DOI 10.5162/sensor2013/C8.3
Martin Kasemann 1 , Karola Rühle 1,2 , Leonhard M. Reindl 1
1 University of Freiburg, Department of Microsystems Engineering, 79110 Freiburg, Germany
2 Fraunhofer Institute for Solar Energy Systems ISE, 79110 Freiburg, Germany
Abstract—The design rules for standard outdoor solar cells are not applicable for cells which are used under low lighting conditions and spectra deviating from AM 1.5. This paper will discuss the major influences on cell efficiencies and their impact on the design of photovoltaic cells for energy selfsufficient sensor systems. This is done for different material classes like crystalline silicon, amorphous silicon and III-V materials.
Keywords–energy harvesting; indoor photovoltaics; lowlighting conditions; photovoltaic cells
I.
I NTRODUCTION
Nowadays, solar cells are optimized with respect to the standard test conditions (STC) with the AM 1.5 sun spectrum and an intensity of 1000 W/m 2 . In fact, these conditions are rarely given in outdoor applications [1], [2] and especially not for indoor or low lighting applications.
A commercially available crystalline silicon solar cell with an efficiency of 18% abs efficiencies of less than 5%
at STC may only provide abs
when it is operated at typical indoor intensities [3], [4]. Similar relations hold for other technologies. The lack of dedicated research on optimizing photovoltaic devices has hindered potential improvement so far. This paper describes the main influences on cell efficiencies that have to be taken into account for a future photovoltaic cell optimization.
II.
M AIN INFLUENCES ON CELL EFFICIENCY
A.
Influence of the Spectrum
The main influences on the cell efficiency can be differentiated between spectra- and intensity-dependent influences. The spectra-dependence is given for losses due to thermalization, spatial relaxation and non-absorption.
These losses relate to the energy gap E g
of the material.
Since indoor spectra, for example, contain shorterwavelength radiation, the optimal energy gap shifts towards higher band gaps for indoor lighting (Fig 1).
Fig. 1: Spectra for different light sources. AM 1.5 is the spectrum of the sun through an air mass of 1.5 atmospheres, ESL is an energy saving lamp, LED is a white light-emitting diode.
Efficiency losses due to spectral variations are caused by thermalization and non-absorption. Thermalization losses occur if the electron-hole pair is generated by a high-energy photon with energies much higher than the band gap. The energy difference between the photon energy and the band-gap energy is lost to lattice heat, due to thermalization of the electron-hole pair to the band edges. Non-absorption losses occur if the incident photon energy is lower than the band gap energy. The total losses and the contributions discussed above are plotted in figure
2 for different spectra in dependence off the band gap energy.
1.5x10
19
1.2x10
19
9.0x10
18
6.0x10
18
The rm al iza tion
3.0x10
18 sunlight
No n-Abso rption
6.0x10
18 fluorescence light bulb
4.5x10
18
3.0x10
18
The rm al iza tion
1.5x10
18
No n-Abso rption
0.0
0 1 2 3 4
0.0
Energy gap (eV)
1 2 3 4
Fig. 2: Thermalization (dash-dot) , non-absorption (dot) and total (solid) losses depending on the energy gap of the cell material. [5]
483

DOI 10.5162/sensor2013/C8.3
B.
Influence of the light intensity
The energy conversion efficiency of photovoltaic cell reduces with decreasing light intensity. This is a fundamental effect caused by the thermodynamic principle of detailed balance. The first treatment of such unavoidable losses was performed by Shockley and
Queisser [6]. According to their treatment, the currentvoltage characteristic of a photovoltaic cell is given by the one diode model 𝑗𝑗 𝑉𝑉 = 𝑗𝑗
!
𝑒𝑒𝑒𝑒𝑝𝑝 𝑒𝑒𝑒𝑒
− 1 + 𝑗𝑗
!"
, (II.1) where the diode saturation current density j the band gap of silicon, the values are j
0
is given by the unavoidable radiative recombination rate only and j sc
is obtained with an external quantum efficiency of one. For and j
0
= 5.5 × 10 -16 A/cm 2 sc
= 42 mA/cm 2 [7]
[6]. Those values are never reached in practice because the typical quantum efficiency is between 90 and 95% and the dark saturation current is usually much higher because of non-radiative recombination. Besides that, the one diode model is typically extended by the series resistance R
S
and the parallel shunt resistance.
Fig 3 illustrates the influence of the different parameters in the one diode equivalent circuit model on the power conversion efficiency under realistic conditions for a silicon photovoltaic cell. The full black line corresponds to equation II.1 with the dark saturation current density j
0
= 10 -12 A/cm 2 . In general, the diode behavior reduces the efficiency towards low intensities. In addition, the shunt resistance has a strong influence on the low intensity efficiency, while the series resistance influences the high intensity efficiency (0.1 to 1 sun, corresponding to 0.01 to 0.1 W/cm 2 ). Solar cell designs for low irradiation intensities thus have the opposite optimization rules regarding series and shunt resistance, when compared to standard outdoor cells operating under one sun intensity conditions.
20
15
R p
( Ω cm
2 )
500
5k
50k
∞
R
S
( Ω cm 2 )
0
0.5
1
5
10
10
Similar observations have been made by Randall et al. in experimental measurements on solar cells (Fig 4).
Fig. 4: Measuremements taken by Randall et al. [3] on different types of solar cells.
III.
T HE POTENTIAL OF DIFFERENT TECHNOLOGIES
The world record power conversion efficiency for different technologies are shown in Fig 5. These efficiencies are measured for AM1.5 conditions, which means an intensity of 100 mW/cm 2 . The different colors indicate different technology groups.
26
24
22
20
18
Emitter doping (cm -3 )
1x10 18
5x10
19
1x10 20
16
5
0
10 -4 10 -3 10 -2 10
-3 W/cm
-1 10 -4
Intensity (W/cm 2 )
10 -3 s
= 0.5 Ohm cm 2 . [5] s
10 -2 p
is important in order to achieve adequate efficiencies at
W/cm 2
10 -1
Fig. 4. Simulation of the intensity-dependent efficiencies for a) different R
Focusing on indoor conditions, it is obvious that the value of R
values with R range of R p
= 5 kOhm and R p values with R p
� ∞.
intensities below 10 efficiency at 10 -3 W/cm resistance of 50 k Ω cm 2
2
2 . To achieve at least 10%
and 5% at 10 -4 a parallel
has to be realized. As a consequence the shunting has to be minimized. The influences of different
R s
values on the efficiencies at indoor intensities differ from the influence of R p
. Below an intensity of 10 values any more, but the efficiency still decreases towards lower intensities, which comes from limiting J
-3 W/cm 2 the intensity-dependent efficiency is not influenced by the R s
01
and J
02
terms.
Cell designs with losses due to high series resistances at outdoor intensities, e.g. back contact cells, benefit from indoor intensities.
14
Fig. 5: Research world record efficiencies 2012 (data from NREL).
12
1E-4 1E-3 0.01
Intensity (W/cm
2
) different emitter doping densities.
0.1
The emerging PV technologies, like a quantum dot or
Fig. 5. Simulation of the intensity-dependent efficiencies for
The reduction (increase) of the emitter doping leads to an overall efficiency increase (decrease). The decrease in efficiency with decreasing intensity is caused by the reduction of V oc
. It has to be considered that the reduction of the emitter doping results in an increased series resistance. This increase is realizable for indoor photovoltaic cells as presented in
Fig. 4., but harmful for solar cell efficiencies at high (outdoor) intensities. This allows reducing the emitter doping of photovoltaic cells to achieve higher efficiencies at intensities below 10 -3 W/cm parameters.
2 . The simulated efficiencies are on a high level because of the idealized assumption of the other
D. Recombination in emitter and base
C. Doping of the emitter
To calculate the influence of J
01 diode-model is used again.
on the efficiency, the two-
To investigate the influence of emitter doping on the efficiency at low intensities, the voltage-dependent current density was simulated with PC1D [6]. The simulations were performed for silicon with E g
= 1.124 eV and other relevant material constants for silicon. The base material was 100 µm thick, 1 Ω cm, p-type silicon with no front or rear reflectance and no recombination at the surfaces. The effective bulk lifetime was set to 5000 µs. The depth of the emitter was 1 µm with an error function profile.
In Fig.5, the calculated intensity-dependent efficiencies for different emitter doping densities are shown. For this simulation other parameters as surface recombination velocities, bulk lifetime, series resistance or parallel resistance were assumed to be ideal.
20
18
16
14
12
10
8
6
4
2
J
01
(A/m 2 )
1x10
-9
5x10 -9
1x10
-8
5x10
-8
1x10 -7
5x10
-7
0
10 -4 10 -3 10 -2
Intensity (W/cm 2 )
10 -1
Fig. 6. Simulation of the intensity-dependent efficiencies for different J
01
values.
In Fig. 6., the influence of different J
01
values is shown; the other parameters, R the efficiency decreases with increasing J decreasing intensity. The efficiency increases by 2% abs decrease of J
01 s
, R p
and J
02
, are ideal. It can be seen that
01
value and
with a
by one order of magnitude. This decrease is

technologies show a quite weak efficiency drop towards low intensities, efficiencies in this intensity range are between zero and 5%. A further deficiency of this technology type is still the low long-term stability of the materials used.
The class of next higher efficiencies is amorphous thinfilm technologies, like amorphous silicon or CIGS. Cells in this technology group show record efficiencies between
10 and 20%. These technologies are already industrially established. However, the record efficiency for industrially available CIGS cells is still only around 12%. At least in the measurements shown in Fig. 4, the CIGS cells show a weak shunt, limiting the low intensity efficiency to values below 5%. Whether processes exist that avoid this shunting is unclear.
Crystalline silicon solar cells form a class of record efficiencies between 20 and 25% at one sun. Silicon solar cell processing is industrially well established and very cheap. Typical industrial cells, however, show a strong decrease towards low efficiencies (eg. Fig 4). This is due to an unoptimized shunt resistance in the order of 5 kΩ that is typically sufficient for outdoor use, but not for low intensity applications. It has, however, been shown [8] that such shunts can be avoided with rather simple measures, leading to experimentally demonstrated efficiencies in the order of 16% at 1 W/m 2 . Flexible silicon solar cells have also been demonstrated with high efficiencies [9].
The highest record efficiencies are reached by cells made from III-V materials. They range from 29% for a single junction cell up to 43.5% for a multi-junction cell.
From the pure efficiency point of view, cells from this materials would be considered best for small-area application at low intensities. However, the area price for this class is so high that widespread application in sensor systems is seen as unlikely. Multi-junction cells have complex requirements regarding the current matching between the different junctions which limits their applicability under varying spectral conditions.
IV.
C ONCLUSION AND OUTLOOK
Solar cells for energy harvesting applications need to be optimized with respect to their spectral response and their low intensity efficiency. Shunting and other parasitic currents in parallel to the diode need to be avoided for a good low-intensity performance. Although the band gap of silicon is not optimized for many indoor lighting spectra, the overall high efficiency and the low price of this technology makes them very feasible for energy harvesting. This holds even more if a flexible application indoors as well as outdoors is intended. Our further research is therefore focused on the improvement of silicon photovoltaic cells in the low intensity range. A concept allowing for industrial large-scale production of such optimized cells will be developed.
DOI 10.5162/sensor2013/C8.3
A CKNOWLEDGMENT
The authors gratefully acknowledge the financial support of the German Research Foundation (GRK 1322).
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