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# Quantum Efficiency｜Definition, Equation, Application, Calculating

#### Contents

A Quantum Efficiency is a parameter which is used to characterize the performance of a photo-electronic device. We describe the definition and information of these photon-electronic devices in different applications, which include solar cells, photodetectors (photodiodes, PD), avalanche photodiodes (APD), charge-couple device (CCD) sensors, CMOS image sensors (CIS), Light Emitting Diodes (LED).

## What is Quantum Efficiency?

A Quantum Efficiency is a parameter which describes the converting ability of the system between “input” and “output”. It is commonly used in modern photoelectrical devices or luminescent materials which is correlated photoelectrical effect. The photon-electronic device can be the solar cell, photodetectors (photodiodes, PD), avalanche photodiodes (APD), charge-couple device (CCD) sensors, CMOS image sensors (CIS), Light Emitting Diodes (LED). In the following, we will introduce the definitions, equations, applications and how to calculate the quantum efficiency in these devices or application.

The definitions of quantum efficiency of different photon-electric devices are described as below:

### Quantum Efficiency of Solar cells

What is the quantum efficiency of solar cells? It is the efficiency of the incident photon-electron conversion which is called IPCE (Incident Photon-Electron Conversion Efficiency) as well. The definition as defined as how many electrons generated by the incident photons. It can help researchers to judge the quality of the solar cells at each or specific wavelength. For more details, please read

### Quantum Efficiency of LEDs

What is the quantum efficiency of LEDs (Light Emitting Diodes)? LED is an active illumination photo-device which has the reverse process of solar cell. The quantum efficiency of LEDs describes that how many injected electrons converted to photons, which is call the electroluminescence phenomena. There are two types of quantum efficiencies of LEDs. One is the external quantum efficiency (EQE) and the other is internal quantum efficiency (IQE). IQE of LEDs is defined as the number of injected electrons per unit time became the number of photons per unit time (inside the LED device). The IQE formula of LED’s is:

EQE of LEDs is defined as the number of injected electrons per unit time converted to the number of “illuminated photons” per unit time (outside the LED device).

The EQE of LED’s formula is:

The difference between IQE and EQE of LEDs is the Light Extraction Efficiency (LEE). The relationship is:

Therefore, the formula of LEE is

The IQE characterizes the ability of LED’s active layer to convert the injected electrons into photons.

The LEE represents the light extraction capability of LED’s device structure design, which includes the layer structure and layer refractive index n matching.

The EQE is the ability of LED electrical energy into light energy outside the whole device.

### Quantum Yield of Luminescent Materials

What is the quantum yield of materials? A Quantum yield (QY) is commonly seen in material science and Chemistry field. It is defined as the number of events per unit time generated by absorbed photons per unit time. In luminescent materials system, the “event” is the emitted photons. Simply speaking, it is coincident and like the previous description about the quantum efficiency: the converting ability between the input and the output.

The Photochemistry and material science, it is important to study the energy levels and the electronics structures of the system. Photoluminescent spectroscopy is the common and essential the technique to characterize the luminescent qualities parameters, including central wavelength, FWHM, and efficiency. Therefore photoluminescent efficiency is also called photoluminescence quantum efficiency or photoluminescence quantum yield.

The symbol of the quantum yield QY is usually represented by Latin  or . Therefore, the quantum yield QY of luminescent materials is defined as:

Quantum yield (QY) is also called PLQY (Photoluminescence Quantum Yield). In some fields like Physics, quantum efficiency (QE) or external quantum efficiency (EQE) term is used to represent the photoluminescent ability of luminescent materials. Therefore, in more common way,

Technical notes on how to measure the quantum yield can be found on the website PLQY.

Figure 1. The Quantum Yield Process. The quantum yield is the quantity describing the ability that the materials converting incident photons to photons. The quantum yield is calculating how many emitted photons divide absorbed photons per seconds.

### Quantum Efficiency of Fluorescence

What is quantum efficiency of fluorescence? Fluorescence is one kind of photoluminescence. When the electron is excited from ground state to excited state, the spin is Singlet state. If the excited singlet state is directly radiative decayed to ground state, there is no spin changing. The emitted light phenomenon is called Fluorescence.

Fluorescence: Excited Singlet State (S1) => Ground State (S0)

Therefore, quantum efficiency of fluorescence is the quantum yield of fluorescence. It characterizes the photoluminescent ability of the material through fluorescent process, which is without spin changing.

Quantum Efficiency of Fluorescence = Quantum Yield of Fluorescence

On counter to fluorescence, phosphorescence is another luminescence phenomenon. It is easily identified the difference between fluorescence and phosphorescence from famous Jablonski-Diagram. After the spin status of excited singlet state (S1) is changed through intersystem crossing (ISC) to excited triplet state, the radiative decay to ground state is called phosphorescence.

Phosphorescence: Excited Triplet State (T1) => Ground State (S0)

Figure 2. Jablonski-Diagram. The photoluminescence process is decried as below.

The first step is the absorption or excitation. The electrons or carriers are excited to the excited singlet states (S2 or S3) and relaxed to the first excited singlet state (S1). This relaxation process is in fs time scale (10-14 sec). S1 have two paths to release its energy: 1. Radiative decay to the ground state and emit photons. 2. Nonradiative decay to the ground state and emit phonons through vibrational energy relaxation. 3. Changing its spin status through intersystem crossing (ISC) process to triplet states. From Jablonski-Diagram we can see these processes. (Source)

### Apparent Quantum Efficiency (AQE)

What is Apparent Quantum Efficiency (AQE)? The apparent quantum efficiency is commonly used in photocatalyst or photochemistry field. The definition can be defined as below:

“In heterogeneous photocatalysis, quantum efficiency has come to define the number of reacted electrons relative to the total number of photons incident in the reaction system, for undefined reactor geometry and for polychromatic radiation, rather than the number of absorbed photons at a given wavelength to satisfy the photochemical definition in homogeneous photochemistry.” (from Photocatalytic Water Splitting on Semiconductor-Based Photocatalysts).

The AQE formula of photocatalyst can be calculated as follows:

The Apparent Quantum Efficiency AQE is also called AQY (Apparent Quantum Yield). It characterizes the efficiency of hydrogen production efficiency in photocatalyst reaction. The AQE (%)= 2* number of H2 reacted/ number of incident photons.

### Detective Quantum Efficiency (DQE) of X-ray imager

What is the Detective Quantum Efficiency (DQE)? DQE is generally used to describe how good of a X-ray image device. It is essential in X-ray medical imaging which tells the user that how radiation exposure dosage to patients. The formula of DQE is expressed in terms of Fourier-based spatial frequencies:

The DQE value can be used to quantify and judge the quality of the X-ray image sensor. However, DQE does not fully represent the quality of the X-ray image due to that X-ray image sensor is one component of the image system. There are other components and factors which will affect the final X-ray image quality.

More details can refer to the external links:

### Quantum Efficiency of image sensor

What is the quantum efficiency of image sensor? Image sensor is an optical device which is the cluster of two-dimensional photodiodes. Quantum Efficiency image sensor is the efficiency of the incident photon-electron conversion, which is like photodiode. One can realize that the quantum efficiency of an image sensor is the “average quantum efficiency” over all of photodiodes of the sensor.

Image sensor can be divided to CCD and CMOS image sensors by device design. In recent years, CMOS image sensor (CIS) dominates the image sensor market due to its low-cost and high performance.

Figure 3. The schematic configuration of CCD and CMOS image sensor. The incident photons get into the photodiode unit of the image sensor, the photoelectrons are generated based on image sensor’s quantum efficiency capability. The charges are transfer out and convert to voltage signal in difference ways for CCD and CMOS image sensor due to their nature device structures.

The structures of image sensor will affect the quantum efficiency performance. For example, BSI (Back-Side Illumination) CSI has around 30% absolute quantum efficiency than traditional FSI (Front-Side Illumination) CSI due to the photo-sensing area increased.

The quantum efficiency curves of CIS are usually tested through non-destructive method. By using special optical beam modulation technique and measuring the variation of images generated by CIS, the digital image variance can transfer to analog quantum efficiency curves. The best benefit is that you do not need to break the CIS and use probe tip to test the photodiode element of CIS. If you are interested in testing system, please read SG-A.

Figure 4. The quantum efficiency curves of CIS with R, G, B Byer filters. The black curve is the summation of RGB curves, which is usually summed to represent the CIS overall quantum efficiency capability. These curves are measured by SG-A system.

### Quantum Efficiency of CCD

What is the quantum efficiency of CCD? CCD is an image sensor type, which is composed by photodiode arrays. The quantum efficiency of CCD is an ability which characterize the photon-electron conversion capability. The quantum efficiency of CCD is describing the whole device performance; therefore, it is also called EQE (external quantum efficiency) of CCD.

Figure 5. Quantum efficiency of CCD and Human Vision Photopic sensitivities. With different device structures and different processing conditions, the quantum efficiency curves of CCD are quite different. For the highest quantum efficiency of CCD is the black-thinned CCD which can reach and exceed 90%. (Source: Hamamatsu)

How to measure the quantum efficiency of CCD? The testing method of CCD quantum efficiency is similar to CIS quantum efficiency measurement. By using nondestructive and modulated light beam, the images under different light beams are measured and analyzed. The digital image signals are re-convoluted to analog quantum efficiency curves.

Figure 6. Most popular CCD’s QE comparison chart. The manufacturers of these CCDs are from Kodak (KAF-3200, KAF-1603ME, KA11002, KAF-8300, KAF-6303, KAI-4022, KAF-16803) and Sony (ICX285, ICX694). (Source)

### Quantum Efficiency of PMT

What is the quantum efficiency of PMT? Before that, we should understand what a PMT is:

“A photomultiplier tube is a vacuum tube consisting of an input window, a photocathode, focusing electrodes, an electron multiplier and an anode usually sealed into an evacuated glass tube.”  From Hamamatsu PMT handbook

Figure 7. Schematic construction of a photomultiplier tube. The light is incident into the faceplate of PMT and then pass-through photocathode, focusing electrode, electron multiplier ad the anode. The incident photons are converted to electrons based on photocathode’s quantum efficiency capability. The generated electrons are multiplied in dynodes through high voltage, which can detect very low photon condition, even in single photon situation.

PMT is a photo-electrical device which can convert the incident photons into electrical signals. Therefore, quantum efficiency of PMT is a parameter which characterize the ability of how many incident photons are converted to photoelectron.

Figure 8. Quantum efficiency of PMT with different photocathodes. The curve codes and photocathode materials are matched in the following table. The theoretical quantum efficiency curve of photocathodes are also plotted. The photocathode materials is the dominant in PMT. It can alter the spectral response wavelength range and repones intensity. (Source: Hamamatsu)

Curve CodePhotocathode MaterialWindow Material
150MCs-IMgF2
250SCs-TeQuartz
250MCs-TeBorosilicate
350KSb-CsUV
351USb-CsUV
452UBialkaliUV
456ULow dark bialkaliUV
552UMultialkaliUV
555UMultialkaliUV
650UGaAs(Cs)UV
650SGaAs(Cs)Quartz
851KInGaAs(Cs)Borosilicate

### Quantum Efficiency of photodiode (PD)

What is the quantum efficiency of the photodiode (PD)? A photodiode is also called photodetector which can convert the incident photons into electrons. Therefore, the quantum efficiency of a photodiode is a character which describing photon-electron converting efficiency.

The formula of the quantum efficiency of PD:

SR(λ) is the Spectral Responsivity in Amp/Watt. In photodiode or photodetector characterizing field, the spectral responsivity (SR) is more usual to describe the performance of a photodiode device than quantum efficiency. The quantum efficiency of photodiode is the same as external quantum efficiency (EQE).

Figure 9. the quantum efficiency of different photodiodes with different wavelength response range. The Si photodiodes have response wavelength range from 300nm to 1100nm. For Ge photodiode, the quantum efficiency curve is from 900nm to 1800nm. The green line is the quantum efficiency curve of Si solar cell, which has over 95% external quantum efficiency. Unlike solar cells, the quantum efficiency curve design of photodiodes is not arm at extremely high EQE, but the balance of quantum efficiency and dark noise current or photo detecting application wavelength range, such as UV or NIR range. Therefore, the quantum efficiency curve is important for photodiode devices, but it is not the most essential parameter to pursue for a photodiode. (Source: Enlitech)

In many applications, the photodiode is operated at certain bias voltage, which can narrow down the PN junction band diagram and increase the responses speed of the photon detection. Therefore, the quantum efficiency curve of photodiode is also common shown at certain bias voltage.

Figure 10. A packaged Si photodiode. The Si photodidoe is S1337 from Hamamatsu. The enclosured package is anodized aluminum body. The black anolized coating can effectively eliminate the scattering stray light which can keep the accuracy of the photodiode and not affect the quantum efiiiceincy of it.

Figure 11. A package Ge photodiode. The Ge photodiode is a TO package and covered the anodized aluminum body. The photons is converted to electron and current signal by the Ge PN junction and according its quantum efficiency ability. The electrical current signal is connected to external circuit through BNC connectors.

### Quantum Efficiency of APD

What is the quantum efficiency of the avalanche photodiode (APD)? The APD is a photodetector which is operate at a high bias voltage. It can generate the “avalanche effect” to increase the gain of the APD. The quantum efficiency of a APD is:

Figure 12. The quantum efficiency curves of APD and PMT. Generally, APD has higher quantum efficiency performance than PMT. The spectral response wavelength range in quantum efficiency curve of APD is much broader than any photocathode type of PMT, especially in NIR wavelength range. They are main advantages of APD from the quantum efficiency curves. (Source: Wiley.com)

The quantum efficiency of APD may not much higher than normal PD’s quantum efficiency. However, the avalanche effect of APD can enhance the signal-to-noise ration and overcome the electronical noise. Therefore, APD is usually, like PMT, used to low-light-detection application.

For Further understanding that how to measure the quantum efficiency of photo-electrical device, we will use solar cells as an example to explain the quantum efficiency related information.

## Quantum Efficiency and Spectral Responsivity of Solar cells

Before explaining what quantum efficiency (Quantum Efficiency) is, let’s first understand the spectral response.

Spectral Response (SR) is an index to evaluate the photoelectric conversion capability of optical radiation detection devices (such as photodetectors, photometers, solar cells, etc.), that is, the efficiency of incident photon-electron conversion efficiency, IPCE. For example, solar cells are also photoelectric devices that convert light into electrical energy, so the spectral response is also an important index for evaluating their conversion efficiency.

Spectral Response SR(λ)

Among them, P(λ) is the incident light energy of each wavelength, in Watts (Watt); I(λ) is the current converted by the solar cell after receiving the incident light, in amperes (Amp). Its physical meaning is: the ability of a solar cell to generate ampere current when receiving one watt of light energy.

The spectral response can also be called Quantum Efficiency (QE) or IPCE (Incident Photon-Electron Conversion Efficiency. The incident light energy is converted into the number of photons, and the current generated by the solar cell and transmitted to the external circuit is converted into the number of electrons. The spectral response can represent the ability of each incident photon to be converted into electrons transported to the external circuit, called Quantum Efficiency (QE), the unit is expressed as a percentage. This can also be called the incident photon-electron conversion efficiency IPCE.

Figure 13. Schematic diagram of solar cell quantum efficiency/spectral response/IPCE principle.

## How to calculate the quantum efficiency? (The formula of quantum efficiency)

The conversion between spectral response and quantum efficiency can be written as the following formula:

q is electron quantity,  h is Plank Constant,  v is photon frequency, λ is the wavelength of incident photons (nm).

According the the above formula, the external quantum efficiency formula can be rewritten as:

Figure 14. The conversion between spectral response (SR) and external quantum efficiency (EQE).

Figure 15. The definition and illustration of EQE (External Quantum Efficiency) and IQE (Internal Quantum Efficiency).

## What is External Quantum Efficiency (EQE) ?

From the formula and the unit of spectral response (Amp/Watt), the ampere Amp is converted to the number of electrons per unit time (electron/sec), and the Watt is converted to the number of photons per unit time (Photons/sec). The quantum efficiency obtained by incorporating the above formula is called the external quantum efficiency.

Generally speaking, the quantum efficiency QE refers to the external quantum efficiency EQE, also known as the incident photon-electron conversion efficiency IPCE (Incident Photon-Electron Conversion Efficiency).

QE=EQE=IPCE

The external quantum efficiency EQE calculates the number of electrons produced by the total number of incident photons. Taking Figure 15 as an example, suppose there are a total of 10 photons incident on the solar cell, 2 photons are reflected on the surface of the solar cell, and finally 6 charges are generated. Therefore, by definition, the external quantum efficiency of this solar cell is

EQE=number of generated charges/total number of incident photons=6/10=60%

## What is Internal Quantum Efficiency (IQE)?

Internal Quantum Efficiency (IQE) is also the calculation of photon-electron conversion efficiency. Different from the external quantum efficiency EQE, it calculates the number of photons that actually enter the solar cell and the number of electrons it generates. Taking Figure 15 as an example, suppose there are a total of 10 photons incident on the solar cell, and 2 photons are reflected on the surface of the solar cell. Then the number of photons that actually enter the solar cell material is (10-2)=8 photons and 6 electrons are generated. Then the internal quantum efficiency of this battery

IQE=number of generated charges/number of photons incident into the internal material=6/(10-2) =75%

## What is the relation between internal quantum efficiency IQE and external quantum efficiency EQE?

The internal quantum efficiency is only calculated when incident on the inside of the material. The external quantum efficiency does not consider the interface  reflection or penetration, and calculates the total number of incident photons.

If the reflectivity of the interface is R, the relationship between the two is:

Figure 16. The external quantum efficiency EQE, internal quantum efficiency IQE, and reflectance R spectra of Si solar cells.

## Why is quantum efficiency the best tool for creating high-efficiency solar cells?

Quantum efficiency/spectral response reflects the photoelectric conversion efficiency of solar cells at different wavelengths. The conversion efficiency of solar cells is affected by factors such as the material, manufacturing process, and structure of the cell itself, so that different wavelengths have different conversion efficiencies. Using spectral response/quantum efficiency measurement technology to detect and analyze the changes in the conversion efficiency of the solar cells under different conditions, we can analyze the pros/ cons of the process and find out the key factors related to improving efficiency.

Figure 17 shows the measured spectral responses A and B of the two silicon crystal cells with two different processes. From the spectral response results, it can be seen that the efficiency of cell A is higher, mainly because of the conversion in the 700~1100 nm band. The efficiency is higher than that of the B cell, and the short-circuit current contributed by it is 0.897 mA/cm2 higher than that of the B cell. But in 300~500 nm wavelength range, the efficiency of A is slightly lower than that of B cell, and the short-circuit current density is 0.675 mA/cm2 lower than that of B cell. Therefore, the overall short-circuit current density of cell A is still higher than cell B (0.897-0.675)=0.222 mA/cm2.

The different wavelength ranges represent the structure and manufacturing process of different layers of the solar cells. It will be introduced in more detail in the next section. Therefore, according to the results reflected in different wavelength bands, the process of A cell in the short wavelength range can be improved to further. From the results of the spectral response, it is easy to analyze the pros and cons of solar cells in different manufacturing processes, which is a guideline for improving efficiency.

Figure 17. Schematic diagram of solar cell spectral response and AM1.5G under different manufacturing process conditions.

## Quantum efficiency/spectral response/IPCE application in silicon solar cell process improvement

Quantum efficiency/ spectral response/ IPCE spectrum reflects the characteristics of each layer of the solar cell. Taking silicon solar cells as an example, interface reflection will occur at the incident interface. Different wavelengths reflect different phenomena of device physics. Generally, the loss caused by reflection in the UV and the infrared wavelength band is higher, and the loss in the visible wavelength range is the lowest.

In the 350 nm ~ 500 nm band, the spectral response curve increases as the wavelength increases. Because the penetration depth of long-wavelength photons is deeper, close to the pn junction, the conversion efficiency is improved. Generally, the most efficient part is in the band of the PN junction, because the internal electric field of the pn junction can efficiently disassemble the electron-hole pairs after absorbing photons. Therefore, the highest efficiency is in the 500-800 nm band, which reflects the characteristics of the pn junction layer. The 800~1100 nm wavelength range penetrates to the lowest p-layer. The external quantum efficiency of the single crystal silicon solar cell in Figure 18 can be used to observe the reaction characteristics of each layer.

Figure 18. Schematic diagram of the quantum efficiency spectrum of a silicon solar cell and the response of each wavelength. The illustration shows the component structure of a silicon solar cell.

The previous figure 17 is an example, and the following figure 19 can be obtained by converting the spectral response into quantum efficiency. The efficiency of A cell is lower than that of B cell at 300 nm ~ 500 nm. To further improve the efficiency of the A cell, it should focus on the process of anti-reflection layer (300 nm ~ 350 nm) and n layer (350 nm ~ 500 nm) as the directions of efficiency improvement.

Figure 19. Quantum efficiency spectra of two cells with different processes.

## How to calculate the quantum efficiency? (The formula of quantum efficiency)

The conversion between spectral response and quantum efficiency can be written as the following formula:

q is electron quantity,  h is Plank Constant,  v is photon frequency, λ is the wavelength of incident photons (nm).

According the the above formula, the external quantum efficiency formula can be rewritten as:

## What is quantum efficiency formula?

As described above, the quantum efficiency of solar cells is the electrons generated by the incident photons, which is also called External Quantum Efficiency (EQE). Therefore, the formula of quantum efficiency is:

## Instrumentation for quantum efficiency measurement for solar cells

The Instruments that measure the external quantum efficiency of solar cells typically have the following main components:

### 1.Monochromatic light generation system:

The monochromatic light generation system of the solar cell quantum efficiency measurement includes

#### 1.1 Continuous-wavelength bulb /Light Source:

What kind of bulb/light source is suitable for quantum efficiency measurement system? In solar cell quantum efficiency testing applications, xenon bulbs are most used as continuous-wavelength white light sources. The emission wavelength of xenon lamp covers 250nm to 2700nm, which is very suitable for the solar cell quantum efficiency spectrum range. It not only covers current mainstream and new type solar cells, including Si solar cells (300nm ~ 1200nm), CIGS solar cells (300 ~ 1300nm), organic solar cells OPV (300nm ~ 1000nm), perovskite solar cells (300nm ~ 800nm), etc. While the halogen bulb QTH has a relatively smooth luminous radiation spectrum, its radiation intensity at short wavelengths (< 400 nm) is insufficient, and it cannot be used to test the quantum efficiency of solar cells from 300 nm to 400 nm. Therefore, most of the light sources used in the quantum efficiency measurement system are mainly xenon light sources.

#### 1.2 Light collection system:

The photons radiated by the bulb require optics to collect and guild into the monochromator. The optical elements used can be lenses or mirrors. Different optical designs of the light collection system will affect the final monochromatic light radiant intensity. The light-emitting structure of the short-arc xenon lamp (How a Xe Lamp Works?) is the bulb closest to the point light source. With paraxial optics, it can collect more photons into the monochromator than the halogen bulb, which produces monochromatic light with higher light intensity. In quantum efficiency measurements, more incident photons can generate more electrons. In this way, a better signal-to-noise ratio can be achieved, and the uncertainty of quantum efficiency test results can be greatly reduced (Uncertainty Analysis of Certified Photovoltaic Measurements at the National Renewable Energy Laboratory). Therefore, the design of the light collection system plays an important role for an accurate quantum efficiency test system.

#### 1.3 Monochromator in quantum efficiency measurement:

What is a monochromator? A monochromator is an indispensable part in quantum efficiency measurement system. it is an optical device that can separate, filter and output specific wavelengths of white light of continuous wavelengths in space by the principle of refraction (Prism) or diffraction (grating). At present, the monochromator mainly adopts the grating Czerny-Turner form as the mainstream due to that it can provide good spectral resolution and sensing intensity. In its optical layout, light passes through an entrance slit and is reflected by a curved collimator mirror onto the grating plane. The light is dispersed into a series of monochromatic rays by diffraction grating. Then a mirror is used to pass the diffracted monochromatic light through the exit slit at a specific angle.

#### 1.4 Auto Filter wheel:

The purpose of filter wheel is holding filters which can filter out the high-order stray light of the diffraction grating. Every diffraction grating has high-order term of monochromatic rays. It is the nature of the grating. The wavelength detective range of quantum efficiency measurement usually covers several hundred nanometers which is also covers the high-order term of diffraction for each optical grating. These high-order diffraction light is usually the un-desired wavelength rays in quantum efficiency measurement. Therefore, it is common and necessary to utilize the band pass optical filters to get rid of this stray light. The auto filter wheel can be controlled to change different optical filters at different wavelength range of monochromator, which can make the quantum efficiency measurement automatically through whole interested wavelength range.

Where should I place the auto filter wheel in quantum efficiency measurement system? In quantum efficiency measurement, the white light is collected to the entrance site of the monochromator and became the monochromatic light beam output at the exit slit. The auto filter wheel is usually placed behind the exit slit of the monochromator. It can filter out the monochromator stray light as most as possible.

### 2.Monochromatic light beam modulation system:

What is a monochromatic light beam modulation system? A monochromatic light modulation system modulates a DC monochromatic light beam into an AC alternating beam of a specific frequency f. In solar cell quantum efficiency measurement systems, mechanical optical chopper system is most used to modulate monochromatic light beam. (Schematic diagram of DC modulation to AC)

What is an optical chopper system? The optical chopper system is a fan-type blade controlled by electronic feedback circuits, which modulates continuous light into periodic intermittent light of a specific frequency f at a certain rotatngl speed. Its composition includes a control unit, a chopper head device, a chopper blade.

Why have an optical chopper to modulate monochromatic light? Optical choppers are usually used along with lock-in amplifiers. The optical chopper controls the chopper blades and the chopper head through the control unit, and modulates the continuous DC monochromatic light into an AC beam with a fixed frequency f. The control unit will also send out a TTL reference electrical signal with modulation frequency f, which is connected to the receiving reference frequency signal channel of the lock-in amplifier. The lock-in amplifier filters out the various frequencies received at the signal input, leaving only the signal with the same frequency as the reference frequency f.

Where should I place the optical chopper in EQE measurement system? The optimal position of the optical chopper is in front of the light entrance slit of the monochromator. This position can best chop the incident light beam and avoid the multi-reflection of monochromatic light being modulated by the chopper, which may be reflected to the DUT, resulting in noise signals. In the quantum efficiency measurement system, the position of the chopper and the shielding of the diffusely reflected light are very important. If the optical path design is poor, it will cause a large error in the results of the quantum efficiency test.

Figure 20. Chopper location within the system.

What kind of optical chopper should I choose?  The Optical chopper is generally accompanied with the lock-in amplifier for precision spectroscopy measurements. The SR540  optical chopper from Stanford Research Systems, a well-known lock-in amplifier manufacturer, has been very famous in the field of optical choppers since it came out in 1986. However, with the great progress of electronic component technology in the past three decades, the SR540 does not have much design changes and improvements. Therefore, there are already many optical choppers whose performance greatly exceeds that of the SR540 optical chopper. Especially the frequency stability and frequency drift of the optical chopper, the frequency drift of the SR540 is 2%. However, if the repeatability of the quantum efficiency measurement is to be above 99%, the frequency jitter of the optical chopper should be in 0.1% capacity. The frequency feedback control capability of the Phase-lock-loop circuits of the optical chopper is very important. The table shows essential performance parameters of different chopper manufacturers.

SRS SR540 ChopperNewport 3502 chopperEnli chopper
Suitable Blade for EQE6/5 slot2 slot3 slot
Frequency range of the Blade in EQE4 Hz ~ 400 Hz4 Hz ~ 213 Hz4 Hz ~ 450 Hz
Frequency Resolution1 Hz0.1 Hz0.01 Hz
Frequency Stability2%> 0.12%> 0.05%

In quantum efficiency system, the light source is not coherent laser source. Therefore, the beam spot and divergent angle is quite huge compared to normal coherent laser beam. The slots density of the chopper blade should not be too high, that is the number of slots usually are not greater than 5 slots.

It is more proper to use 2 or 3 slots blade in the quantum efficiency testing due to the area of the slot is bigger which is more capable to completely “chop” the non-coherent monochromatic light beam. If the monochromatic light beam is not “completely chopped” by the blade slot, the beam will not be modulated into a single frequency. The signal read by the lock-in amplifier will be unstable, which will cause the wrong EQE curve in the quantum efficiency measurement.

### 3.Photocurrent amplification and signal demodulation in EQE system:

When the monochromatic light beam gets incident into the solar cell or DUT, it will generate the photocurrent due to the Photoelectric Effect.

The incident light beam is modulated by the chopper with frequency f, therefore, the generated photocurrent will also be a modulated AC current signal. The AC current usually be connected to the preamplifier which can convert the current signal into voltage signal by the OP or JFET and amplified the intensity. The amplified signal is sent to the lock-in amplifier and de-modulated by it with the modulation frequency f.

It should be noticed that the generated photocurrent in the quantum efficiency measuring system is usually from few nA to few hundreds nA, which is in cable noise range. Therefore, the noises from the cable and electrical-magnetic induced by other instruments should be shielded and avoided. If the noise current cannot be effectively suppressed, the quantum efficiency curve will not be smooth. The repeatability and reproducibility of the EQE will not be high, which will cause the measuring uncertainty as described above.

It is common to use the frequency modulation by chopper and de-modulation by lock-in amplifier in the quantum efficiency measurement system. One of the benefits is the high signal/noise ratio when using the lock-in amplifier. The second benefit using modulation and lock-in technique is that one can apply the DC voltage bias or DC light bias on the solar cells or DUT. Below we will describe the main reasons for applying light bias and voltage bias.

### 4.Bias Light System:

What is the bias light system in the quantum efficiency measurement system? It is a continuous wavelength white lamp with optics which can generate stable DC light intensity with time.

There are two situations that you may need to apply the DC bias light to the solar cells or DUT.

The first purpose of the DC bias light system is used to fill out the traps inside the solar cells. In 1980’s, scientists found that the quantum efficiency curve is dependent with the bias light intensity. When increasing the bias light intensity, the quantum efficiency intensity and spectral shape are changed as well. At that time, the purification technology is not as good nowadays (99.9999%), therefore there are many traps and defects inside the Si wafer. Generally, the AC monochromatic light beam intensity in quantum efficiency measurement is less than uW, which is much smaller than one sun intensity (1000 W/m2). The solar cell is working under one sun intensity. To get the reasonable quantum efficiency, one should use the DC light bias illumination to “create” the one-sun condition for quantum efficiency measurement. The DC bias light photons will fill up the traps, which avoids the AC photocurrent generated by the monochromatic light beam.

However, the DC bias light is also a kind of “Noise” to AC photocurrent signals. Although the lock-in amplifier can “lock” the photocurrent signal with modulation frequency f and electrically filter out the DC signals. It still causes the lock-in amplifier “overload” and un-working, if the DC photocurrent, generated by the DC bias light, is too high.

What the DC bias light intensity level should I apply to the quantum efficiency measurement? If you are interested in the details, click the bottom to let us know then we will write the article about this topic.

The second purpose of the bias light is that when measuring the tandem or multijunction solar cells. It is required the “color” bias light illumination to “saturate” the sub cell/cells to get each sub cell’s quantum efficiency curve. The details of how-to measurement the quantum efficiency of solar cells is described in IEC 60904-8-1:2017.You may click the bottom to let us know then we will write the article about this topic.

The bias light is incident into the solar cells or DUT, it

### 7.Reference Photodiode：

What is a Reference photodetector in quantum efficiency measurement?

Usually, there are three kinds of detector which are acceptable in the calibration of the monochromatic light source in quantum efficiency testing.

1. Spectrally calibrated photodiode, photodiode irradiance detector, or solar cell, which are calibrated in power or irradiance mode.

It should be noted that a spectrally calibrated photodiode should have calibration data that includes the entire spectral response range of the device before performing the quantum efficiency testing. If a part of the range is lacked, it will limit the spectral measuring range.

## How to measure the EQE in solar cells?

The quantum efficiency of a photovoltaic device is defined as the output current per input irradiance or radiant power at a given wavelength. It is normally reported over the wavelength range to which the device responds, is determined by the following procedure:

1. A monochromatic, chopped beam of light is directed (closed to) at normal incidence onto the cell. Simultaneously, a continuous white light beam (bias light) is used to illuminate the DUT at certain irradiance levels between 0 ~ 1 sun intensity.
2. The magnitude of the AC chopped component of the current at the short-circuit condition (Vterminal=0) is monitored as the wavelength of the incident light is varied over the quantum efficiency range of the device.
3.  The total power or irradiance of the monochromatic beam incident on the device is determined by the reference photodetector. The absolute quantum efficiency of the device can then be computed using the measured device photocurrent and the power or irradiance of the monochromatic beam.

Figure 21. The setup of optical and electrical components for quantum efficiency measurement. The quantum efficiency measurement system is composed with white-light lamp system, chopper, auto-filter wheel, two lock-in amplifier one for signal and the other for monitor photodetector.

## The procedures of quantum efficiency measurement

1. Place and mount the reference photodiode in the testing plane which is aligned with the plane of the device under test.
2. Adjust or control the temperature to keep the temperature of reference photodiode at 25℃. The photodiode calibration temperature is usually carried at 25℃.
3. Use the reference photodetector to measure the light irradiance in the spectral range of the quantum efficiency to be measured. Taking the Si photodiode as an example, the light irradiance response has a wavelength range of 300nm ~ 1100nm. The wavelength step for spectral responsivity calibration is 10 nm. Therefore, in quantum efficiency test of solar cells, the wavelength step is mostly 10nm in the irradiation calibration.
4. When doing the irradiance intensity calibration at each wavelength by the reference photodetector, the partial light intensity is collected by the monitor photodiode. The monitor photodiode signal is also recorded by an independent lock-in amplifier, m1.
5. Place and mount the device to be tested in the test fixture. Set the temperature to 25 ℃or the temperature of interest, and connect it to the lock-in amplifier to recorded the modulated current signal.
6. If you turn on the DC bias light, record the bias current in the device to be tested. Make sure that the bias light current does not saturate the lock-in amplifier during the whole quantum efficiency measuring process.

## Why the calibration is important for quantum efficiency measurement?

The reference photodetector must have a known linear current versus incident light intensity ratio over the range of intensities and wavelengths of the monochromatic light source. The calibration of the reference photodetector must be traceable to SI units through NIST, PTB, or any ISO 17025 accredited laboratory which can deliver spectral responsivity scale or other radiometric scale.

## What is “Power mode” and what is “Irradiance mode” in EQE measurement?

The kinds of measurements that can be performed depend on the calibration mode of the reference photodetector and the relationship between the size of the reference photodetector, DUT, and monochromatic beam. “Smaller” means the entire beam reaches the photosensitive surface of the reference detector or DUT. “Larger” means the entire detector or device is illuminated. “Uniform” means the part of the beam that intercepts the reference detector or DUT is uniform. “Defined” means the beam power is known because the irradiance is uniform over the area of an aperture placed between the source and the DUT. Where “absolute” measurement capability is indicated, it is implied that “relative” measurements can also be performed.

A photodetector calibrated in power mode must have spatially uniform spectral responsivity over its photosensitive region. A photodetector calibrated in irradiance mode may have spatially non-uniform spectral responsivity characteristics and must only be used with a uniform monochromatic beam larger than its surface area.

## Quantum efficiency/spectral response/IPCE application in Copper Indium Gallium Senillide (CIGS) solar cells

Copper Indium Gallium Selenium CIGS (Copper Indium Gallium Selenium) is a quaternary compound semiconductor and is classified as a single-junction solar cell. Figure 22 shows its common device structure.

Figure 22. Typical CIGS solar cell device structure. [2]

Copper indium gallium selenide affects the size of its energy gap with the difference of indium gallium content, so that its absorption wavelength range can be from 1.02 ev to 1.68 ev. The quantum efficiency/spectral response/IPCE can test the energy gap of different solar cells. As shown in Figure 23, when the content of gallium in the copper indium gallium selenide increases, and the quantum efficiency/spectral response/IPCE spectrum results show that the energy gap increases. Therefore, it can be used as a detection of the gallium component in the process monitoring.

Figure 23. Under the same device structure, different gallium components changing the quantum efficiency spectra shows that as the composition of gallium increases, the energy gap of copper indium gallium selenide also increases, from 1 eV to 1.67 eV. [2]

The current research direction is to reduce costs and improve photoelectric conversion efficiency for this technology. As shown in Figure 24, the characteristics of each part of the device structure corresponding to the quantum efficiency/spectral response/IPCE spectrum of different bands are drawn. For example, the quantum efficiency of the Window layer (ZnO) can be observed at a wavelength of 300 nm ~ 400 nm, the quantum efficiency of the Buffer layer (CdS) can be observed at a wavelength of 400 nm ~ 540 nm, and the Absorber layer can be observed at a wavelength of 540 nm ~ 1200 nm (CIGS) quantum efficiency.

Figure 24. Quantum efficiency spectrum of the copper indium gallium selenium solar cell and the characteristics of each layer of the reaction cell in different wavelength ranges. [3]

The quantum efficiency spectrum in Figure 25 changes the film thickness of CdS without changing the process conditions of CIS. The results show that the 400-500 nm band changes with the thickness of CdS (15 nm ~ 80 nm) and the efficiency changes accordingly. In the wavelength band> 500 nm, it shows that there is no significant difference in the efficiency of CIS, which means that the process conditions are stable. From the final result, it can be clearly judged that the optimal film thickness condition of CdS is 15 nm. If the CIS process conditions are the same but the spectrum > 500 nm changes, it means that there are other factors that affect the experimental results of different CdS film thicknes. Then we can analyze the impact of the related processes to achieve the effect of obtaining the most effective information in a single process experiment. Through the spectra of quantum efficiency/spectral response/IPCE, the detailed effects of process changes can be observed, and a database can be established to find problems and improve conditions when the production line yield changes.

Figure 25. Adjusting the thickness of different CdS layers can find the difference in 400~500nm wavelength range from the quantum efficiency/spectral response/IPCE spectrum. [2]

Figure 26. The current and voltage curves of solar cells made by using different Buffer layer materials. [2]

Figure 27. Quantum Efficiency curves of CdS and ZnS(O,OH) Window layers. [2]

From the above description, we can realize that the quantum efficiency/spectral response/IPCE spectrum provides the information of copper indium gallium selenide solar cells (CIGS) as follows:

1. The photoelectric conversion efficiency of each layer such as Window/ Buffer/ Absorber.
2. The identification of the material energy gap by the concentration of gallium in the Absorber copper indium gallium selenide.
3. The degree of change in efficiency of each layer due to changes in process conditions.

In today’s fiercely competitive solar industry, continuously reducing costs and improving photoelectric conversion efficiency are necessary conditions for solar manufacturers to stand out! The key to the improvement of solar cell conversion efficiency lies in the improvement of manufacturing process and materials. Measuring the quantum efficiency/spectral response/IPCE of solar cells can understand the photoelectric conversion efficiency of solar cells under different light wavelengths. Users can quickly find process problems and improve them based on the results of the spectral response, which is more conducive to promote efficiency.

Reference

[2] A. Pudov “IMPACT OF SECONDARY BARRIERS ON CuIn1-xGaxSe2 SOLAR‐CELL OPERATION” Dissertation, Dep. Of Physics, Colorado State University, 2005

[3] Markus Gloeckler “DEVICE PHYSICS OF CuIn1-xGaxSe2 SOLAR‐CELL” Dissertation, Dep. Of Physics, Colorado State University, 2005

[4] A.V. Shah et al./Solar Energy Materials & Solar Cells 78 （2003） 469-491

[5] Oerlikon Solar – Constantine, 24 Sep 08