Variable Bias Completes The PLDC Model And Offers Superior MPC Results

This is the third in a three-blog series on PLDC. The first installment was “Improving Uniformity and Linearity for All Masks,” from January 29, 2025. The second blog was “Three Ways Curvy ILT Together with PLDC Improves Wafer Uniformity,” from April 18, 2025.

In 2024, the eBeam Initiative Luminaries Survey found that the number one concern in adoption of curvilinear mask features was mask software infrastructure. Pixel-level dose correction (PLDC) is the answer to the mask process correction (MPC) part of that concern. In this blog, we will take a detailed look at one of the advanced features of PLDC, variable bias, and present results of PLDC performance tests by Micron Technology, as presented by Paris Spinelli at Photomask Japan 2025 and reprised in this eBeam Initiative video. The paper, “Full Reticle Inline Linearity Correction Including Variable Bias with No Turnaround Time,” won the award for Best Paper at the conference.

The mask model used by PLDC, D2S TrueModel for Mask, uses two components: dose models and variable bias models. With these two components, PLDC performs both linearity correction and uniformity enhancement. Both components are critical because both dose-based and variable bias effects contribute significantly – and differently – to the linearity problem.

Variable bias

Variable bias includes a combination of resist and etch effects that occur when processing a photomask. As we discussed in our first blog, after the resist is exposed and dose-based effects have taken place, other mask-making steps occur, including etching. After some of those steps, some areas of the mask are protected by hardened resist from etching, while other areas are left open to etching that “drills” down into the material under the resist a certain known distance. Even though this etching process is sophisticated and accurate in drilling down much more than drilling to the side, a certain amount of etching to the side is inevitable, which effectively increases the etched area. Whether that’s open or closed is subject to definition and whether resist is positive or negative. The linearity issue from variable bias occurs because the amount of that sideways etching is not identical everywhere.

To model this, we must consider etched areas on exterior points along the contour edge. We also observe that variable bias applied by looking at the non-etched area’s interior points along the contour edge can be an effective model form to predict manufacturing effects accurately. The same variable-etch model form is therefore applied both in the etched area and in the unetched area, though with different model parameters for each (exposed and unexposed is etched or not depending on negative or positive resist).

In figure 1, we see etched and unetched areas: etched shown here in blue in this positive resist example, and unetched in white. There are two radii, one on the exterior area outside the etched feature and one on the interior area of the etched feature.

Fig. 1: To model variable bias effects, we must apply a variable-etch model on the exterior edge and the interior edge, taking into account both etched and non-etched areas (Source: Micron).

PLDC mask results

In their recent paper, Micron Mask Technology Center presented mask results from a module. Test structures included clear line (exposed target); dark, unexposed lines (which are exempted features); exposed holes; and dark, unexposed pillars. In figure 2, results from the clear line structures are shown, with the leftmost graph showing the error range with no correction. Reducing this as much as possible is the goal of MPC. The next three graphs from left to right show correction with offline MPC from each of three vendors. The rightmost graph shows correction with full inline correction using PLDC for the MPC function with both the dose model and variable bias model for linearity correction, and using edge-dose enhancement to improve uniformity. The error range was reduced between 42% to 21% by the various offline MPC vendors compared to no correction. Inline PLDC range reduction versus no correction was 67%, exceeding the best performance of offline MPC.

Fig. 2: Micron’s mask results for clear line test structures demonstrated that PLDC reduces error range by 67% from uncorrected baseline, compared to 42% to 21% for offline MPC (Source: Micron).

The results for dark unexposed lines and exposed holes were very similar to those for clear lines, with PLDC offering far greater error reduction. For dark unexposed pillars, offline MPC solutions had an error reduction of 69% to 54%. In this case, inline PLDC only reduced the error by 38%. This was the only case where offline MPC performed better than PLDC MPC. However, the author added the caveat that the next version of PLDC is expected to improve this significantly and showed early, printed results confirming the expected improvements.

The complete results presented in Micron’s paper, which also include a full reticle and curvilinear test structures, demonstrate that PLDC has superior linearity correction for both Manhattan patterns and curvilinear patterns. This is only practical with pixel-based correction equipped for both dose-based effects and variable-bias-based effects with a mask model that is not overfit for Manhattan patterns.

Zero impact on turnaround time

Micron’s presentation also demonstrated that PLDC MPC correction has zero impact on turnaround time (TAT) during processing. This is because PLDC computes the corrected pixel doses as the mask is being written by the multi-beam machine. The fact that PLDC runs inline saves substantial computation time in both rasterizing and contouring. Rasterization of the incoming target contours must be performed by any multi-beam mask writer, even without PLDC. There is no additional time required for contouring in PLDC because the act of eBeam pixels exposing the resist is the physical form of contouring in the PLDC flow.

Figure 3, also from Micron, shows four separate writes of the full reticle. The three in gray are write times of three different runs without PLDC applied and the one purple write time is with PLDC applied. The author noted that write times of machines ordinarily vary, and because the write time with PLDC is well within that ordinary variability, he considers PLDC to have 0 TAT impact on mask processing.

Fig. 3: Mask write times with PLDC are within expected variations, meaning that PLDC has zero impact on mask processing TAT (Source: Micron).

PLDC offers a faster, cost-effective, and high-quality solution for MPC

Variable bias is an important part of the linearity challenge. It is a required element – along with dose models – for an accurate MPC solution. The TrueModel for Mask model employed in PLDC includes both dose-based effects and variable-bias-based effects, as part of an inline MPC solution with zero impact on mask processing TAT. The recently published Micron studies demonstrated that PLDC provides a faster, more cost-effective solution to implement high-quality MPC that both corrects for linearity and improves uniformity for both Manhattan and curvilinear masks.