Plasma Sheath Physics, Bohm Criterion & Sidewall Passivation Kinetics

01Plasma Sheath Dynamics & The Bohm Criterion

Because electrons have significantly higher thermal velocities than heavy positive ions ( $v_{e} ≫ v_{i}$ ), an isolated substrate immersed in plasma rapidly acquires a negative electric potential relative to the bulk plasma. This potential repels electrons and attracts positive ions, creating a non-neutral positive space-charge boundary layer known as the Plasma Sheath.

Process schematicSchematic · source diagram

The Bohm Criterion

For a stable, stationary sheath to form, positive ions entering the sheath edge from the bulk plasma must reach a critical minimum velocity, the Bohm Velocity ( $u_{B}$ ):

u_{B} = \frac{k _{B} T _{e}}{M _{i}}

where $T_{e}$ is electron temperature, $k_{B}$ is Boltzmann's constant, and $M_{i}$ is ion mass. Ions are accelerated across a quasi-neutral "pre-sheath" region by a potential drop $Δ V_{p re} \approx \frac{k _{B} T _{e}}{2 e}$ to satisfy this criterion before entering the high-voltage sheath.

Child-Langmuir Law for Collisionless Sheaths

The ion current density ( $J_{i}$ ) traversing a collisionless sheath of thickness $d_{s}$ under a sheath DC self-bias potential $V_{s}$ follows the Space-Charge Limited Current equation:

J_{i} = \frac{4}{9} ε_{0} \frac{2 e}{M _{i}} \frac{V _{s}^{3/2}}{d _{s}^{2}}

This mathematical relationship dictates that increasing RF bias voltage expands the sheath thickness $d_{s}$ , altering ion transit times and ion energy distribution functions (IEDF).

02Thermochemical Surface Reaction Kinetics & Passivation

Anisotropic profile control in silicon gate etching relies on inhibitor-driven sidewall passivation. When etching silicon with chlorine/bromine chemistries ( $Cl_{2} / HBr / O_{2}$ ), the primary chemical reaction produces silicon tetrahalides:

Si + 4 Br^{*} Ion Impact SiBr_{4} ↑

Incoming Ions & RadicalsSchematic · source diagram

In-Situ Passivation Layer Generation: Oxygen additives react with etched silicon reaction products to deposit an ultrathin silicon oxyhalide passivation layer ( $SiO_{x} Br_{y}$ or $SiO_{x} Cl_{y}$ ) on all exposed surfaces.
Selective Removal: Directional ions continuously bombard the trench floor, sputtering away the $SiO_{x} Br_{y}$ passivation layer and exposing fresh silicon to chemical radicals.
Sidewall Protection: Unbombarded vertical sidewalls retain the passivation film, preventing lateral etching and enabling vertical feature profiles with aspect ratios exceeding 50:1.

03Micro-loading, Aspect Ratio Dependent Etching (ARDE) & Profile Anomalies

As features scale down, transport phenomena inside narrow trenches limit etch performance:

Process schematicSchematic · source diagram

Aspect Ratio Dependent Etching (ARDE / RIE Lag): Etch rates decrease as trench aspect ratios increase. Conductance limits Knudsen diffusion of neutral species to the trench bottom, while charging of insulating sidewalls deflects incoming ions.
Micro-Trenching: Ions grazing against vertical sidewalls deflect toward the outer corners of the trench bottom, creating localized over-etch grooves.
Notching: Charge separation at the bottom of insulating layers (e.g., STI trench stops) causes electron accumulation at feature tops and positive ion accumulation at the bottom, creating a lateral electric field that drives ions sideways, carving out notch defects.

→Prerequisites & continue reading

Prerequisites: ["p06-t6.1-t2-chamber-hardware-rf-bias-plasma-kinematics"]

Also in Topic 6.1, Reactive Ion Etching & Plasma Physics:

Tier 1 · Plasma Etching & Reactive Ion Etching (RIE): Core Fu…Tier 2 · ICP/CCP Etch Chamber Mechanics, Dual-Frequency RF Bi…