Measuring Boltzmann’s constant with a low-cost atomic force microscope: An undergraduate experiment

We discuss a low-cost atomic force microscope that we have designed and built for use in an undergraduate teaching laboratory. This microscope gives students hands-on access to nano-Newton force measurements and subangstrom position measurements. The apparatus relies mainly on off-the-shelf components and utilizes an interferometric position sensor known as the interdigitated ͑ID͒ cantilever to obtain high resolution. The mechanical properties of the ID readout enable a robust and open design that makes it possible for students to directly control it. Its pedagogical advantage is that students interact with a complete instrument system and learn measurement principles in context. One undergraduate experiment enabled by this apparatus is a measurement of Boltzmann's constant, which is done by recording the thermal noise power spectrum of a microfabricated cantilever beam. In addition to gaining an appreciation of the lower limits of position and force measurements, students learn to apply numerous concepts such as digital sampling, Fourier-domain analysis, noise sources, and error propagation.