A mathematical model for a plasma-assisted downstream etching reactor

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Abstract
A mathematical model was developed for a plasma-assisted downstream etching reactor of the impinging jet configuration. Finite-element methods were employed to solve for the two-dimensional fluid velocity, temperature, and active species concentration distributions. Etching of a polymer (e.g., photoresist) using pure oxygen was analyzed with emphasis on the effect of reactor design and operating conditions on etching rate and uniformity. For a given flow rate, an optimum value of pressure was identified which maximized the etching rate. The etching rate increased monotonically with power, but decreased exponentially with distance between the plasma and the wafer. Under the conditions examined, the etching rate was found to be highest at the wafer center. Local loading was observed around the periphery of the wafer at high wafer temperature. The etching uniformity was found to depend on the gas-flow distribution. A new reactor design was proposed to achieve efficient gas dissociation in the plasma, rapid transport of the dissociated gas to the etching chamber, and nearly uniform flow distribution over the wafer. The new design resulted in improvement in both etching rate and uniformity.