The halftone technique renders different levels of "gray" by varying the density of very small geometry on the photomask. The geometry is large enough to resolve on the photomask but too small to resolve in the photoresist. Even though it doesn't print on the photoresist, the density of this geometry attenuates the amount of energy the photoresist receives. This allows you to create very special three-dimensional structures in the photoresist.
To design a grayscale mask for optical lithography you'll first need to know how varying the optical density on the mask will affect your specific lithography process. You characterize your process by first running a calibration mask to quantify this relationship. The information gained from the calibration mask is used to develop a model to produce masks that are optimized for your specific lithography process.
Contact us if you need assistance with this process. At PhotomaskPORTAL, we help researchers design and build low-cost, high-quality photomasks.