Analyzing Carrier Escape Mechanisms in InAs/GaAs Quantum Dot
p-i-n Junction Photovoltaic Cells
Supporting Information
Sample Growth
GaAs solar cells incorporating InAs quantum dots were grown by metal-organic vapor
phase epitaxy (MOVPE) at NASA Glenn Research Center (GRC). The device consisted of a p-in design with a ~195 nm i-region, incorporating InGaP2 front and back surface fields. Specifics
on device structure have been described in more detail elsewhere. 1 Ten repeat units of a
periodic QD superlattice were grown centered in the i-region, buffered on both sides by intrinsic
GaAs. The QD repeat unit consisted of: first intrinsic GaAs layer, followed by the InAs QDs
grown by the Stranski-Krastanov method, an intrinsic GaAs capping layer, and finally a GaP
strain compensation layer.2 QD diameters, heights, and densities were approximately 20nm,
2nm, and ~5x1010 cm-2, respectively, as measured from test structures grown with uncapped
surface QDs and analyzed with atomic force microscopy,
Cells were fabricated using standard photolithographic techniques, and a wet chemical
mesa etch to isolate and define active areas of 1 cm2. Metallization was applied through a
thermal evaporation and lift-off process, using Au/Ge/Ni/Au for n-type contacts, and Au/Zn/Au
for p-type. Anti-reflective coatings were not used in this study; contact grid shadowing was
approximately 4%.
Experimental Diagram
Figure S1. Diagram of the experimental setup for photocurrent measurements under sub-band
gap illumination.
Current-Voltage Measurements
2
Current (mAmp/cm )
0.20
0.15
0.10
I-V scan, 350mW 1.17eV
I-V scan, 350mW 1.17eV + 625mW 0.80eV
Single-Shot, 350mW 1.17eV
Single-Shot, 350mW 1.17eV + 625mW 0.80eV
0.05
0.00
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Volatge (V)
Figure S2. I-V data under 70mW 1064nm illumination (red) and 350mW 1.17eV + 625mW
0.80eV illumination (black) taken as voltage scan or a single-shot reading at -1.0V, -0.5V, 0.0V,
and 0.5V.
Current–voltage (I–V) curves were measured using a Keithley 2400 source measure unit.
The photocurrent was measured under 1.17 eV (or 0.80 eV) CW laser illumination with powers
ranging from 5 mW to 1125 mW depending on the experiment. For illumination with 1.17 eV +
0.80 eV light, the 1.17 eV and 0.80 eV laser beam paths are aligned collinearly and focused on to
the sample with an off-axis parabolic mirror. I-V curves were measured by scanning the voltage
from -1.0 V to 1.0 V. Single-shot photocurrent measurements at a fixed voltage were taken using
a mechanical shutter timed such that photocurrent measurements were made within a few
milliseconds after the shutter opened to permit sample illumination. In all cases the measurement
was taken first under 1.17 eV illumination then repeated with the addition of the 0.80 eV laser
illumination.
The CW 0.80 eV laser had insufficient energy to promote carriers from the valence band
to the discrete states of the quantum dots. Consequently, 0.80 eV photons can only be absorbed
through the promotion of carriers from the quantum dot or conduction band edge to states higher
in the continuum conduction band. Effective mass approximation calculations suggest that the
absorption coefficient for bound to continuum transitions in InAs/GaAs QDs falls off rapidly as
the photon energy exceeds the value necessary to promote carriers to the GaAs band edge.3,4
Regardless of the absolute absorption coefficient for 0.80 eV photons, the number of incident
photons and thus the number of promoted carriers is linear with the laser excitation power.
We observe that single-shot photocurrent measurements at the respective applied voltages
do not overlay with the photocurrent in the I-V scan at the respective voltage. For example, for
1.17 eV illumination under 0.0 V the single-shot photocurrent reading is 4.6 μAmp/cm2 less that
the scanned photocurrent at the same voltage. This disagreement is amplified when additional
intensity of the 0.80 eV laser is added. We also note that the disagreement between single-shot
and I-V measurement increases as the voltage is scanned from -1.0 V to 1.0 V. We hypothesized
that the disagreement arises from sample heating during the I-V scan. The voltage scan takes 20
seconds to scan from -1.0 V to 1.0 V, thus the sample has been illuminated for a longer length of
time at 0.0 V than -1.0 V. We correlate the artificial increase in photocurrent with sample heating
below. All measurements presented in the manuscript are obtained under single-shot excitation
conditions where sample heating is not an issue.
Sample Heating Experiments and Discussion
As a means to attribute the artificial increase in photocurrent to localized sample heating
from laser illumination, we take single-shot current readings as a function of illumination time
(shown Figure S3). Sample illumination was with 350 mW/cm2 1.17 eV and 625 mW/cm2 0.80
eV light. For simplicity the experiment was done under short-circuit conditions only. The
photocurrent increased significantly with illumination time from 0 to 30 seconds then slightly
after that until leveling off. The total change in photocurrent was 33.5 μAmp/cm2. The inset will
be discussed below.
0.230
0.0V
0.225
0.120
2
Current (mAmp/cm )
0.220
0.215
Sample was heated for 60 seconds
2
Current (mAmp/cm )
0.118
0.210
0.205
0.200
0.116
0.114
0.112
0
100
0.195
0
50
100
150
200
300
Time (seconds)
200
250
400
500
300
Time (seconds)
Figure S3. Single-shot photocurrent readings at 0.0 V taken as a function of 350 mW/cm2 1.17
eV and 625 mW/cm2 0.80 eV illumination time. Inset, single-shot photocurrent readings taken as
a function of time following sample illumination for 60 seconds.
It is practical to assume that under high-intensity fluences and small illumination area
that sample heating would impact the accuracy of the photocurrent measurement. We confirm
our assumption by indirectly measuring a localized lattice temperature (T) as a function of subbandgap illumination time. We do this by measuring electroluminescence from the lowestenergy transition of GaAs and using the well-established Varshni equation, which correlates T
with bandgap (BG) energy.5 Under 1.10 applied bias, strong electroluminescence from the GaAs
band edge is observed (Figure S4a). We use the GaAs electroluminescence band to determine
and then monitor the BG energy while the sample is being illuminated with sub-BG light.
Wavelengths of 1.17 eV and 0.80 eV are not energetic enough by themselves to directly excite
GaAs (only the embedded InAs quantum dots).
Figure S4b-d shows electroluminescence measurements for several sub-BG illumination
intensities. Electroluminescence spectra were taken using a Princeton Instruments liquid nitrogen
cooled CCD coupled with a SpectraPro2750 spectrometer. Measurements were taken are a
function of sub-BG 1.17 eV and 0.80 eV illumination time at three different intensities (Fig. S4b
= 200 mW/cm2 1.17eV and 200 mW/cm2 0.80 eV; Fig. S4c = 400 mW/cm2 1.17eV and 400
mW/cm2 0.80 eV; Fig. S4d = 350 mW/cm2 1.17eV and 625 mW/cm2 0.80 eV). The CCD
integration time was 0.20 seconds for all spectra. Electroluminescence spectra in the absence of
any sub-BG illumination are shown in black for comparison. Measurements taken at time zero
upon sub-BG illumination (navy line, Fig. S4b-d) show a negligible red-shift compared to the
spectrum with no sub-band gap illumination. The BG of a semiconductor is known to shift to a
lower-energy when the T of the lattice is increased. Thus the absence of a red-shift in the
electroluminescence spectrum at time zero illumination indicates a negligible T change. For all
sub-BG intensities a red-shift in the electroluminescence spectra was observed when the
illumination time increased. The magnitude of the red-shift increased with increasing
illumination intensity (1.2 to 2.1 nm red-shift). The red-shift saturates (discontinues red-shifting)
between 16 and 24 seconds for all illumination intensities with the exception of the lowestenergy intensity (200 mW/cm2 1.17eV & 200 mW/cm2 0.80eV) which saturates between 24 and
32 seconds. We believe that the saturation in red-shift corresponds to the point when the lattice
reaches thermal equilibrium under the illumination conditions. Under illumination intensities
identical to photocurrent measurements taken as a function of illumination time (Fig. S3), the
saturation time shown in Figure S4d is in good agreement with the ~30 second photocurrent
saturation shown above. We correlate the magnitude of the electroluminescence red-shift with a
change T using the Varshni Equation.5 The Varshni equation for T dependence of semiconductor
BGs is
𝛼𝑇 2
𝐸𝑔 (𝑇) = 𝐸𝑜 − 𝑇+𝛽
(1)
where Eg is the BG energy at a given T, Eo is the BG at room temperature, and α and β are fitting
parameters characteristic of a given material.6 We calculate a 4.4°C, 7.3°C, and 7.7°C increase in
the lattice T for illumination intensities used in figures b, c, and d, respectively. The T change
increases with increasing illumination intensity. While the change in lattice T is not drastic, it
does confirm that (1) the observed increase in photocurrent as a function of time, and (2) the
inconsistency between I-V scanned photocurrent and single-shot photocurrent measurements is
due to localized sample heating resulting from sub-BG illumination. Building on this conclusion
we realize that sample heating could complicate our analysis of competing carrier escape
pathways by potentially changing in the rate of thermal escape of carriers from the intermediates
states. Thus, all photocurrent data presented in this manuscript are taken using single-shot
measurements to avoid sample heating.
The inset in Figure S3 displays the photocurrent recovery time following sample
illuminations. This was done to ensure that an increase in T was not building with sequential
single-shot measurements. The sample was illuminated with 350 mW/cm2 1.17 eV and 625
mW/cm2 0.80 eV light for 60 seconds, turned off, then at a given time another single-shot
measurement was taken. This was repeated, for time intervals from 0 to 500 seconds. The
photocurrent decreased dramatically from 0 to 50 seconds before leveling off at 0.228
mAmp/cm2 indicating that the photocurrent was fully recovered within 60 seconds. The singleshot measurements presented in this manuscript the sample was illuminated for ~1 millisecond,
drastically different than the 60 second high-intensity illumination time presented in Figure S3
inset. However the recovery time data provides us an upper limit, such that single-shot
illumination measurements taken 60 seconds apart are guaranteed to be each at thermal
equilibrium irrespective of illumination intensity.
Bias Mapping of Sample Electroluminescence
560.0
752.7
945.3
1138
1331
1523
1716
1909
2101
2294
2487
2679
2872
3065
3257
3450
850
Wavelength (nm)
875
900
925
950
975
1000
1025
0.90
0.95
1.00
1.05
(b)
Normalized Intensity
(a)
825
No Illum.
0 sec
2 sec
4 sec
8 sec
16 sec
24 sec
32 sec
45 sec
60 sec
1.0
PL Intensity
V: -1.0V to +1.0V // exposure: 0.5s
0.8
0.6
2
0.4
The red-shift saturates at 24 seconds
Red-Shift: ~ 1.2 nm
Red-Shift after 2 seconds: ~0.2 nm
860
1.10
865
870
0.8
0.6
0.8
0.6
2
0.4 The red-shift saturates at 16 seconds
Red-Shift: ~ 2.0 nm
Red-Shift after 2 seconds: ~0.7 nm
870
885
No Illum.
0 sec
2 sec
4 sec
8 sec
16 sec
24 sec
32 sec
45 sec
60 sec
(d)
2
0.4 The red-shift saturates at 16 seconds
865
880
1.17: 350mW/cm ; 0.80: 625mW/cm
2
1.17: 400mW/cm ; 0.80: 400mW/cm
860
1.0
Normalized Intensity
Normalized Intensity
No Illum.
0 sec
2 sec
4 sec
8 sec
16 sec
24 sec
32 sec
45 sec
60 sec
(c)
2
875
Wavelength (nm)
Applied Voltage (V)
1.0
2
1.17: 200mW/cm ; 0.80: 200mW/cm
Red-Shift: ~ 2.1 nm
Red-Shift after 2 seconds: ~0.9 nm
875
Wavelength (nm)
880
885
860
865
870
875
880
885
Wavelength (nm)
Figure S4. (a)Bias mapping of sample electroluminescence (0.85 V to 1.10 V; no sub-bandgap
illumination). (b-d)Electroluminescence from the lowest-energy transition of GaAs measured as
a function of sub-bandgap illumination time (+1.10 V applied bias, 0.20 second CCD integration
time). Sub-bandgap illumination intensities were (b) 200 mW/cm2 1.17eV and 200 mW/cm2 0.80
eV, (c) 400 mW/cm2 1.17eV and 400 mW/cm2 0.80 eV, (d) 350 mW/cm2 1.17eV and 625
mW/cm2 0.80 eV.
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