Efficiency of solar water splitting using semiconductor electrodes

International Journal of Hydrogen Energy 31 (2006) 1999 – 2017 www.elsevier.com/locate/ijhydene

Efficiency of solar water splitting using semiconductor electrodes A.B. Murphya, c , P.R.F. Barnesa, c , L.K. Randeniyaa, c , I.C. Plumba, c,∗ , I.E. Greyb, c , M.D. Horneb, c , J.A. Glasscocka, c a CSIRO Industrial Physics, P.O. Box 218, Lindfield NSW 2070, Australia b CSIRO Minerals, Box 312, Clayton South VIC 3169, Australia c CSIRO Energy Transformed Flagship, Australia

Available online 13 March 2006

Abstract Reliable measurement of the photoconversion efficiency for semiconductor electrodes is essential to the assessment of electrode performance. In this paper, the influence of the choice of light source on measured photoconversion efficiencies for semiconductor photoelectrodes is examined. Measurements of efficiency performed under xenon lamp and solar illumination are compared with efficiencies calculated by integrating the incident photon conversion efficiency (IPCE) over the lamp and solar spectra. It is shown that use of a xenon lamp as the light source can lead to a large overestimate of the photoconversion efficiency, relative to that obtained under standard AM1.5 solar illumination. The overestimate is greater when a water filter is fitted to the xenon lamp, and when a wide-band gap semiconductor such as TiO2 is used as the photoelectrode. Achievable photoconversion efficiencies using rutile TiO2 are calculated taking into account the losses due to imperfefct absorption, reflection and charge-carrier recombination; these calculated efficiencies agree with the measurements to within experimental uncertainties. It is demonstrated that many photoconversion efficiencies presented in the literature are overestimated. It is concluded that reliable estimation of efficiency under standard conditions is best obtained by measuring the IPCE as a function of wavelength, and integrating over the AM1.5 solar spectrum, or by measuring under sunlight with a similar zenith angle to that of the AM1.5 spectrum. 䉷 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Hydrogen generation; Solar energy; Photoelectrochemistry; Photoelectrolysis; Photocatalysis; Spectral irradiance; Xenon lamp; Solar spectrum; Semiconducting materials; Titanium dioxide

1. Introduction Photoelectrochemical splitting of water to produce gaseous hydrogen using solar energy has been researched intensively since its initial demonstration in 1972 [1]. The most important figure of merit for a semiconductor photoelectrode is the photoconversion efficiency for water splitting, which is defined as the ∗ Corresponding author. CSIRO Industrial Physics, P.O. Box 218, Lindfield NSW 2070, Australia. Tel.: +61 2 9413 7351; fax: +61 2 9413 7631. E-mail address: [email protected] (I.C. Plumb).

ratio of the chemical potential energy stored in the form of hydrogen molecules to the incident radiative energy. The benchmark efficiency is 10%, which is generally considered to be required for commercial implementation [2]. Most measurements of the photoconversion efficiency are performed under illumination by artificial light sources. This is convenient for many reasons—the artificial sources are stationary, and their intensity is essentially constant with time, while the spectrum and intensity of solar radiation reaching the ground depends on the time of day, atmospheric conditions such as cloud cover, water vapour content and ozone column,

0360-3199/$30.00 䉷 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2006.01.014

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albedo of the surrounding ground, etc. However, the comparison of photoconversion efficiencies obtained for different semiconductor materials requires that these efficiencies are presented for a standard solar spectrum, usually the AM1.5 global solar spectrum, and artificial light sources do not accurately replicate such spectra. An examination of the literature reveals that in most cases the photoconversion efficiency values presented are obtained using illumination by a particular artificial light source. For example, Nozik [3] used a UV source with radiation between 300 and 400 nm to measure photoconversion efficiencies of up to 4% for TiO2 photoelectrodes. Giordano et al. [4] obtained an efficiency of 2.7% for a TiO2 electrode doped with platinum using a mercury lamp. Khan and Akikusa [5] quoted an efficiency for flame oxidised titanium of 2.0%; the publication indicates a xenon lamp was used, but Akikusa’s PhD thesis [6] reveals that a mercury–xenon lamp was used. Akikusa and Khan [7] reported an efficiency of 1.6% for a similar photoelectrode under xenon lamp illumination. Khan et al. [8] claimed an efficiency of 8.35% for a flame-pyrolysed titanium photoelectrode with a band-gap extended to 535 nm by carbon doping; again xenon lamp illumination was used. Mishra et al. [9] obtained photoconversion efficiencies as high as 3% for TiO2 photolectrodes using a mercury–xenon lamp source. Tang et al. [10] reported an efficiency of 2.5% for a mesoporous anatase photoelectrode using a xenon lamp. Radecka et al. [11] obtained an efficiency of 1.9% using a xenon lamp for a mixed anatase and rutile thin film deposited by radio-frequency sputtering. As will be shown later, all of these efficiency figures are close to or higher than those that are thermodynamically possible for the standard AM1.5 global solar spectrum, given the band gap of the semiconductor material used and the bias voltage applied. It therefore seems likely that the efficiencies are larger than those that would be obtained for sunlight. In this study, we investigate the influence of the light spectrum on the photoconversion efficiency for cells with semiconductor photoelectrodes. We consider in particular the most widely used source, the xenon arc lamp. We have had the spectrum of our lamp characterised by an accredited standards laboratory. We examine the influence on efficiency of the spectrum of the lamp, both with and without a water filter fitted. Water filters are widely used to absorb the infrared output of the lamp, thereby decreasing the heating of the irradiated surfaces. We also investigate the influence of the age of the lamp tube on the spectrum. The photoconversion efficiency depends on many factors in addition to the spectrum of the incident

radiation. These include the band gap of the semiconductor, reflection of radiation before reaching the semiconductor, the level of absorption of the radiation in the semiconductor, and the transport of charge carriers through the semiconductor. We examine the influence of each of these factors on the achievable efficiency, both for solar illumination and xenon lamp illumination. We have measured the photoconversion efficiency for a cell with a rutile TiO2 photoelectrode under both xenon lamp and solar illumination. We have also measured the incident photon conversion efficiency (IPCE), which is the efficiency of conversion of photons incident on the photoelectrochemical cell to photocurrent flowing between the working and counter electrodes, as a function of wavelength of the incident radiation. This allows the photoconversion efficiency to be calculated for any radiation spectrum. The efficiencies obtained from the measurements are compared with those calculated taking into account the spectrum of the radiation, the band-gap, the absorption and reflection of the radiation, and transport of the charge carriers. The measurements reported here were obtained at room temperature (T = 295 K). The effect of increased temperatures on water splitting efficiencies has been investigated by Licht [12,13]. In Section 2, we present the details of our measurements, including the characterisation of the light sources, and the results of these measurements. Our calculations of the efficiency limits for the different light sources are given in Section 3. The measurements are compared with the calculations in Section 4; in addition, the results of other workers are discussed in the light of our results, and possible means of increasing the photoconversion efficiency of semiconductor electrodes are considered. Conclusions are presented in Section 5.

2. Experimental details and results 2.1. Sample preparation The specimen used in this study was prepared by oxidising a titanium substrate in a methane and oxygen flame. Before oxidation, the titanium sheet (Sigma Aldrich, 99.7%, 0.25 mm thick) was polished and then etched in Kroll’s solution (one part 40% HF, one part 70% HNO3 and three parts water) for 5 s. A small (6 mm × 6 mm) piece of the sheet was held in a methane–oxygen flame for five minutes, at a position at which the flame temperature was measured to be 850 ◦ C using a K-type thermocouple. The oxygen to methane volume ratio of the gas mixture was 1.15, so

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Specular reflectance

Diffuse reflectance

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700

800

Measurement Best fit, h = 280 nm

0.04 0.03 0.02 0.01 0.00 300

400

Wavelength (nm) Fig. 1. Diffuse and specular reflectance of the rutile TiO2 film formed by flame-oxidising a titanium substrate. The reflectance is measured relative to a matt Teflon standard. The best fit to the specular reflectance (assuming 15% by volume of the TiO2 film is air) is also shown. The specular reflectance fit is performed only for wavelengths greater than 400 nm, since the strong absorption at shorter wavelengths precludes the formation of an interference pattern.

the flame was lean with respect to stoichiometry. An oxide layer was formed on both sides of the titanium substrate. The side of the substrate exposed directly to the flame is analysed here. The colour of the oxide layer was mid-grey, with some red and green colours indicating the formation of an interference pattern. The preparation and characterisation of a range of similar samples have been described in more detail elsewhere [14]. 2.2. Sample characterisation X-ray diffraction analysis of the sample was performed using a Philips diffractometer with a Cu K
source. The measurements indicated that the oxide layer had a rutile structure. The diffuse and total reflectance of the sample were measured as functions of wavelength from 250 to 800 nm using the diffuse reflectance attachment of a Cary 5 spectrophotometer. The reflectances were measured relative to a Teflon standard. The specular reflectance was obtained by subtracting the diffuse reflectance from the total reflectance. The diffuse and specular reflectances are shown in Fig. 1. The diffuse reflectance curve shows a strong decrease in the reflectance at wavelengths below 400 nm, indicating an absorption edge at around 3.1 eV, close to the band gap of rutile.

The thickness of the oxide layer was derived from the interference pattern evident in the specular reflectance spectrum. This was done using a least squares fit of the specular reflectance from 400 to 800 nm to the expression [15] for the reflection coefficient of an absorbing film of a given thickness on an absorbing substrate. The real part of the refractive index of rutile was taken from Cardona and Harbeke [16] and DeVore [17], as reported by Ribarsky [18] and the imaginary part from the work of Eagles [19]. Scanning electron microscope images indicated that the sample had a porosity of 15 ± 10%. The refractive index was accordingly reduced to allow for 15 ± 10% by volume of air, using the formula given by Mergel [20], based on the Bruggeman approximation. The best fit was obtained for TiO2 film thickness h = 280 ± 40 nm, with the uncertainty allowing for the estimated range of air volumes. The best fit curve for 15% air by volume is shown in Fig. 1. The feature of the fitted curve that determines h is the separation of the peaks of the interference pattern. The amplitude of the fitted curve is normalised to have the same standard deviation from the mean specular reflectance as the measured curve. 2.3. Light sources The spectrum of a light source is usually described by the spectral irradiance E
(
) (units W m−2 nm−1 ),

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defined by E
= dES /d
, where
∞ E
(
) d
ES =

(1)

0

is the incident irradiance. The incident spectral photon flux I
(units m−2 nm−1 s−1 ) is related to the spectral irradiance by I
(
) =

E
(
)
, hc

(2)

where h is Planck’s constant and c is the speed of light in a vacuum. The spectral photon flux is the more relevant quantity in water splitting applications, since at most one electron–hole pair is produced per absorbed photon, and photon energy above the required energy to split a water molecule is lost. 2.3.1. AM1.5 global solar spectrum The standard reference solar spectra for calculating the conversion efficiency of solar energy to electrical or chemical energy are the AM1.5 spectra, defined by the American Society for Testing and Materials [21]. The AM, or air mass, factor characterises the effect of the Earth’s atmosphere on the solar radiation, and is given by AM=1/ cos , where  is the solar zenith angle (the angle between the overhead and actual position of the sun). Two AM1.5 spectra are defined. They describe respectively the direct, and the total, or global, spectral irradiance at air mass 1.5 under standard atmospheric and surface conditions. AM1.5 corresponds to a solar zenith angle of 48.2◦ , at which angle the sun’s radiation has to pass through 1.5 times the thickness of atmosphere relative to a solar zenith angle of 0◦ . The receiving surface is inclined at 37◦ , so the incidence angle is 11.2◦ . The global AM1.5 spectrum includes radiation incident from all angles, and therefore includes scattered light. The direct AM1.5 spectrum includes only the component of the global spectrum that is directly incident from the sun. The global spectrum is the relevant quantity for solar water splitting experiments, since both direct and scattered light will be incident on a water-splitting reactor. 2.3.2. Solar spectrum for efficiency measurement The spectrum of sunlight at the time and location of photoconversion efficiency measurement was calculated using the SMARTS code, version 2.9.2 [22,23]. (This is the same code that has been used to derive the standard AM1.5 spectra.) The measurement was made in Sydney, Australia (latitude 33.87◦ S, longitude 151.22◦ E) at midday on 28 May 2004. There was no cloud cover.

The zenith and azimuthal angles of the sun were, respectively, 55.4◦ and 357.8◦ . The surface of the detector was tilted to face the sun. The calculation uses these parameters. Values corresponding to the AM1.5 standard spectrum were used for all other parameters (e.g., atmospheric composition and surface albedo). The calculated solar spectrum is similar to the AM1.5 global solar spectrum. The spectral irradiance of the calculated spectrum is slightly lower at ultraviolet and visible wavelengths, and similar at infrared wavelengths. The total irradiance of the calculated spectrum was 962 W m−2 , consisting of 835 W m−2 direct and 127 W m−2 diffuse irradiance. The respective figures for the AM1.5 global spectrum are 1000 W m−2 , consisting of 900 W m−2 direct and 100 W m−2 diffuse irradiance. 2.3.3. Xenon arc lamp We used an Oriel 6271 ozone-free xenon lamp, with an Oriel 61945 water filter fitted. The water filter was filled with deionised water, and removed infrared radiation above about 1000 nm and ultraviolet radiation below about 250 nm. An Oriel digital exposure control was used to maintain the total radiant power of the lamp constant. The spectral irradiance of the xenon lamp was measured by the Australian National Measurement Institute [24]. Measurements were performed using a photomultiplier detector for wavelengths from 240 to 400 nm, a silicon detector from 300 to 1010 nm, an indium gallium arsenide detector from 900 to 1680 nm, and a lead sulphide detector from 1300 to 2500 nm. The use of overlapping regions ensured that the measurements made using the different detectors were comparable. The measurement intervals used were 2 nm for wavelengths below 400 nm, 5 nm for wavelengths between 400 and 1200 and 10 nm for longer wavelengths. Spectra were measured both with and without the water filter fitted to the xenon lamp. While the water filter was used in our efficiency measurements, calculations for both spectra are presented in order to broaden the relevance of our results. The spectrum of the lamp without the water filter extends to wavelengths longer than 2.5 m, which is the limit for which the measurements could be performed. However, by measuring the total radiant power flux with a thermopile, and comparing this to the power obtained by integrating the lamp spectrum to 2.5 m, it was determined that less than 5% of the power was at wavelengths longer than 2.5 m. Fig. 2 shows the spectral photon flux of the xenon lamp with and without the water filter. Both spectra have

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Xenon lamp, without water filter Xenon lamp, with water filter AM1.5 global sunlight

35

Spectral photon flux (1018 m-2 s-1 nm-1)

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6 5

25

4 20 3 2

15

1 10 0 200

300

400

500

600

700

5

0 200

400

600

800 1000 1200 1400 1600 1800 2000 2200 2400

Wavelength (nm) Fig. 2. Spectral photon flux for the xenon lamp, with and without the water filter, compared to the AM1.5 global solar spectrum. The lamp had logged 1250 h of operation when the spectrum was recorded. The inset shows detail of short wavelengths. In all cases, the total irradiance is normalised to 1000 W m−2 . Measurements were performed by the National Measurement Institute.

been normalised to a total irradiance of 1000 W m−2 , to facilitate comparison with the AM1.5 global solar spectrum. The lamp spectra are almost identical for wavelengths up to around 900 nm, apart from the influence of the normalisation factor. The water filter absorbs a significant fraction of the light at wavelengths between 900 and 1100 nm, and all of the radiation at longer wavelengths. In total, the filter absorbs about 50% of the lamp irradiance; hence when the spectra were normalised to the same total irradiance, the spectral irradiance of the lamp without the filter is approximately 50% lower for wavelengths less than 900 nm. Fig. 2 indicates that at short wavelengths, the spectral photon flux of the xenon arc lamp is greater than that of AM1.5 global sunlight. The lamp emits a significant photon flux for wavelengths from 250 nm, whereas the solar photon flux is minimal at wavelengths below 300 nm. The enhanced photon flux at short wavelengths is greater for the lamp with the water filter, as a consequence of the normalisation. The xenon lamp spectrum is similar to that presented by the manufacturer [25]. However, arc lamp spectra vary from lamp to lamp, depending on the age of the tube and other variables. The tube used here had logged 1250 h of operation before calibration. To investigate the extent of the variability of the lamp spectrum, we also measured the spectrum of the lamp near the end of the tube life (1337 h), and near the start of the life

of a replacement tube. These measurements were performed by measuring the lamp irradiance with a thermopile, after passing the light through a monochromator with 12 nm pass band. The thermopile is described in Section 2.4. The measurements were performed with the water filter fitted to the lamp, and the total irradiance was normalised to 1000 W m−2 in each case. To check the method of measurement, the spectrum was also measured for the tube with 1250 h of operation; the results are almost identical to those shown in Fig. 2 apart from the poorer wavelength resolution. The spectral photon flux for the three cases is shown in Fig. 3. The new tube has a greater proportion of the photon flux in the ultraviolet. Towards the end of tube life, the proportion of the photon flux in the ultraviolet decreases rapidly. Unless otherwise noted, the results presented in the remainder of the paper pertain to the spectra measured for the tube with 1250 h of operation. Other lamps, such as non-ozone-free xenon arc lamps, mercury–xenon arc lamps, and mercury lamps, are also used for measurement of photoconversion efficiencies. Such lamps emit more strongly in the UV range than ozone-free xenon lamps [25]. 2.4. Measurement of efficiency Two light sources were used for the water-splitting efficiency measurements, the xenon lamp with water filter, and sunlight (at midday on 28 May 2004 in

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Spectral photon flux (1018 m-2 s-1 nm-1)

10 9

Tube 2, 5.7 h of operation Tube 1, 1250 h of operation Tube 1, 1337 h of operation

8 7 6 5 4 3 2 1 0 200

300

400

500

600

700

800

Wavelength (nm) Fig. 3. Spectral photon flux for the xenon lamp with the water filter, for two different tubes and for three different tube ages. In all cases, the total irradiance is normalised to 1000 W m−2 . Measurements were performed using a monochromator with a 12 nm bandpass.

potentiostat

A -V W-R

R

W

C

VW-C N2(g)

quartz window

hv

working SCE reference porous glass frit

Pt counter

Fig. 4. Schematic of the photoelectrochemical cell used for xenon lamp measurements. A simplified equivalent circuit of the potentiostat is included. VW.C and VW.R denote voltmeters measuring the voltages between the working and counter-electrodes, and the working and reference electrodes, respectively. A denotes an ammeter measuring the photocurrent.

Sydney, Australia). Details of these sources were given in Section 2.3. The xenon lamp measurements were performed using a standard three-electrode photoelectrochemical cell, shown in Fig. 4. The three electrodes were the working electrode (the oxidised titanium sample), a platinum wire counter electrode, and a saturated calomel

reference electrode. A Utah Electronics Model 0152 potentiostat was used to control the voltages. The electrodes were immersed in 5M KOH electrolyte. A glass frit separated the counter electrode from the working and reference electrodes. Gaseous oxygen was purged from the counter electrode compartment using a continuous flow of bubbled nitrogen gas. The presence of the glass frit did not make a significant difference to the photocurrent. However, allowing oxygen to dissolve in the electrolyte surrounding the counter electrode led to an increased photocurrent at a given cell bias voltage (VW.C in Fig. 4), by up to a factor of two at low bias voltages. This is attributed to the reduction of oxygen molecules rather than the generation of hydrogen molecules at the counter electrode. Measurements performed in an oxygen-rich electrolyte can thus lead to erroneously large efficiency values. The cell was constructed of glass, with a quartz window to allow the incident radiation to enter with minimal attenuation. The working electrode was placed 10 mm from the window. Swapping the positions of the working and reference electrodes had a negligible effect on the photocurrent, showing that attenuation by the electrolyte and the resistance of the electrolyte were both insignificant. The sunlight measurements were also performed using a three-electrode cell. In this case, the electrodes were immersed in 5M KOH electrolyte in a shallow tray. Sunlight was directly incident on the electrolyte,

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and the working electrode was oriented so that it faced the sun. The counter and reference electrodes were the same as for the xenon lamp measurements, and a flow of nitrogen gas was again used to purge oxygen from the counter electrode. The irradiance was measured using an Oriel 71751 sapphire window thermopile. The thermopile was calibrated against a standard thermopile by the Australian National Measurement Institute, using a standard lamp with filament temperature of approximately 2700 K as the light source. The uncertainty in the calibration is ±2%; spatial variations in the incident light intensity increased the uncertainty in irradiance measurement to 10%. The cell efficiency  for the water splitting reaction was determined using

irradiance was measured to be 880 ± 90 W m−2 . This agrees, within the uncertainty of measurement, with the 960 W m−2 calculated in Section 2.3.2. Fig. 5 shows the measured photoconversion efficiencies for different bias voltages. The maximum efficiency was found to be 0.54% at a bias voltage of 0.6 V for xenon lamp illumination, and 0.28% at the same bias voltage for solar illumination. The experimental uncertainty for the measured photoconversion efficiencies is estimated to be ±20%. The random repeatability error, which is a consequence of variation in factors such as electrolyte purity, working electrode alignment, and time for the photocurrent to reach equilibrium, was approximately 15%. The largest measurement error was the 10% uncertainty in the irradiance measurements by the thermopile.

 = jP (VWS − VB )/ES ,

2.5. Measurement of IPCE

(3)

where jP is the photocurrent produced per unit irradiated area, VWS = 1.229 V is the potential corresponding to the Gibbs free energy change per photon required to split water, and VB is the bias voltage applied between the working and counter electrodes (VW.C in Fig. 4). The irradiance ES was measured at a position outside the cell. The quartz window used in the xenon lamp measurements reflects 4% of this irradiance. No correction is made for this loss, since a window is likely to be required in a working water-splitting reactor. In the solar measurements, no window is used; however, the water is at an angle to the direct solar radiation equal to the solar zenith angle of 55◦ . We calculate that 7% of the direct solar radiation will be reflected by the water. To ensure comparability with the lamp measurements, the measured solar irradiance was reduced by 3%. Some workers [5,7,8,11] have used the voltage between the working and reference electrodes VW.R (relative to the open-circuit value of this voltage) in place of the bias voltage VB . This is often the only voltage that is reported. However, the bias voltage is applied across the working and counter electrodes, and the photocurrent flows between these electrodes, so the electrical power loss that has to be subtracted in calculating the efficiency of the cell is the product of the photocurrent and the voltage applied across the working and counter electrodes. Typically VW.R < VB , so using VW.R instead of VB leads to an overestimate of the cell efficiency. The photocurrent was measured for a range of applied bias voltages, and the photoconversion efficiency calculated using Eq. (3). The irradiance for the xenon lamp illumination was 820 ± 80 W m−2 . The solar

The IPCE provides a measure of the efficiency of conversion of photons incident on the photoelectrochemical cell to photocurrent flowing between the working and counter electrodes. An IPCE of 100% corresponds to the generation of one photoelectron for each incident photon. Losses associated with the reflection of incident photons, their imperfect absorption by the semiconductor, and recombination of charge carriers within the semiconductor before they reach the electrolyte, all contribute to the IPCE values falling below 100%. The IPCE was measured by interposing a monochromator between the xenon lamp and the photoelectrochemical cell. Similar results were obtained both with and without the use of a water filter. The bandpass of the monochromator was 12 nm (FWHM), which is sufficiently narrow to have insignificant effect on the measured IPCE values. The irradiance within the pass band was measured using the thermopile, averaging the measurement over a 20 s period. The IPCE was then calculated as a function of wavelength using IPCE(
) = jP (
)/[eI (
)],

(4)

where I (
) is the incident photon flux passed by the monochromator when set to wavelength
, and e is the electronic charge. The uncertainty of measurement was calculated by combining the standard error on the time average of the irradiance with the errors noted for efficiency measurements in Section 2.4. Fig. 6 shows IPCE(
) for the TiO2 photoelectrode at an applied bias voltage of 0.60 V, at which the maximum photoconversion efficiency is obtained. The IPCE reaches a maximum of just under 60% for a wavelength of 320 nm. The decrease at shorter wavelengths

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Xenon lamp with water filter Sunlight, 28 May 2004, midday

Photoconversion efficiency (%)

0.6

0.5

0.4

0.3

0.2

0.1

0.0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

Bias voltage (V) Fig. 5. Photoconversion efficiency for the cell with TiO2 electrode as a function of bias voltage VB . Results are given for illumination by the xenon lamp with water filter, and the sun.

70

60

IPCE (%)

50

40

30

20

10

0 300

320

340

360

380

400

420

440

Wavelength (nm) Fig. 6. Measured incident photon conversion efficiency, expressed as a percentage, as a function of wavelength for the TiO2 photoelectrode.

is associated with an increase in reflection from the photoelectrode (see Section 3.3). At longer wavelengths, weaker absorption of photons and the recombination of charge carriers lead to a decreased IPCE. These factors are considered in detail in Section 3.4. Using the IPCE measurements, it is possible to calculate the photocurrent expected to be generated for illumination by light with any spectral dependency,

assuming that the photocurrent is not dependent on the irradiance. The photoconversion efficiency can then be determined using
∞  = e(VWS − VB ) IPCE(
)I
(
) d
/ES . (5) 0

The cell photoconversion efficiency for rutile TiO2 calculated for different spectra is given in Table 1.

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Table 1 Photoconversion efficiencies for cells with rutile TiO2 photoanodes for different incident light sources Spectrum

Photoconversion efficiency From IPCE (Eq. (5)) (%)

AM1.5 global sunlight Sunlight, midday, 28 May 2004, Sydney Xenon lamp without water filter (1250 h) Xenon lamp with water filter (1250 h) Xenon lamp with water filter (5.7 h) Xenon lamp with water filter (1337 h)

0.25 ± 0.05 0.21 ± 0.04 0.32 ± 0.07 0.51 ± 0.10 0.66 ± 0.15 0.30 ± 0.06

Directly measured (Eq. (3)) (%) 0.28 ± 0.06 0.54 ± 0.11 0.66 ± 0.12

Comparison of directly measured values with efficiencies calculated from the measured IPCEs integrated over the different source spectra.

The values given in Table 1 for sunlight and the xenon lamp with the water filter can be compared to the photoconversion efficiencies measured directly with those sources. These efficiencies, given in Section 2.4, are repeated in Table 1 and are equal to the values derived from the IPCE measurements within the experimental uncertainty. The age of the xenon lamp tube, and the presence of the water filter, can strongly influence the measured cell photoconversion efficiency for rutile TiO2 . In particular, the efficiency determined using the lamp tube near the end of its lifetime (1337 h of operation) is much less than determined using a new tube or a tube that has been operated for 1250 h. The presence of a water filter increases the measured efficiency by around 50%.

3. Calculated photoconversion efficiency There are fundamental thermodynamic limits to the photoconversion efficiency, which depend on the band-gap of the semiconductor being used, and on the spectrum of the incident radiation. In practice, these limiting efficiencies cannot be achieved, due to losses such as the incomplete absorption of the incident radiation in the semiconductor, reflection of the incident radiation from the surface of the semiconductor and other surfaces, and recombination of conduction band electrons before reaching the electrolyte. In this section we consider first the thermodynamic limits to efficiencies, and then the relevant loss factors. 3.1. Thermodynamic limits to efficiency We consider here an idealised semiconductor, in which all photons of energy greater than the bandgap energy Ug are absorbed. The resulting conduction band electrons are transferred to the electrolyte, and a

hydrogen molecule is produced for each pair of such electrons. The absorbed photon flux is then

g I
(
) d
(6) JS = 0

where
g =hc/Ug is the band-gap wavelength. An upper bound to the photoconversion efficiency is given by ⎧ 0 ⎨ JS G (1 − loss ) if Ug
G0 + Uloss , C = (7) ES ⎩ 0 if Ug < G0 + Uloss , where G0 =eV WS =1.229 eV is the Gibbs free energy change per electron for the water-splitting reaction. The factor loss represents the radiative quantum yield; i.e., the ratio of re-radiated photons to absorbed photons. Hence 1−loss gives the proportion of absorbed photons converted into conduction band electrons. The reradiation of photons is due to blackbody radiation from the excited state. Bolton et al. [26] have calculated that the value of loss that corresponds to a maximum value of the efficiency is given by loss

P

≈ 1/ ln(JS /JBB ),

(8)

where JBB is the blackbody photon flux at wavelengths below the band-gap wavelength. loss P is small, less than 0.02 for the range of band-gap wavelengths of interest, and is practically independent of the spectrum of the incident radiation. The term Uloss is the energy lost per photon. This is a significant loss term, and provides a lower limit to the band-gap energy of a semiconductor that can be used for water splitting. There are two major contributions to Uloss . The first is thermodynamic, and can be shown [26] to be equal to T Smix , where T is the temperature and Smix is the increase in entropy of mixing associated with production of conduction band electrons by photon absorption. This contribution is at least 0.4 eV.

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Maximum efficiency (%)

30

Xenon lamp, without water filter Xenon lamp, with water filter AM1.5 global sunlight

25

20

15

10

Maximum band-gap wavelength

5

0 200

250

300

350

400

450

500

550

600

650

700

750

Band-gap wavelength (nm) Fig. 7. The maximum photoconversion efficiency possible as a function of semiconductor band-gap wavelength. Results are given for AM1.5 global solar illumination, and illumination by the xenon arc lamp with and without the water filter. The maximum band-gap wavelength of 610 nm is indicated; materials with greater band-gap wavelengths cannot be used to split water.

The second contribution is a kinetic loss due to the overpotentials for oxygen and hydrogen production. This has been estimated [27] to be at least 0.4 eV. Therefore, we estimate Uloss
0.8 eV, which is in accordance with Bolton et al.’s assessment [28]. This increases the minimum band gap energy from G0 = 1.23 eV to G0 +Uloss 2.03 eV, corresponding to a limiting bandgap wavelength of 610 nm. Note that there are two other loss factors implicit in Eq. (7). First, although only photons with energy greater than Ug can be utilised to excite electrons from the valence band to the conduction band, the fraction of the photon energy greater than Ug is lost through rapid thermal equilibration with the semiconductor lattice. Second, even though Ug has to be significantly greater than the energy G0 that is ultimately stored as chemical energy, the difference between Ug and G0 is lost. Fig. 7 shows the maximum efficiency for water splitting, calculated using Eq. (7), with loss =loss P . A cutoff band-gap wavelength corresponding to Uloss =0.8 eV is indicated on the graph. The efficiency increases with band-gap wavelength, since more photons with energies greater than the band-gap energy are available as the band-gap wavelength increases. The relative efficiencies of different radiation sources at a given band-gap wavelength depend on the proportion of the photon flux at wavelengths shorter than the band-gap wavelength. For band-gap wavelengths below about 410 nm, the

maximum efficiency is greater for incident radiation from the xenon lamp, both with and without a water filter, than for AM1.5 solar radiation. At band-gap wavelengths above 410 nm, the maximum efficiency obtainable with the xenon lamp without a water filter falls below that of AM1.5 solar radiation, while the maximum efficiency for the xenon lamp with a water filter remains larger for all band-gap wavelengths. Table 2 gives the maximum photoconversion efficiencies obtainable for a range of semiconductors of interest in water splitting, for the different radiation sources. It can be seen that the maximum photoconversion efficiencies for all materials are overestimated when using a xenon lamp fitted with a water filter. The overestimate is particularly severe for wide band gap materials such as SrTiO3 and TiO2 . Use of a xenon lamp without a water filter leads to overestimates of the efficiencies of wide band-gap materials, and underestimates of the efficiencies of narrow band-gap materials. The efficiencies under xenon lamp illumination and the efficiency ratios will vary depending on the tube age and other characteristics of the xenon lamp. Using the spectra shown in Fig. 3 we calculate that the maximum efficiency obtainable for cells using rutile TiO2 electrodes is 4.8% for the new tube (5.7 h operation), and 2.3% for the tube at the end of its lifetime (1337 h operation). These compare with 3.8% for the tube that has been used for 1250 h. Hence, the ratio of the AM1.5

A.B. Murphy et al. / International Journal of Hydrogen Energy 31 (2006) 1999 – 2017

2009

Table 2 Maximum possible photoconversion efficiencies for semiconductors of different band gaps, for AM1.5 global solar illumination, and illumination by a xenon arc lamp with and without a water filter fitted Material

SrTiO3 Anatase TiO2 Rutile TiO2 WO3 CdS TaON C-doped TiO2 [8] Fe2 O3 Ta3 N5 Hypothetical ideal material

Band-gap

Band-gap

Maximum efficiency (%)

energy (eV)

wave-length (nm)

AM1.5

Xe lamp without filter

Xe lamp with filter

AM1.5/Xe lamp without filter

AM1.5/Xe lamp with filter

3.70 3.20 3.00 2.70 2.40 2.38 2.32 2.20 2.07 2.03

335 388 413 459 517 520 535 564 600 610

0.22 1.3 2.2 4.8 9.1 9.3 10.5 12.9 15.9 16.8

0.69 1.7 2.3 3.7 6.0 6.1 6.7 7.9 9.6 10.0

1.0 2.6 3.8 6.2 10.4 10.7 11.7 14.0 16.9 17.7

0.32 0.77 0.98 1.32 1.52 1.53 1.57 1.63 1.67 1.68

0.22 0.49 0.60 0.78 0.87 0.88 0.90 0.92 0.94 0.95

efficiency to that for the xenon lamp with water filter can vary from 0.95 to 0.45 for rutile TiO2 , depending on the tube age. For most of the tube lifetime, the ratio is between 0.45 and 0.60. 3.2. Effect of imperfect absorption on efficiency The results presented in Section 3.1 were calculated assuming the semiconductor absorbs all radiation at wavelengths below the band-gap wavelength; i.e., it was assumed that the absorbed photon flux is given by Eq. (6). The absorption coefficients of real semiconductors in fact decrease as the wavelength approaches the band-gap wavelength from below. To take this into account, the absorbed photon flux should be calculated using JS =



g 0

(
)I
(
) d
,

(9)

where (
) = 1 − exp[−k(
)h]

(10)

is the fraction of incident radiation absorbed in the wavelength band from
to d
, k(
) is the absorption coefficient and h is the thickness of the semiconductor. It is assumed that absorption only takes place at wavelengths shorter than the band-gap wavelength
g of the semiconductor. In this section, we investigate the effect of taking into account real absorption coefficients, using the data of Eagles [19] for the absorption coefficient of single-crystal rutile. The absorption coefficient is

Ratio of efficiencies

6.9 × 107 m−1 at 300 nm, but falls by almost four orders of magnitude to 9.1 × 103 m−1 at the band-gap wavelength of 413 nm. Fig. 8 shows the absorbed spectral photon flux (
)I
(
) for different thicknesses of rutile, calculated using Eq. (9), for AM1.5 global solar radiation. It can be seen that a thickness of about 1 mm is required for essentially all photons with wavelengths below the band-gap wavelength to be absorbed. Fig. 9 shows the maximum photoconversion efficiency, calculated using Eq. (7), for rutile semiconductors of different thicknesses, taking into account the imperfect absorption. Results are given for AM1.5 global solar radiation and for the xenon lamp with and without a water filter. The band-gap energy is assumed to be 3.0 eV (corresponding to wavelength 413 nm), for which C = 2.25% for AM1.5 sunlight, if all radiation at wavelengths below the band-gap wavelength is absorbed. Fig. 9, shows that this maximum efficiency is only obtained for thicknesses approaching 1 mm. For a thickness of 1 m, the efficiency is 1.2%, and for a thickness of 0.1 m, the efficiency is only 0.65%. For xenon lamp illumination, particularly with the water filter, the efficiency is greater, owing to the greater proportion of the more strongly absorbed UV radiation. The calculations presented here do not take into account reflection from the rear surface of the TiO2 layer. The reflection coefficient from this surface is calculated to be about 30% for the titanium substrate used in the experiments. It is therefore likely that the calculations presented here slightly underestimate the absorbed power, particularly under conditions when a substantial proportion of the incident radiation is transmitted by the TiO2 layer.

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A.B. Murphy et al. / International Journal of Hydrogen Energy 31 (2006) 1999 – 2017

Spectral photon flux / 1018 (m-2 nm-1 s-1)

3.0

1 nm 10 nm 100 nm 1 µm 10 µm 100 µm 1 mm AM1.5 global sunlight

2.5

2.0

1.5

1.0

0.5

0.0 300

320

340

360

380

400

420

Wavelength (nm) Fig. 8. Wavelength dependence of the absorbed spectral photon flux for different thicknesses of rutile, for AM1.5 global solar illumination. 4.0 3.5

Xe lamp without water filter Xe lamp with water filter AM1.5 global sunlight

Efficiency (%)

3.0 2.5 2.0 1.5 1.0 0.5 0.0 10-9

10-8

10-7

10-6

10-5

10-4

10-3

Rutile thickness (m) Fig. 9. Dependence of maximum photoconversion efficiency on thickness of rutile layer, taking into account absorption of photons in the rutile. Results are given for AM1.5 global solar illumination, and illumination by the xenon arc lamp with and without the water filter.

3.3. Effect of reflection on efficiency A proportion of the incident light is reflected at any interface at which the refractive index changes. In a typical water-splitting reactor, a semiconductor electrode is immersed in an aqueous solution of a salt, an acid or a base, and light enters through a quartz window. Therefore reflection occurs at the interface between the air and the quartz, the quartz and the solution, and the solution and the semiconductor.

For collimated radiation passing from medium 1 to medium 2 at normal incidence to the boundary between the media, the reflection coefficient is given by R12 =

(n2 − n1 )2 + (2 − 1 )2 (n2 + n1 )2 + (2 + 1 )2

,

(11)

where Ni = ni + ii is the complex refractive indices of medium i. Here ni is the real part of the refractive index (usually referred to as simply the refractive index) and

A.B. Murphy et al. / International Journal of Hydrogen Energy 31 (2006) 1999 – 2017

2011

0.40 0.35

Air-quartz Quartz-water Water-TiO2 Total

Reflection coefficient

0.30 0.25 0.20 0.15 0.10 0.05 0.00 250

300

350

400

450

500

550

600

Wavelength (nm) Fig. 10. Reflection coefficients at the interfaces between air and quartz glass, quartz glass and water, and water and rutile TiO2 . The coefficients are for specular reflection at normal incidence.

i is the extinction coefficient, related to the absorption coefficient k by k = 4i /
. We consider here as an example the reflection losses for a TiO2 electrode immersed in water, with a quartz window between the water and the air. This was the arrangement used for the xenon lamp measurements. It was noted in Section 2.4 that the solar measurements were performed in a vessel with no quartz window; however, it is likely that reactors will use such a window. Refractive index data for water and quartz were taken from the SOPRA optical constant database [29], and for rutile TiO2 as noted in Section 2.2. The TiO2 absorption coefficient was assumed to be constant at wavelengths below 300 nm, as suggested by the data of Eagles [19]. The relevant reflection coefficients, calculated using Eq. (11), are shown in Fig. 10. Reflection losses at the interface between the quartz glass and water are very low, and those between the air and quartz glass are about 4%. The reflection losses at the TiO2 surface are substantial, reaching more than 30% at short wavelengths. It is interesting to note that while large absorption coefficients are required to minimise absorption losses, they have the undesirable effect of increasing reflection losses. The influence of reflection on the efficiency of conversion of solar energy to stored chemical energy can be calculated by modifying the absorbed photon flux JS : JS =



g 0

[1 − R(
)](
)I
(
) d
,

(12)

where R(
) is the total reflection coefficient (i.e., the sum of the individual reflection coefficients). Fig. 11 shows the influence of reflection on the photoconversion efficiency for different thicknesses of TiO2 . Reflection leads to a decrease in efficiency of between 24% and 33%, depending on the thickness of the TiO2 . The decrease is essentially independent of the light source. Reflection reduces the maximum efficiency for AM1.5 sunlight to 1.7% for a thick rutile layer, and to 0.45% for a 0.1 m layer. There are several sources of uncertainty in the reflection coefficient calculations. First, the refractive index of water has been used instead of the refractive index of a basic solution. However, this makes only a small difference to the calculated reflection coefficients. The refractive index of water at 589 nm is 1.333, while that of 5M KOH is 1.376 [30]. The total reflection coefficient at 589 nm is reduced from 15.9% to 14.8% when the refractive index of water is replaced by that of 5M KOH. Second, the reflection coefficients have been calculated for normal incidence. Reflection coefficients, and therefore losses, increase as the angle of incidence (which is zero at normal incidence) increases. For global solar irradiation, a proportion of the radiation is scattered from the atmosphere, and therefore has a non-zero angle of incidence even when the electrode is facing the sun. Hence, reflection losses will be larger than those presented in Fig. 11. We estimated the influence of this by calculating diffuse reflection coefficients (averaged over all angles of incidence) for the air–quartz, quartz–water and water–rutile interfaces,

A.B. Murphy et al. / International Journal of Hydrogen Energy 31 (2006) 1999 – 2017 4.0 3.5

1.0

Xe lamp without filter Xe lamp with filter AM1.5 global solar

0.8

Efficiency (%)

3.0 2.5

0.6

2.0 0.4

1.5 1.0

0.2 0.5 0.0 10-9

0.0 10-8

10-7

10-6

10-5

10-4

10-3

Efficiency with reflection / efficiency without reflection

2012

Rutile thickness (m) Fig. 11. Dependence of photoconversion efficiency on thickness of rutile layer, taking into account reflection from the quartz, water and rutile, and absorption of photons in the rutile. Results are given for AM1.5 global solar illumination, and illumination by the xenon arc lamp with and without the water filter. Also shown is the ratio of photoconversion efficiency achievable including and excluding reflection.

taking into account refraction of the rays at the first two interfaces. The reflection at the first interface increases significantly, resulting in an increase in the total reflection coefficient by a factor of about 30%. We applied these reflection coefficients to the diffuse component of the global AM1.5 spectrum, and the normal incidence reflection coefficients to the remainder of the spectrum. The photoconversion efficiency decreased by a factor of between 9% (for a 1 nm thick rutile layer) and 6% (for a 1 mm thick rutile layer). Again, these changes are relatively small. Finally, the reflection coefficients have been calculated assuming that the TiO2 layer has a smooth surface, while the surface is rough, which may reduce the total reflectance, integrated over a hemisphere. Scanning electron microscope images show that the rms roughness of the surface is much less than 100 nm. Calculations using a physical optics model [31] indicate that the total reflectance from such a surface is at least 97% of that from a smooth surface. 3.4. Calculation of diffusion length of charge carriers from IPCE measurements The measured incident photon conversion efficiency for the TiO2 electrode, shown in Fig. 6 was used in Section 2.5 to calculate the photoconversion efficiency under illumination by different light sources. In this section, we use the measured IPCE to estimate the dif-

fusion length of charge carriers in the TiO2 . We use the simple Schottky-barrier model presented by Ghosh and Maruska [32,33], in which the semiconductor layer of thickness h is assumed to behave like a conventional Schottky barrier. There is a barrier region (carrier depletion, or space charge, region) of width lb at the semiconductor–electrolyte interface. All carriers produced in the barrier region, or that reach the barrier region by diffusion, are assumed to reach the electrolyte. Carriers produced outside the barrier region (i.e., a distance greater than lb from the semiconductor–electrolyte interface) have to diffuse through the bulk of the semiconductor, with diffusion length L, to reach the barrier region. A similar model was used by Butler [34]. The number of carriers produced per unit time within the interval dx at a distance x from the surface is proportional to GI
k exp(−kx) dx, where G is the quantum conversion efficiency. Assuming that G is constant with respect to x and writing  = 1/L gives  k IPCE = G [1 − exp(−kl b )] + exp(lb ) k+  × {exp[−(k + )]lb − exp[−(k + )]h} . (13) A least-squares fit of the IPCE, calculated using (13), to the measured data shown in Fig. 6 was performed. The three terms that were fitted were L, lb and G. The measured IPCEs were divided by (1−R) to compensate

A.B. Murphy et al. / International Journal of Hydrogen Energy 31 (2006) 1999 – 2017

measured model, best fit (L = 180 nm, lb = 8 nm, G = 0.96)

100 90

barrier contribution bulk contribution α(λ)

80 70

IPCE (%)

2013

60 50 40 30 20 10 0 320

340

360

380

400

420

Wavelength (nm) Fig. 12. Measured IPCE at 0.6 V bias voltage, modified to compensate for reflection losses, for the flame-oxidised TiO2 electrode, with the best fit of the Schottky barrier diode model to the measurements. The contribution of the barrier region and the bulk region to the IPCE are shown for the best fit. Also shown is , the percentage of the radiation absorbed in the TiO2 layer.

for reflection losses. The thickness h = 280 ± 40 nm measured by reflectometry was used. The best-fit values of lb , L and G were found to be 8 ± 7 nm, 180 ± 30 nm and 0.96±0.05, respectively, for h=280 nm. The uncertainties reflect the values for which the fit becomes noticeably less accurate. The values are only weakly dependent on h; for example, varying h by ±40 nm altered L by only ±10 nm. The calculated dependence of IPCE on wavelength is shown in Fig. 12 together with the components due to photons absorbed in the barrier region (x lb ) and the bulk region (lb < x L). These components correspond respectively to the first and second terms on the right-hand side of Eq. (13). The agreement between the calculation and the measured data is reasonable for wavelengths up to 380 nm; it is not clear whether the discrepancy at longer wavelengths is a consequence of deviations of the absorption coefficient from the singlecrystal rutile data that was used, or deficiencies in the simple Schottky barrier model. Also shown in Fig. 12 is (
), calculated using Eq. (10) with h = 280 nm, which corresponds to the IPCE assuming that all photons absorbed within the thickness of the TiO2 layer participate in electrochemical reactions. The measured IPCE is significantly smaller than this curve for wavelengths above 330 nm, indicating that recombination of charge carriers is significant. For shorter wavelengths, where absorption occurs close to the surface of the semiconductor, the quantum yield is consistent with the radiative limit of (1 − loss P ) ≈ 0.98 calculated in Section 3.1.

The value of L = 180 ± 30 nm indicates that only photons absorbed in about the top 200 nm of the TiO2 can produce charge carriers that are used in electrolysis. This suggests that, for the present sample, there is little benefit in having a layer of thickness much greater than 200 nm, and that diffusion of carriers through the bulk is the main contribution to photocurrent generation.

4. Discussion 4.1. Comparison of measured and calculated efficiencies The photoconversion efficiencies calculated for different radiation sources are compared with measured efficiencies in Table 3. For each source, six calculated efficiency figures are given. The first is the theoretical maximum value, calculated using Eq. (7). The second takes into account losses due to imperfect absorption, and the third due to reflection as well as imperfect absorption and charge transfer. The influence of the bias voltage of 0.6 V that is applied in the measurements is taken into account in the fourth figure using  = (VWS − VB )/1.23 V,

(14)

where  and  are, respectively, the efficiencies calculated excluding and including the effect of the bias voltage.

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A.B. Murphy et al. / International Journal of Hydrogen Energy 31 (2006) 1999 – 2017

Table 3 Comparison of measured photoconversion efficiencies for rutile TiO2 with those calculated for various effective rutile thicknesses h , reflection coefficients R and bias voltages VB Efficiency

AM1.5 global sunlight

Sunlight, 28 May 2004, midday, Sydney

Xenon lamp with water filter

Xenon lamp without water filter

2.25%

1.94%

3.75%

2.29%

h = 280 ± 40 nm R=0 VB = 0

0.92 ± 0.04%

0.76 ± 0.04%

2.09 ± 0.06%

1.35 ± 0.04%

h = 280 ± 40 nm R from Fig. 10 VB = 0

0.66 ± 0.03%

0.54 ± 0.03%

1.47 ± 0.05%

0.94 ± 0.03%

h = 280 ± 40 nm R from Fig. 10 VB = 0.6 V

0.34 ± 0.02%

0.28 ± 0.02%

0.75 ± 0.02%

0.48 ± 0.01%

h = 180 ± 30 nm R from Fig. 10 VB = 0

0.57 ± 0.03%

0.47 ± 0.03%

1.34 ± 0.06%

0.86 ± 0.03%

h = 180 ± 30 nm R from Fig. 10 VB = 0.6 V

0.29 ± 0.02%

0.24 ± 0.02%

0.69 ± 0.03%

0.44 ± 0.02%

0.25 ± 0.05%

0.21 ± 0.04% 0.28 ± 0.06%

0.51 ± 0.10% 0.54 ± 0.11%

0.32 ± 0.07%

Calculated h = ∞ R=0 VB = 0

Measured From IPCE Direct

The first four figures are calculated assuming that the quantum efficiency reaches its maximum possible value, so that all charge carriers produced in the full thickness of the TiO2 layer participate in water-splitting reactions. The fifth and sixth figures take into account charge transfer between the semiconductor and the electrolyte, using an effective TiO2 layer thickness equal to the diffusion length of 180 ± 30 nm derived in Section 3.4. The sixth figure, which takes into account the bias voltage as well, is the best estimate of efficiency from our calculations. It is compared in Table 3 to the efficiencies measured both directly and derived from the measured IPCE. It can be seen that the calculated efficiency for sunlight agrees well with the measurements, while that for the xenon lamp is slightly higher. There are many uncertainties in the calculated efficiencies, such as the influence of roughness of the TiO2 surface on reflection coefficients, the use of absorption and reflection coefficients for single crystal rutile, the neglect of absorption of radiation reflected from the TiO2 –Ti interface, and the use of a simple model to calculated the effective thickness of the film. These uncertainties account for the small discrepancies between

the measured and calculated efficiencies. Similar calculations for different semiconductors would provide a useful guide to the achievable efficiencies. Of particular interest is the large difference between the theoretical maximum efficiency, and that achievable once loss mechanisms are taken into account. The losses are of the order of a factor of 7 to 8 for sunlight. This is a major concern, given that the theoretical maximum efficiency for a semiconductor with an ideal band-gap energy of 2.0 eV is only 17%. Clearly to obtain the target efficiency of 10% will require substantial effort to minimise losses. If possible, the flat-band potential of the conduction band should be more negative than the hydrogen redox potential to remove the need for a bias voltage. A thick nanostructured or mesostructured semiconductor photoelectrode could be used to ensure all the incident light is absorbed, while allowing the electrolyte to penetrate the semiconductor to minimise recombination losses [35]. 4.2. Influence of the light source on efficiency Our results show that the spectrum of the light source has a large impact on the measured photoconversion

A.B. Murphy et al. / International Journal of Hydrogen Energy 31 (2006) 1999 – 2017

efficiency. We have investigated the most widely-used light source, an ozone-free xenon lamp. The measured efficiency is overestimated, relative to that for the AM1.5 global solar spectrum, for wide bandgap semiconductors and when a water filter is fitted. Other commonly-used lamps, such as mercury lamps, mercury–xenon lamps and non ozone-free xenon lamps have spectra more heavily weighted to the ultraviolet than ozone-free xenon lamps, and will lead to more severe overestimates of efficiency. Even when the spectrum of the light source is known, it is not possible to derive a universal conversion factor to convert measured photoconversion efficiencies to efficiencies under AM1.5 solar illumination. The conversion factor would depend on the band gap, and on the wavelength dependence of the absorption and reflection characteristics of the semiconductor, and hence would vary from material to material. A further difficulty is that the spectrum of a given type of lamp depends on its age. We have shown that the conversion factor can vary by a factor of around two, depending on the age of the tube. Our results indicate that measurement of efficiency under AM1.5 solar illumination has to be performed either directly, or by measuring the IPCE as a function of wavelength and integrating over the AM1.5 spectrum. There are significant uncertainties for solar measurement, since the spectrum can vary depending on the zenith angle of the sun, and atmospheric conditions, particularly the ozone column, and ground conditions. We have found, for example, differences of 15% to 20% in the efficiencies calculated for AM1.5 global spectrum and for the solar spectrum relevant to our measurement performed under solar illumination. Probably the most reliable means of relating measured efficiencies to the AM1.5 global solar spectrum, or any other standard spectrum, is to measure the IPCE and integrate over the chosen spectrum using Eq. (5) 4.3. Relevance to other work 4.3.1. Measurements under solar illumination Few previous publications have compared photoconversion efficiencies obtained under solar and artificial illumination. Houlihan et al. [36] presented data for TiO2 and doped TiO2 electrodes, finding larger efficiencies under sunlight than under xenon lamp illumination (for example, 0.70% under sunlight and 0.26% under xenon lamp for a TiO2 electrode). However, the solar irradiance was assumed to be 400 W m−2 at around midday in June in Pennsylvania, USA [37]; this is too low by a factor of around 2.5. Fujishima et al. [38] similarly

2015

underestimated the solar irradiance as 290 W m−2 , obtaining an efficiency of 0.4% for TiO2 produced by flame oxidation; using a more realistic irradiance would reduce the efficiency to well below 0.2%. The most reliable published solar measurement is probably that of Ghosh and Maruska [32] who obtained an efficiency of 0.6% for aluminium-doped TiO2 under solar illumination for an irradiance of 1.05 kW m−2 . The efficiency for undoped TiO2 was about 35% of the Al-doped TiO2 , and is hence about 0.21%, which is consistent with our result. 4.3.2. Measurements under artificial illumination It was noted in Section 1 that many workers have quoted efficiencies obtained under artificial illumination, and that some of these efficiencies are close to or higher than the theoretical thermodynamic limits for the semiconductors used. Here we examine some specific cases in the light of our results. Khan et al. [8] reported obtaining an efficiency of 8.35% with carbon-doped TiO2 with an extended bandgap wavelength of 535 nm. Table 2 shows that the maximum efficiency under AM1.5 global solar illumination is 10.5% for this band-gap wavelength. The stated bias voltage was 0.3 V; taking this into account using Eq. (14) gives a maximum efficiency of 8.0%. A similar maximum efficiency figure of 8.1% was calculated by Hägglund et al. [39]. Losses due to imperfect absorption, reflection and recombination will almost certainly reduce the efficiency to below 2%. It should also be noted that Khan et al. measured the bias voltage between the working electrode and the reference electrode, and defined the cell bias voltage as the difference between this in the open and closed circuit state. The actual bias voltage was likely to be closer to 0.5 V than the stated 0.3 V. This will decrease the efficiency by a further factor of around 20%. Additionally, no precautions were taken to eliminate oxygen from the electrolyte surrounding the counter electrode, which may cause a further overestimate of efficiency. Khan et al. used a xenon arc lamp with an infrared filter as their light source. Table 2 indicates that this will contribute strongly to the discrepancy between the reported efficiency of 8.35% and the maximum efficiencies estimated here. It is also possible that the spectral response of the photometer used by Khan et al. to measure the irradiance was weighted to short wavelengths, which would lead to an underestimate of the incident power and therefore an overestimate of the photoconversion efficiency. We note that Khan et al. [8] obtained an efficiency of 1.08% for oven-oxidised TiO2 , with a standard rutile band gap of 3.0 eV. This is substantially

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A.B. Murphy et al. / International Journal of Hydrogen Energy 31 (2006) 1999 – 2017

above the values we presented in Table 3 even for xenon arc lamp illumination. The photoconversion efficiencies we have obtained for oven-oxidised TiO2 have generally been lower than those we have obtained for flameoxidised TiO2 . Other workers have also presented photoconversion efficiencies above those possible under AM1.5 global solar illumination. For example, the 2.5% reported by Tang et al. [10] for an anatase photoelectrode under xenon lamp illumination is clearly greater than the 1.3% possible for AM1.5 illumination (and the 1.7% possible for a xenon lamp without a water filter). The discrepancy here is due to an underestimate of the total irradiance [40]. Mishra et al. [9] reported efficiencies up to 3% for TiO2 photoelectrodes using a mercury–xenon lamp source; again this is much higher than is possible for AM1.5 illumination. The 1.9% efficiency obtained by Radecka et al. [11] using a xenon lamp for a mixed anatase-rutile photoelectrode is greater than is possible for anatase or rutile under AM1.5 illumination when the stated 0.2 V bias voltage is taken into account. An earlier paper by Khan and Akikusa [5] quoted an efficiency of 2.0% for flame-oxidised titanium with a bias voltage of 0.7 V; the maximum achievable under AM1.5 sunlight is 0.9% in this case. A number of workers have presented IPCE measurements, but have not taken the next step of integrating these data over the AM1.5 solar spectrum to obtain an efficiency that is easily comparable with the results of others.

sources, without taking into account the differences between the spectra of the light source and the AM1.5 solar spectrum. Other problems are also evident in some efficiency measurements, such as the use of the voltage between the working and reference electrodes, rather than the working and counter electrodes, as the bias voltage, and incorrect measurement of the total irradiance. We have calculated the thermodynamically achievable photoconversion efficiency for semiconductors of different band gaps, and investigated the absorption, reflection and recombination losses for rutile. These losses, and the loss due to the requirement for a bias voltage, are found to account for the discrepancy between the theoretically achievable efficiency and the measured efficiency. The losses lead to a major reduction in the efficiency, and will have to be minimised if photoconversion efficiencies approaching 10% are to be obtained. Acknowledgments We thank Mr. Paul Gwan of CSIRO Industrial Physics for assistance with preparing the rutile electrode, Ms. Christina Li of CSIRO Minerals for assistance with the IPCE measurements, and Mr. Errol Atkinson and Dr. Frank Wilkinson of the Australian National Measurement Institute for calibrating the xenon lamp and the thermopile. References

5. Conclusions We have demonstrated that the use of a xenon lamp as the light source can lead to significant overestimates of the photoconversion efficiencies, compared to efficiencies under the standard AM1.5 solar illumination. The overestimate is particularly large when a water filter is used on the xenon lamp, and for wide-band gap semiconductors such as TiO2 . We conclude that reliable estimation of efficiency under standard solar conditions is best performed by measuring the IPCE at the cell bias voltage of maximum efficiency as a function of wavelength, and integrating over the AM1.5 solar spectrum. Measurements under sunlight should also provide reasonable estimates of efficiency, provided that the solar zenith angle is close to the 48.2◦ used for the AM1.5 spectrum. Many of the photoconversion efficiencies presented in the literature are of limited usefulness, since they have been measured with xenon lamps and other light

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