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Observation of photon recycling in strain-balanced
quantum well solar cells
D. Johnson, I. Ballard, A. Bessière, K. Barnham, J.P. Connolly, M. Mazzer,
C. Calder, G. Hill, J.S. Roberts
To cite this version:
D. Johnson, I. Ballard, A. Bessière, K. Barnham, J.P. Connolly, et al.. Observation of photon recycling
in strain-balanced quantum well solar cells. Applied Physics Letters, American Institute of Physics,
2007, 90 (21), pp.213505. �10.1063/1.2742334�. �hal-02927569�
Observation of Photon Recycling in Strain-Balanced Quantum Well Solar Cells
D.C. Johnson
1
, I.M. Ballard
1
, A. Bessière
2
, K.W.J. Barnham
1
, J.P. Connolly
1
,
M. Mazzer
1
, C. Calder
3
, G. Hill
3
, J.S. Roberts
3
1
Experimental Solid State Physics, Blackett Laboratory, Imperial College London,
SW7 2AZ, UK,
2
1LECA (UMR 7575 CNRS), Ecole Nationale Supérieure de Chimie de Paris, 75005
Paris
3
EPSRC National Centre for III-V Technologies, University of Sheffield, Mappin
Street, Sheffield S1 3JD, UK
Photon recycling in strain balanced quantum well solar cells grown on distributed
Bragg reflectors has been observed as a suppression of the dark current and a change
in electroluminescence spectra. Comparing devices grown with and without
distributed Bragg reflectors we have demonstrated up to a 33% reduction in the
ideality n = 1 reverse saturation current. Furthermore, to validate the observations we
demonstrate how both the measured dark currents and electroluminescence spectra fit
very well to a photon recycling model. Verifying our observations with the model
then allows us to calculate optimised device designs.
Strain-balanced quantum well solar cells (SB-QWSC) have exhibited
efficiencies similar to GaAs p-n devices [1] and are proving to be a viable path to
achieving efficiencies beyond the long-standing GaAs single junction world record
[2]. Growing strain balanced quantum wells in the intrinsic region of a GaAs p-i-n
solar cell increases the short-circuit current (J
SC
), due to the lower absorption
threshold energy in the well. The increase in J
SC
exceeds the reduction in open-circuit
voltage (V
OC
) provided the compressively strained InGaAs wells are balanced by the
tensile strained GaAsP barriers [1]. Further efficiency enhancement has been achieved
by growing the devices on a distributed Bragg reflector (DBR) such that incident
photons, which are not absorbed by the device initially, are reflected back into the
device. The second pass absorption further increases J
SC
[3]. Another benefit of
growing SB-QWSCs on a DBR substrate, as we report here, is that the device dark
current is suppressed when compared to devices grown on GaAs substrates.
Reduction in dark current is only observed when the device is operating in a regime
where radiative recombination is the dominant recombination mechanism [4]; this
behaviour is indicative of photon recycling (PR) or photon self-absorption effects. In
this letter we will present experimental and theoretical evidence of PR in SB-QWSCs.
PR occurs when photons that are emitted from a semiconductor device are
subsequently re-absorbed. Considering that this process may occur several times for a
single photon, the effect is often observed experimentally as an increase in the
minority carrier lifetime [5, 6]; therefore, one can also expect to observe PR as a
reduction in the dark current. Dumke [7] was one of the first to describe PR
quantitatively while more recently Asbeck’s photon recycling factor [8] has been used
widely both theoretically and experimentally. Evidence of PR has been readily
demonstrated in semiconductor devices such as double-heterostructures [9, 10] or
light emitting diodes (LED) [11-13], whereas, results from solar cells have been rather
more elusive [14]. Patkar et al [15] were one of the only groups to demonstrate PR as
a reduction of the dark current, however, this was in LEDs rather than solar cells.
Here we present the first direct evidence for dark-current reduction due to PR in solar
cells and confirm this through the observation of changes in the electroluminescence
(EL) spectra.
Results presented here have been observed in devices with three different SB-
QWSC designs (referred to as Design 1, 2 and 3) which vary only in the number and
depth of the quantum wells. Each SB-QWSC device design was gown on both a DBR
and a GaAs substrate for comparison. To ensure that the wafers with and without
DBRs were grown in as similar conditions as possible a pre-grown DBR wafer and a
n-type GaAs substrate were placed down- and up-stream, respectively, in the metal
organic vapour phase epitaxy (MOVPE) reactor and both overgrown in the same gas
flow. The quantum wells are grown with alloys of In
X
Ga
1-X
As from x = 0.11 to x =
0.22 and the barriers are grown with alloys of GaAs
y
P
1-y
where y = 0.91. The DBRs
were grown using alternating layers of material with low (Al
0.8
Ga
0.2
As) and high
(Al
0.13
Ga
0.87
As) refractive indices. The DBR layer thicknesses were designed to
maximize absorption of normal incident light by the quantum wells. To reduce the
series resistance presented by the DBR, intermediate layers of Al
0.5
Ga
0.5
As are grown
between each DBR layer. Further details of the DBR design can be found in Ref 3.
Devices were processed into fully metalised, 800um diameter, mesa structures
for dark current characterization as well as concentrator devices with 3.7mm diameter
mesas and 11% metalisation [16] for EL characterisation. Fully metalised devices are
used such that series resistance effects on the ideality n = 1 behaviour of the devices
can be kept to a minimum while operation under illuminated conditions can still be
predicted [17]. All devices were grown and processed at the EPSRC National Centre
for III-V Technologies.
A computer controlled Keithley 238 SMU was used to measure the dark
current response of the fully metalised devices. Measurements were made using the
four point method and pulsed current sourcing to reduce heating. All measurements
were taken at 25° C using a Peltier cooled stage. The measurements made in the high
current region of 20 control and DBR devices of Design 2 are presented in Fig.1 The
measurements were subsequently fit to a two exponential model, based on the ideal
Shockley diode equation [18], shown below:
)/()(
02
)/()(
01
21
TknRJVqTknRJVq
ss
eJeJJ
⋅⋅⋅−⋅⋅⋅⋅−⋅
⋅+⋅=
(1)
where J
01
and J
02
are reverse saturation currents, n
1
and n
2
are ideality factors, V is the
applied bias, R
S
is the series resistance, k is the Boltzmann constant and T is the
temperature. For the purposes of fitting, the ideality factor n
1
is fixed at 1. The first
term in eqn. 1 dominates at high bias and corresponds to quantum well radiative
recombination, which we have shown to be more important than the ideal Shockley
recombination in the field-free p and n regions [4]. The ideality n
2
in the second term
is fit to a value of ~ 2 which corresponds to non-radiative Shockley-Read-Hall (SRH)
recombination.
By fitting the measured data to eqn 1 we obtain values for J
01
, J
02
, n
2
and R
S
.
The average J
01
and J
02
values obtained by fitting results on ~ 15 devices for each
design are listed in Table I. The ideality n = 1 reverse saturation current (J
01
) obtained
from the fit is reduced by >25% for all three device designs and by 33% for Designs 1
and 3. The latter reduction would result in absolute efficiency enhancement of ~0.3%
at concentration levels of ~500x entirely due to PR as a result of the DBR substrate.
One can see that while J
01
for the DBR cell is reduced compared to the control in all
cases, the non-radiative contribution J
02
is largely unchanged for Designs 1 and 2; the
third design exhibited irregular behaviour in the ideality n ~2 region, which is why the
J
02
values could not be fit.
To validate the observed reduction in the J
01
reverse saturation current a
photon recycling model has been developed. The EL spectra and, therefore, dark
current are calculated using the method outlined in Refs [19, 20]. The net photon flux
exiting the surface of a semiconductor device can be described using the generalised
Planck equation for a non-black body. Integrating the photon flux density over
energy, one can obtain the radiative dark-current for a given bias or quasi-Fermi level
separation. This method requires calculation of device absorptivity. The absorptivity
of an arbitrary device design is calculated using a complex refractive index which is
calculated from an experimental quantum efficiency and device thickness. The
resulting refractive index is then used along with the matrix method [21] to calculate
the absorptivity of a stack of thin films including anti-reflection coatings, the window
layer, active layer and DBR. This method takes into account multiple passes of
photons and interference effects in the structure; these effects are important to
consider in SB-QWSCs since the quantum wells have relatively low absorptivity,
which can result in multiple reflections before emitted photons are re-absorbed. All
calculations are done using the low-AOD spectrum (913W/m
2
) while assuming ideal
behaviour with zero series resistance and 5% optical shading.
EL spectra are measured by driving devices into forward bias using a Keithley
238 source measure unit (SMU); while maintaining the device at 25° C using a Peltier
cooled stage. The resulting emission spectrum is measured using a computer
controlled charge-coupled device. Fig. 2 shows a comparison between the resulting
measured EL spectrum and the modeled spectrum of a SB-QWSC grown on a DBR
(Design 1). In both the measured and modeled spectrum one can see the distinct
Fabry-Perot oscillations in the emission and that the results from our model fit the
experiment quite well. By integrating the EL spectrum over energy we are also able to
calculate the expected radiative contribution to the device dark current. Fig. 1 shows
both the measured dark currents for the control and DBR devices of Design 2 as well
as the predicted radiative contribution to the dark current as calculated from our
model. The reduction of the dark current is evident in both the measurements and the
calculated values from our model. Table I compares the calculated reverse saturation
currents with the average measured parameters for all three designs. One can see that
the model quite accurately describes the ideality n = 1 component of the measured
dark currents in both relative and absolute terms.
Given close agreement between the model and experiment we have calculated
DBR designs in an effort to achieve the highest overall device efficiency. As we have
seen previously, a DBR can enhance the J
SC
of a SB-QWSC considerably [3].
Similarly, we have shown here that a SB-QWSCs grown on a DBR benefits from an
increase in V
OC
due to PR. However, to increase both J
SC
and V
OC
it is desirable to
maximise the DBR optical “stop band” magnitude and width while reducing the
angular dependence of the reflectivity. Given the DBR material (Al
1-X
Gas
X
As) and
series resistance limit imposed on the number of DBR periods, the DBR reflectivity
can be optimised in one of two ways - growing multiple DBRs with varying stop band
wavelengths and growing chirped DBRs (CDBR) [22].
Using the model, we calculated the efficiency of a 50 shallow quantum well
CDBR (20½ period 1% chirp) SB-QWSC at 350x concentration while varying the
initial thickness of the DBR layers. One can see in Fig. 3 that there are two distinct
efficiency maxima. The bottom left (indicated by the letter A) corresponds to a DBR
optimised to reflect normal incident photons of energies which are readily absorbed
by the quantum wells and so the efficiency enhancement is primarily due to an
increase in J
SC
. On the other hand, the peak at the bottom right of the plot (indicated
by the letter B) corresponds to a DBR which primarily reflects photons of energies
which are absorbed by the quantum wells at off-normal incidence resulting in PR. The
critical angle for photons to escape from the GaAs-Air surface is ~16 degrees and so
any photons emitted towards the front surface at an angle greater than this will be
reflected back into the device. If the reflected photons are not re-absorbed by the
quantum wells, they may also be reflected at the back of the device by the off-normal
incidence reflectivity of the DBR. Therefore, photons emitted outside of the GaAs-Air
escape cone may then be re-absorbed by the quantum wells and thus result in a
reduction of the device dark current. By designing a device with two 10½ period 1%
chirped DBRs each of which is designed for one of the peak efficiencies in Figure 3,
the calculated device J
SC
and V
OC
values were both enhanced. Table II summarises the
results of calculated efficiencies for devices 50 well SB-QWSC devices grown with
no DBR, and grown on CDBRs optimized for V
OC
, J
SC
, and both. An further increase
in efficiency can be realised by growing the SB-QWSC on two CDBRs with different
reflectivity.
In conclusion PR in SB-QWSCs has been demonstrated in both the dark
current and the EL for the first time in a solar cell. Both effects are also well described
by a model based on radiative recombination. We have also demonstrated that PR can
have a considerable impact on the overall conversion efficiency of a SB-QWSC. We
