How N14 challenges what we think we know about photomasks

The semiconductor industry continuously shrinks the dimensions of circuit features to deliver increased functionality at lower cost. Current leading edge production follows design dimensions at the 20nm technology node, and it will soon shrink by 30% to the 14nm technology node (N14). In principle, this will deliver lower cost manufacturing. But in order to benefit, we need to improve our optical proximity correction (OPC) models.

Mark Twain probably was not talking about OPC models when he said “It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so,” but that's just the case with photomasks at N14. We depend on accurate process models to faithfully represent imaging system outputs. The models for OPC and post-OPC verification describe the entire patterning process, including mask, optics, resist, and etch, as a set of separately characterized modules. The parameters that represent the models can be gathered from known input values or empirically tuned during calibration. The parameters that are directly measurable, or known as designed-in values, are associated with the mask and optical system. They include mask film stack thickness and refractive indices, wavelength, numerical aperture, illumination profile, and wafer and resist film stack optical constants. These measurements can contain inaccuracies, which in the past were easily absorbed into the models. However, at N14, inaccuracies in the photomask representation can lead to significant errors in the accuracy of the wafer image critical dimensions (CDs).

We explored the impact of errors associated with the physical mask on 14nm OPC models in a new paper, presented in an invited talk at the SPIE Photomask conference in Monterey on September 10, 2013.^{1} We looked at a number of different error types, including photomask errors such as the difference between as-designed and drawn test patterns used in model calibration, and approximations of 3D electromagnetic fields (EMF). In this class of mask errors, we found that using a model that understands random mean-to-target errors can more accurately predict wafer behavior.

**Figure 1. **Mask critical dimension (CD) error (4X) versus target with 5.36nm root-mean-square (RMS) error relative to the baseline, and residual error after mask process simulation (1.11nm RMS).

**Figure 2. **Effect of absorber sidewall angle on root-mean-square (r.m.s.) error at nominal and through focus. MoSi: Molybdenum silicide. T: Thickness. n: Real refractive index. k: Imaginary refractive index. CTR: Constant threshold model.

Also in this class of errors, we found that the systematic variations in mask CD versus pitch or target dimension in photomask manufacturing can be represented with mask proximity models.^{2,3} Without mask proximity models, these contribute more than 0.5nm root-mean-square (RMS) error (relative to the baseline) to the error budget.^{4} Our model, which was calibrated by referencing actual mask measurement data, faithfully predicted the actual mask CD to within 1.1nm RMS error. We found a strong improvement in RMS fitness when using a mask process model to represent the actual mask manifestation of the test patterns. The strong benefit in improved constant threshold model (CTR) RMS fitness of using a mask proximity model to represent the actual mask manifestation of the test patterns is shown in Figure 1.

We looked at corner rounding errors, which are regarded as systematic for a given process. They can be empirically tuned during OPC model calibration using direct mask scanning electron microscope corner rounding measurements. Doing so results in over 1.5nm of CTR RMS error improvement over assuming the mask has sharp corners.

We also examined the impact of many parameters of a photomask 3D EMF model. Two of those are molybdenum silicide (MoSi) absorber refractive index and thickness, and mask absorber sidewall angle and top corner rounding. Small deviations in these parameters led to significant RMS CD difference. The impact of sidewall angle, which is the most sensitive parameter, can be seen in Figure 2.

The thin mask or Kirchhoff approximation can leave more than 1nm RMS of nominal focus CD error and much higher errors for defocus conditions. Creating a 3D EMF mask model requires information associated with the physical and optical properties of the photomask.

With shrinking total CD control budgets, it is more important than ever to account for all sources of error because the cumulative consequence of those errors can become significant to the computational lithography model at N14. In our work, we show that the proper representation of the mask to a wafer model can improve the modeling accuracy significantly.

There are lessons in this research for wafer OPC modeling teams, mask suppliers, and the International Technology Roadmap for Semiconductor lithography committee. First, wafer OPC modeling teams should trace the origin of all mask-related inputs into a model calibration engine and establish the uncertainty associated with these inputs. They should ensure that the mask corner rounding is properly represented, use a 3D mask model, and account for mask CD target deviations.

Second, mask suppliers should confirm XZ topography, especially sidewall angle, and any dependence on feature type, proximity, or local pattern density. They should also confirm XY corner rounding and pattern dependency, and they should address post-processing thickness, real and imaginary refractive indices, and associated uncertainties. Mask suppliers can also calibrate mask proximity models for systematic CD errors to remove such errors at mask write and improve the wafer OPC model. Third, mask suppliers need to understand the impact of transient effects beyond anchor CD. It would also be helpful if the International Technology Roadmap for Semiconductor lithography committee tightens the specifications for CD, phase, and transmission errors for N14 technology.

The N14 node will require aggressive CD control budgets. Assuming 50% of that budget is allocated to the photomask, that equates to about 2nm of reticle scale CD control. But at N14, some mask errors can manifest 4nm errors at wafer scale. It is imperative to account for such errors appropriately and not merely absorb them into the photoresist black box model. One way to do this is through the use of mask proximity models and correction. Another approach is to create a virtual mask that references the mask process models for use in calibrating wafer OPC model accuracy. It will also be important to simulate corner routing and 3D EMF effects.

Our future work will investigate, among other things, the impact of potential non-constant mask sidewall angles across various patterns. We will also demonstrate various flows that use mask proximity models.

John Sturtevant

Mentor Graphics

Wilsonville, OR

John Sturtevant presented this work at the 2013 SPIE Photomask Technology Conference. He is the director of modeling and verification solutions, and can be reached at john_sturtevant@mentor.com.

References:

1. J. Sturtevant, E. Tejnil, T. Lin, S. Schultze, P. Buck, F. Kalk, K. Nakagawa, The impact of 14-nm photomask uncertainties on computational lithography solutions,

*Proc. SPIE* 8683, p. 868307, 2013.

doi:10.1117/12.2013748
2. T. Lin, T. Donnelly, S. Schulze, Model based mask process correction and verification for advanced process nodes,

*Proc. SPIE* 7274, p. 7274A, 2009.

doi:10.1117/12.814362
3. T. Lin, T. Donnelly, G. Russell, S. Jung, J. Jeong, Application of mask process correction (MPC) to monitor and correct mask process drift,

*Proc. SPIE* 7971, p. 797107, 2011.

doi:10.1117/12.879119
4. J. Sturtevant, E. Tejnil, Roadmap to sub-nanometer OPC model accuracy,

*Proc. SPIE* 8441, p. 84410H, 2012.

doi:10.1117/12.978190