Theoretical assessment of surface waviness on work function

Jacqueline R Malayter,Allen L Garner

doi:10.1063/5.0016116

Abstract

The work function may affect the physical, electrical, and chemical behavior of surfaces, making it important for numerous applications and phenomena, including field emission, gas breakdown, and nanotechnology. Despite this importance, studies examining the impact of surface roughness on the work function have only examined the amplitude and not the period of the waviness, which becomes increasingly important with reduced device size. This paper extends these previous scanning Kelvin probe (SKP)-based mathematical models for predicting the work function of a metallic surface with surface waviness by explicitly including the period. For a given ratio of surface roughness amplitude to the distance from the SKP to the center of the waviness, increasing the period or reducing the SKP step distance reduced the surface’s effective work function. In the limit of infinite period (or low SKP step size) and low surface roughness amplitude, the work function approached that expected with a concomitant reduction in the gap distance with no surface roughness. The effective surface work function approaches zero and may become negative as the SKP tip approaches the surface, suggesting the importance in these corrections for nanoscale measurements. As the SKP step size approaches the surface roughness period, the effective work function becomes infinitely large. Implications of these results on gas breakdown, field emission, and nanoscale device design will be discussed.

Highlights

The work function, the minimum energy required to extract an electron from the surface of a solid to an infinite distance,1 is highly sensitive to physical and chemical changes on the surface, including surface topology.2 Changes in the work function may have important effects on the physical, electrical, and chemical properties of the surface, which may be important in numerous applications, including nanoelectromechanical and microelectromechanical devices (MEMS and NEMS), carbon nanotubes, and semiconductors.3 For example, low voltages may induce high electric fields in NEMS and MEMS devices to cause damaging electrical breakdown.4 Microplasma systems intentionally induce gas breakdown to generate plasma species for various applications, including combustion and medicine.5As device size decreases, reliability under these extreme conditions becomes increasingly important
This study proposed a simple model for calculating the change in work function of a rough surface, it neglected the effect of the periodicity of the surface roughness
We propose a mathematical model for predicting the effective work function of a sample as a function of a copper sample’s amplitude and periodicity of the surface roughness

Summary

INTRODUCTION

The work function, the minimum energy required to extract an electron from the surface of a solid to an infinite distance, is highly sensitive to physical and chemical changes on the surface, including surface topology. Changes in the work function may have important effects on the physical, electrical, and chemical properties of the surface, which may be important in numerous applications, including nanoelectromechanical and microelectromechanical devices (MEMS and NEMS), carbon nanotubes, and semiconductors. For example, low voltages may induce high electric fields in NEMS and MEMS devices to cause damaging electrical breakdown. Microplasma systems intentionally induce gas breakdown to generate plasma species for various applications, including combustion and medicine.. Gas breakdown for microscale gaps at atmospheric pressure is driven by field emission (FE), where the high electric fields strip additional electrons from the cathode, which ionize the surrounding gas molecules near the cathode.7 These positive ions subsequently enhance the secondary emission coefficient γSE, leading to a modified Paschen’s law (PL), which is the standard theory used for predicting gas breakdown.. One approach to unifying FE and PL involves mathematically accounting for the additional positive space-charge introduced by gas ionization near the electrode by rewriting ES in (1) as ES + E+, where E+ is the space-charge electric field, and rewriting the secondary electron emission coefficient γSE as γSE + γ′SE, where γ′SE is a function of E+.15 This leads to a breakdown condition that may be solved numerically..

MODEL DERIVATION

CONCLUSION