Regularization method for quantizing lithography masks
In an electronic design automation technique for optical proximity correction, an optimized mask function that has values other than those allowed for a particular mask type, such as 0 and 1 for a chrome-on-glass binary mask, evolves it to a solution restricted to these values or narrow intervals near them. The technique “regularizes” the solution by mixing in a new cost functional that encourages the mask to assume the desired values. The mixing in may be done over one or more steps or even “quasistatically,” in which the total cost functional and the mask is brought from pure goodness-of-fit to the printed layout for given conditions to pure manufacturability by keeping the total cost functional minimized step-by-step. A goal of this gradual mixing-in is to do thermodynamically optimal work on the mask function to bring it to manufacturable values.
1. A method comprising:
altering a first non-pixelated mask in a frequency domain to obtain a second mask, wherein the altering comprises determining a first cost functional, wherein the first cost functional comprises a first cost term and a second cost term, and wherein the first cost term is weighted in a first proportion relative to the second cost term; and
altering the second mask to obtain a third mask, wherein the altering comprises determining a second cost functional, wherein the second cost functional comprises the first cost term and the second cost term, and wherein the first cost term is weighted in a second proportion relative to the second cost term, wherein the second proportion is different than the first proportion,
wherein the altering the first non-pixelated mask and the altering the second mask are performed using an electronic processor.
2. The method of claim 1 wherein the first cost term measures a fit of a predicted print to a target layout, and wherein the second cost term measures a regularization cost.
3. The method of claim 2 wherein the weighting of the first cost term is lower in the second cost functional than in the first cost functional.
4. The method of claim 2 wherein the regularization cost comprises a cost of the first and second masks taking values other than allowed or favored quantized values.
5. The method of claim 2 , further comprising altering the third mask to obtain a fourth mask, wherein the altering comprises determining a third cost functional, wherein the third cost functional comprises the first cost term and the second cost term, and wherein the weighting of the first cost term is lower in the third cost functional than in the second cost functional.