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Sandbox Physics

E19 · Ion milling

FIB Milling: Remove Without Ruining

Balance dose, beam width, local yield and redeposition to reach a clean cross-section endpoint.

Interactive modelFIB Milling: Remove Without Ruining
Mean trench depth—\text{—}
Trench depth RMS—\text{—}
Mean central substrate loss—\text{—}
Mean assigned damage-length proxy—\text{—}
Expected incident ion number—\text{—}
Gross removed atom number—\text{—}
Returned atom number—\text{—}
Escaped atom number—\text{—}
Expected writing duration—\text{—}
Selected-cell net depth—\text{—}
Experiment target—\text{—}

Physics tutorial

FIB Milling: Remove Without Ruining

BackgroundBalance dose, beam width, local yield and redeposition to reach a clean cross-section endpoint.

Why it mattersReach a 250 nm mean within 25 nm, RMS at most 15 nm, central loss at most 10 nm and damage proxy at most 10 nm.

Start with the essentials

Focus question
Can you mill two trenches while preserving the central specimen?
One-sentence intuition
Material removal and returned material must share one ledger.

Core mathematical model

From fluence to depth

hg=FYnNg=n∑iAihg,iNescape=Ng−Nreturn\begin{aligned}h_g&=\frac{F Y}{n}\\N_g&=n\sum_i A_i h_{g,i}\\N_{\rm escape}&=N_g-N_{\rm return}\end{aligned}

Yield is assigned atoms per ion; the material ledger includes sacrificial-layer atoms. Returned atoms remain on the specimen.

Count charge to set time

T=e∑iFiAiIT=\frac{e\sum_i F_i A_i}{I}

Fluence is per specimen area, so incidence does not add another cosine factor to the delivered charge. Current also changes the assigned ion spot.

Roughness across the trench

h‾=1M∑i∈ThiR=1M∑i∈T(hi−h‾)2\begin{aligned}\overline h&=\frac{1}{M}\sum_{i\in\mathcal T}h_i\\R&=\sqrt{\frac{1}{M}\sum_{i\in\mathcal T}(h_i-\overline h)^2}\end{aligned}

Mean and RMS are evaluated across both declared trench footprints, including their edges.

Common difficulties

Model parameters need calibration

Typical misconceptionA successful preset is a recipe for a real instrument.

Better mental modelContinuum teaching simulation, not experimental data or a milling recipe. Assigned Ga/Xe yield, silicon-like number density, striped yield variation and a damage-length proxy. Uniform one-event return to trench floors; no collision cascade, repeated sputtering, evolving shadowing, implantation, thermal damage, crystal orientation or lift-out mechanics. A central sacrificial layer has silicon-equivalent density and yield, not calibrated platinum. Fluence is per actual specimen area. Beam paths refer to the initial planar surface; relief shows the final snapshot. Fixed 48 by 48 grid at 50 nm pitch; hardware and relief magnified separately. This Lab covers trench preparation, not certification of a complete lamella lift-out.

Run the experiment

  1. 01

    Predict the compromise

    Try the rough trench preset. Compare mean depth, RMS and the separate damage proxy.

    What to observe: Depth alone cannot certify a usable section.
  2. 02

    Prepare a cleaner endpoint

    Use the low-energy preset, then reduce rocking averaging or remove the sacrificial cap.

    What to observe: Rocking reduces the authored yield stripes; the cap is consumed before the substrate.
  3. 03

    Track returned material

    Increase redeposition and compare gross removal, return and escape.

    What to observe: Net depth is smaller even if the incident ion dose is unchanged.
  4. 04

    Check the full target

    Reach a 250 nm mean within 25 nm, RMS at most 15 nm, central loss at most 10 nm and damage proxy at most 10 nm.

    What to observe: The task checks a model endpoint, not a real lift-out protocol.