Quantum efficiency of CMOS sensors

Overview

Most sensor datasheets don't provide the quantum efficiency (QE) directly. Instead, they provide photosensitivity graphs of A/W versus wavelength. In this article we show how to calculate QE from photosensitivity graphs.

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Photosensitivity graphs

Below is an example of a typical CMOS photosensitivity graph:

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The photosensitivity is given in [A/W] and can be converted to QE using the following steps:

1. Extract the image of the graph from the datasheet
2. Digitize the graph using either AI or a graph digitizing tool and generate a CSV file
3. Import the digitized data (CSV of [A/W] versus [nm]) into Excel
4. Postprocess the data and calculate the QE

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Calculate QE from photosensitivty

Photosensitivity consists of:

• Current in [A]: This gives the number of electrons per second
• Light power in [W]: This gives the number of photons per second

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Electrons per second (Fe)

The electron flux, Fe, can be calculated by dividing the current by the elementary charge e^-:

          Fe [e^-/s] = Current [A] / Q_e = Current [A] / 1.60217663 x 10^-19 [Coulomb]

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Photons per second (Fp)

The photon flux can be calculated by using Planck's law for the energy of a photon:

          Ep [J] = h.F = h.c / L,

where h is Planck's constant (6.62607015 x 10^-34 J.Hz^-1), c the speed of light (299.792458 x 10⁶ m.s^-1) and L the wavelength in [m]. The photon flux, Fp, is the number of photons required to provide 1 W of power:

          Fp [p/s] = 1 W / Ep

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Quantum efficiency

The QE is given by the number of electrons per photon:

          QE = Fe / Fp

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Results

The above graph was digitized and postprocessed as described. This is the equivalent QE vs. wavelength:

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Observations about CMOS sensors:

• The peak QE is around 70% @ 600 nm
• The QE in the UV range is around 30%
• Above 800 nm the QE drops sharply and is around 10% @ 1000 nm