Dual-Lift-Off Method in Measurement & Patterning

• Dual-lift-off method is a process employing two sequential lift-off events to reduce parasitic effects and enhance pattern integrity in measurements and fabrication.
• It integrates multi-stage sacrificial layer usage and amplitude-frequency signal compensation to accurately recover target parameters, with errors controlled between 2% and 7.5%.
• Applications span non-destructive testing, epitaxial film transfer, and etching-free oxide patterning, enabling high-fidelity measurements and reliable material processing.

The dual-lift-off method is a process framework deployed in multiple contexts—inductive property measurement, thin-film patterning, and epitaxial lift-off—where sequential or coupled physical or chemical “lift-off” events are used to eliminate parasitic effects or optimize material and pattern integrity. In technical terms, dual-lift-off comprises either sensor manipulation (as in electromagnetic induction), multi-stage sacrificial/etchable layer usage (as in epitaxial or oxide film patterning), or combined amplitude-frequency signal compensation. The defining characteristic is the leveraging of two distinct lift-off events or measures—physical separations, chemical removals, or signal features—to accurately recover target physical parameters or pristine patterned structures.

1. Dual-Lift-Off Methods in Electromagnetic Induction Measurements

In the field of eddy current testing for magnetic plates, dual-lift-off denotes an algorithmic strategy that reduces permeability measurement errors induced by sensor liftoff variations. The approach is formally introduced in "Reducing the Lift-Off Effect on Permeability Measurement for Magnetic Plates From Multifrequency Induction Data" (Lu et al., 2019). The method addresses two concurrent liftoff-driven phenomena: shift in zero-crossing frequency (the frequency at which Re{L(ω)} = 0) and decrease in the amplitude of inductance changes (denoted as L). By encoding both effects, an algorithmic compensation is achieved such that the resultant compensated zero-crossing frequency is almost invariant with respect to liftoff. The predicted permeability, derived from the Dodd and Deeds model, thus approaches the true value regardless of sensor separation, with residual permeability error suppressed within 7.5%.

The algorithm relies on the foundational equation

$\mu = \mu_0 \sigma \frac{\pi \omega_0}{L_0}$

as well as the exponential decay relation

$\ln(L_0 / L_m) = -2\alpha_0 l_0$

to correct for liftoff. The steps encompass multifrequency inductance measurement, amplitude ratio extraction, computation of characteristic spatial frequency (α_0), and quadratic solution for the true zero-crossing frequency, finally mapping to permeability. The experimental protocol employs an SL1260 impedance analyzer, with extensive validation across simulated and measured datasets.

2. Lift-Off Compensation Algorithms in Phase-Sensitive Measurements

A related class of dual-lift-off techniques is described in "Measurement of permeability for ferrous metallic plates using a novel lift-off compensation technique on phase signature" (Lu et al., 2019). Here, liftoff-induced reductions in the phase of the impedance signal (θ_r) and simultaneous reductions in signal amplitude are jointly processed. The compensation algorithm computes a corrected phase by quantifying and subtracting the error induced by liftoff: $\theta = \theta_r - \Delta\theta$ with Δθ derived from the difference between measured and baseline phase or (alternatively) via inversion of a sensor model

$$\phi(\alpha)_0 = \frac{1}{1 + 1/\mu_r + rj\omega\sigma\mu/(\dots)}$$

Phase correction is tied to the compensated zero-crossing frequency,

$$\omega_0 = \frac{\pi \omega_m}{\pi + 4\ln(\Delta L_0 / \Delta L_m)}$$

enabling robust permeability inference using multi-frequency data, with error controlled to below 2% over a range of liftoffs. The technique is compatible with dual-lift-off sensor geometries—one as a reference, another as a variable probe—enabling precise, online permeability monitoring even when sensor position fluctuates.

3. Thickness Measurement Algorithms Immune to Lift-Off Variations

"A Novel Compensation Algorithm for Thickness Measurement Immune to Lift-Off Variations Using Eddy Current Method" (Lu et al., 2019) generalizes dual-lift-off principles for thickness determination. Here, the physically relevant index—peak frequency of the imaginary component of the inductance spectrum—shifts due to lift-off, as does amplitude. By mathematically relating the amplitude decay (exponential in liftoff) to the frequency shift via the Dodd and Deeds integral model,

$$L(\omega) = K \int_0^{\infty} [A(\alpha)\phi(\alpha)]\,d\alpha$$

and applying a quadratic correction to the spatial frequency variable α_0, one recovers the compensated peak frequency: $$\omega_0 \approx (2\alpha_0\pi + 4\ln[\mathrm{Im}(L_m)]) / (\pi\sigma\mu c_0)$$ The final thickness is computed as a function of ω_0, with error tightly bounded (within 2%), provided sensor and sample conditions respect the validity of the exponential decay and small-angle assumptions. This indicates systematic compensation for lift-off via feature amplitude and frequency indices, obviating dependence on empirical calibration.

4. Dual-Lift-Off in Epitaxial Thin-Film and Nanostructure Lift-Off

The method finds application in selective etching and transfer of crystalline films. In "Selective etching of (111)B-oriented $Al_xGa_{1-x}As$-layers for epitaxial lift-off" (Henksmeier et al., 2021), dual-lift-off refers to the process of undercutting an AlₓGa₁₋ₓAs sacrificial layer via hydrofluoric acid etching, mechanically assisted by wax deposition, resulting in controlled upward bending and detachment (“lift-off”) of epitaxial GaAs films. The rate of lateral etching,

$$R_{\text{lat}} = \frac{d_{\text{lateral}}}{t_{\text{etch}}}$$

is empirically modulated by aluminum concentration (optimal above 70%) and orientation ((111)B vs (100)), allowing fine process control. AFM and HRXRD measurements confirm that film quality is maintained post-lift-off, enabling the fabrication of nanostructures for nonlinear optics, particularly those exhibiting efficient second harmonic generation.

5. Etching-Free Dual-Lift-Off for Patterning Oxide Thin Films

A direct application of dual-lift-off to oxide heterostructure processing is described in "Etching-free dual-lift-off for direct patterning of epitaxial oxide thin films" (Qin et al., 1 Sep 2025). The workflow comprises:

1. Spin-coating and patterning photoresist on TiO₂-terminated SrTiO₃ substrate.
2. Room-temperature pulsed laser deposition of amorphous Sr₃Al₂O₆ (aSAO) or Sr₄Al₂O₇ (aSAO427) as a sacrificial layer.
3. Lift-off of the photoresist in isopropanol, leaving patterned aSAO.
4. High-temperature PLD growth of the functional oxide (e.g., LSMO or BFO) atop patterned aSAO.
5. Water-based dissolution of aSAO, completing the second lift-off to yield the final patterned film.

This method substitutes high-temperature-resistant, water-soluble oxides for traditional photoresists, enabling the patterned deposition of functional films without etching—preserving film integrity and environmental viability. The patterned films retain intrinsic electronic and ferroic properties, as verified by XRD, AFM, transport, and PFM measurements. Resolution is determined by photolithographic mask dimensions, with sub-μm pattern fidelity achievable.

6. Technical Considerations, Limitations, and Optimization Strategies

Across electromagnetic implementations, dual-lift-off formulations depend on robust mathematical modeling of amplitude and frequency features as functions of lift-off and target geometry. The compensation steps require that amplitude decay faithfully tracks physical separation—exponential for ideal plate geometries—and that signal zero-crossing or spectral peak frequency shifts can be attributed directly to liftoff rather than secondary materials effects. In thin film patterning, dual-lift-off success is contingent on the thermal stability and solubility of the sacrificial layer (aSAO, AlₓGa₁₋ₓAs), optimal layer thickness matching, and clean boundary transfer during chemical dissolution. Minimal linewidth is ultimately limited by lithography and chemical compatibility, and crystallization or incomplete removal of the sacrificial layer must be experimentally monitored. In all cases, two-lift-off process design must be optimized for the specific physical measurement or fabrication target, with simulation and empirical calibration supporting the implementation.

7. Applications and Broader Impact

Dual-lift-off methodologies enable precision permeability and thickness measurement in non-destructive evaluation, structural health monitoring, and quality control in magnetic and conductive materials. In fabrication science, they facilitate high-fidelity patterning of functional heterostructures such as ferroelectric or ferromagnetic oxides and nonlinear GaAs nanostructures. The demonstrated compatibility with broadband induction and high-temperature deposition processes allows broad integration into automated manufacturing, spintronics, and photonics. A plausible implication is the continued expansion of dual-lift-off based patterning for more complex multi-material architectures, contingent upon development of compatible, dissolvable sacrificial layers and scalable process controls.