Thermally Activated Selective Topography Equilibration (TASTE)

• TASTE is a nanofabrication technique that uses dose-dependent EBL and thermal reflow to form asymmetric, wedge-like facets in PMMA.
• The method involves grayscale lithography to pattern multilevel staircases, followed by selective polymer reflow driven by capillary forces.
• It enables high-efficiency diffraction gratings with controlled facet roughness and blaze angles, critical for EUV and soft X-ray spectroscopic applications.

Thermally Activated Selective Topography Equilibration (TASTE) is a two-step nanofabrication technique enabling the formation of blazed, sawtooth relief profiles in polymer resists. The method integrates grayscale electron-beam lithography (GEBL) to pattern multilevel staircases in polymethyl methacrylate (PMMA), followed by thermally induced selective polymer reflow. TASTE facilitates the creation of asymmetric, continuous wedge-like facets without dependence on substrate crystallography, allowing arbitrary groove layouts suitable for advanced applications in diffraction gratings for astronomical x-ray and extreme ultraviolet (EUV) spectroscopy (McCoy et al., 2021, McCoy et al., 2020, McCoy, 2021).

1. Physical Foundations and Principles

TASTE exploits the dose-dependent reduction of polymer molecular weight $M_w(D)$ in positive-tone resists such as PMMA, induced by electron exposure during GEBL. This reduction locally depresses the glass transition temperature $T_g(D)$ according to the relation $T_g(D) < T_g(0)$ for increasing dose $D$. Controlled thermal annealing at a temperature $T$ satisfying $T > T_g(D)$ in exposed regions and $T < T_g(0)$ in unexposed regions renders only the exposed areas viscous while unexposed regions remain glassy and rigid.

The ensuing flow is governed by Mullins’ surface-tension-driven evolution equation in the lubrication (thin-film) regime:

$$\frac{\partial h}{\partial t} = \frac{\gamma}{3\eta} \nabla \cdot\left[h^3 \nabla \nabla^2 h\right]$$

where $h(x,t)$ is the local surface height, $\gamma$ the surface tension, and $T_g(D)$0 the polymer viscosity described by an Arrhenius law:

$T_g(D)$1

with $T_g(D)$2 as the activation energy and $T_g(D)$3 the gas constant. Capillary forces dominate, as gravity and disjoining pressures are negligible at submicron scales, and the unexposed resist exhibits $T_g(D)$4 Pa·s, preventing flow (McCoy et al., 2021).

2. Grayscale Lithography and Contrast Calibration

The fabrication workflow commences with the spin-coating and baking of PMMA resist ($T_g(D)$5 kg·mol⁻¹ in 3% anisole, thickness $T_g(D)$6 ≈ 130 nm), followed by GEBL patterning to form multilevel staircases. The dose-to-thickness response is mapped by measuring a contrast curve using spectroscopic ellipsometry and fitting to a Cauchy model. Dose increments typically range from 50 μC/cm² (full thickness) to 200 μC/cm² (fully cleared). Patterns are divided, for example, into 4 or 6 levels per period, with precisely controlled dose delivery via proximity-effect correction (3DPEC) or EBPG sequencing (McCoy et al., 2021, McCoy et al., 2020).

Pattern layouts for period $T_g(D)$7 nm (6 levels of 140 nm) or $T_g(D)$8 nm (4 levels of 100 nm or modified widths to reduce plateauing) are encoded such that each step’s thickness $T_g(D)$9 matches a calibrated dose $T_g(D) < T_g(0)$0. This enables beam-write strategies that are compatible with both rapid serial (sequencing) and high-precision (3DPEC) strategies.

3. Selective Thermal Reflow and Facet Formation

Thermal reflow is performed on an automated hotplate at temperatures straddling the $T_g(D) < T_g(0)$1 depression window. For PMMA, $T_g(D) < T_g(0)$2(unexposed) ≈ 130°C, while $T_g(D) < T_g(0)$3 in exposed regions drops to 110–120°C. Hold times from 20 s to 120 s modulate the degree of leveling; optimal facet formation occurs at 120°C for 60 s, which rounds intermediate steps, yielding near-linear facets, but preserves the uppermost step to maintain apex sharpness.

Facet angle $T_g(D) < T_g(0)$4 emerges as $T_g(D) < T_g(0)$5, with AFM-measured values of $T_g(D) < T_g(0)$6 (840 nm period) and $T_g(D) < T_g(0)$7 (400 nm period) for PMMA relief depths of 130 nm and 100 nm, respectively. RMS facet roughness is 2–4 nm, with field-stitch artifacts up to 5 nm but suppressible via optimized reflow (McCoy et al., 2021).

4. Application to X-ray and EUV Reflection Gratings

TASTE was applied to fabricate reflection gratings with periods of 400 nm and 840 nm, serving as PMMA templates for subsequent functionalization. Metal coatings (e.g., 10–20 nm Au with Ti adhesion) are deposited via EBPVD for grazing-incidence reflectivity. For prototyping (McCoy et al., 2020), a grating of period $T_g(D) < T_g(0)$8 nm and blaze angle $T_g(D) < T_g(0)$9 was produced over $D$0, achieving facet roughness of $D$1 nm as confirmed by AFM.

EUV/SXR measurements (ALS 6.3.2 beamline) showed absolute peak first-order diffraction efficiencies up to 75% at $D$2 nm ($D$3 eV), with total relative efficiency exceeding 90% of the gold Fresnel limit across much of the SXR range. Performance was quantitatively described by the Nevot–Croce roughness factor,

$D$4

where $D$5 is the facet roughness and $D$6 the grazing angle (McCoy et al., 2020, McCoy, 2021).

5. Design Guidelines and Process Parameters

Guidelines for grating design with TASTE include:

• Period and Facet Angle: Choose grating period $D$7 and desired facet angle $D$8, leading to a required relief depth $D$9.
• Staircase Quantization: Assign $T$0 steps per period with widths $T$1 summing to $T$2; target resist thickness after development, $T$3.
• Dose Assignment: Invert the measured contrast curve $T$4 to determine $T$5 for each level.
• Thermal Timescale: Leveling time $T$6 for lateral scale $T$7 and feature height $T$8, using $T$9 and $T > T_g(D)$0 mN/m for PMMA.
• Optical Equation: The blaze wavelength for order $T > T_g(D)$1 is $T > T_g(D)$2.

Limits arise for periods $T > T_g(D)$3 nm due to quantization of GEBL step heights and electron-backscatter effects, necessitating further optimization for higher facet steepness and roughness control (McCoy et al., 2021).

6. Strengths, Limitations, and Prospects

TASTE enables the fabrication of high-fidelity blazed gratings on arbitrary (non-crystallographic) layouts, decoupling groove geometry from substrate orientation. Custom fanned, curved, or variable-line-space motifs are directly accessible via dose mapping in GEBL. The technique is not constrained by silicon crystallography, unlike KOH-etched Si gratings.

Key limitations include apex rounding, possible nonuniformity in facets for higher orders ($T > T_g(D)$4), and achievable period limits set by lithographic contrast and reflow dynamics. Surface roughness near 1.5 nm RMS is sufficient to meet the Rayleigh criterion for soft X-ray reflection at grazing incidence, but further reductions (<1 nm) are needed for improved efficiency, especially for smaller periods.

Future work aims to extend TASTE to smaller pitches (<200 nm) by enhancing resist chemistry, contrast, and thermal management. The process is compatible with master imprinting (e.g., NIL, SCIL) for mass manufacturing, and offers promising potential for next-generation instruments such as reflection grating spectrometers in x-ray astronomy (McCoy, 2021).

7. Comparative Performance and Integration Pathways

The table below summarizes key experimental parameters and outcomes for TASTE-based X-ray reflection gratings:

Parameter	400 nm grating (McCoy et al., 2020)	840 nm grating (McCoy et al., 2021)
Polymer resist & thickness	PMMA, 130 nm	PMMA, 130 nm
Staircase levels per period	4	6
Facet (blaze) angle (AFM)	~27° ± 0.5°	~9° ± 1°
Facet RMS roughness (pre-/post-metal)	1.3–1.5 nm	2–4 nm
Peak 1st-order diffraction efficiency	75% at λ~11 nm	30–50% (simulated)

Measured groove placement jitter is below 1 nm per write field; facet uniformity and minimized stitching artifacts are critical for high spectral resolving power ($T > T_g(D)$5). TASTE-fabricated gratings with gold overcoating exhibit total efficiency in the EUV/SXR regime $T > T_g(D)$6 relative to the Fresnel limit, satisfying soft x-ray grating requirements for missions such as Lynx (McCoy, 2021, McCoy et al., 2020).