Optimisation of High Efficiency AlGaAs MQW Solar Cells
J.P.Connolly, K.W.J.Barnham, J.Nelson, P. Griffin, G. Haarpaintner, C.Roberts, M.Pate, J.S.Roberts
aa r X i v : . [ c ond - m a t . m e s - h a ll ] J un Optimisation of High Efficiency Al x Ga − x As MQW Solar Cells
J.P.Connolly, K.W.J.Barnham, J.Nelson, P. Griffin, G. Haarpaintner
Blackett Laboratory, Imperial College of Science, Technology and Medicine, London SW7 2BZ
C.Roberts
IRC for Semiconductor Materials, Imperial College of Science, Technology and Medicine,London SW7 2BZ
M.Pate, J.S.Roberts
EPSRC III-V Facility, University of Sheffield, Sheffield S1 3JD
The GaAs / Al x Ga − x As materials system is well suited to multi-bandgap ap-plications such as the multiple quantum well solar cell. GaAs quantum wellsare inserted in the undoped Al x Ga − x As active region of a p − i − n structure to extend the absorption range while retaining a higher open cir-cuit voltage than would be provided by a cell made of the well materialalone. Unfortunately aluminium gallium arsenide (Al x Ga − x As) suffers frompoor transport characteristics due to DX centres and oxygen contaminationduring growth, which degrade the spectral response. We investigate threemechanisms for improving the spectral response of the MQW solar cell whilean experimental study of the open circuit voltage examines the voltage en-hancement. An optimised structure for a high efficiency GaAs / Al x Ga − x Assolar cell is proposed.
One of the best materials for single band-gap solar cells is GaAs. Single crystal GaAshas high minority carrier mobility and a direct bandgap close to the optimum for singleband-gap solar cells. A novel high efficiency design, the quantum well solar cell (QWSC),is illustrated in figure 1. The multiple quantum wells (MQWs) in the depletion regionextend the absorption range below the barrier band-gap. Comparison of AL . Ga . As Preprint submitted to Elsevier Preprint 10 October 2018 indow graded p i n ✛ x p ✲ x wp ✛ x i ✲ x wn ✛ x n ✲ ✲ Depth ✻ electronenergy ❤❤❤❤ PPPP ❛❛ ◗◗◗ ◗◗◗◗◗◗◗◗◗◗ ◗◗◗ PPPP ◗◗◗ ◗◗◗◗◗◗◗◗◗◗ ◗◗◗ PP E F Fig. 1. QWSC band diagramme. The structure is a p − i − n photodiode design with quantumwells in the intrinsic region. A high band-gap Al x Ga − x As window is grown on the top surfaceto reduce surface recombination. devices with and without quantum wells has shown that the J sc is more than doubled insamples with 50 MQWs. Furthermore, the V oc provided by QWSCs is higher than wouldexpected from a cell with the quantum well effective bandgap. This provides the potentialfor a QWSC cell with a higher fundamental efficiency limit than a single band-gap cell. Inorder to test this idea in the GaAs / Al x Ga − x As materials system the short circuit current( J sc ) must be increased further. This can be achieved through improved growth and celldesign.Bulk Al x Ga − x As cells generally suffer from a relatively poor photon to photocurrentconversion effeciency (quantum efficiency or QE) Part of this poor performance stemsfrom a DX centre associated with the proximity in energy of the Γ, X and L band gapsin energy at approximately 35% aluminium (Al) [11]. Oxygen contamination from the Alsources during growth contributes further to decreasing minority carrier lifetimes withincreasing Al fraction X .Three methods of optimising the QE are described. The first is investigated in [9] andconsists of thinning the p layer thickness. This improves minority carrier collection by2educing the mean distance carriers must diffuse before reaching the junction. Moreover,the absorptivity of the p layer is reduced, allowing more light to reach the efficient intrinsic( i ) region. However, the J sc current enhancement is offset by increased p layer seriesresistance.The second method consists of linearly grading X in the p layer so that the bandgapdecreases with depth. This also reduces the p layer absorptivity, and enhances the i regionphotocurrent. Furthermore, minority carriers generated in the p are swept towards thejunction with the intrinsic region by the band-gap gradient. This only affects the QEat energies above the Al x Ga − x As band-gap. At very high Al content, carrier collectionefficiency tends to decrease because of a deterioration in material quality.The third improvement consists of etching off the GaAs substrate and coating the back ofthe cell with a mirror. This is very effective for a QWSC design because the wells absorb arelatively small fraction of the incident light but convert it into current with nearly 100%efficiency.The following discussion outlines the voltage study described in [5]. Thinner p regions aredescribed in [9] while the present work mainly investigates samples with graded layers andmirrors. Experimental and modelling results incorporating these methods are presented,with particular regard to to QE enhancement in samples with graded p layers and mirrorbacked samples. The model is used to design an optimised structure for a 50 quantumwell QWSC. Measurements in [5] have shown that the QWSC V oc as a function of effective band-gap is higher than expected from detailed balance arguments. This has been seen inthe GaAs / Al x Ga − x As indium gallium arsenide / indium phosphide and also the indiumgallium phosphide / gallium arsenide materials systems. Photoluminescence and pho-tocurrent studies of Al x Ga − x As samples presented in [12] indicate that the quasi-Fermilevel separation in the wells is also greater than expected. This phenomenon is not fullyunderstood but may be due to the high thermal escape efficiencies observed at roomtemperature.The observed voltage in a ungraded QWSC with 20% Al fraction in the barrier X barr was1% higher than exptected for a cell with the well bandgap. Similar voltage enhancementsin cells with higher Al fraction were 7% with a X barr =30% and 11% with X barr =40%.However, V oc optimisation is limited by the decreasing QE at high X barr .3 Theory
The QE model differs from previous work by [9] and [7] by considering inhomogeneousmaterial with position dependent materials parameters. We compare the modelled QEwith experimental data for graded p layer devices. The QE of the cell is calculated bysolving minority carrier transport equations at room temperature. The calculation ofphotocurrent from doped layers applies equally to p and n regions, with appropriatematerials parameters. The n region contribution is small because little light with sufficientenergy reaches it. For this region, the following discussion concentrates on photocurrentcontributions from the p and i layers. Under illuminated conditions, the excess minoritycarrier generation rate as a function of depth x from the surface of the p layer is given by G ( x, λ ) = F ( λ )(1 − R ( λ )) α ( x, λ ) × exp ( − R x [ α ( x, λ )] dx ) (1)where R ( λ ) is the surface reflectivity, α ( x, λ ) is the absorption coefficient and F ( λ ) isthe incident photon flux. Current and continuity equations determine the excess minoritycarrier concentration n ( x ). Since the cell operates in the low injection limit we use theEinstein relationship between mobility and diffusion constant. The excess carrier concen-tration n ( x ) in the p layer can then be found by solving d ndx + qE ( x ) k B T dndx − nL n ( x ) + G ( x,λ ) D n ( x ) = 0 (2) L n and D n are the electron diffusion length and diffusion constant respectively. E ( x ) isthe depth dependent effective electric field due to the bandgap gradient. The expressionsfor the band-gap are due to [3] (direct gap) and [8] (indirect). The smaller contributions tothe effective field from the bulk photovoltaic effect, the mobility gradient and the Demberpotential are neglected.The boundary condition at the surface is determined by matching the drift and diffusioncurrents to the surface recombination current. For the p layer, this takes the form qDE ( x ) KT n ( x ) + qD n ( x ) ∇ n ( x ) = S n n ( x )at x = 0 (3)4here S n is the minority electron surface recombination velocity. The second boundarycondition in the depletion approximation is that of zero excess minority carrier concen-tration at the edge of the depletion region for p respectively: n ( x wp ) = 0 (4)Equation 2 has an analytical solution for ungraded samples with constant transport pa-rameters in the doped layers. For graded samples with depth dependent transport char-acteristics, a standard numerical method is used. The photocurrent J p ( λ ) from the p isgiven by the diffusion current at the depletion edge J p ( λ ) = qD n ∇ n ( x wp ) (5)where x wp is the position of the p depletion edge. This expression assumes zero excessminority carrier concentration at the edge of the junction within the depletion approxi-mation.The validity of the this approximation on the minority carrier gradient at the edge of thejunction was verified by analytically calculating the photocurrent in the light at x wp foran ungraded sample with a high current density. This was compared with the numericalresult for the same device. The largest error was was of the order of 0.1% for a GaAs cellin the resulting photocurrent from the p layer.Assuming 100% collection efficiency, the current J i ( λ ) from the i region is calculated fromthe integral of the generation rate over the depleted regions J i ( λ = q x p + X i + x wn Z x p − x wp [ G ( x, λ )] dx (6)The short circuit current is then the sum of the contributions from the three regions J sc ( λ = J p ( λ + J i ( λ + J n ( λ (7)where the n region photocurrent J n is calculated in a similar fashion to J p . The QE isdefined in terms of J sc and the incident flux QE ( λ ) = " J sc ( λqF ( λ ) (8) The normal incidence mirror model treats the cell as a cavity with uniform light intensityfor a given wavelength. The refractive index is an average over the structure.5he light intensity in the QWSC is calculated as a function of wavelength by summingelectric field amplitudes due to successive reflections. The wavelength dependence of thefront and back surface reflectivities is neglected. A wavelength independent back surfacereflection phase change is included. The mean light intensity in the cell is given by thesquared modulus of the total electric field amlpitude. The QE enhancement above thewell is neglected because of the low levels of light reaching the back mirror at thesewavelengths.
The main model parameters are the reflectivity, the absorption coefficient, S n , D n and L n .Reflectivities were measured on a separate set of large area calibration samples describedin section 5. An average reflectivity is used in the modelling since the measured data varyby no more than a few percent. Modelling of the absorption coefficient is described in [9].The surface recombination velocity S n is very dependent on sample growth and processingand is essentially used as a fitting parameter at wavelengths below 400nm. L n is also sensitive to growth and processing. A wide range of values exist in the literature([1], citehamaker85) and reliable published data can only be found for X compositionsbelow approximately 40%. A number of simpler ungraded QWSC structures were grownat different values of X in order to increase our knowledge of L n . The following methodwas used to extract values of this parameter.Inspection of the analytical solution to equation 2 and equation 5 shows that the expres-sion for the QE is independent of D n if D n is a constant. The only free parameters in thiscase are S n and L n . S n mainly influences the QE at short wavelengths whereas L n affectslonger wavelengths. The ungraded p layer QE can therefore be modelled in terms of S n at short wavelengths and L n at long wavelengths.Fitting QE measurements of p − i − n and QWSC samples without grades have enabledus to extract values of the diffusion length for X ranging from 20% to 47%. Since we haveno samples outside this range, we use the paramterisation in [6] for X compositions above47%.We use the values of L n descibed above to model graded QWSC samples. This assumesthat the X dependance of the diffusion length in the graded p is similar to the behaviourobserved in separate ungraded structures with different X compositions. In graded sam-ples, however, D n is no longer a constant, and has a significant effect on the QE.Inspection of equations 2 and 8 shows that for a graded sample the QE depends on thegradient of the diffusion constant with X composition ∇ X D n but not on the it magnitude6f D n . The graded p layer QE can therefore be modelled in terms of ∇ X D n . In the absenceof detailed D n measurements, we assume a constant gradient ∇ X D n between the two Alfractions for each p layer and use this constant as the main fitting parameter. Modelling the mirrors involves three parameters. We find that for low front surface re-flectivities the back surface reflectivity mainly determines the level of QE increase in thewells. The amplitude of Fabry-Perot oscillations is set by the front surface. The phasechange upon reflection from the back surface is a poorly understood quantity, but partlydetermines the position of Fabry-Perot peaks.
The MBE samples were grown on a V80H Vacuum Generators machine. The growthtemperature was at 630 ◦ C. Temperature monitoring was carried out using an opticalpyrometer backed up by a substrate thermocouple and RHEED observation of oxygendesorbtion from the surface at 590 ◦ C. The flux ratioes (As:Ga 10:1) were measured witha beam monitoring ion gauge.A series of ungraded 30 well QWSCs and control p − i − n structures were grownby MBE at nominal Al fractions of 20%, 30% and 40%. These samples have 0.03 µ mwindows grown at X =67%. The Al fraction is subject to increasing uncertainty up toabout X =50% because of Ga source flux fluctuations. The controls are identical in everyrespect except that the well material is replaced by Al x Ga − x As with the barrier Alfraction. A Al . Ga . As double heterostructure p − i − n was also grown.A set of three graded QWSCs was grown on the same MBE machine. The X compositionswere calculated from the photocurrent spectra. The Al fraction in the graded p regionsvaries from X =44% at the front surface to X =22% at the p - i interface in sample U4033.Analoguous grades in samples U4034 and U4035 ranged from 67% to 34% and 67% to47% respectively.MOVPE growth details are given in [10]. Sample QT468a is a 30 well ungraded QWSCwith a 80% 0.02 µ m Al x Ga − x As window.The samples were processed to circular 1mm gold ring contact photodiode devices with acircular 600 µ m optical window. The devices are mounted on TO5 headers.The anti-reflection (AR) coating consists of 75nm of SiN. Large area pieces of wafer fromeach sample were AR coated to allow reflectivity measurements to be carried out.Coating the back of a device with a mirror is achieved by etching the substrate down tothe n layer, which acts as an etch-stop. A metallic mirror is then evaporated directly onto7 ample Type Modelled p Al Diffusion S n fraction (%) Length ( µm ) cm /s U2027 mqw 22 0.075 10 − U2028 ∗ pin DHet 22 0.075 10 − U4036 pin 22 0.075 10 − U2029 mqw 35 0.06 10 − U2030 pin 35 0.05 10 − U2031 mqw 47 0.06 5 × − U2032 pin 47 0.075 5 × − Table 1Modelled diffusion lengths for ungraded samples at three aluminium fractions. The values of l n show remarkable consistency at low Al fractions. Poorer consistency at high Al fractions ispartly due to variable device performance. the back surface of the n region. p QWSC
More detailed discussion of thin p cells is given in [9]. Preliminary studies indicate thatseries resistance has a significant effect on unconcentrated AM1.5 performance for thick-nesses below about 0.1 µ m. L n fromUngraded Devices The model reproduces the QE of pin and QWSC samples with very similar values of L n and S n . These are given in table 1. Also shown in the table are the band-gaps extractedfrom the photocurrent spectra. We note that consistency between different types of sam-ples is very good for X =20% but deteriorates at higher Al fractions. Theory and QE datafor the 30% Al sample are given in figure 2.Modelling shows that L n decreases more slowly with increasing Al fraction than has beenreported in [6]. It increases near the direct - indirect transition in the region of 40% Al.This trend is consistent with published measurements in the review article [1] althoughour values are substantialy lower for reasons which are not fully understood.8 ig. 2. Experimental data and model for a 33% Al fraction 30 MQW solar cell used to determinevalues of L n . ∇ X D n from Graded QWSCs Graded samples were used to establish diffusion constant gradients between the fourdifferent Al fractions and are given in table 2. The QE data and theory for the 33% Algraded QWSC U4034 are given in figure 3.Figure 5 shows the experiment and theory for the mirror backed MOVPE sample QT468a.The integrated J sc enhancement for this device was 49% in the well and of 28% in J sc overall. Fabry-Perot peaks are visible, showing that front and back surface interfaces aresmooth. Other samples with accidentally roughened back mirrors have shown higher J sc enhancements. This is attributed to non-specular reflection at the back surface whichincreases the optical path length in the cell and hence improves light absorption.9 ig. 3. Experimental data and model for a 33% Al fraction 30 MQW solar cell incorporating a p region compositionally graded from 33% to 67% Al. Comparison with figure 2 shows significantlyimproved QE at short wavelengths.Sample p grade ∇ X D n Front Al fraction (%) Back Al fraction (%) (cm/s)U4033 22 44 − . × U4034 34 67 − . × U4035 44 67 − . × Table 2Gradients of the diffusion constant in Al x Ga − x Aswith respect to Al fraction. These values arederived from modelling the QE of graded QWSC samples using the L n values given in table 1. The model was used to design an optimised 50 well QWSC with a thinned and graded p layer. We chose to concentrate on a nominal barrier aluminium fraction of 30% and to10 ig. 4. mirrored 30% cell QT468a showing Fabry-Perot effects. The short circuit current en-hancement for this device was 25% overall. base the design on our best previous G951 cell which is described in [9].The p layer was thinned to 0.1 µ m. Modelling values of J sc predict little current enhance-ment for grades with a top Al fraction above about 44%. We have therefore limited thisoptimisation to 44% in view of increasing impurity incorporation at higher Al fractionsand greater uncertainty in modelling parameters in this region.The modelled J sc under standard AM1.5 illumination for a mirror backed device was 27.9mAcm − for our contact design which has a 7% shading loss. Comparison with G951 givesus an rough value for the efficiency we expect from this sample. G951 has a V oc of 1.07V,a fill factor of 78% and a J sc of 17.5mA cm − . The V oc is a little low for the optimised cellbecause of its higher J sc . If, however, we use these parameters to estimate the efficiencyof the optimised cell on the basis of the modelled J sc we obtain an efficiency of of 22.3%.This compares favourably with a GaAs cell described in [4] which has an efficiency of25.1% for a fill factor of 87%, a V oc of 1.022V and a J sc of 28.2mA cm − . We note thatthe QWSC efficiency would improve substantially if the fill factor QWSC were increased.11 ig. 5. Optimised 50 well QWSC consisting of a 0.1 µ m p region compositionally graded form30% - 44% Al and mirror backed. I sc =25.5 mA ( IEC − AM . cm − . Also shown the experimentfor the best 30% QWSC prior to optimisation. Previous work has demonstrated current enhancement and promising voltage performancein QWSCs. Further theoretical and experimental investigation has shown that useful J sc enhancements can be made in different wavelength ranges. Improved design of the p layercan enhance the disappointing QE of Al x Ga − x As cells below 400nm, while a back mirrorcoating is seen to double the MQW current in 30MQW samples.Theoretical predictions combining these improvements in a single cell indicate that anGaAs / Al x Ga − x As cell can be grown with efficiencies close to the unconcentrated GaAscells. Further improvements are expected if fill factors in particular can be increased.The design may be attractive for the high bandgap component of a concentrator system,either as an optimised Al x Ga − x As cell, or a QWSC. The QWSC may be attractive forthis purpose since its current output can be tuned to that of the lower bandgap componentby varying the number and/or width of the quantum wells.12 eferences [1] Ahrenkiel R K (1992), Minority – Carrier Lifetime and Diffusion Length in AlGaAs. In:Adachi S (Ed) Properties of Aluminium Gallium Arsenide, EMIS Datareviews Series No. 7,INSPEC, London, pp. 221 – 224.[2] Barnham K et al. (1994), Quantum well Solar Cells, Optoelectronics – Devices andtechnologies 9(4), Mita Press, Tokyo, pp. 483 – 498[3] Casey H C, Panish B (1978), Heterostructure Lasers, part B. Academic Press,New York[4] Green M A et al. 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