**7. Suggestions for modeling**

334 Solar Cells – New Aspects and Solutions

included) is of the order of 1012 to 1013 cm-2 per eigen-state. Thermionic current density values have been found to be near order of 30mA/cm2 and open-circuit voltage values above 1V, at one sun. Overall (for a composite cell see figure 3) collection efficiency values are initially projected well in excess of 35%, which is a key for immediate improvement to even higher collection efficiency. Total current density is dominated by the lowest of the two sub-cell currents, and open-circuit voltage values are the sum of the two sub-cell Voc values. Total current from the bottom cell is the sum of thermionic and nearest neighbor hopping currents. Preliminary results reach estimates of efficiencies from each of the two (latticematched) sub-cells in excess of 21% per cell (predicted synergy of the two sub-cells in excess of 40%). Loss mechanisms at interfaces and quantum wells and their role in overall

i. Solar spectrum matching in both visible and IR ranges through layer band gap-

iii. Increased carrier transport due to GaAs. It is conceivable that even the 40%-plus target

Heterostructure and (most recently) multijunction solar devices exhibit better performance in transport properties, when compared to bulk solar cells: especially in quantum well devices, photo-excitation causes carrier accumulation in discrete energy levels, with subsequent escape to the conduction band (minus recombination losses) via standard mechanisms such as tunneling, thermal escape or nearest neighbor hopping conduction. Full spectrum absorption and triple junction solar cells have become key factors for high efficiency collection in PV structures of various geometries. Most recently, successful photovoltaic device (PV) designs have shown high efficiency values well above 30%, and efficiency levels in excess of 40% have been reached by means of triple junction metamorphic solar cells and under high sun concentration (good candidate for concentrated PV or CPV). Multijunction solar cells offer a great advantage over their bulk counterparts: by incorporating lattice-matched alloys, one may succeed in designing a device with more than one energy gaps thus increasing the number of absorbed solar photons. During the last decade, various groups have modeled and developed *multijunction* solar cells in order to increase overall collection efficiencies. Emphasis has been given in two types of PV devices (a) lattice-matched solar cells and (b) metamorphic (lattice-mismatched) solar cells. In particular, III-V multijunction solar cells have shown the greatest progress in overall efficiency. The broader impact of this project is a new design proposal for high efficiency solar cells. The target is to exceed 45% collection efficiency for very efficient photovoltaic devices. It is more than clear that once such a cell is realized, the field of concentration photovoltaics (CPV) will benefit greatly: solar cells with (a) record high efficiency values (b) under several hundred suns (Fresnel optics at 500+ suns) and (c) small in size (low area hence less material) is already attracting interest for mass production in many places in the world. In recent years, it has been proposed by us a new design for a high efficiency and lattice-matched solar cell (HESC), where both visible and infrared portions of the solar spectrum are absorbed according to the structure's geometric material arrangement: simultaneous absorption of both short and long wavelengths. In this on-going research enterprise, the synergy between a highly efficient triple junction cell and a highly efficient superlattice or a multi-quantum well region, is presented as a new and innovative way for further efficiency increase. It is well established by now, that triple junction solar cells are exceeding the upper threshold of collection efficiency to ever higher levels, namely

efficiency determination will also be included. Advantages of the design are:

of conversion efficiency can be reached with such designs

matching selection. ii. Lattice-matching

> Fully develop a theoretical model of PV composite PV devices by first principle calculations and computations based on realistic device parameters; propose a composite PV structure with two major cells: a triple junction and multi-layer tuned cell, with the prospect of high efficiency near 50%. Modeling tools include several established math software packages. Seek for a composite photovoltaic device that combines properties of direct-gap crystalline semiconductors and absorption in the entire spectrum, mainly in the visible and in the infrared (NIR/IR) wavelength ranges, and which is configured as a two-part solar cell: a top triple junction and a multi-layer p-i-n bottom unit tailored to IR infrared wavelengths. The solar spectrum (a 6,000 oK, see in Figure 5) offers the option of finding suitable band gaps for highest absorption. Material selection shows a blue shift in the absorption via wide gap materials as shown (AlAs). Low gap materials offer wavelength matching in the IR range (note the dashed arrows indicating optical gaps corresponding to various wavelengths. It is of advantage to exploit quantum wells grown on n-type or low-doped substrates.

Fig. 7. Tuned quantum wells at 1eV solar photons: shown are energy levels and optical gap increase

High Efficiency Solar Cells via Tuned Superlattice Structures: Beyond 42.2% 337

5. reduced carrier trapping and recombination (carriers in MQW region separate from

Fig. 8. Proposed cell structure: top cell p-n junction, tunnel junction (TJ) (purple) and p-i-n bottom cell with superlattice in the middle; P region (green), N region (yellow). Top cell is the window facing the sun (anti-reflected coating and surface texturing not shown).

Tuned Superlattic

As seen from the figure above, there are several options for further design and optimization (a) top region offers the possibility of another superlattice tuned at selected wavelengths (b) layers and alloys other than GaAs can be used (in the lattice-matched fashion) (c) tuned superlattice (bottom cell) can be split is more than one narrow units tuned at desired solar spectrum peaks

Concentrated light on small solar cells can become of great advantage: a small size cell (~2 mm2 area) may be placed at the focal point of a Fresnel optical system. Concentrated light causes higher carrier absorption from the bulk of the device and therefore higher

(d) cell can be of small area (less material used) or of large area for higher exposure.

**8. Some thoughts on concentrated photovoltaics (CPV)** 

their corresponding holes as being away from the quantum wells)

3. less complexity in the structure overall

6. faster growth conditions attainable

7. lower fabrication costs

4. reduced scattering of drifting and diffusing carriers

Superlattice structures in both cases mentioned above are at the designer's disposal, in the sense that appropriate quantum well geometries may lead to desired solar photons absorption. Enhancement of cell performance can be achieved by replacing the intrinsic region with *tuned* multi-quantum well (MQW) layers, designed for specific wavelengths. Thermionic emission, hopping conduction and tunneling are dominant mechanisms of photo-carrier transport in heterostructures (against losses due to recombination processes). Photo-excited layers thermally escape from quantum wells (minus recombination losses): incident solar photons typically generate 1012 to 1013 net photo-excited carriers per unit area (cm2), after recombination effects have been taken into account. This population is expected to migrate to the conduction band assisted by the escape mechanisms named above and the built-in electrostatic field in the p-i-n region.

By selecting suitable geometry of the quantum wells that leads to one or two energy levels in the quantum wells, ground state of electron-hole pairs at 1eV may be formed, and a second state at the very edge of the GaAs layer conduction band (see Fig 2): this event has been shown to act in favor of nearest neighboring hopping electrons from site to site (QW). Thus a three-fold advantage of the superlattice/MQW region is that (1) excess (in addition to carriers from the bulk part of the device) carriers are trapped and thermally escape to the conduction band and (2) nearest neighbor hopping conduction (NNH) becomes a second conduction mechanism and (3) band gaps of other materials may be represented via energy levels in quantum wells. The total current from the intrinsic region will be the sum of the thermionic and the NNH current components (minus recombination losses). Subsequent well width selection may lead to further refinement of solar photon absorption. Near infrared and infrared portions of the solar spectrum can be covered by suitable width selections, with equal amount of modeling effort (from the point of view of computations, it is a mere change of parameters for slightly different optical gaps). It is also interesting to note at this point that quantum well width could be modeled as a random variable, leading to a random distribution of optical gap values (as function of well width) and hence a smeared distribution of optical gap values and absorbed photon wavelengths, for the benefit of the photovoltaic device. Thus, IR photon absorption in the neighborhood of 1eV is feasible. In addition, the superiority of transport properties of the proposed quantum-PV device should be noted compared to its III-N-V "high" efficiency counterpart: our proposed superlattice cell is mainly a GaAs device perturbed by thin Ge layers, and therefore this region exhibits much higher electron mobility. In the absence of tunneling (thick potential barriers) total currents are in essence the sum of (a) bulk currents from the mainly bulk pin device (b) thermionic and (c) hopping current components, due to free electrons in the GaAs conduction band, assisted by the overall electrostatic field in the intrinsic region. Recent modeling and simulation have shown that the top cell retains visible absorption (AlAs/ (Al) GaAs/GaAs at ~21%) or to include a highly efficient triple junction cell (in this proposal, our own choice (InP/GaAs/GaAs at 30% efficiency). The bottom multi-well cell operates at longer wavelengths (1eV or 1,240nm), and therefore the whole of the unit absorbs in both regimes visible and IR respectively. Since germanium and gallium arsenide layers are lattice-matched, it is conceivable that a superlattice would fit in between the p- and nregions of the device. Advantages of such designs are summarized below:


Superlattice structures in both cases mentioned above are at the designer's disposal, in the sense that appropriate quantum well geometries may lead to desired solar photons absorption. Enhancement of cell performance can be achieved by replacing the intrinsic region with *tuned* multi-quantum well (MQW) layers, designed for specific wavelengths. Thermionic emission, hopping conduction and tunneling are dominant mechanisms of photo-carrier transport in heterostructures (against losses due to recombination processes). Photo-excited layers thermally escape from quantum wells (minus recombination losses): incident solar photons typically generate 1012 to 1013 net photo-excited carriers per unit area (cm2), after recombination effects have been taken into account. This population is expected to migrate to the conduction band assisted by the escape mechanisms named above and the

By selecting suitable geometry of the quantum wells that leads to one or two energy levels in the quantum wells, ground state of electron-hole pairs at 1eV may be formed, and a second state at the very edge of the GaAs layer conduction band (see Fig 2): this event has been shown to act in favor of nearest neighboring hopping electrons from site to site (QW). Thus a three-fold advantage of the superlattice/MQW region is that (1) excess (in addition to carriers from the bulk part of the device) carriers are trapped and thermally escape to the conduction band and (2) nearest neighbor hopping conduction (NNH) becomes a second conduction mechanism and (3) band gaps of other materials may be represented via energy levels in quantum wells. The total current from the intrinsic region will be the sum of the thermionic and the NNH current components (minus recombination losses). Subsequent well width selection may lead to further refinement of solar photon absorption. Near infrared and infrared portions of the solar spectrum can be covered by suitable width selections, with equal amount of modeling effort (from the point of view of computations, it is a mere change of parameters for slightly different optical gaps). It is also interesting to note at this point that quantum well width could be modeled as a random variable, leading to a random distribution of optical gap values (as function of well width) and hence a smeared distribution of optical gap values and absorbed photon wavelengths, for the benefit of the photovoltaic device. Thus, IR photon absorption in the neighborhood of 1eV is feasible. In addition, the superiority of transport properties of the proposed quantum-PV device should be noted compared to its III-N-V "high" efficiency counterpart: our proposed superlattice cell is mainly a GaAs device perturbed by thin Ge layers, and therefore this region exhibits much higher electron mobility. In the absence of tunneling (thick potential barriers) total currents are in essence the sum of (a) bulk currents from the mainly bulk pin device (b) thermionic and (c) hopping current components, due to free electrons in the GaAs conduction band, assisted by the overall electrostatic field in the intrinsic region. Recent modeling and simulation have shown that the top cell retains visible absorption (AlAs/ (Al) GaAs/GaAs at ~21%) or to include a highly efficient triple junction cell (in this proposal, our own choice (InP/GaAs/GaAs at 30% efficiency). The bottom multi-well cell operates at longer wavelengths (1eV or 1,240nm), and therefore the whole of the unit absorbs in both regimes visible and IR respectively. Since germanium and gallium arsenide layers are lattice-matched, it is conceivable that a superlattice would fit in between the p- and n-

regions of the device. Advantages of such designs are summarized below:

1. less material to grow

2. small area (exposed to sun-light cell aperture)

built-in electrostatic field in the p-i-n region.

Fig. 8. Proposed cell structure: top cell p-n junction, tunnel junction (TJ) (purple) and p-i-n bottom cell with superlattice in the middle; P region (green), N region (yellow). Top cell is the window facing the sun (anti-reflected coating and surface texturing not shown).

As seen from the figure above, there are several options for further design and optimization (a) top region offers the possibility of another superlattice tuned at selected wavelengths (b) layers and alloys other than GaAs can be used (in the lattice-matched fashion) (c) tuned superlattice (bottom cell) can be split is more than one narrow units tuned at desired solar spectrum peaks (d) cell can be of small area (less material used) or of large area for higher exposure.
