Quantum Efficiency: How to Calculate It

This guide explains how to calculate quantum efficiency (QE) for a photodetector, solar cell, or similar device. You input the measured photocurrent, the incident light power, and the wavelength of the light; the calculation returns the QE as a percentage (or a ratio) indicating how many incoming photons are successfully converted into charge carriers.

Formula

The quantum efficiency is the number of charge carriers generated per incident photon. For a photodetector, it is calculated from the measured photocurrent and the known incident light power:

QE = (I × h × c) / (P × λ × e)

Where:

• I = measured photocurrent (amperes, A)
• h = Planck’s constant (6.626 × 10⁻³⁴ J·s)
• c = speed of light (2.998 × 10⁸ m/s)
• P = incident optical power (watts, W)
• λ = wavelength of light (meters, m)
• e = elementary charge (1.602 × 10⁻¹⁹ C)

In practice, the constants are combined into a single factor. When wavelength is in nanometers, the formula simplifies to:

QE (%) = (I × 1239.8) / (P × λ_nm) × 100

This gives the external quantum efficiency (EQE). If you instead want the internal quantum efficiency (IQE), you divide the EQE by the fraction of light absorbed by the device (1 minus reflectance and transmittance).

Worked Example

Using the default values from the calculator:

• Photocurrent (I) = 0.001 A (1 mA)
• Incident power (P) = 0.01 W (10 mW)
• Wavelength (λ) = 550 nm

Step 1: Multiply the photocurrent by the constant 1239.8:

0.001 × 1239.8 = 1.2398

Step 2: Multiply the incident power by the wavelength:

0.01 × 550 = 5.5

Step 3: Divide the first result by the second:

1.2398 / 5.5 = 0.225418…

Step 4: Convert to a percentage by multiplying by 100:

0.225418 × 100 = 22.54%

The calculator shows 22.54%, matching the manual calculation.

When to Use This Calculation

Quantum efficiency is a key performance metric for:

• Photodetectors – to compare sensitivity across wavelengths.
• Solar cells – to evaluate how well each wavelength of sunlight is converted to electricity.
• Image sensors – to assess color response and low-light performance.
• Photodiodes – to verify datasheet specifications.

The result tells you the percentage of photons that produce a measurable charge. A QE of 100% means every photon is converted, but real devices are lower due to reflection, transmission, and recombination losses.

Common Mistakes

• Mixing units – Using wavelength in nanometers without adjusting the constant, or power in milliwatts instead of watts, will give a wildly wrong answer.
• Forgetting the electron charge – The simplified formula already includes the elementary charge. If you use the full formula with I in amperes and P in watts, you must include e = 1.602×10⁻¹⁹ C.
• Confusing EQE and IQE – The formula here gives external quantum efficiency. Internal quantum efficiency requires knowing the absorbed light fraction, which is not the same as incident power.
• Ignoring dark current – The measured current should be the photocurrent only, not the total current including dark current. Subtract the dark current first.
• Rounding too early – Rounding intermediate values can shift the final percentage noticeably, especially for low QE values.

Tips

• Always measure the incident power at the exact wavelength you are testing. A broadband source needs a monochromator or bandpass filter.
• Use a calibrated photodiode or power meter to verify your light source power.
• For solar cells, measure under standard test conditions (AM1.5G spectrum, 1000 W/m²) to compare with published data.
• If you are measuring a device with a reflective surface, account for reflectance to get internal quantum efficiency.
• Repeat the measurement at several wavelengths to plot a QE spectrum, which is more informative than a single point.

Troubleshooting

QE exceeds 100%
This usually means the photocurrent is overestimated or the power is underestimated. Check for stray light, incorrect calibration, or that you are not including current from other sources. In some avalanche photodiodes, QE can appear above 100% due to internal gain, but that is a special case.

QE is very low (below 1%)
Verify the wavelength is within the device’s spectral response range. A silicon photodiode, for example, has low response below 400 nm and above 1100 nm. Also check that the light actually reaches the active area – a misaligned beam or a protective window can block it.

Results vary between measurements
Ensure the light source is stable. Use a lock-in amplifier or chopper to eliminate ambient light interference. Also confirm the device temperature is constant, as QE can drift with temperature.

Negative QE
This indicates the photocurrent is negative, meaning the device is generating current in the opposite direction. Check the polarity of your connections and the bias voltage.

Frequently Asked Questions

What is the difference between external and internal quantum efficiency?
External QE (EQE) counts all incident photons, including those reflected or transmitted. Internal QE (IQE) counts only photons that are actually absorbed by the device. IQE is always higher than EQE.

Can quantum efficiency be above 100%?
In standard photodetectors, no. But in devices with internal gain, such as avalanche photodiodes or photomultiplier tubes, the measured current per photon can be more than one electron, leading to an apparent QE above 100%.

Why is QE important for solar cells?
It shows how efficiently the cell converts each wavelength of sunlight. A high QE across the visible and near-infrared spectrum means the cell can harvest more energy, leading to higher overall efficiency.

What is the typical QE of a silicon photodiode?
Good silicon photodiodes have peak EQE around 80–90% in the visible range (500–800 nm), dropping off in the UV and infrared.

How do I measure photocurrent accurately?
Use a picoammeter or a lock-in amplifier. Ensure the device is shielded from electromagnetic interference and that the dark current is subtracted from the total current.

Does QE depend on light intensity?
In ideal devices, QE is independent of intensity. However, at very high intensities, nonlinear effects like recombination or saturation can reduce QE. At very low intensities, noise can make measurements unreliable.

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in i | Photocurrent (I) | A | 0.001 | 0
in p | Incident power (P) | W | 0.01 | 0
in w | Wavelength (λ) | nm | 550 | 0
out qe | Quantum efficiency | % | (i * 1239.8) / (p * w) * 100 | 2
out n | Photon flux | photons/s | p * w / (1.2398e-6) | 0
out nc | Converted photons | photons/s | i / 1.602e-19 | 0