Solar cells have been made from a wide variety of materials, including polycrystalline silicon, germanium, and III-V compounds such as Gallium-Arsenide (GaAs), Indium Phosphide (InP), and others in various combinations. Solar cells have a p-n junction that absorbs photons of light that match the bandgap energy of that p-n junction, which depends on the exact semiconductor material used. Electron-hole pairs are created when photons are absorbed, and these flow as current generated by the solar cell.
Semiconductor materials such as silicon (Si) and GaAs can be grown as large crystals and sliced into thin wafers that act as substrates. One or more epitaxial or epi layers can be grown on the wafer substrate. For example, a GaAs epi layer can be grown on a silicon wafer substrate.
Wafer substrates can have different orientations. FIG. 1 shows (111) and (100) planes in a crystal. FIG. 1 shows a face-centered-cubic (FCC) structure that is repeated in three dimensions in a FCC crystal. The six surfaces of the FCC cube are (100) surfaces that define (100) planes, or planes parallel or perpendicular to (100). If a grown crystal is cut along the (100) plane, it is considered to be a (100) substrate. The flat surface of the (100) substrate is parallel to one of the (100) planes.
The (111) plane passes through atoms 902, 904, 906 at 3 of the 8 corners of the FCC cube. A crystal cut along this plane is considered to be a (111) substrate. The flat surface of the (111) substrate is parallel to the (111) plane.
In semiconductor manufacturing wafers of (100) silicon are commonly used, although (111) silicon is sometimes used. Silicon has a diamond structure that has two inter-penetrating FCC structures that are offset from one another by (¼, ¼, ¼), where 1 is the distance along one side of the FCC cube.
GaAs has a different crystal structure than silicon. GaAs has a zincblende crystal structure with two inter-penetrating FCC structures, one for Ga atoms and the other for As atoms. In the GaAs zincblende crystal structure the As FCC structure is (¼, ¼, ¼) away from the Ga FCC structure. Since GaAs has both Ga and As atoms, its crystal structure is polarized in the (111) direction.
FIG. 2 shows a silicon epi layer grown on a silicon substrate. When the silicon epi layer is grown, such as by silane gas in a gas-phase reactor, the silicon atoms form the gas attach to the silicon atoms exposed on the surface of the silicon substrate to grow the epi layer. Several atomic layers are grown as the epi layer.
The lattice constant A of the silicon substrate is the same as the lattice constant B of the silicon epi layer, since the epi layer is made of the same material as the substrate. Also, the orientation of the epi layer matches that of the substrate when the epi growth is controlled. The density of crystal defects in the epi layer can be very low, perhaps matching or even exceeding that of the substrate.
FIG. 3 shows a GaAs epi grown on a Si substrate. GaAs does not have exactly the same lattice constant as Si. For example, only 25 Ga and 25 As atoms may fit in the same amount of linear space as 26 Si atoms. Silicon's lattice constant A is slightly smaller than GaAs's lattice constant B. This slight mis-match is ultimately caused by the difference in atomic sizes and properties of Ga, As, and Si.
When GaAs is grown as an epi layer over a Si substrate, such as in a chemical-vapor-deposition (CVD) reactor, the Ga and As atoms may initially have the same spacing A as the Si atoms in the substrate. However, after a few layers of GaAs are grown, the lattice strain from the difference in lattice constants causes the GaAs lattice to adjust back to the spacing of its lattice constant B. This creates a dislocation. For example, there may be one such dislocation for every 26 Si atoms, since there are only 25 Ga and 25 As atoms in the same linear spacing. The density of dislocations may be proportional to the lattice mismatch.
These dislocations are undesirable since they can reduce the efficiency of a solar cell. Dislocations can trap electron-hole pairs, allowing them to recombine and reduce the current produced by the solar cell. Dislocations can also increase resistance to current flow. The stress due to lattice mismatch can cause bowing and warping of the whole wafer during or after epitaxial layer growth, which is also undesirable.
FIGS. 4A-B highlight differences in step height at terraces in (100) silicon and GaAs substrates. In FIG. 4A, GaAs (100) substrate 230 has a zincblende lattice structure. GaAs (100) substrate 230 is cut in the (100) orientation. However, the cut is not exactly parallel to the (100) crystal planes, and may be off by a small angle, such as 0.5 degree. This non-exact cut produces a vicinal substrate surface.
The misorientation from an exact orientated singular surface causes steps and ledges on a vicinal surface. The vicinal surface has flat areas known as terraces 244 that are atomically flat. Steps 242 are ledges between terraces 244. The height of these steps 242 depends on the lattice structure, orientation, and substrate material. For example, the GaAs (100) substrate has a step height of ½ of the lattice constant.
FIG. 4B shows Si (100) substrate 212 which also has a vicinal surface. Si (100) substrate 212 has a diamond structure. Due to the diamond structure, steps 222 between terraces 246 have a step height of only ¼ of the lattice constant. Thus Si (100) substrate 212 has a step height of only ¼ while GaAs (100) substrate 230 has a step height of ½.
GaAs has to have layers for both Ga and As atoms to be stable, whereas Si needs only one layer of Si for stability. Thus the step height of GaAs is double that of Si. The roughly double-size step height of GaAs (100) substrate 230 relative to Si (100) substrate 212 makes is difficult to grow low-defect GaAs epi layers on Si (100) substrate 212.
FIGS. 5A-C highlight defects created when GaAs is grown on Si (100) substrates. Epitaxial layers first grow from steps rather than from the terraces of a vicinal substrate. These steps provide a nucleation site that allows gas-phase atoms to adhere to the substrate and begin growth of the epitaxial layer.
In FIG. 5A, Si (100) substrate 212 is exposed to a gas mixture that provides Ga and As atoms, such Tri-methyl-gallium gas and Arsine gas. Ga and As atoms are first deposited at and adhere to steps 222, 223, 224 and begin forming GaAs epi films 216, 217, 218. These GaAs epi films 216, 217, 218 grow outward from steps 222, 223, 224 along the terraces of Si (100) substrate 212.
Since GaAs has a step height of ½, while Si has a step height of ¼ on the (100) orientation, as shown in FIGS. 4A-B, GaAs epi films 216, 217, 218 grow in a layer that is ½ of the lattice constant thick, or double the height of silicon steps 222, 223, 224. This double-height step of GaAs causes GaAs epi films 216, 217, 218 to extend above the top of steps 222, 223, 224 as shown in FIG. 5A.
Since GaAs has both Ga and As atoms, its crystal is polarized in the (111) direction. Adjacent Silicon step terraces have different surface reconstruction that causes GaAs layers grown on adjacent terraces to have different orientations, one turned 90 degree from the other.
As growth of the epi films continues along the terraces, outward from steps 222, 223, 224, eventually the edge of the terrace is reached. In FIG. 5B, GaAs epi film 216 has grown across its terrace, reaching the end of the terrace at step 223. Likewise, GaAs epi film 217 has grown to the end of its terrace at step 224. GaAs epi film 216 has grown to the right along the terrace to touch adjacent GaAs epi film 217 at step 223. Likewise, GaAs epi film 217 has grown to the right along the terrace to touch adjacent GaAs epi film 218 at step 224.
Since GaAs epi films 216, 217 have opposite crystal phases, GaAs epi film 216 cannot continue growing to the right over GaAs epi film 217. Also, GaAs epi film 217 has a ¼ step height relative to the terrace of Si (100) substrate 212. This ¼ height step blocks further growth to the right of GaAs epi film 216 beyond step 223 and over GaAs epi film 217. Instead of continuing to grow sideways, GaAs epi films 216, 217, 218 grow upward after reaching the edge of the terraces, as shown in FIG. 5C.
Since GaAs epi films 216, 217 have opposite crystal phases, a boundary between GaAs epi films 216, 217 is formed within the crystal as the crystal phase changes from +90 degrees to +0 degrees. This boundary is known as an anti-phase boundary (APB). An APB also is formed between GaAs epi films 217, 218 over step 224.
APB's are a type of stacking fault. These phase boundaries are propagated upward in the new epi layer as GaAs epi films 216, 217, 218 grow, as shown in FIG. 5C. These APB's were formed due to the crystalline nature of a compound of two kinds of atoms (Ga and As) growing on an elemental substrate having only 1 kind if atom (Si). These APB's are undesirable since they are a type of defect in the epi crystal.
FIGS. 6A-B highlight similarities in step heights of (111)-orientated silicon and Gallium-Arsenide. In FIG. 6A, a vicinal surface of GaAs (111) substrate 228 has a step height of 1/SQRT(3) of the lattice constant of GaAs, or about 0.577 of the lattice constant of GaAs. In FIG. 6B, a vicinal surface of Si (111) substrate 202 has a step height of the reciprocal of the square root of 3, 1/SQRT(3), of the lattice constant of Si, or about 0.577 of the lattice constant of Si. Since the lattice constants of Si and GaAs are near each other, although not exactly equal, these step heights for Si (111) substrate 202 and GaAs (111) substrate 228 are quite close to each other. In contrast, FIGS. 4A-B showed that the step height of GaAs was about double that of Si for the (100) orientation. Thus a much better match of step heights of Si and GaAs occurs on the (111) surfaces than on the (100) surfaces.
FIGS. 7A-B highlight epitaxial layers of GaAs grown on a Si (111) substrate. In FIG. 7A, Si (111) substrate 202 is exposed to a gas that provides Ga and As atoms, such as Tri-methyl-gallium and Arsine gases. Ga and As atoms are first deposited at and adhere to steps 204 and begin forming GaAs epi films 206, 207. These GaAs epi films 206, 207 grow outward from steps 204 along the terraces of Si (111) substrate 202.
Since GaAs has a step height of 1/SQRT(3) of the GaAs lattice constant, while Si has a step height of 1/SQRT(3) of the Si lattice constant on the (111) orientation, as shown in FIGS. 6A-B, GaAs epi films 206, 207 grow in a layer that is close to the height of silicon steps 204. This similar-height step of GaAs causes GaAs epi films 206, 207 to be close to flush with the top of steps 204 as shown in FIG. 7A.
GaAs crystal is polarized. GaAs can be though of as a FCC crystal lattice of a GaAs molecule, with one GaAs molecule occupying each lattice point in the FCC lattice. However, the GaAs molecule is polarized so that the Ga atom is in the (111) direction while the As atom is in the (−1 −1 −1) direction.
The Burgers vector of the FCC structure is ½<110>. On the (111) surface with GaAs on top of Si in a coincidence site lattice, for every 25 Ga (or As) atoms, there are 26 Si atoms. These two rows of atoms form a Burgers vector in one of the <110> directions parallel to the surface. In a triangle in the (111) direction with 25 Ga (or As) atoms at each side of the triangle with 26 Si atoms right below, we have 3 Burgers vectors in 3 different <110> directions all parallel to the (111) surface on this triangle, and they cancel out. Burgers vectors with 3 different <110> directions cancel out at the interface between the Si substrate and the GaAs epi layer.
In a more complicated structure such as zincblende or diamond, ½<110> dislocations might be separated into ⅙<112> partial dislocations. These ⅙<112> partial dislocations also cancel out (See C. B. Carter, G. Anderson, F. Ponce Phil. Mag. A 63 (1991) 279). Thus, in a coincidence site lattice in the <111> direction, all dislocations are cancelled at the interface, and do not propagate into the epitaxial layers. If no additional defects are introduced through lattice mismatch and APBs, the epitaxial layer should have the same defect density as the starting substrate.
As growth of the epi films continues along the terraces, outward from steps 204, eventually the edge of the terrace is reached. In FIG. 7B, GaAs epi film 206 has grown across its terrace, reaching the end of the terrace at the next step 204. GaAs epi film 206 has grown to the right along the terrace to touch adjacent GaAs epi film 207 at step 204.
Since GaAs epi films 206, 207 have the same crystal phase, GaAs epi film 206 can continue growing to the right over GaAs epi film 207. Also, GaAs epi film 207 has a nearly equal step height relative to the terrace of Si (111) substrate 202. This nearly equal step height allows further growth to the right of GaAs epi film 206 beyond step 204 and over GaAs epi film 207. GaAs epi films 206, 207 can also grow upward after reaching the edge of the terraces.
Since GaAs epi films 206, 207 have identical crystal phases, no boundary between GaAs epi films 206, 207 is formed within the crystal at steps 204, unlike the case of Si (100) substrate 212 shown in FIG. 5B. The anti-phase boundary (APB) and any stacking faults have been avoided.
The inventor has realized that the much better match of step heights and the lack of multiple crystal phases of Si (111) substrate 202 should yield GaAs epitaxial layers with much lower defect densities than for Si (100) substrate 212. The lower defect densities should produce higher efficiency devices such as solar cells, lasers, and light-emitting diodes.
FIG. 8 is a graph of solar cell efficiency as a function of dislocation density. For a solar cell within a single p-n junction, the efficiency is about 25% when the dislocation density is less than 5×105 defects per cm2 of surface area. However, when defects increase above 5×105, the efficient drops off. Efficiency drops to about 7% for high defect densities such as 108.
Efficiencies are higher for solar cells with multiple p-n junctions. The multi-junction efficiency is about 36% when the dislocation density is less than 5×105 defects per cm2 of surface area. When defects increase above 5×105, the efficient drops off to about 19% for high dislocation densities such as 108.
Of course, the actual efficiency of any solar cell varies, but the effect of dislocation density on efficiency should be similar.
Solar cells, lasers, and light-emitting diodes that are constructed from GaAs epitaxial layers grown over Si (111) substrates are thus desirable. Low-defect-density epi layers grown over (111) silicon substrates is desirable since multi-junction solar cells having many epi layers could be produced with high efficiencies. Multiple layers of GaAs and other III-V and similar materials grown over Si (111) substrates is desired.