulation methods which show that the operations described in this paper are experimentally realizable.
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