= Photoelectron binding energy reference
{title2=$E_B=h\nu-E_{\rm kin}-\phi_{\rm analyzer}$}
Let a conducting sample and conducting analyzer be in good electrical contact, unbiased, at equilibrium, and without appreciable charging during illumination. Their <Fermi levels> then coincide. Choose that common <Fermi level> as zero. Define $E_B>0$ as the <binding energy> relative to this zero: removing an <Electron> into the <Electron> reservoir at the <Fermi level> costs $E_B$. It is not the cost of removing the <Electron> all the way to the sample's <vacuum> level.
Write the sample and analyzer <work functions> as $\phi_s$ and $\phi_a$. Their local <vacuum> levels lie at $\phi_s$ and $\phi_a$ above the common <Fermi level>. <Conservation of energy> for an <Electron> emitted without additional losses gives total outgoing <energy> $h\nu-E_B$, where $h$ is the <Planck constant> and $\nu$ the <photon> <frequency>. Immediately outside the sample its <kinetic energy> is $K_s=h\nu-E_B-\phi_s$. The contact-related <electric potential> changes this to
$$
E_{\rm kin}=K_s+\phi_s-\phi_a
=h\nu-E_B-\phi_a,
\qquad
E_B=h\nu-E_{\rm kin}-\phi_a.
$$
Thus the sample <work function> cancels when the measured <kinetic energy> is referenced to the analyzer. Substituting $\phi_s$ for $\phi_a$ in the final conversion would mix two different <energy> references. An instrument's calibrated <binding energy> scale can incorporate its effective analyzer <work function>, so the correction need not appear as a separate operator-entered number.
As an original numerical example, stipulate $h\nu=1486.6\,\mathrm{eV}$, $\phi_a=4.5\,\mathrm{eV}$ and a line at $E_B=284.0\,\mathrm{eV}$. The predicted analyzer <kinetic energy> is $1198.1\,\mathrm{eV}$. If $\phi_s=5.0\,\mathrm{eV}$, the surface value is instead $K_s=1197.6\,\mathrm{eV}$; the contact-related increase is $0.5\,\mathrm{eV}$. A second line at $286.0\,\mathrm{eV}$ gives $1196.1\,\mathrm{eV}$ at the analyzer. A $+2.0\,\mathrm{eV}$ <chemical shift in photoelectron spectroscopy> therefore appears as a $-2.0\,\mathrm{eV}$ shift in measured <kinetic energy>. These are chosen values, not a measured <carbon> spectrum.
Charging breaks the assumed reference. If a uniformly charging sample rises by <electric potential> $V>0$ relative to the analyzer, an escaping <Electron> loses an additional <energy> $eV$, with $e$ the positive <elementary charge>. Applying the unbiased conversion consequently returns
$$
E_{B,\mathrm{apparent}}=E_{B,\mathrm{true}}+eV.
$$
Two features from the same stable potential retain their separation. Features from regions at different potentials acquire different offsets, which can mimic chemical differences or broaden a line. A conducting holder alone does not establish electrical contact through an insulating surface layer. Compare repeat scans, electrical contact and charge-compensation settings before interpreting an offset as a change in <chemical bonds>.
<Measurement calibration> is a separate issue: a known reference line tests the scale, while charge compensation controls the specimen's <electric potential>. In an original offset model $E_{B,\mathrm{read}}=E_{B,\mathrm{true}}+b$, one known line determines $b$. An unknown scale factor in $E_{B,\mathrm{read}}=aE_{B,\mathrm{true}}+b$ requires two distinct known lines to determine both $a$ and $b$. Re-reading a reference after a sample checks drift. Treating an unidentified contamination peak as a universally fixed reference would assume the chemical identity and electrical behavior that the measurement should test.
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