E07 · Electron microscopy / specimen physics

Vacuum, Charging & Conductive Coatings

Can you stop charging without hiding the surface? Only if the charge has a path to ground. A conductive coating drains charge only when it is actually connected to ground. Waiting, or pumping the chamber to a lower pressure, will not remove a layer that has already been deposited on the surface, and that layer can hide the detail you wanted to see.

Compare a grounded coating with the same coating disconnected from ground. Run one scan starting from an uncharged surface, then blank the beam: the charge drains away, but the distortion in the scan and the deposited layer stay.

Potential at end of scan $0\,\mathrm{V}$

Effective ground conductance $0\,\mathrm{pS}$

Hydrocarbon layer $0\,\mathrm{nm}$

Retained surface contrast $0\,\mathrm{\%}$

More measurements and target

Chamber pressure $0\,\mathrm{Pa}$

Selected coating $\text{—}$

Final residual potential $0\,\mathrm{V}$

Charge relaxation time $0\,\mathrm{s}$

Coating ground contact $\text{—}$

End-of-scan displacement proxy $0\,\mathrm{nm}$

Gas transmission proxy $0\,\mathrm{\%}$

Experiment task $\text{—}$

Simulated examples; each plot identifies its data source.

Connect coating to groundOpen removes the coating path; bare specimen leakage remains.Chamber pressure exponent

\log_{10}(p/\mathrm{Pa})

-5

Coating: 0 carbon, 1 gold

m

0

Coating thickness

h

0\,\mathrm{nm}

Beam current

I

50\,\mathrm{pA}

Advanced settings

Bare specimen conductance exponent

\log_{10}(G_0/\mathrm{pS})

-2

Pixel dwell

\tau

10\,\mathrm{\mu s}

Scan exposure duration

T

30\,\mathrm{s}

Beam-off recovery duration

T_{\mathrm{off}}

0\,\mathrm{s}

Learning goal and model limits

Instrument settings

Vacuum, Charging & Conductive Coatings

During the scan, keep the potential's magnitude below 2 V, the contamination layer below 1 nm and the surface contrast above 75 percent. Recovering afterwards cannot make an unstable exposure pass.

Why does the chamber stay at higher pressure?

Chamber · nitrogen equivalent

0

Pump inlet · nitrogen equivalent

0

Calibrated He flow

0

Last ion gate

0

Drag the gold valve handle. Keep a run to compare the pressure observations below.

Chamber gauge principle

Valve opening

0.8

Pipe diameter

30\,\mathrm{mm}

Pump inlet speed

80\,\mathrm{L/s}

Wall gas load

1\times10^{-9}\,\mathrm{Pa\,m^3/s}

He flow during tracer pulse

2\times10^{-12}\,\mathrm{mol/s}

Measurement limits and reference conditions

The diaphragm signal depends on total pressure, not the gas sensitivity of ionization. This 10 Pa full-scale teaching device resolves 0.3 mPa; supported indications, including uncertainty, lie between 5 and 10 mPa. The comparison begins at 9 mPa and 23°C after two hours of operation. Its early readable points remain saved as pumping takes it below the usable interval. Signal, ion-gauge and He records remain separate.

Initial trapped-gas pressure

1\times10^{-5}\,\mathrm{Pa}

This run begins after rough pumping, in molecular flow. Chamber and pump-inlet volumes are 20 and 2 litres; the pipe is 0.6 metres long. Valve opening multiplies an illustrative calibrated conductance.

The ion gauges report nitrogen-equivalent pressure for an unknown mixture. Their illustrative He sensitivity is 0.18 relative to nitrogen. Ion counts are seeded stochastic rounding of integrated expected ions, without a full shot-noise model.

He flow uses a blank, a known whole-path standard and a separate heldout. Changing the valve, pipe or pump requires calibration again. A pressure trace alone cannot identify a real or virtual leak; a helium response supports a tracer-responsive path. An unresolved response shows an approximate upper bound under the counting-noise and affine-background assumptions.

Flow in moles per second converts to pressure-volume throughput at the stated gas temperature. Throughput is not heater power. Permeation, pump compression curves and atmospheric pump-down are omitted.

Gas reference temperature

293.15\,\mathrm{K}

Model assumptions

This is an RC circuit model, averaged over the beam duty cycle and started from a fresh surface; it is not recorded SEM data. The capacitance is fixed and the net current is negative. The coating's continuity and conductance are assumed. Beam-induced deposition stops during recovery, but material already deposited stays. Gas transmission, scan displacement, surface masking and the spectral markers are illustrative. Ripple from individual pixel pulses, neutralization by gas ions, positive charging, self-consistent fields and material calibration are not modeled.

Retained detector observations

Import run

Early readable interval and the first withheld point. The readable-point plot expands the first 10 seconds; the raw-voltage plot keeps the full run.

Actual acquisition times · diaphragm indication
Time / s	Pressure / Pa	Standard uncertainty / Pa

Raw channels and calibration

Exports retain voltages, integer ion gates, gas and valve commands, exact gate times, reference flow temperatures, blank and heldout observations. JSON also labels the separate generating reference. CSV contains raw observations and calibrations only.

Scroll the table sideways to see every column.

Last six gates in the selected retained run
End / s	Chamber / V	Pump / V	He ions	Valve	Diaphragm / V	Supported / Pa

Start with the essentials

Focus question: Does a coating still drain charge when its ground contact is open?
One-sentence intuition: What matters for the image is the charge during the scan, not what is left after blanking, and neither waiting nor lower pressure removes a layer already deposited.

Core mathematical model

Charging up from an uncharged surface

C\frac{dV}{dt}=-I_{\mathrm{net}}-GV,\qquad V(t)=-\frac{I_{\mathrm{net}}}{G}\left(1-e^{-t/\tau_c}\right),\quad \tau_c=\frac{C}{G}

The capacitance is fixed at 2 pF. The net negative current is 35 percent of the incident current, times the duty fraction. That averaged duty fraction comes from the dwell time and an assumed 10 microsecond blanking interval per pixel; the rapid on-off switching itself is not resolved.

Charge draining after the beam is off

V(T+t_{\mathrm{off}})=V(T)e^{-t_{\mathrm{off}}/\tau_c},\qquad G=G_0+cG_{\mathrm{coat}}

The contact switch is one when the coating is connected and zero when it is open. The bare specimen's own leakage stays in both cases. Conductance here means the effective path to ground, not the bulk conductivity. Waiting changes the final potential, not the scan that came before.

Deposited layer and surface masking

h(t)=r_{\mathrm{dep}}\min(t,T),\qquad S(t)=\exp\left[-\frac{b_{\mathrm{coat}}+h(t)}{15\,\mathrm{nm}}\right]

Only beam-induced deposition is modeled, and material already deposited stays during recovery. Each scan row uses the state of the surface at the time that row was scanned. The masking and the displacement scale are illustrative; they are not a resolution calibration or an electrostatic transport calculation.

Common difficulties

Waiting afterwards does not fix the image

Typical misconceptionA small final potential means the preceding scan was stable.

Better mental modelThe target uses the potential at the end of the scan. The recovery time does not change the scan image, and it does not clean away deposited material.

What the model covers

Typical misconceptionThis is a calibrated SEM charging or coating calculation.

Better mental modelThis is an RC circuit model, averaged over the beam duty cycle and started from a fresh surface; it is not recorded SEM data. The capacitance is fixed and the net current is negative. The coating's continuity and conductance are assumed. Beam-induced deposition stops during recovery, but material already deposited stays. Gas transmission, scan displacement, surface masking and the spectral markers are illustrative. Ripple from individual pixel pulses, neutralization by gas ions, positive charging, self-consistent fields and material calibration are not modeled.

Run the experiment

01
Compare a grounded and a floating coating
Select Thin carbon coat, then Disconnected coat. The film thickness and masking stay the same, but the charge drainage changes.
What to observe: A floating coating still shows its spectral marker and still masks the surface, but it no longer adds a path to ground.
02
Blank the beam after the scan
Select Bare scan, then blank. Compare the potential at the end of the scan with the final residual potential, then change the Beam-off recovery duration.
What to observe: The charge decays once the beam is off, but the scan image and the contamination stay the same, and an unstable exposure still fails the target.
03
Find a stable preparation
During the scan, keep the potential's magnitude below 2 V, the contamination layer below 1 nm and the surface contrast above 75 percent. Recovering afterwards cannot make an unstable exposure pass.
What to observe: A thin, grounded carbon coat meets this teaching target. Thick gold hides surface detail, and a poor vacuum raises the assumed deposition rate. Lowering the pressure alone does not ground an insulator.

Read the instrument principle, sources and limits

Start with the essentials

Focus question: Does a larger pump or a wider pipe lower chamber pressure more?
One-sentence intuition: Effective speed depends on the entire gas route. Gauge response depends on composition, and helium flow requires standards that travel the same path.

Core mathematical model

Gas inventory in each volume

p_iV_i=n_iRT,\qquad V_i\dot p_i=Q_i+\sum_jC_{ij}(p_j-p_i)-S_ip_i

At fixed gas temperature, nitrogen and helium inventories evolve separately. Every internal flow enters one volume and leaves its neighbour; pumping removes gas at the inlet.

Connecting the pump to the chamber

S_{\mathrm{eff}}=\frac{CS}{C+S},\qquad Q_{pV}=\dot nRT

A narrow route makes effective speed approach its conductance. Converting molar flow to pressure-volume throughput uses the recorded gas temperature. Throughput is not heating power.

Common difficulties

Nitrogen-equivalent pressure

Typical misconceptionA voltage trace directly gives the true total pressure of any mixture.

Better mental modelIonization response depends on gas species. An unidentified mixture retains a nitrogen-equivalent pressure until composition is independently known.

Allowing the signal to recover

Typical misconceptionResidual helium can be ignored as soon as tracer delivery stops.

Better mental modelThe acquired reference tail must lie within two percent of the late-pulse response relative to the blank, allowing for both signs and count uncertainty. Incomplete recovery withholds helium-flow inference.

Run the experiment

01
Compare a narrow route with a larger pump
Compare Open path, Narrow path and Larger pump.
What to observe: Conductance changes the pressure difference and evacuation curve.
02
Move the valve while the apparatus runs
Drag the gold handle, calibrate the path again and keep the run.
What to observe: The network updates before release. Old plots and exports retain their original settings.
03
Mark gas outside the chamber
Compare External leak with Trapped gas and select helium ion counts.
What to observe: An external tracer path produces helium response. Absence of that response does not establish a virtual leak from pressure alone.

Vacuum, Charging & Conductive Coatings

Retained detector observations

Can you stop charging without hiding the surface?

Core mathematical model

Charging up from an uncharged surface

Charge draining after the beam is off

Deposited layer and surface masking

Common difficulties

Waiting afterwards does not fix the image

What the model covers

Run the experiment

Compare a grounded and a floating coating

Blank the beam after the scan

Find a stable preparation

Gas crosses the pipe before reaching the pump

Core mathematical model

Gas inventory in each volume

Connecting the pump to the chamber

Common difficulties

Nitrogen-equivalent pressure

Allowing the signal to recover

Run the experiment

Compare a narrow route with a larger pump

Move the valve while the apparatus runs

Mark gas outside the chamber

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