The Transition to Paschen's Law for Microscale Gas Breakdown at Subatmospheric Pressure

Area of Science:

• Physics
• Electrical Engineering
• Materials Science

Background:

• Miniaturization of electronic devices requires understanding gas breakdown at microscale.
• Paschen's Law, based on Townsend avalanche, is inadequate for gap distances below 15 μm.
• Field emission and Townsend avalanche are key mechanisms in microscale breakdown.

Purpose of the Study:

• Derive a new analytic equation for breakdown voltage (V_B) at microscale.
• Validate the equation against numerical results and experimental data.
• Investigate the influence of various parameters on breakdown behavior.

Main Methods:

• Development of a novel analytical model for gas breakdown.
• Numerical simulations to verify the derived equation.
• Comparison with experimental data for subatmospheric pressures and gap distances from 1-25 μm.

Main Results:

• The new equation predicts V_B within 4% of numerical and experimental results.
• Breakdown voltage transitions to Paschen's Law (PL) behavior near the Paschen minimum at atmospheric pressure.
• At lower pressures, the transition to PL occurs to the left of the Paschen minimum.
• Work function significantly influences the transition side, while field enhancement and secondary emission coefficient have lesser roles.

Conclusions:

• The derived analytic equation provides accurate predictions for microscale gas breakdown.
• Understanding parameter influence (work function, field enhancement) is key to predicting breakdown transitions.
• Results explain extended plateaus observed in microscale gas breakdown experiments.