Fig. 2. Heat transfer model and parameters affecting temperature and nanoscale thermal reaction kinetics under the tip.

a Heat transfer model of a resistively heated cantilever: Heat is conducted from the source through the tip and the air gap into the sample material and the substrate. b Effect of tip apex size and opening angle on the tip-sample contact temperature and resolution. Typically, with larger tip opening angles and large apex radius, a higher contact temperature can be achieved at the cost of resolution. c Effect of film thickness on the temperature distribution for a typical situation where the thermal conductivity of the film (e.g., polymer) is lower than the substrate (e.g., Si). The tip-sample contact temperature decreases with decreasing film thickness. d Qualitative sketch of how the temperature distribution in the material relates to the corresponding converted volume of material in the film. For most reactions relevant to t-SPL, the thermally converted volume is smaller than the spreading of heat, which benefits the lateral resolution. e Plot of a first-order reaction where the fraction of converted material with respect to the total material is plotted as a function of the tip temperature. The points where 1%, 50% and 99% of the material is converted are indicated. The following plots show how the temperature is affected by activation energy, tip-sample contact duration and indentation force. f When the activation energy of a thermally driven process increases, a higher temperature is required to induce a material modification. g The longer the tip is in contact with the material, the lower the temperature required to induce a modification and the narrower the temperature range over which the conversion takes place (x-axis is logarithmic). h The temperature required for certain chemical reactions to complete can be lowered by increasing the pressure. In t-SPL, this can be achieved by increasing the indentation force