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SPM Principles

Force Modulation microscopy


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Under realization of Force Modulation mode (FM-mode) along with scanning of sample surface as in Constant Force mode  (CFC-mode) the scanner (or the sample) executes a vertical periodic motion [1]. Under this periodic motion cantilever "feels out" the sample surface. At that the pressure of the probe tip on the sample surface does not remain constant but has periodic component, usually sinusoidal. In accordance with the local elasticity of the sample value of corresponding indentation will change under scanning. On the stiff areas of the sample surface depth of indentation will be smaller, and on the compliant areas - larger.
Tracing of the sample surface relief height is conducted by the usage of the averaged cantilever deflection in the feedback circuit [2]. If values of the scanner vertical displacement Dz, the probe tip vertical displacement D and cantilever force constant кс are known, one can determine the local elasticity of the sample under investigation кs
кs = кс· (Dz/D - 1)


In turn with known value of the local elasticity one can to determine the modulus of elasticity of the sample. It can be done with usage of the calibrating measurements or with usage of the Hertzian model [3]. Force Modulation mode is widely used in polymers, semiconductors, biological, especially in composite materials investigations.


  1. US Pat. 5092163. 
  2. Nanotechnology 2, 103 (1991). 
  3. Jonson KL. Contact mechanics. Cambridge University press: Cambridge, 1995. 
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