Abstract
A thickness distribution model of photoresist spin-coating on concave spherical substrate (CSS) has been developed via both theoretical studies and experimental verification. The stress of photoresist on rotating CSS is analyzed and the boundary conditions of hydrodynamic equation are presented under the non-lubricating condition. Moreover, a multivariable polynomial equation of photoresist-layer thickness distribution is derived by analyzing and deducing the flow equation where the evaporation rate, substrate topography, interface slip between liquid and CSS, and the variation of rotational speed and photoresist parameters are considered in detail. Importantly, the photoresist-layer thickness at various CSS rotational speeds and liquid concentrations can be obtained according to the theoretical equation. The required photoresist viscosity and concentration parameters of different photoresist coating thickness under a certain coating speeds can be also solved through this equation. It is noted that the calculated theoretical values are well consistent with the experimental results which were measured with various CSS rotational speeds and liquid concentrations at steady state. Therefore, both our experimental results and theoretical analysis provide the guidance for photoresist dilution and pave the way for potential improvements and microfabrication applications in the future.
Highlights
The detailed mathematical analysis of spin coating was first conducted by Emslie et al in 1958.22 They presented the model of spin coating on the plane and gave the initial force balance equation on concave spherical substrate (CSS) from fluid mechanics principle
A polynomial equation of film thickness was brought forward which related to evaporation rate, substrate topography, interface slip between liquid and CSS, the variation of rotational speed and photoresist parameters
In the present work, the distribution model of photoresist-layer thickness on CSS by spincoating has been presented and the theoretical solutions for the film thickness have been compared with a sequence of experimental results
Summary
Spin-coating photoresist films have attracted numerous investigations because of their versatile applications in micro-electromechanical systems, microelectronics processing, magnetic storage, etc.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] Among these applications, the thickness uniformity determined by flow and evaporation processes strongly affect on the quality of photoresist films.[19,20] coating with a uniform photoresist film on the CSS is the first and most crucial step in the preparation process.[21]. There are some studies in spin-coating photoresist such as mentioned above, but the reports about an exact model (considering evaporation rate and interface slip between liquid and CSS) and its correctness verification by experiments are limited. The boundary condition of hydrodynamic equation was presented on the basis of substrate topography when considering the interface slip between photoresist and substrate. The evaporation rate was constructed when spinning coating on different substrates and the derivation course was shown in detail. A polynomial equation of film thickness was brought forward which related to evaporation rate, substrate topography, interface slip between liquid and CSS, the variation of rotational speed and photoresist parameters. The most important is that the numerical profiles are in close agreement with the experimental data, indicating the general model we proposed in the paper can be applied to actual device structures as a guiding tool
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