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Production sequence of Si-spheres and interferometrical determination of the sphere volume

Influence of surface roughness on the measured indentation modulus of crystalline silicon


As part of a dissertation funded by the Indonesian state, the influence of surface roughness on the mechanical properties of crystalline silicon measured by means of nanoindentation was investigated at PTB. Three different crystal planes of silicon were studied: (100), (110) and (111). Starting with four-inch crystalline Si wafers, these surfaces were roughened using reactive ion etching (ICP). Different levels of high-frequency power resulted in different surface roughness (see Fig. 1). The Si (100) surfaces could be roughened the most with this method (Ra = 168 nm), the Si (111) surfaces least (Ra = 6 nm). The surface roughness of the samples produced was measured with high resolution using an atomic force microscope (AFM) in tapping mode. Subsequently, nanoindentation measurements were carried out with a Hysitron Triboindenter TI950 up to indentation forces of 10 mN and with a Fischerscope HM2000 up to 1 N indentation force. Reference measurements were also carried out on non-roughened reference samples which showed roughness values of the order of Ra = 0.1 nm.


The surface roughness generated by etching was modeled to investigate the influence of the rough surface on the contact area of the indenter and thus on the measured reduced indentation modulus Er. In this model, the rough surface is described by sinusoidal profile peaks and the contact area of the indenter increases proportionally to the mean roughness value Ra. This leads to systematically smaller measured indentation moduli. According to the model, the measured reduced indentation modulus Er decreases non-linearly with the mean roughness value Ra and this effect is stronger the smaller the wavelength of the rough surface structures is (see Fig. 2). To determine the mean wavelength, the spectral distribution of the surface waves was calculated from the AFM topography measurements carried out for the roughness measurement and the mean wavelength for each sample was determined from this. The measured indentation modules can be described quite well with this simple model. The deviation between the measured and the modeled values is a maximum of 5%.

To correct the indentation moduli measured on the rough crystalline Si surfaces, a new method was developed in which the measured contact depth hc is corrected with the help of a correction table determined for the respective crystalline material [1]. After correction, the reduced indentation moduli measured on rough crystalline Si surfaces only deviate by a maximum of 1 % from the reference value of a smooth comparison surface.



[1] Puranto, P. Indentation testing of silicon micropillars obtained from cryogenic dry etching 2022 submitted dissertation, Faculty of Electrical Engineering, Information Technology, Physics of the Technical University Carolo-Wilhelmina in Braunschweig.



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