3. A. Hubert, R. Scha¨fer, Magnetic Domains (Springer,Berlin, 1998).4. J. Raabe et al., J. Appl. Phys. 88, 4437 (2000).5. T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, T. Ono,Science 289, 930 (2000).6. M. Pratzer et al., Phys. Rev. Lett. 87, 127201 (2001).7. S. Heinze et al., Science 288, 1805 (2000).8. A. Kubetzka, M. Bode, O. Pietzsch, R. Wiesendanger,Phys. Rev. Lett. 88, 057201 (2002).9. The Cr film thickness dependent reorientation tran-sition may be caused by the surface anisotropy thatdominates at small thickness.10. M. Bode, M. Getzlaff, R. Wiesendanger, Phys. Rev.Lett. 81, 4256 (1998).11. O. Pietzsch, A. Kubetzka, M. Bode, R. Wiesendanger,Phys. Rev. Lett. 84, 5212 (2000).12. D. Wortmann, S. Heinze, Ph. Kurz, G. Bihlmayer, S.Blu¨gel, Phys. Rev. Lett. 86, 4132 (2001).13. The spin polarizations of the tip and the sample aredefined as PS,T(E) ⬅ (nS,T2(E) ⫺ nS,T1(E))/(nS,T2(E) ⫹nS,T1(E)) with nS,T2(E) and nS,T1(E) being the densityof states of majority and minority electrons.14. O. Pietzsch, A. Kubetzka, D. Haude, M. Bode, R.Wiesendanger, Rev. Sci. Instr. 71, 424 (2000).15. U. Gradmann, G. Liu, H. J. Elmers, M. Przybylski,Hyperfine Interactions 57, 1845 (1990).16. The tiny bright spots randomly distributed in bothimages are caused by adsorbates that appear asdips in the topograph (Fig. 2A) and locally changethe value of C in Eq. 1; i.e., the signals are not ofmagnetic origin.17. The simulations were performed with the OOMMFprogram, release 1.2 alpha 2 (http://math.nist.gov/oommf/) using a lateral grid with a cell size of 1 nm2.The shape as well as the averaged island height of 8 nmwas taken into account. Because the height of the Feislands of about 8 nm is only 2.5 to 3 times larger than公A/Kd, the magnetization was assumed to be indepen-dent of the z coordinate (3, 18).18. U. Gradmann, J. Korecki, G. Waller, Appl. Phys. A 39,101 (1986).19. The small deviation between experimental andsimulated data at dvc⫽ 10 to 15 nm in thepresence of external fields is caused by the lateralmovement of the vortex core (Fig. 4B), which hasnot been considered in the simulations. At the rimof the Fe island, the magnetization tilts strongerinto the direction of Hextthan in the island center.20. Financial support from the BMBF (grant no.13N7647) and SFB 508 is gratefully acknowledged.20 June 2002; accepted 4 September 2002Microfluidic Large-ScaleIntegrationTodd Thorsen,1Sebastian J. Maerkl,1Stephen R. Quake2*We developed high-density microfluidic chips that contain plumbing networkswith thousands of micromechanical valves and hundreds of individually ad-dressable chambers. These fluidic devices are analogous to electronic integratedcircuits fabricated using large-scale integration. A key component of thesenetworks is the fluidic multiplexor, which is a combinatorial array of binaryvalve patterns that exponentially increases the processing power of a networkby allowing complex fluid manipulations with a minimal number of inputs. Weused these integrated microfluidic networks to construct the microfluidic an-alog of a comparator array and a microfluidic memory storage device whosebehavior resembles random-access memory.In the first part of the 20th century, engineersfaced a problem commonly called the “tyrannyof numbers”: there is a practical limit to thecomplexity of macroscopically assembled sys-tems (1). Using discrete components such asvacuum tubes, complex circuits quickly be-came very expensive to build and operate. TheENIAC I, created at the University of Pennsyl-vania in 1946, consisted of 19,000 vacuumtubes, weighed 30 tons, and used 200 kW ofpower. The transistor was invented at Bell Lab-oratories in 1947 and went on to replace thebulky vacuum tubes in circuits, but connectivityremained a problem. Although engineers couldin principle design increasingly complex cir-cuits consisting of hundreds of thousands oftransistors, each component within the circuithad to be hand-soldered—an expensive, labor-intensive process. Adding more components tothe circuit decreased its reliability, as even asingle cold solder joint rendered the circuituseless.In the late 1950s, Kilby and Noyce solvedthe “tyranny of numbers” problem for electron-ics by inventing the integrated circuit. By fab-ricating all of the components out of a singlesemiconductor—initially germanium, then sili-con—Kilby and Noyce created circuits consist-ing of transistors, capacitors, resistors, and theircorresponding interconnects in situ, eliminatingthe need for manual assembly. By the mid-1970s, improved technology led to the devel-opment of large-scale integration (LSI): com-plex integrated circuits containing hundreds tothousands of individual components.Microfluidics offers the possibility of solv-ing similar system integration issues for biologyand chemistry. However, devices to date havelacked a method for a high degree of integra-tion, other than simple repetition. Microfluidicsystems have been shown to have potential in adiverse array of biological applications, includ-ing biomolecular separations (2– 4), enzymaticassays (5, 6), the polymerase chain reaction (6,7), and immunohybridization reactions (8, 9).These are excellent individual examples ofscaled-down processes of laboratory tech-niques, but they are also stand-alone function-alities, comparable to a single component with-in an integrated circuit. The current industrialapproach to addressing true biological integra-tion has come in the form of enormous roboticfluidic workstations that take up entire labora-tories and require considerable expense, space,and labor, reminiscent of the macroscopic ap-proach to circuits consisting of massive vacuumtube– based arrays in the early 20th century.There are two basic requirements for a mi-crofluidic LSI technology: monolithic microv-alves that are leakproof and scalable, and amethod of multiplexed addressing and controlof these valves. We previously presented acandidate plumbing technology that allowsfabrication of chips with monolithic valvesmade from the silicone elastomer polydi-methylsiloxane (PDMS) (10). Here, we de-scribe a microfluidic multiplexing technologyand show how it can be used to fabricatesilicone devices with thousands of valves andhundreds of individually addressable reactionchambers. As possible applications of fluidicLSI technology, we describe a chip that con-tains a high-density array of 1000 individuallyaddressable picoliter-scale chambers thatserves as a microfluidic