Structure Model and Analysis Method

Figure 5.6(a)

shows a schematic configuration of the proposed structure. The three lattice-matched subcells of the triple-junction solar cell from top to bottom in order are the InGaP, GaAs, and Ge subcells, grown on the p-type Ge substrate by low-pressure metal-organic chemical vapor deposition (MOCVD). Trimethyl sources of aluminum, gallium and indium were used as group-III precursors, and arsine and phosphine were used for the group-V reaction agents. Silane (SiH4) and diethylzinc (DEZn) were used as the n-type and p-type dopant sources, respectively. The InGaP and GaAs subcells are connected to each other by a p-AlGaAs (p=4×10²⁰ cm^-3, 20 nm)/n-InGaP (n=1×10²⁰ cm^-3, 20 nm) tunnel junction, whereas the GaAs middle subcell is connected to the Ge bottom subcell by a p-GaAs (p=6×10¹⁹ cm^-3, 30 nm)/n-GaAs (n=1×10²⁰ cm^-3, 30 nm) tunnel junction. Silver was chosen as the metal electrodes for both the front and backside contacts. The chip size of the individual cell is designed to be 1 cm × 1 cm.

The CdSe QDs are dispensed onto the top AlInP-window layer by spin-cast that covers the metal electrode (further details of the CdSe QDs synthesis procedure is reported in our previous work [5.14]). The sample was dropped by a fixed volume (125 μL) of colloid QDs with different concentrations in toluene solution, and spin-cast at 2500 r.p.m for 10s to dispense CdSe QDs. The undergone sample then stood for 1 minute in the fume hood in the ambient conditions to evaporate toluene for the subsequent light current density vs. voltage (J-V) measurements. The device’s performance was characterized by an Oriel Sol3A solar simulator. The J-V characteristic was obtained using a Keithley 2400 multi-meter in four-wire sensing mode to eliminate the resistance contribution from the probes and the contact resistances.

Fig. 5. 6 (a) Schematic plot of an InGaP/GaAs/Ge triple-junction solar cell with CdSe QDs spread on the top surface to tailor the solar spectrum and enhance the photocurrent of the GaAs middle subcell. (b) Simplified structure of the tandem solar cell to facilitate optical calculations.

To systematically analyze the dependence of the QD’s dimension on the device’s efficiency, we developed a simple model based on the fundamentals of material optics that simulates the energy distribution of the solar spectrum converted by CdSe QDs on each individual subcell. As a result, the power conversion efficiency of the device with CdSe QDs of different sizes can be quantitatively determined and compared. The solar cell device [Fig. 5.6(a)] was simplified as an InGaP/GaAs/Ge multi-stacking layer to facilitate the optical calculation, as shown in

Fig. 5.6(b). The p-type and n-type active

regions are combined as a single layer, and the metal electrode on the top surface is neglected. The solar light was normally incident from the top surface down through the whole device. The optical dispersion is also considered by applying the wavelength-dependent refractive index and the extinction coefficient on each subcell [5.15], [5.16]. As it is well known that the energy bandgap of the QDs is mainly dominated by the diameters, the incident spectrum and radiative intensity of solar light

inside the device can hence be tailored. As shown in

Fig. 5.6 (b), the solar light is

incident on the CdSe QDs, and the high-energy regime of the solar light was partially absorbed by the QDs and re-emitted as radiation with photon energies matching the CdSe QDs’ energy bandgap. Therefore, by applying CdSe QDs with the proper diameters on the top of the tandem solar cell, the tailored solar spectrum combining the rest of solar light with the radiation of CdSe QDs is well-suited to generate more photocurrents for the current-limiting subcell (i.e., the smallest photocurrent among the three subcells) and hence promotes the overall power conversion efficiency of the device. The formula for the incident intensity I0i

and the transmitted light intensity I

0t

can be expressed as follows:

Here, A denotes the absorbance of the CdSe QDs, which can essentially be determined by measuring the absorption spectrum [5.17], and I0i

and I

0t indicate the intensity inside the CdSe QDs. The CdSe QDs’ absorbance can also be defined as follows:

0

0

(ln10) A

  L ^

(5. 2)

where α0 and L0 are the absorption coefficient and the layer thickness of the CdSe QDs, respectively. By considering the optical reflection at the interface between the air and the CdSe QDs, the incident intensity of solar light inside the top of the CdSe QDs is

spectrum [5.18] and nair and nQD are the refractive indices of the air and the CdSe QDs, respectively. Restated, the CdSe QDs absorb the high-energy regime of the incident solar light and re-emit radiation with an energy intensity IPL that is equivalent to the QDs’ band-gap energy, which can be directly acquired by the photoluminescence (PL) measurement. Therefore, by considering the optical conversion of the CdSe QDs and the optical reflection at the dot-InGaP interface, the incident intensity of the solar light inside the top surface of the InGaP subcell can be described as follows:

1_i 0_t (1 1) _PL 0_i 10 ^A (1 1) _PL

I  I   R  I  I 

^

  R  I

(5. 4)

Again, R1 is the optical reflection at the dot-InGaP interface and is defined as

R₁=

(

(n_QD-n_InGaP) / ((n_QD+n_InGaP)

)

^{2, where nInGaP} is the refractive index of the InGaP subcell.

The incident intensity of the solar light I1i is attenuated to I1t as the light travels through the InGaP subcell with a thickness of L1: incident intensities I2i and I3i inside the top surface of the GaAs and Ge subcells can be written as follows:

where R2 and R3 are the optical reflections at the InGaP/GaAs and GaAs/Ge interfaces, respectively, and can also be determined by their wavelength-dependent refractive indices, as illustrated in Eq. [(5.3)]. α2 and L2 are the absorption coefficient and the cell thickness of the GaAs subcell, respectively. Consequently, the optical absorption

(1,2,3)( )

A



of each subcell can be determined by the difference between the incident and transmitted light intensities inside the subcell:

(1,2,3)( ) (1,2,3)_i (1,2,3)_t (1,2,3)_i (1 exp [ (1,2,3) (1,2,3)])

A   I  I  I     L

(5. 7)

where the subscripts 1, 2, and 3 stand for the InGaP, GaAs, and Ge subcells, respectively. To calculate the power generation efficiency of each subcell, we assume that each absorbed photon with an energy larger than the subcell’s band-gap energy generates an electron-hole pair and consider the quantum efficiency of each subcell

(1,2,3)( )

QE



. Therefore, the short-circuit current density J_(1,2,3) versus applied voltage of each subcell is expressed by the sum of the photon-generated current minus the intrinsic current generated by radiative recombination as follow [5.19]:

 

subcell. By substituting the proper values of

I

_(1,2,3)iand_{QE(1,2,3)( )}

_

, we can immediately estimate the J-V characteristics of each subcell. Hence, the dependence of the CdSe QD’s size on the power conversion efficiency of the InGaP/GaAs/Ge triple-junction solar cell can also be determined. This calculation also helps us to determine the dimension of the CdSe QD that optimizes the power conversion efficiency.

5.3 Results and Discussion

Figure 5.7 shows the measured (a) absorbance and (b) PL spectra of CdSe QDs of

different sizes in toluene. Accordingly, the reduced dimensionality of the CdSe QDs

Fig. 5. 7 (a) Absorption and (b) photoluminescence spectra of CdSe QDs of different sizes in toluene.

exhibits quantization of electronic energy levels, and consequently, a blue shift of the optical absorption edge occurs. The optical absorption edge shifts from ~700 nm to

~500 nm as the diameters of the CdSe QDs decrease from D=6.6 nm to D=2.1 nm. At a given diameter, the optical absorption increases as the emitting wavelength of the excitation source decreases. Similarly, the main peak of the CdSe QD emission is blue-shifted as the diameters of the CdSe QDs decrease. The main PL peaks of λpeak=640 nm, λpeak=610 nm, λpeak =590 nm, λpeak =560 nm, λpeak =520 nm, and λpeak

=480 nm were observed at CdSe QD diameters of D=6.6 nm, D=5.0 nm, D=4.2 nm, D=3.3 nm, D=2.5 nm, and D=2.1 nm, respectively. Additionally, all of the PL intensity exhibits a similar full width at half maximum of FWHM=32 nm. The above observations are direct evidence that CdSe QDs demonstrate wavelength conversion for incident photons and that the conversion interval is mainly dominated by the diameters of the QDs.

Fig. 5. 8 Calculated light intensity of the solar spectrum I(1,2,3)i(λ) distributed on each subcell for the device (a) without and (b) with CdSe QDs with diameters of D=2.1 nm. The quantum efficiency QE(1,2,3)(λ) of each subcell is also plotted in the figure.

By substituting the absorbance and the PL intensity measured above into Equations (4)−(6),

Fig. 5.8 plots the calculated light intensity of the solar spectrum I

(1,2,3)i

(λ) distributed on each individual subcell for the device (a) without and (b) with

CdSe QDs with diameters of D=2.1 nm. The quantum efficiency of each subcell

QE

(1,2,3)

(λ) was also plotted in the figure and will be employed with I

(1,2,3)i

(λ) to derive

the J-V characteristic of the device by Eq. [(5.8)]. In this case, the CdSe QDs mainly convert the ultraviolet light into visible light, and hence, the peak intensity of I1i (λpeak

=480 nm) is even stronger than that of the original solar spectrum. Additionally, the InGaP subcell exhibits the highest QE response to the incident wavelength of ~500 nm.

We therefore expect that applying CdSe QDs with diameters of D=2.1 nm primarily enhances the photocurrent of the InGaP subcell. The light intensities of the solar spectra on the GaAs and Ge subcells are also enhanced because the CdSe QDs provide an additional functionality as an antireflection coating for light trapping of the solar light [5.20].

Fig. 5. 9 Calculated J-V characteristics of each subcell by Eq. [(5.8)] for the device (a) without and (b) with CdSe QDs with diameters of D=2.1 nm.

Figure 5.9 plots the calculated J-V characteristics of each subcell by Eq. [(5.8)] for

the device (a) without and (b) with CdSe QDs with diameters of D=2.1 nm. As expected, due to the unoptimized dimensions of the CdSe QDs, the enhancement of the photocurrent is mainly observed in the InGaP subcell. By applying CdSe QDs, the calculated short-circuit current density of the InGaP subcell is considerably enhanced from JSC =8.06 mA to JSC =10.1 mA. However, as in the previous discussion of Fig. 5.8, the enhancement of the solar intensity in the GaAs subcell is insufficient; therefore, the short-circuit current density of that subcell is only slightly boosted from JSC =7.88 mA to JSC =8.56 mA, and the overall power conversion efficiency of the device increases from η=21.12% to η=22.76% (blue dash-line). Restated, the enhanced photocurrents of the GaAs and Ge subcells are mainly attributed to the reduction of optical reflection because the CdSe QDs also serve as an antireflection coating for the long spectral regime.

Fig. 5. 10 (a) Calculated short-circuit current density (JSC) of each subcell and (b) the overall power conversion efficiency (PCE) of the device (bottom) as a function of the CdSe QD’s diameter. The enhancement ratio of the PCE compared to the device without CdSe QDs is also labeled in the figure.

The black dash-line marks the current-matching condition of InGaP and GaAs subcells.

To examine the experimental characteristics of the device after the integration of CdSe QDs, the J-V curves are measured under AM1.5G normal illumination (100mW/cm², 1 sun) at room temperature. The QD’s diameter was selected to be D=4.2 nm as this diameter exhibits the highest power conversion efficiency based on our calculation in reference to

Fig. 5.10. Figure 5.11(a) displays the J-V characteristics of

the bare InGaP/GaAs/Ge solar cell with and without CdSe QDs. The J-V characteristics of the devices with SiNx antireflection coating (ARC) and with CdSe QDs dispensing on top of SiNx ARC are also plotted in the figure for comparison.

The J-V curves shown in

Fig. 5.11 were acquired by the average of five different

samples for each QDs concentration, and the J–V measurements were found to be repeatable, having less than 1% deviation for two separate J–V characterizations of

Fig. 5. 11 (a) Electrical performance of the device after dispensing 7 mg/mL of CdSe QDs with diameters of 4.2 nm compared to the one without CdSe QDs under AM1.5G sunlight illumination. The performances of devices with SiNx antireflection coating (ARC) and with CdSe QDs dispensing on top of SiNx ARC are also plotted for comparison. Inset: photograph of the actual devices with dimensions of 1 cm×1 cm. (b) J-V characteristics with different concentration of CdSe QDs.

each solar cell device. Thus the measured enhancement is mainly attributable to the incorporation of CdSe QDs, and is irrelevant to the intensity fluctuation of solar simulator used in the experiment. A photograph of the actual devices with and without CdSe QDs is also inserted in the figure with dimensions of 1 cm×1 cm. From the photograph of both devices, it is visually evident that CdSe QDs provide an additional benefit of serving as an antireflection layer. Accordingly, with the assistance of SiNx ARC, the short-circuit current density and the power conversion efficiency are clearly boosted from JSC=11.04±0.11 mA/cm² to JSC=11.59±0.19 mA/cm² and from η=23.66%

to η=24.89 %, respectively. However, for the device with CdSe QDs dispensing on top of SiNx ARC, the performance is degenerated to JSC=10.68±0.31 mA/cm² and to

η=22.51%, respectively. It is because that the effective refractive index and the optical

thickness of CdSe QDs are not matched well with those of the underneath SiNx ARC layer to create the destructive interference and to reduce the Fresnel reflection of

incident light. Most importantly, by using 7 mg/mL of CdSe QDs with diameters of D=4.2 nm, the short-circuit current density and the power conversion efficiency are increased to JSC=12.12±0.20 mA/cm² and to η=26.12%, respectively. Since the device’s photogenerated carriers are drifted by the internal electrical field, and then are directly collected by the silver electrodes without passing through CdSe QDs, in principle the additional dispensing QDs does not interfere its distribution of energy-band profile.

Consequently, the integration of CdSe QDs has no obvious impact on the device’s open-circuit voltage (VOC=2.51V) and fill factor (FF=85.4—85.9%). Note that the measurement and the comparison are conducted on the exact same solar cell before and after spreading the CdSe QDs to fairly validate our hypothesis.

Figure 5.11(b) shows

the J-V characteristics of the InGaP/GaAs/Ge solar cells with different concentrations of CdSe QDs (D=4.2nm) to gauge the impact of the QDs on the device’s performance.

A summary of JSC as a function of the QD concentration is also plotted and inserted into the figure. Cleary, the concentration of CdSe QDs significantly affects the J-V characteristics of the device, and the highest power conversion efficiency is observed on the concentration of 7 mg/mL.

To understand the possible influence of various concentrations of CdSe QDs on the J-V characteristics of the device, we have performed the reflectance measurement in

Fig. 5.12 for the devices dispensing CdSe QDs with concentrations of 5 mg/mL, 7

mg/mL, and 9 mg/mL, respectively. The CdSe QD’s diameter is kept as D=4.2nm, and the reflectance of the bare tandem solar cell is also plotted in this figure. After the deployment of CdSe QDs by using spin-cast method, the CdSe QDs dispense uniformly upon the device [inset of

Fig. 5.11(a)], and can therefore be considered as a physical

homogeneous film. The effective refractive index is strongly dependent on the

Fig. 5. 12 Reflectance of the devices dispensing CdSe QDs with various concentrations of 5 mg/mL, 7 mg/mL, and 9 mg/mL, respectively. The reflectance of the bare tandem solar cell is also plotted in the figure.

composited concentration of CdSe QDs, and that profoundly affects the measured reflectance of the device. Accordingly, as compared to the bare tandem solar cell, by spin coating CdSe QDs on the top of the devices, the measured reflectance is obviously reduced, especially for the incident wavelength of λ<1000nm where coincides the QE response regions of InGaP and GaAs subcells. The measured JSC of the device dispensing with CdSe QDs is hence enhanced, as the summary depicted in the inset of

Fig. 5.11(b). The minimal reflectance occurs at the specific concentration of 7 mg/mL,

by which the effective refractive index of CdSe QDs is matched with that of InGaP top subcell to eliminate the Fresnel reflection, serving as an optimal antireflection layer. As a result, most of solar light is emitted into the device and then is converted by the CdSe QDs, yielding the highest power conversion efficiency of η=26.12% in this work.

5.4 Conclusions

In conclusion, we have demonstrated the use of CdSe QDs to tailor the incident spectrum of solar light and achieve efficient solar spectrum utilization in InGaP/GaAs/Ge tandem solar cells. We have also shown that the integration of CdSe QDs can significantly enhance the power conversion efficiency of an InGaP/GaAs/Ge tandem solar cell under AM1.5 illumination by both theory and experiment. Most importantly, because the fabrication and integration of CdSe QDs are simple, low cost, and compatible with the current manufacturing process of the photovoltaic industry, we believe that the proposed scheme is viable and highly promising for future generations of energy devices.

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