Joules to eV Converter for Detector Pair-Creation Energy

What It Costs to Make One Charge Carrier

A radiation detector does not measure energy. It counts charge — electron-hole pairs in a diode, ion pairs in a fill gas, photons in a scintillator — and the number of carriers is what the preamplifier turns into a pulse height. Between the joules a particle deposits and the carriers that eventually reach the electronics sits a single material constant: the average energy needed to create one carrier, universally quoted in electronvolts. Converting a deposited energy into electronvolts is the step that makes a carrier count, and therefore a statistical resolution, calculable.

Conversion factor: 1 J = 6.241509e+18 eV. A deposit of 1 pJ in a silicon diode is 6.241509e+6 eV, and at 3.62 eV per electron-hole pair that liberates about 1.72 million carriers.

Why the Number Is Not Simply the Band Gap

W Is an Average, Not a Threshold

The W-value is the total deposited energy divided by the carriers produced. Much of that energy goes into lattice vibrations and excitations that never free a charge, so W always exceeds the minimum ionisation energy of the medium.

Carriers Are What the Preamp Sees

Pulse height is proportional to collected charge, so the carrier count — not the joule figure — is what sets signal amplitude and what has to beat the electronic noise floor of the front end.

Gases Cost Far More per Pair

A gas needs roughly 26 to 34 eV to make one ion pair against 3 to 4 eV in a semiconductor. Order-of-magnitude fewer carriers is why a proportional counter cannot approach the energy resolution of a cooled diode.

Scintillators Count Photons Instead

In a scintillator the equivalent constant is the energy per emitted photon — near 25 eV in thallium-doped sodium iodide — and the photocathode then throws most of those away, which compounds the statistical penalty.

Turning a Deposited Energy into a Carrier Count

The sequence is always the same: get the deposit into electronvolts, divide by the medium's W-value, then decide whether the resulting count is large enough for the resolution the measurement needs.

Enter the deposited energy in joules

Calorimetric readings, absorbed-energy figures per kilogram and pulse-calibration values all arrive in joules or sub-multiples of one. The electronvolt column resolves as you type, and a decimal comma is accepted alongside a point.

Divide by the W-value of your medium

Use the table below. Silicon takes 3.62 eV per electron-hole pair, germanium 2.96, argon 26.4 per ion pair. The quotient is the carrier count, which is the quantity every noise and resolution estimate is built on.

Reverse it to price a carrier count in joules

The swap arrows run the pair the other way when you already know the electronvolt figure and need the SI energy for an absorbed-energy or calorimetry calculation. The searchable list on each side also reaches keV, MeV and GeV, which is where photon and particle energies usually arrive.

Copy the clean figure into the noise budget

The control above each field yields the number by itself, with no unit and no thousands spacing, ready for the spreadsheet cell where it will be multiplied by the Fano factor and a square root. Ctrl+C in a field does the same.

Deposited is not incident: W-values apply to energy actually absorbed in the sensitive volume. A photon that Compton-scatters and escapes leaves only part of its energy behind, which is why a spectrum has a continuum below the full-energy peak. Convert the deposit, not the beam.

W-values and Pair-Creation Energies for Detector Media

The middle column is the same constant expressed in joules, and the last column is what a 1 MeV deposit yields: 10⁶ divided by the W-value. That final number is the one that decides how good the statistics can possibly be.

Medium	W-value (eV per carrier)	Same in joules	Carriers per 1 MeV
Germanium (77 K)	2.96	4.742443e-19	337 838
Silicon	3.62	5.799879e-19	276 243
Cadmium telluride	4.43	7.097642e-19	225 734
Cadmium zinc telluride	4.64	7.434100e-19	215 517
Diamond	13.0	2.082830e-18	76 923
Xenon (gas)	21.9	3.508767e-18	45 662
Argon (gas)	26.4	4.229746e-18	37 879
Dry air	33.97	5.442594e-18	29 438

The spread from top to bottom is more than a factor of eleven, and since statistical spread scales with the square root of the count, germanium starts a 1 MeV measurement with roughly three times better intrinsic resolution than argon before any other effect is considered. That single column explains why high-resolution gamma spectroscopy means a cooled germanium crystal and why an air-filled chamber is used for integrating charge rather than resolving lines.

What This Pairing Gives a Detector Calculation

Pair-Creation Energies Stay in Exponent Form

A W-value in joules sits near 1e-18, far below the point where the output switches to exponent notation, so the digits survive instead of collapsing into zeros.

keV and MeV Reachable from the Same Field

Photon and particle energies arrive in keV and MeV far more often than in plain eV; both sit in the searchable list on either side, so a 60 keV line needs no manual scaling.

Clean Carrier Figures for a Noise Budget

Copied values carry no unit text and no digit spacing, which is what the cell expects when it is about to be multiplied by a Fano factor and a square root.

Run a Known Line Energy Back to Joules

Press the arrows and a familiar electronvolt line energy becomes the SI figure an absorbed-energy or calorimetric cross-check has to be worked in.

Detector Questions About W-values, Carriers and Resolution

What is a W-value, and why does it exceed the band gap?

W is the mean energy expended per charge carrier created, measured by depositing a known energy and collecting the resulting charge. Silicon's band gap is 1.12 eV but its W-value is 3.62 eV, roughly three times larger, because a fast electron slowing down spends most of its energy on phonons and on excitations that relax without freeing a carrier. Only about a third of the deposit ends up as collectable charge, and W is the bookkeeping constant that accounts for the rest.

How many electron-hole pairs does a 60 keV photon make in silicon?

If it is fully absorbed, 60 000 ÷ 3.62 ≈ 16 575 pairs. In joules that deposit is 9.613060e-15 J, which is why nobody works the problem in SI. Sixteen thousand electrons is about 2.66 fC of collected charge — enough to be measured cleanly by a low-noise front end, but small enough that a preamplifier contributing a few hundred electrons of noise is already a visible share of the peak width.

Why does 33.97 eV per ion pair in air sit under so many measurements?

Because an ionisation chamber measures charge, and air's mean energy per ion pair is what converts that charge back into absorbed energy. Expressed as W/e it is 33.97 J per coulomb. The old roentgen was defined as 2.58e-4 C per kilogram of air, so one roentgen corresponds to 2.58e-4 × 33.97 = 8.76 mJ of energy absorbed in each kilogram. Every free-air chamber calibration still runs through that constant.

What does the Fano factor do to the resolution I should expect?

It shrinks the fluctuation below what pure Poisson counting would give, because the individual ionisation events are not independent — the total energy is fixed, so one event happening constrains the next. The standard deviation in carrier number is √(FN) rather than √N, with F near 0.115 in silicon and 0.11 in germanium. For the 16 575 pairs above that gives σ ≈ 43.7 pairs, or 2.355 × 43.7 × 3.62 ≈ 372 eV FWHM: about 0.6 per cent at 60 keV, and that is the floor before electronic noise is added.

My detector spec says 1.8 keV at 1332 keV — does the arithmetic agree?

Partly, and the gap is informative. A 1 332 keV cobalt-60 line in germanium liberates 1 332 000 ÷ 2.96 = 450 000 pairs; with F = 0.11 the Fano-limited width is 2.355 × √(0.11 × 450 000) × 2.96 ≈ 1.55 keV. A catalogue figure of 1.8 keV is that intrinsic limit with preamplifier noise and incomplete charge collection added in quadrature. If a crystal measures much worse than about 1.9 keV, the problem is in the electronics or the collection, not in the statistics.

Joules to Electronvolts