Improved AFM Measurement Accuracy and Precision Using Quadrature Phase Differential Interferometry for Tip Displacement Sensing

R. Proksch, A. Labuda, J. Lefever, J. Li, F.T. Limpoco, B. Ohler
Oxford Instruments Asylum Research Inc.,
United States

Keywords: atomic force microscopy, piezoresponse force microscopy, quadrature phase differential interferometry, measurement accuracy and precision


We have developed the first commercial atomic force microscope to use quadrature phase differential interferometry (QPDI) to measure the AFM probe tip displacement more accurately and precisely. The vast majority of AFMs instead use the optical beam deflection (OBD) method for cantilever sensing. OBD generates a signal proportional to the angular deflection of the cantilever, which is used as a proxy for the vertical tip displacement. However, several commonly encountered interactions between the probe and sample cause cantilever bending but not tip displacement. That cantilever bending changes the OBD signal, which is erroneously interpreted as tip displacement. This causes errors in AFM measurements including piezoresponse force microscopy (PFM), force-distance curves, and spring constant calibration. Previous work has demonstrated that directly measuring tip displacement with an interferometer, instead of inferring it from the OBD angular deflection, can eliminate or greatly reduce these errors. Indeed, this is not the first AFM to use interferometric cantilever sensing. Several early AFM designs used interferometric detection, but this approach was largely abandoned after the invention of OBD in 1988 because of complexity, limited measurement range, and poor low-frequency noise performance. More recently, a laser doppler vibrometer (LDV) was integrated with an AFM for interferometric detection of the cantilever displacement. Several groups demonstrated significant progress in reducing artifacts in PFM measurements using that design. However, an LDV measures velocity and its output is therefore not DC stable. This prevented the use of that AFM for force-distance curves and any other low-frequency measurements. The QPDI design reported here overcomes these limitations. The quadrature phase interferometer approach enables the measurement of large tip displacements while maintaining high sensitivity. By measuring the tip displacement differentially versus the adjacent stationary probe chip, low-frequency noise and drift are greatly improved over designs using remote reference mirrors. The resulting QPDI displacement signal reaches a noise floor of ~10 fm/rtHz, which is less than half that of a carefully optimized OBD measurement on a small cantilever, and over 10× better than typical OBD performance on conventionally sized cantilevers. Moreover, the QPDI displacement signal is inherently calibrated by the wavelength of the light, which eliminates uncertainties associated with calibration of OBD. We will show results demonstrating that direct measurement of tip displacement using QPDI cantilever sensing greatly reduces systematic errors and improves AFM measurement accuracy and that the much lower noise of QPDI detection improves measurement precision. We anticipate that these improvements to quantitative functional, mechanical, and electrical AFM measurements will have far-reaching impacts in fields of piezo- and ferroelectric materials, 2D materials, polymers, semiconductor process control, and beyond Moore’s law materials.