mask 3d effects

**Mask 3D effects** refer to how the **physical thickness and topography of mask absorber and phase-shift materials** affect the diffraction of light passing through (or reflecting from) the mask, causing deviations from the idealized thin-mask (Kirchhoff) model used in traditional lithography simulation. **Why Mask 3D Effects Matter** - Traditional lithography simulation treats the mask as an **infinitely thin** plane — light either passes through or is blocked, with no interaction with the mask material's finite thickness. - In reality, mask absorbers and phase-shift layers have thickness of **50–100 nm** (for DUV) or **30–70 nm** (for EUV). At feature sizes comparable to the absorber thickness, the 3D structure significantly affects how light diffracts. **Effects of Mask Topography** - **Shadowing**: Light enters the mask absorber at oblique angles (especially for off-axis illumination and high-NA systems). The absorber sidewalls **cast shadows**, effectively shifting the apparent feature position. - **Best Focus Shift**: The 3D mask structure changes the phase and amplitude of diffracted orders, shifting the best-focus position through-pitch — dense and isolated features focus at different heights. - **Pattern Shift**: Features appear to shift laterally depending on illumination angle and absorber profile. - **CD Asymmetry**: Left and right feature edges can print at different widths due to asymmetric shadowing effects. - **Pitch-Dependent CD**: The mask 3D contribution to CD error varies with feature pitch, complicating process control. **Mask 3D Effects in EUV** - EUV lithography uses **reflective masks** at an incident angle of 6° off normal. The absorber thickness (~60–70 nm) interacts with the oblique illumination to create significant 3D effects. - **Shadowing in EUV** is inherently asymmetric — the absorber shadow falls differently on the left and right sides of features due to the tilted illumination. - This is a **major challenge** for EUV patterning, especially at high-NA where the angular range increases further. **Mitigation** - **Rigorous EMF Simulation**: Use electromagnetic field (Maxwell's equations) simulation of the mask instead of thin-mask approximations. More accurate but computationally expensive. - **Thinner Absorbers**: Reducing absorber thickness reduces 3D effects. New materials (high-k absorbers with higher extinction coefficients) achieve the same optical density with thinner films. - **Compensating OPC**: Include mask 3D effects in the OPC model to pre-compensate for the distortions. Mask 3D effects are a **dominant source of patterning error** in EUV lithography — accurately modeling and compensating for them is essential for achieving the tight CD control required at advanced nodes.