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Proceedings of the International Mechanical Engineering Congress and Exposition IMECE2010

November 12-18, 2010, Vancouver, British Columbia, Canada

IMECE2010-38960

nanoFIBrication OF A TWO-DIMENSIONAL PHONONIC CRYSTAL IN A FREE STANDING MEMBRANE

Drew Goettler University of New Mexico Albuquerque, NM, USA

Mehmet Su University of New Mexico Albuquerque, NM, USA

Roy Olsson, III Sandia National Laboratories

Albuquerque, NM, USA

Ihab El-Kady Sandia National Laboratories

Albuquerque, NM, USA

Zayd Leseman University of New Mexico Albuquerque, NM, USA

ABSTRACT

A two-dimensional phononic crystal (PnC) that can operate in the GHz range is created in a freestanding silicon substrate using NanoFIBrication (using a focused ion beam (FIB) to fabricate nanostructures). First, a simple cubic 6.75 x 6.75 μm array of vias with 150 nm spacing is generated. After patterning the vias, they are backfilled with void-free tungsten scatterers. Each via has a diameter of 48 nm. Numerical calculations predict this 2D PnC will generate a band gap near 22 GHz. A protective layer of chromium on top of the thin (100 nm) silicon membrane confines the surface damage to the chromium, which can be removed at a later time. Inspection of the underside of the membrane shows the vias flaring out at the exit, which we are dubbing the ‘trumpet effect’. The trumpet effect is explained by modeling the lateral damage in a freestanding membrane.

INTRODUCTION

Milling anisotropic holes, or vias, with a focused ion beam (FIB) into a material with precise control over size and location is a useful technique for many applications. Circuit editing in the semiconductor industry is one such example. Vias are required to ‘probe’ the circuits that are embedded below the surface [1-3]. Another application is the fabrication of photonic [4-7] and phononic crystals [8-10]. Both crystals require material to be set up in an orderly fashion, and generating vias in a crystalline pattern is one such possibility [9, 11, 12]. This work focuses on fabrication of a two-dimensional phononic crystal using nanoFIBrication (using a FIB to create nanostructures).

Successful nanoFIBrication of a two-dimensional phononic crystal (PnC) in a freestanding membrane requires both an ordered, crystalline pattern and isolation of the crystal from

surrounding material. In this work the crystal is comprised of a silicon matrix material with tungsten inclusions arranged in a periodic array inside the matrix. These materials were chosen because of their ability to be processed with a FIB and their high acoustic impedance mismatch. Large differences in the acoustic impedance of two materials leads to wider band gaps in a PnC [13, 14]. The center frequency of the band gap, however, is determined by the spacing between inclusions and radius of the inclusions [9, 15].

When vias are milled, most often the only direction for sputtered material is up and out of the hole. In a freestanding membrane, however, once the hole emerges from the bottom, there is an additional exit for the sputtered material. A second unique feature of milling vias in a freestanding membrane is direct observation of the vias penetrating the entire thickness of the membrane prior to backfilling the holes with Tungsten (Figure 1). In this article, it is shown that vias can be successfully milled and subsequently filled with a void-free metal deposition inside a FIB chamber.

NOMENCLATURE PnC Phononic Crystal FIB Focused Ion Beam FDTD Finite Difference Time Domain SOI Silicon-on-Insulator BOX Buried oxide PR Photo resist BOE Buffered oxide etch GIS Gas-insertion system t Thickness of membrane a Spacing between vias

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MODELING A numerical simulation of elastic waves propagating

through the PnC was performed using the FDTD method. A detailed description of the FDTD method can be found in Reference 12. Results of the simulation are shown in Figure 2, which show a band gap centered at 22 GHz with a width of 9.1 GHz (equal to 41% of center frequency). The simulation uses tungsten inclusions with a radius of 24 nm spaced 150 nm apart within a silicon matrix.

Additional modeling was performed to observe the effect of ions impinging upon a freestanding silicon surface. This was done with a software package called SRIM, which is able to calculate the stopping and range of ions into matter by using a quantum mechanical treatment of ion-atom collisions [16]. With this model, it can be shown that incoming ions induce damage in a cone, or trumpet shape (Figure 3).

Figure 1: SEM picture of PnC crystal imaged at an angle of 52

degrees with vias spaced 150 nm apart milled into a freestanding membrane comprised of Cr (a protective layer) on top of Si. A 1 μm gap exists between the membrane and Si substrate. Damage to the

substrate below the PnC indicates complete penetration of the membrane for all vias.

Figure 2: FDTD simulation predicts a band gap centered at 22 GHz

for a 2D PnC with tungsten inclusions inside a silicon matrix. Radii of

inclusions equal 24 nm and are spaced 150 nm apart. Width of band gap equals 41% of the center frequency.

FABRICATION OF FREESTANDING MEMBRANE The first step in fabricating 2D phononic crystals requires

the creation of a thin, 100 nm device layer on a SOI wafer. Studies show that either ultra thin membranes (t < a) or ultra thick slabs (t > 10a) produce a band gap unaltered by slab modes [17]. The initial top silicon layer was 450 nm +/- 25 nm, and the BOX layer was 1000 nm +/- 20 nm thick. Growing and removing thermal oxide thinned the device layer to the desired thickness. Because of the long run time required to grow the appropriate thickness of SiO2 in a single step predicted by the Deal-Grove model, thinning was performed in multiple steps to cut down on run time. After each run, the thermal oxide was removed using a 6:1 BOE. The wafers were then cleaned with DI water prior to each growth to minimize contaminants.

Figure 3: Ion induced damage to 50 nm freestanding layer of Si with

N2 gas on backside of Si. Ions enter at midpoint of left-hand face. Red dots indicate position of ions at a specific point in time (not final

resting position).

Figure 4: Fabrication process for creating a thin, freestanding

membrane for 2D PnC’s.

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Once the wafers were thinned, the next step was to pattern the outline of the PnC on the wafer. The process for creating the PnC outlines is shown in Figure 4. First, a thin, protective Cr layer was sputtered onto the thinned wafers. Next, a layer of PR was placed on the Cr. Once the PR was patterned, the wafer was dipped into a Cr etchant to allow the pattern to be traced onto the Cr layer. The wafer was then placed in a bath of KOH to remove the thin device layer. Finally, the devices were undercut by removing the SiO2 using additional 6:1 BOE.

Because of the devices’ dimensions (100 nm thick and 10-20 microns in width), they were prone to stiction failure [18-20]. In order to minimize the possibility of stiction failure, the devices were dried using a CO2 critical dryer. Figure 5A shows a released, freestanding membrane of Cr on Si.

Figure 5: A) SEM image of released, freestanding membrane of Cr on

Si prior to nanoFIBrication. B) SEM image showing top view of nanoFIBricated array of vias with 150 nm spacing.

nanoFIBrication The next step was to nanoFIBricate an array of air holes

and backfill with tungsten. All of the FIB work was performed with FEI’s Quanta 3D FEG dual beam system. The ion gun was used to both mill and backfill the vias with tungsten.

Spacing between holes in both the x and y directions was set to 150 nm to create a square array. As the ion beam moves from one via to the next, the beam is not blanked, or turned off. This means material between the desired holes is also removed. Two steps were taken to minimize the damage to the silicon between adjacent vias. First, the dwell time of the ion beam was maximized so that a minimum number of passes were made. Second, a protective layer of Cr was placed on top of the Si to protect the Si surface from unwanted damage. Upon completion of the PnC, the Cr can then be removed. Using this process, a 6.75 x 6.75 μm array of vias was nanoFIBricated. Figure 5B shows a completed array of vias.

After nanoFIBrication of the air hole array, the next step was to backfill the holes with tungsten. The FIB system is equipped with a GIS needle that flows tungsten hexacarbonyl gas over the device. Ray et al. showed that using an ion beam one-quarter of the via diameter can generate void-free filling of vias [3]. A tungsten-filled air hole array is shown in Figure 6. A cross-section of tungsten-filled holes in a freestanding membrane is shown in Figure 7, and it shows the void-free tungsten deposits. In Figure 7, the via array was covered with a layer of Pt to preserve the array during cross sectioning.

Figure 6: 6.75 x 6.75 μm PnC of tungsten inclusions in a Si

membrane.

RESULTS AND DISCUSSION Referring to Figure 1, it is clear that a freestanding

membrane allows for underside observation. Direct observation of the substrate allows confirmation of the membrane’s penetration. A second observation is the membrane’s uneven underside, which can be seen in Figure 7. Milling vias in the freestanding membrane created a trumpet

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effect as the ions exited the membrane. This result was unexpected, but it can be explained by looking at the SRIM results. As ions bombard a surface, they do not stay confined to the initial cross-sectional area. Results from the SRIM modeling show a spreading of the ions. This lateral spreading of the ions also holds true near the lower surface of the freestanding membrane. Due to lateral damage and the fact that there are fewer ions in the wings of the Gaussian beam, less material will be removed from the backside of the membrane as one moves away from the center of the beam, but material will still be removed. These interactions (lateral spreading and a Gaussian profile) lead to an exit hole that flares out, leaving a cross-section that looks like the end of a trumpet.

Figure 7: Cross-section of tungsten filled vias. Each via in the

membrane is filled with a void-free plug of tungsten. The Pt on top of the Cr helps preserve the vias’ shape during cross sectioning.

CONCLUSION Using a focused ion beam, we nanoFIBricated a 2D PnC

into a freestanding membrane of Si using a protective layer of Cr. The PnC is comprised of tungsten plugs with a diameter of 48 nm in a simple cubic pattern, and the spacing between each inclusion is 150 nm. FDTD simulations predict the 2D PnC to have a band gap centered at 22 GHz and a width equal to 41% of the center frequency. Using a software package called SRIM, we modeled the lateral spreading of ions as they impinge upon a surface. NanoFIBrication of a PnC in a freestanding membrane revealed a number of interesting observations. 1) One could directly observe complete penetration of the membrane. 2) Milling vias in the freestanding membrane created a trumpet effect as the ions exited the membrane. 3) Void-free tungsten plugs can be fabricated in a freestanding membrane.

ACKNOWLEDGMENTS This work was supported by the Laboratory Directed

Research and Development program at Sandia National

Laboratories. Sandia National Laboratories is a multiprogram laboratory operated by the Sandia Corporation, Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract No. DE-AC04-94AL85000. This work was completed in part at the University of New Mexico Manufacturing Training and Technology Center.

REFERENCES 1. V. Ray, presented at the International Symposium for

Testing and Failure Analysis, Worcester, MA, 2004 (unpublished).

2. V. Ray, N. Antoniou, R. Balasubrumanian, N. Bassom, M. Clabby, T. Gannon, C. Huynh and G. Tiani, presented at the International Symposium for Testing and Failure Analysis, Santa Clara, CA, 2003 (unpublished).

3. V. Ray, N. Antoniou, N. Bassom, A. Krechmer and A. Saxonis, Journal of Vacuum Science and Technology B 21 (6), 2715-2719 (2003).

4. K. Balasubramanian, P. J. Heard and M. J. Cryan, J. Vac. Sci. Technol. B 24 (6), 2533-2537 (2006).

5. I. Celanovic, N. Jovanovic and J. Kassakian, Applied Physics Letters 92 (19) (2008).

6. M. Cryan, M. Hill, D. C. Sanz, P. S. Ivanov, P. Heard, L. Tian, S. Yu and J. Rorison, IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS 11 (6), 1266-1277 (2005).

7. T.-C. Lu, S.-W. Chen, L.-F. Lin, T.-T. Kao, C.-C. Kao, P. Yu, H.-C. Kuo and S.-C. Wang, Applied Physics Letters 92 (2008).

8. I. El-Kady, R. H. Olsson and J. G. Fleming, Applied Physics Letters 92 (1) (2008).

9. R. H. Olsson and I. El-Kady, Measurement Science and Technology 20 (2009).

10. R. H. Olsson, S. X. Griego, I. El-Kady, M. Su, Y. Soliman, D. Goettler and Z. Leseman, (2009).

11. E. N. Economou and M. M. Sigalas, Physical Review B 48 (18), 434-438 (1993).

12. M. M. Sigalas and N. Garcia, Journal of Applied Physics 87 (6), 3122-3125 (2000).

13. R. H. Olsson, J. G. Fleming, I. F. El-Kady, M. R. Tuck and F. B. McCormick, in TRANSDUCERS and EUROSENSORS '07 (IEEE, 2007).

14. M. M. Sigalas and E. N. Economou, Journal of Applied Physics 75 (6), 6 (1994).

15. T. Miyashita, Measurement Science and Technology 16, R47-R63 (2005).

16. J. F. Ziegler, J. P. Biersack and M. D. Ziegler, SRIM The Stopping and Range of Ions in Matter, 5 ed. (2008).

17. M. F. Su, R. H. Olsson, Z. C. Leseman and I. El-Kady, Applied Physics Letters 96 (2010).

18. F. W. DelRio, M. P. DeBoer, J. A. Knapp, E. D. R. Jr., P. J. Clews and M. L. Dunn, Nature 4, 629-634 (2005).

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19. D. Goettler, K. Murphy, A. Savkar and Z. Leseman, in ASME IMECE2007 (ASME, Seattle, WA, 2007).

20. Z. C. Leseman, S. P. Carlson and T. J. Mackin, Journal of Microelectromechanical Systems 16 (1), 38-43 (2007).