Complete analytical solutions of film planarization during spin coating

To offer a simple set of equations to designers and researchers for describ ing the degree of planarization (DOP), a first complete analytical solution of film planarization during spin coating is presented. The analytical sol utions are suitable for an isolated feature and periodic features in the wh ole range of Omega(2). The governing dimensionless parameter Omega(2) repre sents the ratio of centrifugal force to surface tension force during spin c oating. For Omega(2) --> 0, surface tension is infinite, and the film is pl anar. For Omega(2) --> infinity, surface tension is zero, and the film is a lways conformal, with an equal thickness everywhere. The analytical solutio ns agree with the existing experiment data and numerical solutions. A compa rison shows that the degree of planarization for an isolated trench is high er than that for an isolated ridge in the range of 10(-5) < Omega(2) < 3 x 10(1), but they gradually become identical and independent of d/h(f) for Om ega(2) > 3 x 10(1) and Omega(2) < 10(-5). For periodic features, DOPP is in dependent of dimensionless film thickness, d/h(f), dimensionless line spaci ng, alpha, and Omega(2) in the range of Omega(2) > 3 x 10(2) and Omega(2) < 10(-2) (C) 1999 The Electrochemical Society. S0013-4651(99)01-014-9. All ri ghts reserved.