Abstract. The ion velocity distribution (IVD) is important in plasma etching of microfeatures. IVD at a rf biased wafer is studied, first analytically using probability theory and then numerically by using a particle simulation method. The analytic expression shows that IVD is governed by the parameter qVri/miuil, where q is the charge of ion, V T f is the rf bias amplitude, w is the rf bias angular frequency, I is the penetration depth of bias potential, and mi is the mass of ion. The analytical expression is applicable to the case when the ion collisions in the penetration depth are negligibly few and the rf period of biasing is much shorter than the time that ions take in traversing the depth I. The IVDs for general conditions are also examined using the self-consistent particle-in-cell/Monte Carlo simulation.
I INTRODUCTIONWeakly ionized plasmas used in materials processing generally consist of positive and negative ions, electrons, and neutral species. In the case when electrons are more abundant than negative ions, a negative potential is formed near the surface of the floating wafer immersed in the plasma. In processing plasmas the electron temperature is few electron volts, while the ion temperature is roughly equal to the background gas temperature. To keep the balance between the negative and positive currents on the floating surface, low energy electrons should be reflected in the sheath region back to the plasma bulk. This is the physical reason why the potential of the floating wafer is lower than the plasma potential.Negative sheath potential (measured from the plasma bulk) accelerates the positive ions to the wafer. If no collision is assumed in the sheath region, the positive ions impinge almost perpendicularly onto the wafer. However, electrons are decelerated and lose the velocity component normal to the wafer.When ions and electrons come into a microscopic trench, electrons are easily sticked near the top of the side of the trench wall while ions can reach the bottom of the trench. This kind of charge separation inside microfeatures causes a charge build-up. The strongly localized electric field due to the charge build-up distorts the trajectories of incident ions, which results in an anomalous etch profile called "notching". The localized charge build-up also causes the electrical breakdown induced by fatal tunneling currents through gate-oxides.In order to suppress the so-called charging damages, new ideas on plasma sources are proposed, e.g., timemodulation of the source power [1] and use of ultra-high frequency (500 MHz) power [2]. These approaches are intended to lower the electron temperature and hence generate more negative ions. To understand the role of negative ions, let us consider the plasma including only positive and negative ions; when the wafer is biased at low frequency (< 3MHz), the positive and negative ions impinge on the bottom of the trench alternately. Thus no charge build-up occurs.The ion energy distribution (IED) and ion angle distribution (IAD) of ions that impinge o...