Direct-Write Electron-Beam Lithography

• Direct-write electron-beam lithography is a maskless method that uses a focused electron beam to directly pattern 2D and 3D micro- and nanostructures.
• It leverages processes like FEBID and direct-write electrodeposition to enable selective material deposition, high resolution, and complex architecture formation.
• Advanced workflows combine controlled e-beam dosing and real-time process monitoring to achieve high aspect ratios and scalable nanofabrication.

Direct-write electron-beam lithography (DW-EBL) encompasses a set of techniques enabling the creation of two- and three-dimensional micro- and nanostructures by directly steering an electron beam over a surface, typically in the absence of masks or multi-step resist processing. The scope of DW-EBL has expanded to include resistless metal additive manufacturing, 3D nanoprinting by focused electron-beam induced deposition (FEBID), electron-beam-enabled confined electrodeposition on insulators, direct-write forming of high-index dielectrics, and advanced patterning workflows such as those for complex photonic and diffractive optics. This article provides a comprehensive technical survey of the principles, instrumentation, kinetics, materials scope, and performance metrics of modern direct-write electron beam lithography across its major implementations.

1. Principles and Process Architectures

DW-EBL fundamentally operates by local electron-beam-induced modification through three principal mechanisms: (i) exposure and modification of an electron-sensitive resist (conventional EBL), (ii) precursor decomposition on a surface (FEBID and molecular precursor direct-write), and (iii) beam-induced electrochemical reduction in a confined liquid environment (direct-write electrodeposition).

In resist-based EBL, a coated resist is locally modified by the e-beam, then chemically developed to leave behind the desired pattern, which is further transferred to functional materials via etching, lift-off, or deposition. In FEBID, a precursor gas is delivered via a gas injection system and dissociates locally under the e-beam to form solid deposits composed of metals, semiconductors, or dielectrics. Direct-write electrodeposition exploits a transient electrolyte meniscus, often formed by electrohydrodynamic ejection, with the electron beam locally reducing ionic species (e.g., Cu²⁺ → Cu⁰) at the substrate to enable metal growth even on insulating surfaces.

Advanced DW-EBL workflows coordinate patterned e-beam exposure, direct material conversion, and in situ or ex-situ planarization steps to achieve multilayer, high-resolution, or three-dimensional architectures without the need for masks or etch/deposition cycles (Nydegger et al., 2023, Skoric et al., 2019, Baspinar et al., 19 Jan 2026).

2. Direct-Write Electrodeposition: Mechanism and Performance

Electron-beam-enabled, confined electrodeposition using EHD-ejected electrolyte microdroplets establishes a new paradigm for direct-write on insulators (Nydegger et al., 2023). A nanoliter-scale electrolyte meniscus is generated and replenished by a pulsed EHD jet from a pulled quartz capillary (opening ~120–200 nm), with a sacrificial metal wire in the capillary acting as the anode. Upon landing, the droplet forms a transient meniscus at the substrate, and the electron beam serves as the local reducing agent, enabling metal growth localized to the focal spot with feature sizes down to ≈200 nm. The entire process operates in an environmental SEM at 30–50 Pa pressure, suppressing substrate charging.

Key process physics include Maxwell stress-driven fluid ejection, Navier–Stokes hydrodynamics, and Nernst–Planck ion transport, with reduction kinetics under the e-beam described by a Butler–Volmer-type expression with the relevant overpotential determined by the local electron flux. Dimensional control depends on both the spatial confinement of the meniscus and the rastering/blanking of the electron beam—continuous e-beam yields continuous lines, while blanking produces discrete features.

Technical specifications demonstrate lateral features of ~200 nm, out-of-plane aspect ratios >400:1, and growth rates ~70 nm/s for higher beam current densities. Pure, polycrystalline copper structures with grain sizes 10–50 nm and high bulk conductivity (σ ≈ 10⁷ S/m, ~80% of bulk) are deposited directly onto insulators such as Al₂O₃, glass, and PE, with robust adhesion and no post-annealing required. Throughput is limited by the electron flux on insulators or droplet flux on conductors, both independently tunable (Nydegger et al., 2023).

3. Focused Electron-Beam Induced Deposition (FEBID): 3D Nanofabrication

FEBID directly writes 2D or 3D nanostructures by decomposing surface-adsorbed precursor molecules via a focused e-beam, yielding feature sizes as small as ~10 nm and the ability to realize complex free-standing architectures (Skoric et al., 2019, Huth et al., 2017, Okasha et al., 22 Jul 2025). The process is governed by a convolution of electron-induced dissociation kinetics (cross-sections σ(E) ~ 5–50 eV), precursor supply, surface diffusion, and desorption dynamics, as encapsulated in reaction–diffusion and local deposition rate equations:

$$\frac{\partial\sigma}{\partial t} = D\nabla^2\sigma - k_{\rm des}\,\sigma - \nu_{\rm el}(x,y)\,\sigma + S(x,y)$$

where σ is the surface coverage, D is diffusion, $k_{\rm des}$ is desorption, $\nu_{\rm el}$ is local electron-induced dissociation, and S is precursor supply.

Three-dimensional structures are realized by STL-based CAD slicing, per-layer dose planning, and proximity-effect correction—similar to advanced EBL but extended into the z-dimension. Dwell-time models, incorporating lateral Gaussian attenuation and thermal scaling, matched to Monte Carlo beam scattering simulations and finite-element thermal maps, support nm-accuracy fabrication of free-standing 3D nanostructures in metals such as Fe, Pt, and Co (Okasha et al., 22 Jul 2025).

FEBID enables arbitrary 3D geometries with resolutions down to 5–10 nm, but is currently limited by (i) material purity (<90 at.% metal in many cases without post-treatment), (ii) throughput (serial write and point-by-point scanning), and (iii) build volume per unit time (typ. 10×10×10 μm³/hour). Co-injection of reactive gases and post-deposition irradiation can partially mitigate purity limitations (Huth et al., 2017, Höflich et al., 2024).

4. Direct-Write EBL for Dielectrics, Metasurfaces, and Grayscale Structures

Direct-write EBL has been extended to the patterning of high-index dielectrics via e-beam-induced conversion of molecular precursors (e.g., Sb–BDCA complex to Sb₂S₃) (Baspinar et al., 19 Jan 2026, Wang et al., 2024). This process eliminates separate deposition/etch steps by forming the functional material in situ. In single-step grayscale EBL, variable local dose yields 3D topographies, enabling fabrication of multilevel diffractive optics such as 4-level Fresnel Zone Plates and metalenses with sub-100 nm lateral features. The dose–height relationship is empirically captured as:

$d(D) \approx \alpha(D - D_\mathrm{th})$

up to a saturation regime well-described by

$d(D) = d_{\max}[1 - \exp(-D/D_{c})]$

where d is the final height, D is e-beam dose, $D_\mathrm{th}$ is the threshold, and $D_c$ is the characteristic saturation dose.

Developed Sb₂S₃ exhibits high refractive index (n ≈ 2.6–4.6) and low optical loss, critical for optical metasurfaces (Wang et al., 2024). Multilayer direct-write lithography reduces layer count per workflow (from 9 to 4 steps per layer), obtains sub-50 nm overlay, and enables fabrication of complex stacked resonant filters with independent layer control (Baspinar et al., 19 Jan 2026).

5. Quantitative Metrics: Resolution, Throughput, and Materials Performance

Method	Feature Size	Throughput	Materials	Purity / Q
Electrodeposition (Nydegger et al., 2023)	~200 nm	0.0056 µm³/s	Cu, direct on insulators	σ ≈ 10⁷ S/m
FEBID (Skoric et al., 2019, Huth et al., 2017)	~10 nm (xy, z)	~10³ nm³/s (varies)	Fe, Pt, Co, Ag, Au, W...	Pt/Au ~90 at.%, Fe/Co <90%
Sb₂S₃ Direct-write (Baspinar et al., 19 Jan 2026)	≤100 nm (xy), 4–6 nm (z)	0.002 cm²/min (per layer at 20 nA)	Sb₂S₃, high-n chalcogenides	n ≈ 2.1 (NIR); Q ~82 (exp)
Grayscale EBL (Wang et al., 2024)	100 nm	~10² µm²/s	Sb₂S₃, 3D optics	n ≈ 2.6–4.6, k ≈ 0

Direct-write EBL approaches attain lateral resolution down to ~10 nm (FEBID), ~200 nm (electrodeposition), and 50–100 nm (dielectric direct-write). Out-of-plane (z) resolution depends on the layer thickness control (FEBID: 3–10 nm, Sb₂S₃: quantized at ~120–400 nm). Grayscale approaches leverage dose–height mapping for multilevel topographies. Throughput is fundamentally limited by the serial nature of the e-beam, but can be optimized using high-current beams (multilayer Sb₂S₃) and parallel nozzle architectures (direct-write electrodeposition).

Material purity ranges from near-bulk values for direct-write electrodeposition (Cu, σ ≈ 10⁷ S/m, >80% dense) to moderate (10–30 at.% metal for Ag-FEBID without post-treatment (Höflich et al., 2024)), with dielectrics achieving high optical quality and tunable refractive index post-annealing. Edge placement and overlay accuracy is determined by tool calibration, with alignment tolerances down to <10 nm.

6. Comparative Advantages, Limitations, and Applications

Direct-write EBL provides unmatched design freedom for 3D nanofabrication, bypassing resist coating, development, and etch/liftoff constraints of mask-based EBL. Key advantages include:

• One-step, maskless, and resistless operation for both metals and high-index dielectrics
• Vertical and lateral patterning in a single tool, including in-plane and out-of-plane geometries with aspect ratios >400:1 (Nydegger et al., 2023)
• Capability for direct deposition on insulators, flexible substrates, and complex topographies
• Superior material properties in electrodeposition compared to FEBID (no carbon matrix, high purity)
• Grayscale patterning for true 3D freeform optics

Limitations comprise:

• Throughput bottlenecked by beam current (serial, pixel-by-pixel writing), meniscus size (electrodeposition), or precursor supply
• Material purity in FEBID remains challenging without post-deposition treatment
• Tool complexity and requirement for low-vacuum or controlled-environment SEMs
• Build height in electrodeposition constrained by electron mean free path (~1–3 µm at 20 keV for a static meniscus)
• Limited industrial scaling, though multi-nozzle and multi-beam systems offer a plausible route forward

Applications span prototyping of MEMS/NEMS, direct-write microelectronic interconnects, vertical capacitors, metamaterials and quantum photonic devices, multilevel diffractive optical components, and site-specific metallic, magnetic, or dielectric architectures unattainable by conventional lithography (Nydegger et al., 2023, Skoric et al., 2019, Baspinar et al., 19 Jan 2026).

7. Outlook and Future Directions

The integration of direct-write EBL with advanced process modeling (Monte Carlo and FEM-based growth maps), real-time characterization (in situ AFM and SEM imaging), and modular multi-material precursor strategies establishes a foundation for further progress in nanofabrication (Okasha et al., 22 Jul 2025, Koop et al., 2010). Continued innovations in precursor chemistry (especially for highly pure metals and high-index dielectrics), multi-beam architectures for throughput scaling, and robust environmental control are essential for translation to larger-scale manufacturing.

The emergence of direct-write multilayer lithography workflows (Sb₂S₃, HSQ, and alternative hybrid processes) significantly reduces processing complexity, cost, and adds degrees of freedom in vertical device design, setting the groundwork for scalable, compact, functional nanostructures in photonic and electronic systems (Baspinar et al., 19 Jan 2026). Predictive path-planning, complex 3D nanosculpting, and multi-material alloy/oxide extension are expected directions for both fundamental research and technological deployment of direct-write electron-beam lithography (Nydegger et al., 2023).