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Photoelectrochemical cells: Laboratory determination of solar conversion efficiencies
Solar Energy Vol. 36, No. 2, pp. 151-157, 1986
0038-092X/86 $3.00 + .00 © 1986 Pergamon Press Ltd.
Printed in the U.S.A.
PHOTOELECTROCHEMICAL CELLS: LABORATORY DETERMINATION OF SOLAR CONVERSION EFFICIENCIES PER CARLSSONand BERTIL HOLMSTROMt Department of Physical Chemistry, Chalmers University of Technology and University of G6teborg, S-412 96 G6teborg, Sweden (Received 23 November 1984; accepted 23 July 1985)
Abstract--To define the solar-to-electricity conversion efficiency TI of a regenerative photoelectrochemical (PEC) cell is a straightforward matter. The actual determination of "q from real laboratory measurements is, however, far from trivial. In this paper the problem is analyzed in detail, based on two types of laboratory measurements: (i) the photocurrent as a function of photoelectrode potential at constant wavelength of illuminating light, and (ii) the photocurrent as a function of wavelength at constant potential. The analysis results in four somewhat different "recipes" for computation of "q, based on two choices: (a) whether or not to "correct" for dark current, and (b) how experiments of type (i) and type (ii) are weighed together. The analysis is applied to experiments on III-V semiconductors. The "q values computed according to the four equations are in good agreement; a recommendation is given to which one(s) to prefer. The "q values depend on the air mass (AM) value assumed for the solar spectrum. Although reported data probably should refer to AM 1, other AM values would be more realistic.
I. INTRODUCTION
Over the last decade, photoelectrochemical (PEC) cells have been established as one of the most promising routes to solar energy utilization producing either electricity (regenerative PEC cells) or chemicals (photoelectrosynthetic cells). A number of reviews are available[l]. To facilitate the following discussion, a schematic band diagram is given in Fig. I. A major concern in designing PEC systems is stability against photocorrosion. Assuming that this can be handled in a satisfactory way, a remaining major criterium for a viable PEC system is its solar conversion efficiency "qso~, defined simply enough as the ratio of " p o w e r o u t " to " p o w e r in" under certain specified conditions: "qsol = Pout/Pin.
(1)
In order to compare results reported from different laboratories it is essential to have universal agreement not only on the interpretation of eqn (l) but also on how to measure it under laboratory conditions. This problem, which certainly is nontrivial, was recently discussed by Parkinson[2], who also cited examples of controversy and misunderstanding when efficiency numbers are discussed both inside and outside the scientific community. We will restrict our discussion to regenerative PEC cells, specifically with an n doped photoelectrode. (Extension to p doped photoelectrode is straightforward. Treatment of photoelectrosyn-
thetic PEC cells, however, presents several additional problems.) F o r a regenerative PEC cell, the proper quantity for Poot is the power output (per unit area) of the illuminated cell when working under optimum load, i.e. at the "working point" (cf Fig. 2): Po~t = ( j U ) wp,
(2)
w h e r e j = current density (A m -2) and U cell voltage (V). To give true values for "q~ot, two conditions are to be fulfilled: (i) the light source used in the experiments should be the sun itself (shining from a clear sky), or else have the same spectral composition (a "solar simulator"), and (ii) the light meter should measure over all wavelengths (like a blackbody detector). If we denote the reading from the bb we have light meter (power per unit area) as P+o~, Pin = Psol. bb
(3)
To complicate the situation further, the spectral composition of terrestrial sunlight varies with the height of the sun above the horizon, with direct overhead ( " A M I " ) sunshine containing comparatively more short wavelength ( " b l u e " ) photons than sunshine in general (say, with the sun 30° above the horizon, " A M 2 " , or at 14°, " A M 4 " ) . The way to define the solar-to-electricity conversion efficiency under AMn conditions would then be xln = (jU)~P/P~. b
f ISES member. 151
(4)
152
P. CARLSSONand B. HOLMSTROM
WE
Sotn.
CE
WE
Sotn.
CE
WE
Soln.
CE
vl" ®
@
©
Fig. 1. Schematic diagram of electric potential V in the working electrode (WE), in the electrolyte solution, and in the counter electrode (CE) (note the convention direction of the V axis!), (a) and (b) Illuminated cell under open circuit condition: (a) An idealized case of negligible parasitic processes. There is no remaining band bending. The fermi potential VF is located at a distance A V~c negative from the redox potential Vredoxof the solution (which coincides with the fermi potential of the CE). (b) A real cell, with A Voc slightly less than A Vid. (c) Dark cell or short circuited illuminated cell. The fermi potential of the WE, the redox potential in the solution, and the potential of the CE are all the same.
where we would expect a wide band device (e.g. using TiO2) to show rh > '114, with the opposite being true for a narrow band device (e.g. using CdSe or GaAs). A clear sky with direct overhead sun is seldom at hand at the time and the place where PEC experiments are performed. Although solar simulators are commercially available they are fairly expensive and usually not very convenient in PEC studies. A blackbody detector is insensitive and inconvenient compared to detectors like a silicon photodiode (which has a specific spectral sensitivity, with a long wavelength cutoff around 1100 nm). In most experiments polychromatic light is used with a spectral distribution different from that of the solar radiation, as well as a detector with a spectral sensitivity different from that of the black body detector. The values for P~, obtained in this
way can at most be transferred from one experiment to the next in the same laboratory, but certainly not much further. Admittedly, reporting " t r u e " values for-q~o~is by no means the most pressing problem in PEC re* search. Nevertheless it is the purpose of this paper to analyze how such values can be deduced from laboratory measurements performed with monochromatic light from any available continuous light source (e.g. a xenon arc lamp or an incandescent lamp) and using any convenient detector. The analysis is applied to some experiments on GaAsyPI_y, 0 ~< y ~< 1. Two types of experiments are needed for the efficiency determination: (i) varying the potential at constant wavelength (conventional voltammetry) and (ii) varying the wavelength at constant potential.
THEORY
A theoretical treatment of how to determine values for "qsol is conveniently divided into three sections: how to describe the spectral distribution of sunshine, how to describe the spectral response of a PEC cell under monochromatic illumination, and how to unite these parameters into a description of a real solar cell.
JPh
\f JWPJSC AVwp voc
I _
\
V
Fig. 2. Schematic diagram showing the variation of photocurrent density vs. electrode potential for a PEC cell with an n doped photoelectrode.
Spectral distribution of solar irradiance There are several different ways to report the spectral distribution of radiation, e.g. of sunlight. One is the function P'(X), the power per unit area and unit wavelength increment (W m -z txm-l), which has been tabulated by several authors[3] for a variety of conditions, including clear direct overhead sun (AM1) and clear sun at 14° above the horizon (AM4). Although the AM1 situation is convenient for reference purpose, the AM4 situation is more realistic for a practical working cell.
153
Photoelectrochemical cells The total incident power, P ,bb , measured by a blackbody detector when irradiated with clear sunlight at air mass n is given by the integral
Pnbb = f P~,(h) dh.
(5)
Spectral response o f a regenerative PEC cell The independent parameters in a wavelength resolved study of a regenerative PEC cell are (in addition to the shutter for switching between light, L, and dark, D, conditions) the wavelength h of the illuminating light, and the potential V of the photoelectrode (WE in Fig. 1), measured with respect to some chosen reference electrode, RE). The measured quantities are the light intensity and the cell current. The input power density, el(h) (W m -z) is obtained from a photometer using a proper calibration curve and knowing the area of the detector. The photocurrent, /oh(h) is the difference between the currents from the illuminated cell, iL(h) and from the dark cell, io(h); the corresponding current densities are obtained by dividing by the electrode area. The photocurrent density depends on light intensity and wavelength, and on electrode potential. As illustrated in Fig. 2, jr(h) decreases from a high value j~¢(h) when the cell operates under short circuit conditions, to zero when the cell is in open circuit condition. In a practical (two electrode) cell the photovoltage, A V, is simply the voltage between the photoelectrode and the counterelectrode (CE in Fig. 1). In addition to the parameters mentioned above, A V depends strongly on the external load of the cell, reaching a maximum (absolute) value at zero load (open circuit) and dropping to zero when the load goes to zero ("short circuit"); cf. Fig. 2. Laboratory PEC studies are usually performed under potentiostatic control, keeping the WE potential fixed by external means (with respect to the chosen reference electrode RE). The potential of the CE (with respect to RE) is determined by the redox couple in the electrolyte solution. The j - V plot has the same shape as in the two-electrode case, but with A V defined as the potential difference between WE and CE. The output power density of the cell, Pout(h), is the product of photocurrent density and the photovoltage. It is zero both under short circuit conditions ( j = f ~ , A V = 0) and under open circuit conditions ( j = 0, A V = V°~). It reaches a maximum at some intermediate potential, the working point ( j = jwo, A V = A VWp), from which we define the fill factor, tiff: xlfr = j w . A Vwp/j ~c A V °~.
(6)
A useful parameter is the quantum conversion efficiency +v(h), a dimensionless quantity defined as the ratio of the number of electrons leaving the cell
to the number of incident photons: d~v(h) _
jv(x)/e _ hc jv(h) Pl(k)/(hc/h) eX Pl(h) "
(7)
We note that the quantum conversion efficiency varies with wavelength (going to zero when h goes to hg) and is dependent on the photoelectrode potential (being zero at the open circuit potential). Two cases are of special interest: +~c, corresponding to short circuit condition (A V = 0), and +'~P, relating to working point condition (A V = A Vwp). It is important to note that the quantum conversion efficiency must not be confused with the quantum yield, which is the ratio of the number of electrons delivered to the number of photons actually absorbed by the photoelectrode. The quantum conversion efficiency is zero for X > h~,, while the quantum yield is undefined in this case. The performance of the cell under monochromatic illumination is described by the monochromatic conversion eJficiency rl(h):
~(h) = jwv(h).AVWp/el(h ).
(8)
Two alternative forms, which sometimes are more convenient, are obtained by introducing the quantum conversion efficiency and the fill factor:
e AV wp rl(h) = ' he' qbwo(h)X,
(8a)
e A V °~ rl(h) - - rife +~c(h) h. hc
(8b)
Solar conversion efficiency The solar conversion efficiency at AMn is obtained by weighing "q(h) over the solar spectrum:
= f
f (h) dX,
(9)
where the weighing factor fn(h) is obtained from the known solar spectral distribution:
f,(h)=
P,(h)/f
P'~(h)dh.
(lO)
Introducing the quantum conversion efficiency, as defined in eqn (7), and the monochromatic conversion efficiency, eqn (8), we get
~n -
e A V wp f hc +wP(h) X f A h ) dh.
(lla)
If we assume that the working point potential is independent of wavelength, we can derive an alternative form: "q. = " q f ef - 8~ V °~ f +~¢(h) h f.(h) dk,
(1 lb)
where -qff is the fill factor as defined in eqn (6).
154
P. CARLSSONand B. HOLMSTRt3M which easily is found to be identical with eqns (1 la) and (ilb). As a final remark it can be pointed out that as "q00 = 0 for h > hg, it is evident that a ceil with a quite high monochromatic conversion efficiency but also a low Xg (a high Eg) will have a low value for ~q and thus be of little interest in practical application. [Some but not all of the controversies pointed out by Parkinson[2] are due to confusion on this point.]
It may be interesting to compare these "operational" equations for the solar conversion efficiency with equations normally encountered in papers analyzing various factors limiting the possible yield[4]. If we imagine an ideal cell, in which all light with h < hg is absorbed by the system, and where each photon contributes an energy of hc/hg, we can calculate an "ultimate" conversion efficiency (also called a "threshold factor" or a "band gap factor")
,/
-% -- ~g
$(h) k f0Q dk,
(12)
3. EXPERIMENTAL
where ~(k) = i for h < ~kg and = 0 elsewhere. Replacing ~(h) with the short circuit quantum conversion efficiency d:c(h) defined in eqn (7) we can define a "practical band gap efficiency": TIg , = ~gi f
(bsc(x)X f(X) dh.
(13)
Even under open circuit conditions, there are unavoidable losses in any real cell which leads to an open circuit photopotential less than that defined by the band gap. This can be formulated as an "open circuit efficiency factor":
~v-
e A V °c
(14)
Eg
Combining eqns (13) and (14) with the fillfactor introduced previously we get an expression for the total solar conversion efficiency: t
rl = "% "qv r l .
(15)
The instrumentation is a multipurpose computerized photoelectrical arrangement[5] schematically shown in Figs. 3 and 4. Although the setup is arranged for rotating ring-disk (RRDE) experiments (as needed for photocorrosion studies), only the disk currents were recorded in the experiments discussed here. (For efficiency determinations, even a stationary electrode would serve just as well.) Computer control. The various pieces of equipment are linked (Fig. 4) to a microcomputer (Commodore CBM 3032) equipped with floppy disk storage system. By means of a homebuilt multiplexer/ interface unit, the computer can (i) set the wavelength of the monochromator and control the light shutter, (ii) acquire and store output data from a chosen set of devices (measuring e.g. light intensity, electrode potentials, currents), (iii) at a later time perform various calculations (including computations involving stored functions like the terrestrial solar spectrum and the photometer calibration curve), and (iv) print or plot data in various ways.
M~OR ( ~ CONTROL
REF (DISK)
i(
'
~ [ ~ _ ] MOTSTEP OR _ }
XENON
LAMP
5r
PHOTO METER
SHUTTER DMM
LIfiHT GUIDES
Fig. 3. Schematic diagram of the experimental arrangement.
155
Photoelectrochemical cells
Illumination. The light source, a 1000 W xenon lamp (Oriel), is fitted with a voltage stabilizer and a water filter to remove excess IR. The lamp spectrum is shown in Fig. 6(a). The monochromator (Joban Yvon) is modified with a geared step motor (one step being equal to 0.1 nm). The setting of the wavelength is controlled from the computer, which also controls the shutter. To increase the flexibility of PEC cell design, the output from the monochromator is focussed Stepmotor Shuffer onto a bifurcated glass fiber light guide, with one 4 Spare Output arm going to the PEC cell, the other to the pho[ontr0tLine'. tometer. The input power density (the light intensity) is Interface obtained as the current output from the photometer (Photodyne 44XL), converted to Px(h) by means of a sensitive curve S(h) provided by the manufacturer (and stored in the computer). The silicon photohead has a long wavelength cutoff where S(h) drops to zero--which might present a problem when working with very narrow band gap materials, but not for the III-V compounds discussed here. (There is also a short wavelength cutoff which in almost most cases is shorter than other limiting parameters and therefore hardly presents a problem.) RE WE [E Electrochemistry. A PAR 173 potentiostat is Fig. 4. Block diagram of the system showing flow of com- used for measurements of photocurrent (at constant mands and data. Single lines: analog, double lines: digital electrode potential) as a function of wavelength of signals. DMM = digital multimeter. illuminating light. In addition, a PAR 175 ramp generator is used for voltammetry experiments with constant wavelength of illuminating light. Motor and control gear for rotating electrode experiments are homebuilt. Electrodes. The experiments discussed here are taken from a larger study of n type III-V semiconductors, either commercial single crystalline GaAs 500 nm or GaP (MCP Electronics) or single crystalline ternary alloys in the series GaAs~_yPv, 0 < y < 1 (prepared at the Department of Solid State Physics, University of Lund, using metal-organic vapour 700 phase epitaxy[6]). Chemicals. All experiments reported here were done in neutral aqueous solution, using potassium hexacyanoferrate as redox couple and potassium 80Onto chloride as auxilliary electrolyte. Triple distilled water was used and all chemicals were p.a. grade.
I
I
++÷
2.o
4. RESULTS AND DISCUSSION
Fig. 5. Current vs. electrode potential under illumination with light of different wavelengths (as marked), and dark current. Photoelectrode: GaAso.87Po.13, reference electrode Pt, electrolyte K4Fe(CN)6 (0. ! M) + KCI (0. I M). Also shown are the working points at different wavelengths.
In Fig. 5 (for an electrode with y = 0.13) the variation of current, iL, vs potential, V, is shown for illumination at four different wavelengths (500, 600,700 and 800 nm). For each of these curves, the working point is located in such a way as to obtain the maximum inscribed rectangle. It is found that the working point potential increases from - 0 . 5 0 V at 400 nm to -0.41 V at 800 nm. (A plausible cause is the decrease in light intensity towards longer wavelength, cf. Fig. 6.) Due to the low intensity of the monochromatic light, the currents of the illuminated cell is of similar
156
P. CARLSSONand B. HOLMSTROM -EpA 3.0
~20
/
o o
l
2.0.
10 1.o. Dark Current
500
600
(a)
700
BOO
660
5oo
~/nm
760
860
-
,
(b)
=
~m
>.
~1.0-
1.0
o o 0.s.
o
c
0.5
8
\ / s00
660
700
\,-. a00
~o ~nm
500
600
700
800
(d)
(e)
~m
Fig. 6. Wavelength dependence of different functions relating to the cell described in Fig. 5. (a) Lamp spectrum. (b) Photocurrent and dark current, at working point potential. (c) Quantum conversion efficiency (based on the photocurrent). (d) "Corrected" quantum conversion efficiency (based on the light current, i.e. the difference between the photocurrent and the dark current). magnitude as the dark current iD, also shown in Fig. 5. At short circuit condition the dark current iV is slightly anodic (0.1 I~A), rendering the photocurrent i~,~ smaller than the light current ist~ by this amount. At the potentials corresponding to the working points at different wavelengths, the dark current is cathodic (0.1 to 0.3 I~A), giving i~'~ larger than i~ p. These problems will be dis-
cussed further below when computing the total conversion efficiencies. The set of curves in Fig. 7 (for an electrode with y = 0.60) gives the wavelength variation of the quantum conversion efficiency as defined by eqn (7), for a number of electrode potentials. In principle, it would be possible to determine -q according to eqn (lla) by integrating along different ~bv(h)
390
582 ,
,
I
I
1 1
,1f / Q5
',
70 Fig. 7. Set of quantum conversion efficiency vs. wavelength plots for 15 different settings of the electrode potential, from -0.4 V (lowest curve) to +0.4 V vs. SCE. Photoelectrode: GaAso.6oPo.4o, electrolyte K4Fe(CN)6 (0.1 M).
Photoelectrochemical cells
157
Table 1. Solar-to-electricity conversion efficiencies calculated according to different equations (cell composition as in Fig. 5) photocurrent
light current
0.075 working point
short circuit + fill factor
0.062*
(0.082)
(0.067)
0.064* (0.070)
0.066 (0.074)
* recommeDded choices Upper values: AMT, lower values
curves for different segments of the h axis. Clearly this is not a very practical approach. Two possibilities remain: (i) to choose one "typical" working point potential, measure +wP(h) for this potential, and compute ~q according to eqn (1 la), or (ii) to measure ~bsc(h) and use eqn (l lb) together with the ~f~ for the chosen wp to compute ~. A further choice to be made is between qbL and ~bp~ (i.e. whether or not to "correct" for the dark current). The lamp spectrum is given in Fig. 6(a). The remainder of Fig. 6 shows measurements on the same cell as used in Fig. 5. The electrode potential, - 0 . 5 0 V vs Pt, is the working point potential obtained form the 500 nm curve in Fig. 5. At this potential, the dark current is cathodic, and the light current is obtained as the difference of the photocurrent and the dark current, both shown in Fig. 6(b). The drop in photocurrent on the long wavelength side reflects the band gap of the photoelectrode, the drop on the short wavelength side is due to light absorption in the electrolyte. The quantum conversion efficiency functions for the two cases are shown in Figs. 6(c) and 6(d). The first one, based on the photocurrent, is a smooth function of h, and can be considered as a correct picture of the ability of the cell to convert light into electricity. The overall solar-to-electricity conversion efficiency for AMI radiation, rl~, is 0.075 when using the photocurrent. As the only current that can be delivered by the cell to an external user is the light current, the latter (and lower) value is the correct one to report as the efficiency of the cell. Under short circuit conditions, the photocurrent curve is similar to that of Fig. 6(b) (although, of course, the values are higher). In this case the dark current is anodic, and the light current is the sum of the photocurrent and the dark current. The quantum conversion efficiency curves are similar to the one in Fig. 6(c). The efficiency values, computed according to eqn (1 lb), are 0.064 (based on the photocurrent) resp, 0.066 (based on the light current). Only the first (and lower) value is a measure of the
(in prantheses):
AM4.
conversion of infalling sun light into electricity, and should be regarded as the efficiency of the cell. The values mentioned (for AMI radiation) are collected in Table I, together with efficiency values calculated for AM4 conditions. Asterisks denote recommended values for describing cell performance. Although most reports to date probably are given for AM1 conditions, we believe that AM4 (or perhaps AM3) values are a better measure of cell performance as averaged over the working day (and year). Methods (i) and (ii) are found to give more or less the same results, so the choice between them is directed by convenience [which probably would turn to method (ii) as the first choice].
Acknowledgements--The work was supported by the Swedish Energy Resource Commission (Efn) and the Swedish Natural Science Research Council (NFR).
REFERENCES
1. E.g., Solar Energy--Photochemical Processes Available for Energy Conversion (Edited by S. Claesson and
2. 3.
4. 5. 6.
B. Holmstr6m). Liber, Stockholm (1982); Supplement I (Edited by B. HolmstrOm) (1983); Photochemical Conversion and Storage of Solar Energy (Edited by J. Rabini). Weizmann Science Press of Israel Jerusalem (1982); Photochemical Conversion and Storage of Solar Energy (Edited by H. Tsubomura). Special issue ofJ. Photochem. 29, 1 (1985). B. Parkinson, On the efficiency and stability of photoelectrochemical devices. Acc. Chem. Res. 17, 431 (1984). (a) M. P. Thekaekara, Solar Irradiance, Total and Spectral, in Solar Energy Engineering (Edited by A. A, M. Sayigh). New York (1977); (b) R. E, Bird, R. L. Hulstrom and L. J. Lewis, Terrestrial Solar Data Sets. Solar Energy 30, 6 (1983). M. D. Archer, Electrochemical Aspects of Solar Energy Conversion. J. AppL Electrochem. 5, 17 (1975). P. Carlsson, B. Holmstr6m, A computerized system for photochemistry with application to solar energy material research. Rev. Sci. Instr. 56, 333 (1985). L. Samuelson, P. Omling, H. Titze and H. G. Grimmeiss, Organic metallic epitaxial growth of GaAsl-xPx. J. Phys. 12, C5-325 (1982).
0038-092X/86 $3.00 + .00 © 1986 Pergamon Press Ltd.
Printed in the U.S.A.
PHOTOELECTROCHEMICAL CELLS: LABORATORY DETERMINATION OF SOLAR CONVERSION EFFICIENCIES PER CARLSSONand BERTIL HOLMSTROMt Department of Physical Chemistry, Chalmers University of Technology and University of G6teborg, S-412 96 G6teborg, Sweden (Received 23 November 1984; accepted 23 July 1985)
Abstract--To define the solar-to-electricity conversion efficiency TI of a regenerative photoelectrochemical (PEC) cell is a straightforward matter. The actual determination of "q from real laboratory measurements is, however, far from trivial. In this paper the problem is analyzed in detail, based on two types of laboratory measurements: (i) the photocurrent as a function of photoelectrode potential at constant wavelength of illuminating light, and (ii) the photocurrent as a function of wavelength at constant potential. The analysis results in four somewhat different "recipes" for computation of "q, based on two choices: (a) whether or not to "correct" for dark current, and (b) how experiments of type (i) and type (ii) are weighed together. The analysis is applied to experiments on III-V semiconductors. The "q values computed according to the four equations are in good agreement; a recommendation is given to which one(s) to prefer. The "q values depend on the air mass (AM) value assumed for the solar spectrum. Although reported data probably should refer to AM 1, other AM values would be more realistic.
I. INTRODUCTION
Over the last decade, photoelectrochemical (PEC) cells have been established as one of the most promising routes to solar energy utilization producing either electricity (regenerative PEC cells) or chemicals (photoelectrosynthetic cells). A number of reviews are available[l]. To facilitate the following discussion, a schematic band diagram is given in Fig. I. A major concern in designing PEC systems is stability against photocorrosion. Assuming that this can be handled in a satisfactory way, a remaining major criterium for a viable PEC system is its solar conversion efficiency "qso~, defined simply enough as the ratio of " p o w e r o u t " to " p o w e r in" under certain specified conditions: "qsol = Pout/Pin.
(1)
In order to compare results reported from different laboratories it is essential to have universal agreement not only on the interpretation of eqn (l) but also on how to measure it under laboratory conditions. This problem, which certainly is nontrivial, was recently discussed by Parkinson[2], who also cited examples of controversy and misunderstanding when efficiency numbers are discussed both inside and outside the scientific community. We will restrict our discussion to regenerative PEC cells, specifically with an n doped photoelectrode. (Extension to p doped photoelectrode is straightforward. Treatment of photoelectrosyn-
thetic PEC cells, however, presents several additional problems.) F o r a regenerative PEC cell, the proper quantity for Poot is the power output (per unit area) of the illuminated cell when working under optimum load, i.e. at the "working point" (cf Fig. 2): Po~t = ( j U ) wp,
(2)
w h e r e j = current density (A m -2) and U cell voltage (V). To give true values for "q~ot, two conditions are to be fulfilled: (i) the light source used in the experiments should be the sun itself (shining from a clear sky), or else have the same spectral composition (a "solar simulator"), and (ii) the light meter should measure over all wavelengths (like a blackbody detector). If we denote the reading from the bb we have light meter (power per unit area) as P+o~, Pin = Psol. bb
(3)
To complicate the situation further, the spectral composition of terrestrial sunlight varies with the height of the sun above the horizon, with direct overhead ( " A M I " ) sunshine containing comparatively more short wavelength ( " b l u e " ) photons than sunshine in general (say, with the sun 30° above the horizon, " A M 2 " , or at 14°, " A M 4 " ) . The way to define the solar-to-electricity conversion efficiency under AMn conditions would then be xln = (jU)~P/P~. b
f ISES member. 151
(4)
152
P. CARLSSONand B. HOLMSTROM
WE
Sotn.
CE
WE
Sotn.
CE
WE
Soln.
CE
vl" ®
@
©
Fig. 1. Schematic diagram of electric potential V in the working electrode (WE), in the electrolyte solution, and in the counter electrode (CE) (note the convention direction of the V axis!), (a) and (b) Illuminated cell under open circuit condition: (a) An idealized case of negligible parasitic processes. There is no remaining band bending. The fermi potential VF is located at a distance A V~c negative from the redox potential Vredoxof the solution (which coincides with the fermi potential of the CE). (b) A real cell, with A Voc slightly less than A Vid. (c) Dark cell or short circuited illuminated cell. The fermi potential of the WE, the redox potential in the solution, and the potential of the CE are all the same.
where we would expect a wide band device (e.g. using TiO2) to show rh > '114, with the opposite being true for a narrow band device (e.g. using CdSe or GaAs). A clear sky with direct overhead sun is seldom at hand at the time and the place where PEC experiments are performed. Although solar simulators are commercially available they are fairly expensive and usually not very convenient in PEC studies. A blackbody detector is insensitive and inconvenient compared to detectors like a silicon photodiode (which has a specific spectral sensitivity, with a long wavelength cutoff around 1100 nm). In most experiments polychromatic light is used with a spectral distribution different from that of the solar radiation, as well as a detector with a spectral sensitivity different from that of the black body detector. The values for P~, obtained in this
way can at most be transferred from one experiment to the next in the same laboratory, but certainly not much further. Admittedly, reporting " t r u e " values for-q~o~is by no means the most pressing problem in PEC re* search. Nevertheless it is the purpose of this paper to analyze how such values can be deduced from laboratory measurements performed with monochromatic light from any available continuous light source (e.g. a xenon arc lamp or an incandescent lamp) and using any convenient detector. The analysis is applied to some experiments on GaAsyPI_y, 0 ~< y ~< 1. Two types of experiments are needed for the efficiency determination: (i) varying the potential at constant wavelength (conventional voltammetry) and (ii) varying the wavelength at constant potential.
THEORY
A theoretical treatment of how to determine values for "qsol is conveniently divided into three sections: how to describe the spectral distribution of sunshine, how to describe the spectral response of a PEC cell under monochromatic illumination, and how to unite these parameters into a description of a real solar cell.
JPh
\f JWPJSC AVwp voc
I _
\
V
Fig. 2. Schematic diagram showing the variation of photocurrent density vs. electrode potential for a PEC cell with an n doped photoelectrode.
Spectral distribution of solar irradiance There are several different ways to report the spectral distribution of radiation, e.g. of sunlight. One is the function P'(X), the power per unit area and unit wavelength increment (W m -z txm-l), which has been tabulated by several authors[3] for a variety of conditions, including clear direct overhead sun (AM1) and clear sun at 14° above the horizon (AM4). Although the AM1 situation is convenient for reference purpose, the AM4 situation is more realistic for a practical working cell.
153
Photoelectrochemical cells The total incident power, P ,bb , measured by a blackbody detector when irradiated with clear sunlight at air mass n is given by the integral
Pnbb = f P~,(h) dh.
(5)
Spectral response o f a regenerative PEC cell The independent parameters in a wavelength resolved study of a regenerative PEC cell are (in addition to the shutter for switching between light, L, and dark, D, conditions) the wavelength h of the illuminating light, and the potential V of the photoelectrode (WE in Fig. 1), measured with respect to some chosen reference electrode, RE). The measured quantities are the light intensity and the cell current. The input power density, el(h) (W m -z) is obtained from a photometer using a proper calibration curve and knowing the area of the detector. The photocurrent, /oh(h) is the difference between the currents from the illuminated cell, iL(h) and from the dark cell, io(h); the corresponding current densities are obtained by dividing by the electrode area. The photocurrent density depends on light intensity and wavelength, and on electrode potential. As illustrated in Fig. 2, jr(h) decreases from a high value j~¢(h) when the cell operates under short circuit conditions, to zero when the cell is in open circuit condition. In a practical (two electrode) cell the photovoltage, A V, is simply the voltage between the photoelectrode and the counterelectrode (CE in Fig. 1). In addition to the parameters mentioned above, A V depends strongly on the external load of the cell, reaching a maximum (absolute) value at zero load (open circuit) and dropping to zero when the load goes to zero ("short circuit"); cf. Fig. 2. Laboratory PEC studies are usually performed under potentiostatic control, keeping the WE potential fixed by external means (with respect to the chosen reference electrode RE). The potential of the CE (with respect to RE) is determined by the redox couple in the electrolyte solution. The j - V plot has the same shape as in the two-electrode case, but with A V defined as the potential difference between WE and CE. The output power density of the cell, Pout(h), is the product of photocurrent density and the photovoltage. It is zero both under short circuit conditions ( j = f ~ , A V = 0) and under open circuit conditions ( j = 0, A V = V°~). It reaches a maximum at some intermediate potential, the working point ( j = jwo, A V = A VWp), from which we define the fill factor, tiff: xlfr = j w . A Vwp/j ~c A V °~.
(6)
A useful parameter is the quantum conversion efficiency +v(h), a dimensionless quantity defined as the ratio of the number of electrons leaving the cell
to the number of incident photons: d~v(h) _
jv(x)/e _ hc jv(h) Pl(k)/(hc/h) eX Pl(h) "
(7)
We note that the quantum conversion efficiency varies with wavelength (going to zero when h goes to hg) and is dependent on the photoelectrode potential (being zero at the open circuit potential). Two cases are of special interest: +~c, corresponding to short circuit condition (A V = 0), and +'~P, relating to working point condition (A V = A Vwp). It is important to note that the quantum conversion efficiency must not be confused with the quantum yield, which is the ratio of the number of electrons delivered to the number of photons actually absorbed by the photoelectrode. The quantum conversion efficiency is zero for X > h~,, while the quantum yield is undefined in this case. The performance of the cell under monochromatic illumination is described by the monochromatic conversion eJficiency rl(h):
~(h) = jwv(h).AVWp/el(h ).
(8)
Two alternative forms, which sometimes are more convenient, are obtained by introducing the quantum conversion efficiency and the fill factor:
e AV wp rl(h) = ' he' qbwo(h)X,
(8a)
e A V °~ rl(h) - - rife +~c(h) h. hc
(8b)
Solar conversion efficiency The solar conversion efficiency at AMn is obtained by weighing "q(h) over the solar spectrum:
= f
f (h) dX,
(9)
where the weighing factor fn(h) is obtained from the known solar spectral distribution:
f,(h)=
P,(h)/f
P'~(h)dh.
(lO)
Introducing the quantum conversion efficiency, as defined in eqn (7), and the monochromatic conversion efficiency, eqn (8), we get
~n -
e A V wp f hc +wP(h) X f A h ) dh.
(lla)
If we assume that the working point potential is independent of wavelength, we can derive an alternative form: "q. = " q f ef - 8~ V °~ f +~¢(h) h f.(h) dk,
(1 lb)
where -qff is the fill factor as defined in eqn (6).
154
P. CARLSSONand B. HOLMSTRt3M which easily is found to be identical with eqns (1 la) and (ilb). As a final remark it can be pointed out that as "q00 = 0 for h > hg, it is evident that a ceil with a quite high monochromatic conversion efficiency but also a low Xg (a high Eg) will have a low value for ~q and thus be of little interest in practical application. [Some but not all of the controversies pointed out by Parkinson[2] are due to confusion on this point.]
It may be interesting to compare these "operational" equations for the solar conversion efficiency with equations normally encountered in papers analyzing various factors limiting the possible yield[4]. If we imagine an ideal cell, in which all light with h < hg is absorbed by the system, and where each photon contributes an energy of hc/hg, we can calculate an "ultimate" conversion efficiency (also called a "threshold factor" or a "band gap factor")
,/
-% -- ~g
$(h) k f0Q dk,
(12)
3. EXPERIMENTAL
where ~(k) = i for h < ~kg and = 0 elsewhere. Replacing ~(h) with the short circuit quantum conversion efficiency d:c(h) defined in eqn (7) we can define a "practical band gap efficiency": TIg , = ~gi f
(bsc(x)X f(X) dh.
(13)
Even under open circuit conditions, there are unavoidable losses in any real cell which leads to an open circuit photopotential less than that defined by the band gap. This can be formulated as an "open circuit efficiency factor":
~v-
e A V °c
(14)
Eg
Combining eqns (13) and (14) with the fillfactor introduced previously we get an expression for the total solar conversion efficiency: t
rl = "% "qv r l .
(15)
The instrumentation is a multipurpose computerized photoelectrical arrangement[5] schematically shown in Figs. 3 and 4. Although the setup is arranged for rotating ring-disk (RRDE) experiments (as needed for photocorrosion studies), only the disk currents were recorded in the experiments discussed here. (For efficiency determinations, even a stationary electrode would serve just as well.) Computer control. The various pieces of equipment are linked (Fig. 4) to a microcomputer (Commodore CBM 3032) equipped with floppy disk storage system. By means of a homebuilt multiplexer/ interface unit, the computer can (i) set the wavelength of the monochromator and control the light shutter, (ii) acquire and store output data from a chosen set of devices (measuring e.g. light intensity, electrode potentials, currents), (iii) at a later time perform various calculations (including computations involving stored functions like the terrestrial solar spectrum and the photometer calibration curve), and (iv) print or plot data in various ways.
M~OR ( ~ CONTROL
REF (DISK)
i(
'
~ [ ~ _ ] MOTSTEP OR _ }
XENON
LAMP
5r
PHOTO METER
SHUTTER DMM
LIfiHT GUIDES
Fig. 3. Schematic diagram of the experimental arrangement.
155
Photoelectrochemical cells
Illumination. The light source, a 1000 W xenon lamp (Oriel), is fitted with a voltage stabilizer and a water filter to remove excess IR. The lamp spectrum is shown in Fig. 6(a). The monochromator (Joban Yvon) is modified with a geared step motor (one step being equal to 0.1 nm). The setting of the wavelength is controlled from the computer, which also controls the shutter. To increase the flexibility of PEC cell design, the output from the monochromator is focussed Stepmotor Shuffer onto a bifurcated glass fiber light guide, with one 4 Spare Output arm going to the PEC cell, the other to the pho[ontr0tLine'. tometer. The input power density (the light intensity) is Interface obtained as the current output from the photometer (Photodyne 44XL), converted to Px(h) by means of a sensitive curve S(h) provided by the manufacturer (and stored in the computer). The silicon photohead has a long wavelength cutoff where S(h) drops to zero--which might present a problem when working with very narrow band gap materials, but not for the III-V compounds discussed here. (There is also a short wavelength cutoff which in almost most cases is shorter than other limiting parameters and therefore hardly presents a problem.) RE WE [E Electrochemistry. A PAR 173 potentiostat is Fig. 4. Block diagram of the system showing flow of com- used for measurements of photocurrent (at constant mands and data. Single lines: analog, double lines: digital electrode potential) as a function of wavelength of signals. DMM = digital multimeter. illuminating light. In addition, a PAR 175 ramp generator is used for voltammetry experiments with constant wavelength of illuminating light. Motor and control gear for rotating electrode experiments are homebuilt. Electrodes. The experiments discussed here are taken from a larger study of n type III-V semiconductors, either commercial single crystalline GaAs 500 nm or GaP (MCP Electronics) or single crystalline ternary alloys in the series GaAs~_yPv, 0 < y < 1 (prepared at the Department of Solid State Physics, University of Lund, using metal-organic vapour 700 phase epitaxy[6]). Chemicals. All experiments reported here were done in neutral aqueous solution, using potassium hexacyanoferrate as redox couple and potassium 80Onto chloride as auxilliary electrolyte. Triple distilled water was used and all chemicals were p.a. grade.
I
I
++÷
2.o
4. RESULTS AND DISCUSSION
Fig. 5. Current vs. electrode potential under illumination with light of different wavelengths (as marked), and dark current. Photoelectrode: GaAso.87Po.13, reference electrode Pt, electrolyte K4Fe(CN)6 (0. ! M) + KCI (0. I M). Also shown are the working points at different wavelengths.
In Fig. 5 (for an electrode with y = 0.13) the variation of current, iL, vs potential, V, is shown for illumination at four different wavelengths (500, 600,700 and 800 nm). For each of these curves, the working point is located in such a way as to obtain the maximum inscribed rectangle. It is found that the working point potential increases from - 0 . 5 0 V at 400 nm to -0.41 V at 800 nm. (A plausible cause is the decrease in light intensity towards longer wavelength, cf. Fig. 6.) Due to the low intensity of the monochromatic light, the currents of the illuminated cell is of similar
156
P. CARLSSONand B. HOLMSTROM -EpA 3.0
~20
/
o o
l
2.0.
10 1.o. Dark Current
500
600
(a)
700
BOO
660
5oo
~/nm
760
860
-
,
(b)
=
~m
>.
~1.0-
1.0
o o 0.s.
o
c
0.5
8
\ / s00
660
700
\,-. a00
~o ~nm
500
600
700
800
(d)
(e)
~m
Fig. 6. Wavelength dependence of different functions relating to the cell described in Fig. 5. (a) Lamp spectrum. (b) Photocurrent and dark current, at working point potential. (c) Quantum conversion efficiency (based on the photocurrent). (d) "Corrected" quantum conversion efficiency (based on the light current, i.e. the difference between the photocurrent and the dark current). magnitude as the dark current iD, also shown in Fig. 5. At short circuit condition the dark current iV is slightly anodic (0.1 I~A), rendering the photocurrent i~,~ smaller than the light current ist~ by this amount. At the potentials corresponding to the working points at different wavelengths, the dark current is cathodic (0.1 to 0.3 I~A), giving i~'~ larger than i~ p. These problems will be dis-
cussed further below when computing the total conversion efficiencies. The set of curves in Fig. 7 (for an electrode with y = 0.60) gives the wavelength variation of the quantum conversion efficiency as defined by eqn (7), for a number of electrode potentials. In principle, it would be possible to determine -q according to eqn (lla) by integrating along different ~bv(h)
390
582 ,
,
I
I
1 1
,1f / Q5
',
70 Fig. 7. Set of quantum conversion efficiency vs. wavelength plots for 15 different settings of the electrode potential, from -0.4 V (lowest curve) to +0.4 V vs. SCE. Photoelectrode: GaAso.6oPo.4o, electrolyte K4Fe(CN)6 (0.1 M).
Photoelectrochemical cells
157
Table 1. Solar-to-electricity conversion efficiencies calculated according to different equations (cell composition as in Fig. 5) photocurrent
light current
0.075 working point
short circuit + fill factor
0.062*
(0.082)
(0.067)
0.064* (0.070)
0.066 (0.074)
* recommeDded choices Upper values: AMT, lower values
curves for different segments of the h axis. Clearly this is not a very practical approach. Two possibilities remain: (i) to choose one "typical" working point potential, measure +wP(h) for this potential, and compute ~q according to eqn (1 la), or (ii) to measure ~bsc(h) and use eqn (l lb) together with the ~f~ for the chosen wp to compute ~. A further choice to be made is between qbL and ~bp~ (i.e. whether or not to "correct" for the dark current). The lamp spectrum is given in Fig. 6(a). The remainder of Fig. 6 shows measurements on the same cell as used in Fig. 5. The electrode potential, - 0 . 5 0 V vs Pt, is the working point potential obtained form the 500 nm curve in Fig. 5. At this potential, the dark current is cathodic, and the light current is obtained as the difference of the photocurrent and the dark current, both shown in Fig. 6(b). The drop in photocurrent on the long wavelength side reflects the band gap of the photoelectrode, the drop on the short wavelength side is due to light absorption in the electrolyte. The quantum conversion efficiency functions for the two cases are shown in Figs. 6(c) and 6(d). The first one, based on the photocurrent, is a smooth function of h, and can be considered as a correct picture of the ability of the cell to convert light into electricity. The overall solar-to-electricity conversion efficiency for AMI radiation, rl~, is 0.075 when using the photocurrent. As the only current that can be delivered by the cell to an external user is the light current, the latter (and lower) value is the correct one to report as the efficiency of the cell. Under short circuit conditions, the photocurrent curve is similar to that of Fig. 6(b) (although, of course, the values are higher). In this case the dark current is anodic, and the light current is the sum of the photocurrent and the dark current. The quantum conversion efficiency curves are similar to the one in Fig. 6(c). The efficiency values, computed according to eqn (1 lb), are 0.064 (based on the photocurrent) resp, 0.066 (based on the light current). Only the first (and lower) value is a measure of the
(in prantheses):
AM4.
conversion of infalling sun light into electricity, and should be regarded as the efficiency of the cell. The values mentioned (for AMI radiation) are collected in Table I, together with efficiency values calculated for AM4 conditions. Asterisks denote recommended values for describing cell performance. Although most reports to date probably are given for AM1 conditions, we believe that AM4 (or perhaps AM3) values are a better measure of cell performance as averaged over the working day (and year). Methods (i) and (ii) are found to give more or less the same results, so the choice between them is directed by convenience [which probably would turn to method (ii) as the first choice].
Acknowledgements--The work was supported by the Swedish Energy Resource Commission (Efn) and the Swedish Natural Science Research Council (NFR).
REFERENCES
1. E.g., Solar Energy--Photochemical Processes Available for Energy Conversion (Edited by S. Claesson and
2. 3.
4. 5. 6.
B. Holmstr6m). Liber, Stockholm (1982); Supplement I (Edited by B. HolmstrOm) (1983); Photochemical Conversion and Storage of Solar Energy (Edited by J. Rabini). Weizmann Science Press of Israel Jerusalem (1982); Photochemical Conversion and Storage of Solar Energy (Edited by H. Tsubomura). Special issue ofJ. Photochem. 29, 1 (1985). B. Parkinson, On the efficiency and stability of photoelectrochemical devices. Acc. Chem. Res. 17, 431 (1984). (a) M. P. Thekaekara, Solar Irradiance, Total and Spectral, in Solar Energy Engineering (Edited by A. A, M. Sayigh). New York (1977); (b) R. E, Bird, R. L. Hulstrom and L. J. Lewis, Terrestrial Solar Data Sets. Solar Energy 30, 6 (1983). M. D. Archer, Electrochemical Aspects of Solar Energy Conversion. J. AppL Electrochem. 5, 17 (1975). P. Carlsson, B. Holmstr6m, A computerized system for photochemistry with application to solar energy material research. Rev. Sci. Instr. 56, 333 (1985). L. Samuelson, P. Omling, H. Titze and H. G. Grimmeiss, Organic metallic epitaxial growth of GaAsl-xPx. J. Phys. 12, C5-325 (1982).