Scaling Issues in Chemical and Biological Sensors MARC J. MADOU AND ROGER CUBICCIOTTI Invited Paper When a system is reduced isomorphically in size (i.e., scaled down with all dimensions of the system decreased uniformly, or iso- morphic scale reduction), the changes in length, area, and volume ratios alter the relative influence of various physical effects that determine the overall operation—often in unexpected ways. As ob- jects shrink, the ratio of surface area to volume increases, rendering surface forces more important. More generally, as the size of an ob- ject decreases, forces scaling with a lower power of the linear di- mension dominate over the ones scaling with a higher power (e.g., surface tension gains over gravity, electrostatics over magnetics, etc.) [see M. J. Madou, Fundamentals of Microfabrication, 2nd ed. (Boca Raton, FL: CRC, 2002)]. In this paper, we are investigating the influence of miniaturiza- tion on various aspects of chemical and biological sensors; we re- view scaling issues faced in sensor construction, the importance of sample size and the effect of sensor size on detection sensitivity 1 in some of the most popular sensing approaches. Keywords—Biosensors, electrochemical sensors, optical sen- sors, scaling laws. I. SCALING ISSUES IN SENSOR FABRICATION 1) Liquid Evaporation: Fig. 1 illustrates isomorphic scaling; the smallest doll has the largest surface to volume ratio (S/V). Fast evaporation associated with large S/Vs has important consequences for the fabrication and storage of miniaturized sensors incorporating liquids. Examples include the evaporation of ejected liquids in drop delivery equipment, the aqueous based chemical cocktails in minia- turized polymerase chain reaction (PCR) chambers and glucose sensors, and the storage of miniaturized “wet” sensors in general. Engineering solutions to evaporation problems include adding a hygroscopic material, mixing the liquid with a lower vapor pressure solvent (e.g., glycerol), Manuscript received February 15, 2003; revised March 2, 2003. M. J. Madou is with the Mechanical and Aerospace Engineering De- partment, University of California, Irvine, CA 92697-3975 USA (e-mail: mmadou@uci.edu). R. Cubicciotti is with NanoMedica, Inc., Newark, NJ 07102-2100 USA (e-mail: cubic@nanomedica.com). Digital Object Identifier 10.1109/JPROC.2003.813577 1 Sensitivity of a sensor is the amount of change in a sensor’s output, , in response to a change at the sensor’s input, , over the entire sensor range (i.e., ). Fig. 1. Russian nesting dolls illustrate isomorphic scaling. When the size of the dolls approaches the same length scale as a boundary layer, be it a thermal, hydrodynamic or diffusion boundary layer, continuum theories break down and macro scaling laws no longer apply. Fig. 2. Contactless dispensed volumes from 5 L down to 25 nL. One can go down to 10 nL routinely, but one has to be pretty fast to take a picture. Courtesy Bart van der Schoot, Seyonic. topping the solution with a low vapor pressure, nonmixing liquid, and working in a solvent-saturated environment. In Fig. 2, we show an array of water droplets ejected contactless from a nozzle with volumes ranging from 5 L to 25 nL. At smaller droplet size, evaporation in air is so fast that it is difficult to take a picture [1]. Moving from microsensors to nanosensors, manufacturing and storage will pose even more daunting liquid management issues. Nature’s solution to the problem involves packaging the sensor molecules (e.g., proteins and nucleic acids) within 0018-9219/03$17.00 © 2003 IEEE 830 PROCEEDINGS OF THE IEEE, VOL. 91, NO. 6, JUNE 2003