How To Calculate Etching Time: A Comprehensive Guide

Etching is a critical process in microfabrication and materials science, used to selectively remove material from a substrate. Accurately calculating etching time ensures precision in creating microstructures, semiconductors, and MEMS devices. This guide details the factors, formulas, and methodologies involved in determining etching time for both wet and dry etching processes.

1. Introduction to Etching

Etching involves two primary methods:

• Wet Etching: Uses liquid chemicals ( e.g., acids, bases) to dissolve material. It is isotropic, etching uniformly in all directions.
• Dry Etching: Employs reactive gases or plasmas (e.g., Reactive Ion Etching, RIE) for anisotropic etching, which is directional and ideal for high-precision patterns.

2. Key Factors Affecting Etching Time

A. Material Properties

• Type of Material: Silicon, SiO₂, metals, or polymers each react differently to etchants.
• Crystal Orientation: Etch rates vary with crystallographic planes (e.g., silicon etches faster in ⟨100⟩ than ⟨111⟩ directions in KOH).

B. Etchant Parameters

• Concentration: Higher concentrations generally increase etch rates (e.g., 30% KOH etches faster than 10%).
• Temperature: Elevated temperatures accelerate reactions (governed by the Arrhenius equation).

C. Process Conditions

• Agitation : Stirring improves etchant replenishment on the surface, enhancing wet etching rates.
• Power and Pressure: In dry etching, RF power and chamber pressure influence ion energy and etch rates.

D. Desired Outcome

• Etch Depth: Directly proportional to time.
• Selectivity: The ratio of etch rates between the target material and mask/layer beneath (e.g., SiO₂/Si selectivity in HF).

3. Fundamental Etching Time Formula

The basic formula for etching time is:

Etching Time (t)=Desired Depth (d)Etch Rate (ER)Etching Time (t)=Etch Rate (ER)Desired Depth (d)​

• Etch Rate (ER): Typically expressed in µm/min or nm/sec, determined empirically or from literature.

4. Calculating Wet Etching Time

A. Isotropic Etch Rate Considerations

Wet etching undercuts the mask laterally by an amount equal to the depth. For critical features, the total lateral loss must be accounted for.

B. Temperature Dependence

Etch rates often follow the Arrhenius equation:

ER=k⋅Cn⋅e−EaRTER=k⋅Cn⋅e−RTEa​​

• $k$ = Pre-exponential factor
• $C$ = Etchant concentration
• EaEa​ = Activation energy
• $R$ = Gas constant (8.314 J/mol·K)
• $T$ = Temperature (Kelvin)

C. Example Calculation

Goal: Etch 50 µm into silicon using KOH at 80°C (ER = 1 µm/min).

t=50 μm1 μm/min=50 minutest=1 μm/min50 μm​=50 minutes

Note: Ensure the mask (e.g., SiO₂) withstands the etchant for the calculated time.

5. Calculating Dry Etching Time

A. Anisotropic Etching

Dry etching focuses on vertical material removal. The etch rate depends on:

• Plasma density
• Reactive gas chemistry (e.g., SF₆ for silicon)
• Ion bombardment energy

B. Loading Effects

High substrate surface area in the chamber can deplete reactive species, reducing etch rates. Adjust time accordingly.

C. Example Calculation

Goal: Etch 10 µm of silicon via RIE with SF₆ (ER = 0.5 µm/min).

t=10 μm0.5 μm/min=20 minutest=0.5 μm/min10 μm​=20 minutes

6. Practical Considerations

A. Calibration and Experimentation

• Conduct test etches on samples to calibrate rates under specific conditions.
• Use profilometers or SEM to measure actual etch depths.

B. Selectivity and Mask Integrity

• Ensure the mask material (e.g., photoresist) does not degrade before etching completes.

C. Endpoint Detection

Advanced systems use optical emission spectroscopy or laser interferometry to halt etching automatically when the desired depth is reached.

7. Advanced Topics

A. Selectivity Calculations

Selectivity (S)=ERmaterialERmaskSelectivity (S)=ERmask​ERmaterial​​

High selectivity (>100:1) minimizes mask erosion.

B. Uniformity and Process Control

Etch rates may vary across the substrate due to temperature gradients or plasma non-uniformity.

Conclusion

Calculating etching time requires understanding material properties, etchant chemistry, and process conditions. While the formula $t=d/ER$ provides a baseline, real-world adjustments for selectivity, anisotropy, and equipment calibration are essential. Always validate calculations with empirical tests to achieve optimal results.