Estimating thermal transport in deep X-ray lithography with an inversion method

This study proposes a general methodology for estimating the depth profile of the heat source of the thermal transport system during deep X-ray lithography. The exposure process in a lithography system is considered as an inverse heat conduction problem with an unknown heat source. The conjugate gradient method is used to solve the inverse problem. Numerical results confirm that the method proposed herein can accurately estimate the heat source even involving the inevitable measurement errors. Furthermore, this methodology can also be applied to estimate the local distribution of temperatures when using scanning thermal microscopy (SThM) to microthermally machine materials and will contribute to increase the quality of microthermally machined products. In addition, a thermomechanical data-storage system, which utilizes a resistively heated atomic-force-microscopy (AFM) cantilever tip to read and write data bits, can also adopt this inverse methodology to control the temperature of a polymer substrate.