The Physics of Energy, page 103
The Shockley–Queisser Bound The Shockley–Queisser bound on single-junction photovoltaic efficiency combines the three factors associated with the three issues raised in §25.4: (a) the bound (25.25) on ; (b) the fill factor from eq. (25.20); and (c) the bound on collection efficiency (25.11), to give an overall efficiency bound
(25.26)
Multiplying out the factors, the best efficiency possible for a silicon photodiode under AM1.5 conditions is . For a silicon photodiode with V the bound is . Improvements in materials to increase may push the efficiency somewhat above 27%, though the true bound for a silicon PV may be below . Green [149] uses recombination properties of electrons in silicon to argue that 28.8% is the highest efficiency possible for single-junction silicon PV cells that respond equally to light coming from all directions (isotropic response).
The analysis given here is intended to provide a general sense of the physical limits for this technology, and not a precise efficiency bound. As of 2015, the highest efficiency achieved for single-junction silicon photovoltaic solar cells under one sun illumination (i.e. without concentrators) was around 25%. Note that while the collection efficiency bound (see §25.4) is maximized for a gap around eV, the electron–hole recombination bound (25.25) favors higher band gaps, as mentioned above, so after all factors are included, the optimal band gap is in the range 1.3–1.4 eV, with a Shockley–Queisser bound around 34%. The Shockley–Queisser bound as a function of band gap is graphed in Figure 25.22 (for incoming AM1.5 radiation).
Figure 25.22 The Shockley–Queisser limit on single-junction PV efficiency as a function of band gap (using the AM1.5 spectrum). Image: S. Byrnes, Harvard University.
Note that although the bounds on efficiency we have discussed in this and the preceding sections are based on physical principles, each bound is predicated on certain assumptions that may be evaded in various ways. For example, the spectrum bound derived in §25.4 may be evaded if a mechanism is found that can make use of the extra energy in an electron excited by a photon of energy above the band gap. It is possible that open-circuit voltages above 0.7 V may be achieved by a clever combination of device geometry and materials. It is possible that the Shockley–Queisser bound on may be violated, for example if the PV material does not itself radiate as a black body. Nonetheless, exceeding these bounds for a single-junction photovoltaic cell represents a major engineering challenge. In §25.9.1 we discuss the possibility of achieving higher efficiencies in photovoltaic cells using multiple materials (multi-junction PV).
25.8Silicon Solar Cells
To date, most deployed solar PV systems are based on the crystalline silicon solar cell described in the preceding sections. At present, the most efficient commercially available silicon solar cells have peak efficiencies of roughly 20%. While energy from photovoltaic cells is still (as of 2017) somewhat more expensive for many applications than energy from fossil fuels such as coal, petroleum, or natural gas, PV systems have become competitive with other sources in some markets in recent years. In this section we briefly review some of the practical issues in engineering inexpensive and efficient silicon solar cells.
Material constraints Because of crystalline silicon's indirect band gap, at least 100 μm of material is needed to absorb a significant fraction of incoming solar radiation. Current solar cells have 100–300 μm thickness of crystalline silicon. While the element silicon is abundant on Earth (crustal abundance 28% by mass), it almost never occurs naturally in pure form. Instead it is usually obtained from quartz (SiO), a very common mineral. To form a semiconductor of quality high enough for use in PV solar cells, silicon is refined typically to a purity of 99.9999% (“six nines”), from which monocrystalline (single crystals) or polycrystalline (many small crystals) stock is grown. Thin wafers are then sawn from the bulk silicon. This process is complex, relatively expensive, and energy intensive. Processing silicon can also release carbon (e.g. in the reduction of silicon dioxide SiO + 2C Si + 2CO). Though new methods are being developed that may reduce the cost and energy requirements of producing pure silicon crystals, the complexity of the crystal growing and wafer production process drives up the cost of silicon photovoltaic cells.
The Shockley–Queisser Limit on Silicon Photovoltaic Efficiency
The Shockley–Queisser limit on the efficiency of a photovoltaic cell constructed from a single type of semiconductor with a band gap is
Here ff is the fill factor determined by the voltage-current relation of the photodiode; is the open-circuit voltage, and is the collection efficiency. This bound limits the efficiency of single-junction silicon solar cells to approximately 33%, assuming AM1.5 radiation and that the cell radiates as a black body. Fundamental materials constraints suggest an upper bound around 29%; current silicon solar cell materials and geometries have achieved 25% conversion efficiency for non-concentrated sunlight.
Degradation Exposure to UV light and high temperatures gradually damages silicon solar cells, causing defects in the crystal lattice and reducing efficiency. Lifetimes of currently produced solar cells are estimated at about 25 years, so any given solar cell has a finite expected energy production over its lifetime.
Figure 25.23 Different PV technologies and maximum research-cell efficiencies realized since 1975. From [154].
Contacts The connection of electrical contacts to the semiconductor junction is a significant engineering challenge in making highly efficient solar cells. Contacts on the front surface can block incoming light, and the interface can reduce cell efficiency. At present, large quantities of silver (Ag) are used for this purpose; on the order of tens of milligrams of Ag are needed per peak watt of solar power. Researchers, however, are actively looking for lower-cost replacements, and the amount of silver used in silicon solar PV manufacturing is expected to drop significantly over the next decade.
Reflectivity Bare silicon is highly reflective, so rough surfaces or an antireflective coating must be used to optimize collection efficiency.
Low-voltage DC current Since the voltage across the cell is typically V, PV cells are usually connected in series to produce higher-voltage systems. A consequence of this is that shading one cell in a series can reduce the power output of the whole system. Furthermore, all solar cells produce direct current, which must be converted to alternating current to be fed into standard electric power distribution systems (see §38).
Substantial science and engineering efforts have gone into addressing these and other technical issues over the last several decades. Silicon solar cells continue to evolve, with costs steadily decreasing and efficiency gradually increasing. For a substantial jump upward in performance, or downward in cost, however, it is possible that a different technology needs to be developed.
25.9Advanced Solar Cells
In most of this chapter we have focused on single-junction silicon-based solar cells. A wide variety of alternatives have been, and continue to be, explored both for improving efficiency and reducing cost of large-scale solar systems. Figure 25.23 gives an overview of some of the technologies that have been explored over the last 50 years, with maximum realized research-cell efficiencies for the different technology types.
Example 25.2 Two-junction PV Cell
A solar cell made from two materials with differing band gaps can collect more solar energy than a single-junction cell. Consider, for example, two materials, one with band gap eV and the other with band gap eV. By arranging the cell so that incoming solar radiation passes first through material 1 and then through material 2 (see figure at right), collection efficiency can be optimized. Assuming a 6000 K blackbody spectrum, electrons in the first material are excited by photons with , collecting a fraction of the total incoming energy
The second material then collects energy from the remaining photons that have ,
so that the total energy collected in usable excited electron energy is more than 60% of the incoming solar radiation.
While the Shockley–Queisser bound (25.26) represents a limit on a certain class of photovoltaic solar cells, the only known absolute physical bound on conversion from solar radiation to electrical energy is the Carnot limit quoted earlier in this chapter, . Present technologies are far from this bound, motivating intense research into novel designs that can operate at higher efficiency (and acceptable cost). Solar PV technologies fall into three categories: first generation, which includes the conventional crystalline silicon cells discussed in depth in this chapter; second generation, including thin-film PV cells that employ semiconductors with a direct band gap, which account for most of the rest of deployed PV capacity at the present time; and third generation, which includes a variety of approaches that are currently either limited to niche applications (e.g. multi-junction PVs, see below) or are still at an early stage in their development (e.g. dye-sensitized cells, organic PVs, quantum dots, and graphene). A full discussion of second and third generation PVs goes well beyond the scope of this book. In this section we give a brief description of some features of two of the main threads of development: multi-junction cells, which can improve photovoltaic efficiency above the 33% efficiency limit for single-junction PV cells (§25.9.1), and thin films, which may significantly reduce the cost of large-scale PV installations (§25.9.2).
25.9.1 Multi-junction Cells
The limit on collection efficiency described in §25.4 assumes that photons can only be excited across one band gap. The idea of a multi-junction photovoltaic cell is to evade this limitation by combining several materials with different band gaps. Assume, for example, that two semiconductors with band gaps are available. By placing a layer of material 1 above a layer of material 2, a photovoltaic cell can gather more energy than either material alone could collect. Material 1 gathers more energy from some photons than could be collected by material 2, and material 2 collects energy from some photons that cannot excite an electron across the band gap of material 1 (see Figure 25.24). For example (see Example 25.2), a two-junction photovoltaic cell composed of materials with band gaps eV and eV can collect over 60% of incoming energy in a 6000 K blackbody spectrum – significantly above the collection efficiency bound for any single-junction cell (based on a material with a single band gap). Even higher collection efficiency can be realized by using three (or more) materials. While the maximum collection efficiency for 6000 K light by a single junction cell is 43.9% (optimized by a band gap eV), this increases to 60.4% for a double-junction cell and 69.2% for a triple-junction cell (Problem 25.8). In recent years, multi-junction solar cells have been constructed with increasingly high overall conversion efficiencies. Triple-junction cells have been built with efficiencies exceeding 40%.
Box 25.2 Materials for Multi-junction PVs
One of the major challenges in constructing multi-junction PVs is to find compatible materials that have band gaps in the specific ranges necessary for optimal collection efficiency. To this end, scientists have been experimenting with a wide range of materials. One broad family of materials that are of interest in this regardare those formed from a combination of elements from columns III and V of the periodic table (see Figure D.1). In general, elements from columns III and V can combine into the zincblende crystal structure, which, like the diamond lattice, consists of two interlaced FCC lattices, but with one FCC lattice containing the group III element and the other containing the group V element (see Figure 25.1(b)). Many III–V crystals of this kind form good semiconductors, with band gaps that can be used effectively in multi-junction PVs. A simple example of a III–V semiconductor often used in multi-junction PV cells is gallium arsenide (GaAs). This material has a direct band gap of eV, which is near the optimum band gap for a single-junction semiconductor, corresponding to a Shockley–Queisser bound around 33.5% (for 6000 K blackbody radiation). The best recorded single-junction cell efficiencies have been realized for GaAs cells – close to 30% efficiency with concentration factors .
An even broader class of materials include alloys that mix elements from one column. For example, indium gallium phosphide (InP), also based on a zincblende crystal, mixes the group III elements indium and gallium with relative weights in one of the FCC lattices. By tuning the relative fraction of the group III elements in the alloy, the band gap can be varied over a range of values, with pure InP and GaP having direct and indirect bandgaps of 1.34 and 2.26 eV at the extremes, respectively. One combination of materials that has been used for triple-junction PV cells with realized efficiencies above 40% uses InP for the highest band gap, for the middle band gap, and germanium (a diamond crystal structure group IV semiconductor like silicon, but with band gap 0.66 eV) for the lowest band gap. As with silicon, using concentrators increases the efficiency of multi-junction cells by increasing through eq. (25.18).
Figure 25.24 A two-junction solar cell containing two materials of energy gaps . Photons with energy above excite electrons in the first material. Photons with energy below but above excite electrons in the second material. Photons with energy below do not excite electrons. Collected energy can exceed that of any single-junction PV cell.
While multi-junction photovoltaic cells provide the highest conversion efficiencies yet realized, there are a number of challenges to large-scale development of power systems using this technology. Although band gaps can be tuned for certain semiconductors (see Box 25.2) the materials involved are often rare and/or expensive. The world's annual production of germanium (Ge), for example, was only ~118 tonnes in 2011, which severely limits the production of triple-junction cells using Ge as the lowest band gap element (Problem 25.17). While using concentrators can make multi-junction cells more cost effective, to date most uses of high-efficiency multi-junction PV cells have been in niche applications such as space exploration (Mars rovers) and military systems (for mobile devices) where light weight and high power density are of critical importance. In addition to materials supply limitations, there are also technical issues with multi-junction cells that complicate the engineering of these systems. In particular, combining different semiconductors into a single functioning photovoltaic cell often requires matching the lattice structures of the materials (heterojunctions); matching the electrical characteristics of the materials can also be often difficult. In some multi-junction cells, tunnel junctions are used in which quantum tunneling plays an important role in connecting the layers of the cell. These technical and engineering issues present a major challenge to large-scale production of cheap and efficient multi-junction photovoltaic cells.
25.9.2 Direct Band Gap Materials and Thin-Film Photovoltaics
Although silicon has a near optimum band gap and is an abundant material, two drawbacks mentioned under the heading of material constraints have motivated intense interest in alternative materials. First, the manufacture of silicon PV cells involves a complicated and expensive multistep process. Second, because of its indirect band gap a single-junction cell made of monocrystalline or polycrystalline silicon must be on the order of 100 μm thick to absorb a substantial fraction of incoming solar radiation. In contrast, a material with a direct band gap can absorb most solar radiation over a distance of order 1 μm. Though a direct band gap also leads to more rapid recombination, the relative rate of non-radiative recombination can be lower, and in direct band gap materials (such as GaAs) emitted photons can sometimes be reabsorbed in a mechanism known as photon recycling that increases the efficiency of the cell. In many cases careful engineering can lead to highly efficient thin-film solar cells requiring much less material than traditional silicon solar cells. Furthermore, it has proved possible to deposit thin films using familiar technologies developed in other branches of the semiconductor industry. As a result, some reasonably efficient thin-film PVs are already cost competitive (on a cost per watt basis) with silicon PVs.
The roll-to-roll production systems that are used in other parts of the technology industry could, in principle, be used to produce large quantities of inexpensive thin-film PV modules, which could radically alter the large-scale deployment of PV systems. Cheap, lightweight, flexible modules could, for example, be adapted for use in gigawatt-scale desert power systems or building-integrated installations where flexible PV sheets could be wrapped around the exposed surfaces of urban buildings.
Unfortunately, all of the thin-film PV materials that have been developed to a commercial level so far make use of chemical elements that are far less abundant than silicon (see below). The quest for an earth-abundant, thin-film PV is one of the most active areas of research in the field of photovoltaic power. This field is developing rapidly, and mostly beyond the scope of this book; we provide a few comments on the main materials that have been used in large-scale commercial photovoltaics of this type.
Cadmium Telluride (CdTe) Like gallium arsenide (see Box 25.2), cadmium telluride forms a zincblende crystalline semiconductor, and has a direct band gap eV. Cadmium is toxic, but relatively plentiful. Tellurium, on the other hand, is one of the least abundant solid elements in Earth's crust, rarer than gold. Nevertheless, tellurium is relatively inexpensive because it is produced (in small quantities) as a by-product of copper refining. Research-cell efficiencies for CdTe had reached by the end of 2016 [156], with commercial efficiencies somewhat lower. Unlike crystalline silicon, CdTe has been deposited and fabricated into an integrated PV cell in a roll-to-roll manufacturing processes. In 2010 CdTe broke the $1/W barrier for PV cell manufacturing cost, and the cost has continued to decline in subsequent years. CdTe photovoltaic cells have entered large-scale production: in 2015 approximately 4% of the global PV market and 60% of thin-film PVs were CdTe [155]. Concerns about the cost and supply limitations on tellurium cloud the future of this otherwise promising technology.
