beams which interfere.The weak excitation beam is chopped and the resulting photocurrent is
measured using a lock-in ampli?er.The obtained signal is proportional toσg?σ(I1),whereσg represents the photoconductivity in the presence of the light interference pattern andσ(I1)is
the photoconductivity due to the illumination with only beam I1.Then the sample is illuminated
again,but this time the beam with the intensity I1is incoherent with the second beam.The
obtained signal is proportional toσg(I1+I2)?σ(I1).The ratio between these signals de?nes the parameterβ:
β=
σg?σ(I1)
σ(I1+I2)?σ(I1)
(5.11)
The parameterβdepends on the ambipolar diffusion length L amb and the grating period in the following way(as derived in reference[40]):
β=1?
2γγ20
[1+(2πL amb/ )2]2
(5.12)
In Equation(5.12),γis a power exponent in the relation of the photoconductivity with the generation rate(σph∝Gγ),andγ0is a factor that characterizes an interference contrast that can change due to,for example,partial coherence between the beams or light scattering (0<γ0≤1).The ambipolar diffusion length is a?tting parameter in the dependence ofβon the grating period and is obtained either from the slope of a plot ?2versus(1?β)?1//2, or from the intersection of the line with the ?2axis.The exponentγis determined from a
ADV ANCED AMORPHOUS SILICON SOLAR CELL TECHNOLOGIES187 plot of the photoconductivity as a function of the light intensity,which is varied using neutral density?lters.
5.3.6Determination of density of states
In the following,we present widely used methods to evaluate the density of states in thin amorphous and microcrystalline silicon layers.
5.3.
6.1Optoelectrical methods
A large group of methods is based on correlating the optical absorption in a-Si:H?lms or devices with the density of states distribution.The subbandgap absorption especially is of major interest since it re?ects transitions involving the localized states within the bandgap. However,the subbandgap absorption is weak and therefore indirect methods,which are based on measurement of some secondary effect,are used to determine the absorption coef?cient. In photothermal de?ection spectroscopy[42],the de?ection of a probe laser beam re?ects a change in the refractive index of a medium which is in contact with the a-Si:H?lm.The change of the refractive index depends on the amount of heat generated by the absorption of monochromatic light in the a-Si:H?lm and dissipated from the?lm into the medium.Other techniques,such as constant photocurrent method[43],dual beam photoconductivity[44], and the recently introduced Fourier transform photocurrent spectroscopy[45]are based on measurement of the spectral dependence of the photoconductivity.
5.3.
6.2Photothermal de?ection spectroscopy
Photothermal de?ection spectroscopy(PDS)is based on the conversion of a fraction of the absorbed photon energy in a?lm into thermal energy(heat),which dissipates and causes a change in the index of refraction of a medium adjacent to the surface of the?lm.By probing the medium’s refractive index change with a laser beam,one can relate the probe beam de?ection to the optical absorption of the?lm.A sample with a-Si:H?lm is immersed in an optically transparent and thermally conductive liquid.A chopped,monochromatic beam,which is called a pump beam,illuminates the sample.The de?ection signal is measured by a position sensitive detector,which is connected to a lock-in ampli?er.
The attractive feature of this technique is its high sensitivity:absorbance values ofαd≈10?5can be measured on thin?lms.For a-Si:H?lms with a typical thickness of1μm,an absorption coef?cient as low as10?1cm?1can be determined.The PDS technique is sensitive to surface states,and for this reason,PDS results can overestimate the bulk density of states.
5.3.
6.3Constant photocurrent method
The constant photocurrent method(CPM)is based on measurement of the photoconductivity as described in the previous section.In CPM measurement,the steady state photocurrent is measured as a function of photon energy in the subbandgap region.In this region,the absorption
188THIN FILM SOLAR CELLS
is weak,which means thatαd 1.The exponential function can be expanded to a power series and exp(?αd)≈1?αc8ab0301a6c30c2259019ebcing this approximation in Equation(5.9),the photoconductivity can be expressed as:
σph=qμτηg 0(1?R)α(5.13) Equation(5.4)describes the relation between the photocurrent I ph and the photoconductivity σc8ab0301a6c30c2259019ebcbining Equations(5.4)and(5.13),the photocurrent can be expressed as:
I ph∝ 0αηgμτ(5.14)
The basic idea of CPM measurement is to ensure that the termηgμτis kept constant during measurement.This is achieved by keeping the photocurrent constant while changing the photon ?ux density.The constant photocurrent means that the positions of the quasi-Fermi levels for holes and electrons in the bandgap,which determine the number of recombination centres,do not change during the experiment.During the whole measurement,the carrier lifetime is,in this way,kept constant.When we assume that the mobility of the carriers and the generation quantum ef?ciency are not spectrally dependent,then the absorption coef?cient is dependent only on the incident photon?ux:
αCPM(E)≈C CPM
0(E)(5.15)
where C CPM is an energy independent constant and 0(E)the number of photons necessary to keep the photocurrent constant.The relative absorption coef?cientαCPM is calibrated to the ab-solute absorption coef?cient,which is determined from re?ection–transmission measurement. This original CPM method was later adapted in order to measure the optical(photocurrent) absorption spectrum directly in absolute units without additional calibration and undisturbed by interference fringes[46].
5.3.
6.4Dual beam photoconductivity
The basic idea of dual beam photoconductivity(DBP)measurement is that in addition to a chopped probe beam of monochromatic light,a second light source is used to illuminate the sample.This additional‘bias’light keeps the splitting of the quasi-Fermi levels constant during the measurement.The ac fraction of the photocurrent is measured using a lock-in ampli?er and depends on both the monochromatic photon?ux and the absorption coef?cient of the a-Si:H ?lm[44].The absorption coef?cient can be extracted from the measured photocurrent and photon?ux density by:
αDBP(E)≈C DBP I ph(E)
0(E)(5.16)
where C DBP is an energy independent constant and 0(E)the photon?ux density.As in the case of the CPM,the relative absorption coef?cientαDBP has to be normalized to the absolute absorption coef?cient.The advantage of the DBP measurement in comparison to the CPM is a shorter measurement time since it is not necessary to adjust the photon?ux density of monochromatic light in order to keep the photocurrent constant.
ADV ANCED AMORPHOUS SILICON SOLAR CELL TECHNOLOGIES189 5.3.6.5Fourier transform photocurrent spectroscopy
Recently,the Fourier transform photocurrent spectroscopy method[45]has been introduced for determining the sub-bandgap absorption.A Fourier transform infrared(FTIR)spectrometer is used as the interferometer and an a-Si:H sample as the external detector.The spectrometer can be equipped with a globar and white light source in order to measure in0.4to1.8eV spectrum range.The sample,which can be a thin?lm deposited on a substrate or a complete solar cell, is connected to an electrical circuit with a low noise voltage source and a current preampli?er. The photocurrent of the sample is ampli?ed,and an A/D converter digitizes the output of the preampli?c8ab0301a6c30c2259019ebcing a computer,the signal is?nally translated from the time domain to the frequency domain by Fourier transformation.The FTIR signal from the sample is normalized to the FTIR signal from a spectrally independent detector.The advantage of this method is its sensitivity to low photon energies;the measurement of the subbandgap absorption is extended from～0.8eV,typical for the CPM and DBP measurement,to0.4eV.The measurement time is strongly reduced and is only a few minutes.
