2.3 External Quantum Efficiency (EQE)
[35]
As mentioned in section 1.2.4, quantum efficiency (QE) measurement is a charac-terization method for photovoltaic devices that gives information on it’s wavelength dependent performance. Such information is highly relevant when experimenting with solar cells under colored light, like is done in this thesis. To perform QE measurements, a monochromatic light beam of known irradiance is needed.
Section 2.3.1 discusses the definition and principles of QE, section 2.3.2 explains how monochromatic light can be produced by using a monochromator and section 2.3.3 contains information on how light beam irradiation can be determined by using a silicon detector.
2.3.1 Concept of quantum efficiency
The number of charge carriers separated by a solar cell is not only dependent on the irradiation intensity, but also on the wavelength of the incident light. This means that a solar cell generates a different amount of electrons per photon depending on the photons wavelength which corresponds to the photons energy according toE = hcλ. To quantify this behavior, a cell’s quantum efficiency is defined as the ratio of the number of charge carriers produced by the solar cell to the number of photons of a given energy incident on the solar cell [35] which leads to the following formula:
QE(λ) :=
electrons sec photons
sec (λ) (2.22)
There are two different quantum efficiency:
internal QE (IQE) is the ratio between separated electrons and photons absorbed by the cell.
external QE (EQE) is the ratio between separated electrons and photons that hit the solar cell
This means that the EQE also includes optical losses such as transmission and re-flection whereas the IQE only considers internal losses like recombination.
An ideal solar cell would transform every incoming photon into one electron and therefore would have a rectangular shape in a QE-λ-diagram like 2.4.
2.3 External Quantum Efficiency (EQE)
Figure 2.4: The quantum efficiency of a solar cell. The green arrow indicates the dif-ference from ideal and real QE. Taken from [35]
The QE is highly material dependent. The main difference is the band gap cut-off as can be seen in figure 2.5. c-Si cells have a very broad response due to a band gap of around 1.1 eV corresponding to light of 1100 nm. GaAs has a band gap of around 1.42 eV. While mc-Si has the lowest QE, a-Si and DSSC (Dye sensitized solar cells) have quite similar QE-curves. An example of a CIGS cells QE can be seen in figure 3.12.
Figure 2.5: Comparison of typical QE-curves of solar cells of different materials.
The ISC can be derived from the EQE data as follows:
2.3 External Quantum Efficiency (EQE) where E(λ) is the spectral irradiance distribution, S is the spectral response corre-sponding to QE according to SR= qλhcQE(λ).
2.3.2 Monochromator
“A monochromator is an optical device that transmits a mechanically se-lectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input.” [36]
A monochromator can either be realized by using the optical phenomenon of op-tical dispersion in a prism, or by using a diffraction grating, making use of opop-tical interference. A diffraction grating can be either transmissive or reflective, however, in monochromators the reflective type is more common, due to space issues. A grating is made of several slits, ideally with the same width and the same spacing d. Due to additive and destructive interference of the light after interaction with the grating, the light of every wavelength is diffracted to different, wavelength dependent directions (having several maxima and minima). The wavelength maxima can be calculated by
θm = arcsin mλ
d −sinθi
. (2.24)
In this equation θi is the angle between the diffracted ray and the grating’s normal vector, λ is the wavelength of the exiting light, m is the number of the maximum of the wavelengthλ and θm the angle at which themth maximum of the wavelength λ is found. θi is the arbitrary angle of the incident light beam from the grating’s normal vector.
In order to get the wavelength dependent beams focused on a measuring spot, a Czerny-Turner monochromator can be used. It focuses the incident light beam (A) onto the diffraction grating (D) with a curved mirror (C), from where the light is diffracted onto another mirror(D), that focuses the beam on the exit slit (F). The diffraction grating can be turned as indicated to focus beams of different wavelength on the exit slit (see figure 2.6).
2.3 External Quantum Efficiency (EQE)
Figure 2.6: Scheme of a Czerny-Turner Monochromator. See text for closer description.
Picture taken from [37]
2.3.3 Calibration by a semiconductor detector
In order to calculate the EQE by equation (2.22) the number of incident photons has to be known. Instead of calculating it from the emittance spectrum of the lamp and the transmittance of the monochromator it is easier and also more precise to detect the number of incident photons at the measuring position by placing a photon detector there. By running through all wavelengths with the monochromator and detecting the number of photons with a photon detector. For this purpose a semiconductor detector can be used.
The semiconductor detector consists of a semiconductive bulk placed between two electrodes. Incident radiation creates electron hole pairs in the semiconductor, as it does in solar cells. By an external electric field, these charge carriers are drawn from the semiconductor to the electrodes where they are collected and then measured by an Ammeter or Voltmeter.
The number of charge carrier pairs does not depend on the energy of the incident photons, except when they have lower energies than the band gap of the semiconductive detection material, leading to no detection. Above the band gap energy, every incident photon creates only one electron (the surplus energy is absorbed by the material by thermal relaxation). This means that the intensity of the incident radiation can be determined from the number of charge carriers.
For EQE, the wavelength dependent irradiance of the setup measured by the semi-conductor detector is saved and later combined with the measurement of charge carriers collected by the sample cell to calculate the EQE.