SCIENCE · INVESTIGATE AND EXPLAIN

Audit a supplied bandgap detector without claiming a real device

In a semiconductor, electronic states form bands rather than only isolated-atom lines. A valence-to-conduction transition leaves both an electron and an unoccupied valence state called a hole. A band gap is an energy separation, not a physical empty layer between two pieces of material. Doping changes available levels and carrier populations; it does not mean every photon is collected or that a material has one universal efficiency independent of wavelength and temperature.

Learning outcome: Compare equal, below and above-gap photons, then hold photon energy fixed while changing gap. Retain photon rate, current and selected energy shares separately. Explain why no full electrical output efficiency follows.

Starting recap

Separate per-event energy, expectation rate and measurement indication. Check particle identities, conservation, threshold branches and calibration roles before making a source or detector claim.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

At gap 1.5 eV and photons2 eV, collected current is0.6×1/2=0.3 nA. The selected branch receives0.6 nW; pair-creation energy rate is0.45 nW and excess thermalization0.15 nW. Their sum is0.6 nW, not the total incident1 nW.

Open the experiment

Predict

In this supplied model, one collected electron-hole pair contributes to external current with charge magnitude:

Your prediction and reason

Experiment

Compare equal, below and above-gap photons, then hold photon energy fixed while changing gap. Retain photon rate, current and selected energy shares separately. Explain why no full electrical output efficiency follows.

Audit a supplied photon-to-carrier energy budget

Worked teaching model · synthetic values · Supplied ideal threshold detector at incident power 1 nW, external collected-pair yield 0.6 only strictly above the gap. Exact equality is an energetic threshold with no finite-yield prediction. Pair creation energy and excess thermalization are tracked for the collected branch only; no complete device efficiency or actual material performance claim.

Ideal direct band gap: 1.5 eV Incident photon energy: 2 eV

Reset keeps your prediction, captures and practice history.

An energy gap is not a complete spectral response

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: sampled supplied response; no interpolation across the ideal threshold (open markers). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for An energy gap is not a complete spectral response

sampled supplied response; no interpolation across the ideal threshold

photon energy (eV)	collected current under stipulated yield (nA)
1	0
1.025	0
1.05	0
1.075	0
1.1	0
1.125	0
1.15	0
1.175	0
1.2	0
1.225	0
1.25	0
1.275	0
1.3	0
1.325	0
1.35	0
1.375	0
1.4	0
1.425	0
1.45	0
1.475	0
1.5	0
1.525	0.393443
1.55	0.387097
1.575	0.380952
1.6	0.375
1.625	0.369231
1.65	0.363636
1.675	0.358209
1.7	0.352941
1.725	0.347826
1.75	0.342857
1.775	0.338028
1.8	0.333333
1.825	0.328767
1.85	0.324324
1.875	0.32
1.9	0.315789
1.925	0.311688
1.95	0.307692
1.975	0.303797
2	0.3
2.025	0.296296
2.05	0.292683
2.075	0.289157
2.1	0.285714
2.125	0.282353
2.15	0.27907
2.175	0.275862
2.2	0.272727
2.225	0.269663
2.25	0.266667
2.275	0.263736
2.3	0.26087
2.325	0.258065
2.35	0.255319
2.375	0.252632
2.4	0.25
2.425	0.247423
2.45	0.244898
2.475	0.242424
2.5	0.24
2.525	0.237624
2.55	0.235294
2.575	0.23301
2.6	0.230769
2.625	0.228571
2.65	0.226415
2.675	0.224299
2.7	0.222222
2.725	0.220183
2.75	0.218182
2.775	0.216216
2.8	0.214286
2.825	0.212389
2.85	0.210526
2.875	0.208696
2.9	0.206897
2.925	0.205128
2.95	0.20339
2.975	0.201681
3	0.2

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

Calculated quantities under the declared measurement model
Quantity	Value	Unit
Energetic threshold wavelength	826.667	nm
Incident photon rate	3120750000	s⁻¹
Strictly above ideal gap	1	flag
Exact threshold, no finite-yield prediction	0	flag
Collected pair rate under supplied yield	1872450000	s⁻¹
Collected current magnitude	0.3	nA
Pair-creation energy rate for collected branch	0.45	nW
Excess-energy thermalization rate for collected branch	0.15	nW
Selected-branch absorbed power	0.6	nW
Selected energy ledger residual	0	nW

Enough photon energy is necessary for a band transition; actual absorption and collection need further material evidence.

A valence-to-conduction transition leaves an electron and a hole, not two independent charge quanta delivered through the same external circuit. With the stipulated external yield, current is e times the collected pair rate. For that selected branch, gap energy plus excess thermalization equals absorbed photon energy; uncollected photons and later recombination are outside this partial ledger. Doping changes carrier populations and available levels; the abrupt ideal threshold does not model an actual material, indirect-gap phonons, temperature, dark current or device conversion efficiency.

Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.

Enough photon energy is necessary for a band transition; actual absorption and collection need further material evidence.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

State the event and measurement model

Reconcile the quantitative evidence

The supplied ideal direct-gap detector accepts a finite yield only for photon energy strictly above Eg. Exact equality is an energetic threshold, not a promised finite absorption rate. At fixed incident power 1 nW, photon supply is P/Ephoton in consistent units. A stipulated external collected-pair yield0.6 gives current e times that pair rate, not2e times it: the electron and hole are complementary carriers in a single circuit-transfer process, not permission to double-count collected charge.

Preserve limits and alternative explanations

For the selected collected branch, each event initially assigns Eg to pair creation and Ephoton−Eg to excess-energy thermalization. Their rates add to the selected absorbed photon power. Uncollected photons, later recombination and any external electrical output require further terms, so this partial ledger is not a conversion-efficiency calculation. Actual absorption edges, indirect-gap phonons, temperature, dark current, contact loss and spectral response are deliberately not inferred from this sharp threshold model. The calculation is virtual and gives no construction, bias-voltage or exposure advice.

Worked original case

Investigation

Changed-case practice

Try the changed case before feedback

At photon energy 3 eV, power 1 nW and stipulated external yield0.6 above the gap, find current magnitude in nA.

Numerical result in the requested units

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and boundaries

Original cases checked 31 October 2026 against the primary explanation. These are bounded virtual models, not instructions to illuminate, accelerate, collect or expose real material. No real laboratory participation, detector certification, personal medical conclusion or independent mastery is claimed. Keep first work, critique, revision and genuinely new assigned evidence separately from public practice.

Supplemental source checks, 31 October 2026: Semiconductor devices. Numerical cases remain original supplied models.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Which independent observation would reject the selected model or calibration premise, and which quantity is not identified by these records?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Separate energy calibration from source identification Next: Balance nuclear identities and a complete mass-energy account

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