Is getCurrentForSystem applying the band fraction twice?

[jessegreenberg]

Noticed during https://github.com/phetsims/totality/pull/161, but I think this has always been present (in the java too?)

At positive or 0 V, all emitted electrons should reach the collector, right? But doesn't this effectively compute photons * bandFraction * bandFraction?

const electronRateAsFractionOfPhotonRate = Math.min(
  photonEnergyBeyondWorkFunction / bandWidth,
  1
);
const electronsPerSecondFromTarget = electronRateAsFractionOfPhotonRate * photonsPerSecond;

Then the band fraction is applied again here:

const fractionMoreEnergeticThanRetardingVoltage = Math.max(
  0,
  Math.min( ( photonEnergyBeyondWorkFunction - retardingVoltage ) /
            bandWidth, 1 )
);

const electronsPerSecondToAnode = electronsPerSecondFromTarget * fractionMoreEnergeticThanRetardingVoltage;

Full code at https://github.com/phetsims/totality/blob/main/photoelectric-effect/js/common/model/PhotoelectricEffectModel.ts#L375.

[jessegreenberg]

Confirmed that the same pattern was used in the java.

[marlitas]

But doesn't this effectively compute photons * bandFraction * bandFraction?

I'm not following... I don't see the bandwidth being part of the photonsPerSecondCalculation... Maybe would be good for us to check in synchronously on this because I'm confused.

[jessegreenberg]

Yes, agreed. But here is my rationale:

electronsPerSecondFromTarget is computed as photonsPerSecond * electronRateAsFractionOfPhotonRate, and electronRateAsFractionOfPhotonRate is photonEnergyBeyondWorkFunction / bandWidth.

Then electronsPerSecondToAnode multiplies that by fractionMoreEnergeticThanRetardingVoltage, which is also divided by bandWidth.

When voltage is 0, the second fraction becomes the same band fraction: photonEnergyBeyondWorkFunction / bandWidth.

If bandFraction is photonEnergyBeyondWorkFunction / bandWidth, we have
photonsPerSecond * bandFraction * bandFraction.

I guess I am wondering why electronsPerSecondToAnode isn't simply this:

const fractionReachingCollector = Math.max(
  0,
  Math.min( ( photonEnergyBeyondWorkFunction - retardingVoltage ) / bandWidth, 1 )
);

const electronsPerSecondToAnode = photonsPerSecond * fractionReachingCollector;