5.3.5.1Dark conductivity
The dark conductivityσd of device quality intrinsic a-Si:H is less than1×10?10 ?1cm?1. To determine it and its activation energy,a very low current is measured,in the order of picoamperes.Such measurements are usually carried out on samples with two1to2cm long coplanar metal electrodes deposited less than1mm apart from each other on a single a-Si:H layer on highly resistive glass,such as Corning1737.Care has to be taken that moisture or
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diffusing impurities do not affect the measurement of current.Therefore,the measurement is usually taken in vacuum or in an inert atmosphere and before the measurement,the sample is annealed at150?C for half an hour to evaporate all moisture present on the surface of the ?lm.A voltage of typically100V is applied to a sample with an a-Si:H layer of about1μm thick in order to obtain a current of tens of picoamperes through the sample that can be reliably measured.
The dark conductivity is determined as:
σd=I
U w
ld
(5.4)
where U is the applied voltage,I is the measured current,l is the length of the electrodes (～1to2cm),w is the distance between the electrodes(0.5to1mm),and d is the thickness of the?lm.
5.3.5.2Activation energy of the dark conductivity
The measurement of the temperature dependence of the dark conductivity is used to evaluate the activation energy of the dark conductivity,E A,which gives a good approximation of the position of the Fermi level in a-Si:H?lms.The temperature dependence of the dark conductivity σd(T)is described as
σd(T)=σ0exp(?E A/kT)(5.5) whereσ0is a conductivity prefactor,T the absolute temperature and k Boltzmann’s constant. From the slope of the Arrhenius plot,which in this case is the relationship between log(σd(T)) and1/T,the activation energy is determined.In combination with the optical bandgap,the activation energy is a good measure to evaluate the presence of impurities in the?lm.The impurities often act as dopants,and even a small concentration of impurities,1×1017cm?3 of O or N,causes a shift of the Fermi level.For undoped a-Si:H,the activation energy should be higher than0.80eV.
The low dark conductivity of undoped a-Si:H is a result of the low mobility of charge carriers and the high mobility gap of a-Si:H.This is also re?ected by the high activation energy of the dark conductivity.The mobility of the charge carriers in the extended states of a-Si:H is about two orders of magnitude lower than in single crystal silicon.Typically,intrinsic a-Si:H is characterized by electron mobility values of10to20cm2V?1s?1,and the hole mobility is 1to5cm2V?1s?1.
5.3.5.3Photoconductivity
The photoconductivity can be determined by illuminating the same samples as used for the dark conductivity measurement with appropriate light.Often the AM1.5light spectrum with an incident power of100mW cm?2is used.With these conditions,the photoconductivity of device quality undoped a-Si:H,calculated from the photocurrent similarly to Equation(5.4),should be higher than1×10?5 ?1cm?1.The ratio of the photoconductivity and dark conductivity is called the photoresponse.This parameter gives an indication of the suitability of a material
ADV ANCED AMORPHOUS SILICON SOLAR CELL TECHNOLOGIES185 for use as a photoactive layer in a solar cell.A good photoresponse value for a-Si:H is higher than105.
Photoconduction is a complex process of generation,transport and recombination of excess photogenerated carriers.The optical generation rate of carriers G depends on the absorption coef?cient,α,and the quantum ef?ciency for carrier generationηg.The latter represents the number of electron–hole pairs generated by one absorbed photon.When we assume that the current in a-Si:H is dominated by electrons,transport and recombination are characterized by the extended state mobilityμof electrons and their lifetime,τ.Its photoconductivity can be written as:
σph=qμ n=qμτG(5.6) where q is the unit charge and n the concentration of photogenerated electrons.The average optical generation rate over the whole thickness,d,of the?lm is related to the absorbance,A, which can be calculated from the Lambert–Beer absorption formula:
A= 0(1?R)(1?exp(?αd)),(5.7)
where 0is the incident photon?ux density and R the re?ectance of the air–a-Si:H interface. Neglecting the spectral dependence of the re?ectance,the average generation rate can be approximated by:
G=ηg A
d
=ηg
0(1?R)(1?exp(?αd))
d
(5.8)
By combining Equations(5.6),(5.7)and(5.8),the photoconductivity can be expressed as:
σph=qμτηg 0(1?R)(1?exp(?αd))
d
(5.9)
The quantum ef?ciency mobility lifetime productηgμτis a useful and often used?gure of merit that combines the photoabsorption,transport and recombination in an a-Si:H?lm. This quantity is determined by measuring photocurrent when illuminating the sample with a monochromatic light of a relatively long wavelength.At such a wavelength,the absorption coef?cient is small,which results in almost uniform carrier generation in the a-Si:H?lm. Usually,600nm light is chosen as the probe c8ab0301a6c30c2259019ebcing Equation(5.9)combined with the geometry factors of the sample as in Equation(5.4),theηgμτproduct is obtained as:
(μτηg)600=
I ph w
qUl 0(1?R)(1?exp(?αd))
(5.10)
When we assume thatηg=1in amorphous silicon,it means that one absorbed photon generates one electron–hole pair and the mobility lifetime product at600nm for device quality a-Si:H isμτ≥1×10?7cm2V?1.
5.3.5.4Ambipolar diffusion length
Theμτproduct determined from the photoconductivity measurement characterizes the charge carriers that dominate the transport,i.e.the electrons in amorphous silicon.However,solar
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cell performance is often determined by the transport properties of minority carriers,which
are holes in a-Si:c8ab0301a6c30c2259019ebcmonly the steady state photocarrier grating(SSPG)technique is used
to determine the ambipolar diffusion length in amorphous silicon[40,41],from which the
mobility lifetime product of the holes is calculated.
When an excess of photogenerated carriers is not distributed uniformly throughout a semi-
conductor,diffusion of the excess carriers takes place.The excess carriers will diffuse in the
semiconductor until they recombine.In the absence of an electric?eld,the photogenerated
electrons and holes diffuse in the same direction.This process is called ambipolar transport.
The average distance that the excess carriers can diffuse due to ambipolar transport before
being annihilated is de?ned as the ambipolar diffusion length.The ambipolar diffusion length
is therefore a good?gure of merit for applying a semiconductor material as a photoactive layer
in a solar cell.In case of intrinsic amorphous silicon,ambipolar transport is determined by the
mobility of the less mobile charge carriers,holes.
The same samples as for the conductivity measurements can be used for the SSPG technique.
The principle of the SSPG technique is based on the creation of a steady state interference
pattern in the concentration of photogenerated carriers in the a-Si:H?lm.This concentration
pattern is made by illuminating the sample with two interfering beams generated from one
laser.The concentration fringes are parallel to the electrodes of the sample.The photocarriers
diffuse from highly populated regions to regions of lower concentration,which leads to a
reduction of the amplitude of the modulated carrier population.This reduction depends on the
period of the grating pattern and results in a change in the photoconductivity of the sample,
which is measured perpendicular to the grating fringes.
In the SSPG experiment,the laser beam is split into two beams,where the intensity of one
beam I1is larger than that of the second beam I2.First,the sample is illuminated with both
