LATTICE-GRADED EPILAYERS

Abstract: Lattice-graded epilayers (13, 43) composed of materials belonging to the cubic crystal system. The epilayers (13, 43) are disposed on curved-surface regions (11, 41) of crystalline substrates (21, 49). If the lattice constant of the epilayer (13 or 43) adjacent to the curved-surface regions (11 or 41) is greater than the lattice constant on the opposite side (9 or 39) of the epilayer (13 or 43), concave-shaped curved-surface regions (11) are used, and if the converse is true, then convex-shaped curved-surface regions (41) are used.

Description: LATTICE-GRADED EPILAYERS Technical Field The present invention relates to epitaxial layers ("epilayers") having a crystal structure that belongs to the cubic crystal system and which are graded in lattice constant ("lattice-graded") from an initial value adjacent to the substrate on which they are disposed to a final value which differs from this initial value. Background Art The atoms in a crystal are arranged in a three- dimensional array known as the lattice. In a crystal of uniform composition, a unit cell can be identified which repeats itself to generate the lattice. The unit cell contains complete information regarding the arrangement of atoms in a lattice and can be used to describe the crystal. Crystals can be allocated into seven crystal systems, one of which is the cubic crystal system. In the cubic crystal stem, a unit cell can be specified by a single scalar quantity known as its lattice constant which is the length of one edge of a cube containing the unit cell. Disclosure of Invention The present invention is concerned solely with lattice-graded epilayers having a crystal structure belonging to the cubic crystal system. Such materials include, for example, such group III elements as silicon and germanium, and such III-V compound materials as the phosphides, arsenides, and antinimides of gallium, alumi¬ num and indium. Lattice-graded epilayers can be used to grade the lattice constant from that of an available low-cost substrate to that of a material possessing properties of interest but which is costly or is not available in the form of a substrate. Since the active regions of many electronic and electro-optical devices are only a few micrometers thick, an epilayer of a desired material may be grown over a lattice-graded epilayer for the purpose of producing such devices. The materials of which a lattice-graded epilayer is composed may also have differing values of energy bandgap. As a consequence, the lattice-graded epilayer may also be graded in energy bandgap value ("bandgap- graded") . It is an object of the present invention to provide lattice-graded epilayers composed of materials belonging to the cubic crystal system. It is an additional object of the present inven¬ tion to provide lattice-graded epilayers composed of mate¬ rials belonging to the cubic crystal system which are bandgap-graded. Briefly, in accordance with the principles of my invention and in the preferred embodiment thereof, a lat¬ tice-graded epilayer is disposed on a plurality of sub¬ strate surface regions which are not flat but are curved in shape ("curved-surface regions") . The curved-surface regions are convex in shape ("convex-shaped") when the lattice constant at points in the lattice-graded epilayer increases as a function of a distance from the curved- surface regions on the substrate and are concave in shape ("concave-shaped") when the lattice constant at points in the lattice-graded epilayer decreases as a function of distance from the curved-surface regions on the substate. In general, when a section is taken by passing a flat plane through a curved-surface region at a point, the radius of curvature of the intersection of this plane with this surface that appears o_, this section at that point will be a function of the orientation of this plane with respect to this surface and will differ for different such orientations. For reasons that will become clear later and for the purposes of the present application, the convention is hereby established that when the radius of curvature at a point on a curved-surface region is referred to, what will be meant will be that radius of curvature of the various possible intersections of such planes with the curved-surface region at that point which has the largest magnitude. (This radius of curvature will establish, in conjunction with other variables, the mini¬ mum thickness of the lattice-graded epilayer required at that point for strain-free growth of the epilayer.) It will also be assumed that the point is not what is referred to in mathematics as a saddle-point. The lattice-graded epilayers are formed on the curved-surface regions on the substrates by a growth process, e.g., chemical vapor deposition or molecular beam epitaxy can be used for this purpose. The growth process commences with the growth of epitaxial material having an initial lattice constant compatible with the growth of high-quality material on the substrate, and ends with the growth of epitaxial material having a desired final value of lattice constant. For certain applications of lattice- graded epilayers, this final value of lattice constant may be required to be compatible with the growth of a high- quality epitaxial layer of a desired material over the surface of the lattice-graded epilayer. The change in the material composition of the lattice-graded epilayer during its growth which results in the change in its lattice constant can be achieved by varying the material composi¬ tion of the nutrient medium supplying the materials for the growth of the epilayer, as is well-known in the art. The curved-surface regions on the substrate can be formed from an initially-flat surface using techniques well-known in the art. For example, photolithographic techiques can be used in conjunction with liquid or reactive-ion etchants to form the curved-surface regions. It is well-known in the art that it is prefer- able to use single-crystal crystalline substrates rather than multi-crystal crystalline substrates and to use substrates with low defect counts per unit of surface area in order to obtain high-quality epilayers. In a particular example, a plurality of convex- shaped curved-surface regions are formed on the surface of a crystalline silicon substrate. These convex-shaped curved-surface regions have surfaces that conform well to portions of spherical surfaces of-radii Rl equal to 100 micrometers and intercept adjacent flat regions on the surface of the substrate at circles of diameter D equal to 50 microme-ters separated from each other by center-to- center distances of D plus 10 micrometers. A lattice- graded silicon-germanium epilayer disposed on the plural¬ ity of curved-surface regions and that is graded from the lattice constant of silicon (5.431 Angstroms) to the lat- tice constant of germanium (5.657 Angstroms) is desired. For reasons that will become clear below, the thickness of this epilayer must exceed 4.2 micrometers. The epilayer is grown by means of the thermal decomposition of a nutrient mixture containing silane and germanium tetra- chloride as the relative proportions of these materials in the nutrient mixture is varied during the growth process, starting the epilayer growth with a substrate temperature of 1100 degrees Centrigrade with the growth of silicon from silane and ending the epilayer growth with a substrate temperature of 850 degrees Centigrade with the growth of germanium. If desired, an epilayer of gallium arsenide can be grown over the germanium surface of the lattice-graded epilayer since the lattice constant of gallium arsenide is compatible with the lattice constant of germanium for such growth. In a lattice-graded epilayer, the strain at a point is a function of the lattice constant of the mate¬ rial at that point as well as of the spatial distribution of the lattice constants of the material of the epilayer and the substrate in the vincinity of that point. If the strain exceeds the elastic limit of the material at the point, defects appear in the epilayer which may be detri¬ mental for devices which incorporate the lattice-graded epilayer, and thus such defects should be avoided. The present invention provides lattice-graded epilayers in which the appearance of defects arising from strains that exceed the elastic limits of the epilayer materials is minimized. Consider the strain produced in an element of volume of a very thin, initially flat, lattice-graded epilayer by bending the epilayer into a spherical shape with a radius of curvature R. This strain is a function of R, the differential epilayer thickness in the radial direction dR, the lattice constant a(R), and the differen¬ tial change in the lattice constant in the radial direc- tion da(R). The relationship is: strain = dR/R -da(R)/a(R). If the strain is zero, then: da(R, /a(R) = dR/R, or da(R)/dR = a(R)/R. An actual lattice-graded epilayer can be con¬ sidered to result from the composite effect of many thin constituent lattice-graded epilayers, each of thickness dR. It is possible to interleave thin epilayers of constant lattice constant with the lattice-graded thin epilayers since growth of epitaxial material of constant lattice constant equal to that of its substrate can be produced on a surface of arbitrary shape without intro¬ ducing strain (although strain may be transmitted to such epilayers from adjacent material), i.e., the epilayer growth may be viewed ' as a linear combination of lattice- graded and constant lattice constant growth. Thus, as long as the rate of change in the lattice constant as a function of epilayer thickness is less than the limit imposed by the equality in the above equations for the variation of a(R) as a function of R, the lattice-graded epilayer can be strain-free despite the change in the lattice constant. Two cases arise. If the lattice constant is increased during the growth of the lattice-graded epi- layer, strain-free growth of the epilayer can be achieved if da(R)/dR is maintained less than or equal to a(R)/R and the epilayer is grown on convex-shaped curved-surface regions. If R2 is greater than Rl, then a(R2)/a(Rl) must be less than or equal to R2/R1. In the second case, the lattice constant is decreased during the growth of the lattice-graded epilayer and the epilayer is grown on concave-shaped curved-surface regions. If R2 is less than Rl, then a(R2)/a(Rl) must be greater than or equal to R2/R1 for strain-free growth of the epilayer. From the above results, it can be shown that if R' is the radius of curvature at a point on a curved- surface region of a substrate, then the minimum thickness of a lattice-graded epilayer grown without strain is equal to R' multiplied by the absolute magnitude of the total change in lattice constant of the epilayer and divided by the lattice constant of the epilayer adjacent to that point. It is now clear why the convention was established above that the largest value of the various radii of curvature of the intersections of flat planes of different orientations with the curved-surface region at a point is taken as the radius of curvature of the curved-surface region at that point since it is the minimum thickness of the lattice-graded epilayer required for strain-free growth of the epilayer that is of concern. After a plurality of curved-surface regions are formed on a given crystalline substrate, the lattice- graded epilayer is grown on these curved-surface regions. After the lattice-graded epilayer has been grown over the curved-surface regions, epilayer growth may be continued if desired, e.g., with material of constant lattice con¬ stant. This may involve some overgrowth of regions adja- cent to the curved surface regions by the epilayer. Such overgowth is well-known in the art. Brief Description of Drawing In the drawing, in which the views are not drawn to scale: FIG. 1 is a cross-sectional view of a lattice- graded epilayer disposed on a concave-shaped curved-sur¬ face region of a substrate; FIG. 2 is a view of the surface of a substrate on which a plurality of concave-shaped curved-surface regions has been formed; FIG. 3 is a cross-sectional view of a lattice- graded epilayer disposed on a convex-shaped curved-surface region of a substrate; and FIG. 4 is a view of the surface of a substrate on which a plurality of convex-shaped curved-surface regions has been formed. Modes ' for Carrying Out the Invention In FIG. 1, a cross-sectional view is shown of a portion of a substrate 21 on which a concave-shaped curved-surface region 11 has been formed. The curved- surface region 11 conforms well to a portion of a spheri¬ cal surface with radius of curvature 17 having a center 19. A lattice-graded epilayer 13 is disposed on the curved-surface region 11. The lattice constant of this epilayer 13 adjacent to the curved-surface region 11 of the substrate 21 is a(radius of curvature 17), and this value of lattice constant is, preferably, compatible with the lattice constant of the substrate 21 so that epilayer material of good crystalline quality can be grown over the curved-surface region 11. As previously mentioned, it is assumed that the crystal structures of the lattice-graded epilayers disclosed herein belong to the cubic crystal system. Thus, epilayer 13 is assumed to have a crystal structure belonging to the cubic crystal system. For- the epilayer 13 to have good crystalline quality, it is usually beneficial if the crystal structure of the crystalline substrate on which the epilayer is grown also belongs to the cubic crystal system, although this is not always necessary. The upper surface 9 of the lattice-graded epi¬ layer 13, preferably, conforms well to a portion of a spherical surface of radius of curvature 15 having a center 19. The lattice constant of the lattice-graded epilayer at surface 9 is a(radius of curvature 15). For strain-free growth of the epilayer, radius of curvature 17 divided by radius of curvature 15 is equal to or greater than a(radius of curvature 17) divided by a(radius of curvature 15) . In FIG. 2, a view is shown of surface 23 of substrate 21. On surface 23, a plurality of concave- shaped curved-surface regions 11 separated by flat region 25.is shown. In FIG. 3, a cross-sectional view is shown of a portion of a substrate 49 on which a convex-shaped curved- surface region 41 has been formed. The curved-surface region 41 conforms well to a portion of a spherical surface of radius of curvature 45 having a center 37. A lattice-graded epilayer 43 is disposed on the curved- surface region 41. The lattice constant of the epilayer 43 adjacent to the curved-surface region 41 is a(radius of curvature 45) , and this value of lattice constant is, preferably, compatible with the lattice constant of the substrate 49 so that epitaxial material of good crystal quality can be grown over the curved-surface region 41. As previously mentioned, it is assumed that the crystal structure of the lattice-graded epilayer 43 belongs to the cubic crystal system. For the epilayer 43 to have good crystal quality, it is usually beneficial if the crystal structure of the crystalline substrate also belongs to the cubic crystal system. The upper surface 39 of the lattice-graded epi¬ layer 43, preferably, conforms well to a portion of a spherical surface of radius of curvature 47 having a center 37. The lattice constant of the lattice-graded epilayer 43 at surface 39 is a(radius of a curvature 47). For strain-free growth of the epilayer 43, radius of curvature 47 divided by radius of curvature 45 is equal to or greater than a(radius of curvature 47) divided by a(radius of curvature 45). While the sections shown in FIGS. 1 and 3 each have a single curved-surface region that conforms well to a portion of a single spherical surface, i.e., have a single radius of curvature, it is not necessary that each entire curved-surface region have a single radius of cur- vature. Rather, it is to be explicitly understood that an actual curved-surface region may be regarded as being constituted by differential surface elements of area, each of which has a different radius of curvature, and the conditions disclosed herein for strain-free lattice-graded epilayers are applicable to each such differential surface element of area considered as a curved-surface region on which the epilayer growth takes place. The minimum thickness of a lattice-graded epilayer at each point of a curved-surface region where the epilayer has been grown without strain due to the lattice-grading is equal to the radius of curvature of the curved-surface region at that point multiplied by the absolute magnitude of the difference between the lattice constant of the epilayer adjacent to the substrate and the lattice constant of the epilayer on its side opposite to its side adjacent to the substrate and divided by the value of the lattice constant of the epilayer adjacent to the substrate. If the curved-surface regions have a maximum radius of curvature, then a minimum thickness of the epilayer can be taken to be the product of this maximum radius of curvature multiplied by the absolute magnitude of the difference in lattice constants on the two sides of the epilayer and divided by the value of the lattice constant of the epilayer adjacent to the curved-surface regions of the substrate. In FIG. 4, a view is shown of surface 53 of substrate 49. On surface 53, a plurality of convex-shaped curved-surface regions 41 separated by flat region 51 is shown. In general, a lattice-graded epilayer according to the present invention is disposed on convex-shaped curved-surface regions of a substrate if the lattice constant of the epilayer adjacent to the curved-surface regions is less than the lattice constant of the epilayer on the side of the epilayer opposite to the side of the epilayer adjacent to the substrate, and is disposed on concave-shaped curved-surface regions of a substrate if the lattice constant of the epilayer adjacent to the curved-surface regions is greater than the lattice constant of the epilayer on the side of the epilayer opposite to the side of the epilayer adjacent to the substrate. Industrial Applicability Lattice-graded epilayers may be incorporated in electronic and electro-optical devices. Bandgap-graded epilayers are utilized in certain types of detectors and solar cells, for example.

Claims: Claims 1. An epitaxial layer composed of materials belonging to the cubic crystal system disposed on a plu¬ rality of curved-surface regions of a substrate; charac- terized in that: said epitaxial layer has a first lattice constant on a first side of said epitaxial layer, said first side of said epitaxial layer being adjacent to said substrate, and a second lattice constant on the side of said epitaxial layer opposite to said first side; said first lattice constant differs from said second lattice constant; and said curved-surface regions are convex-shaped where said first lattice constant is less than said second lattice constant, and said curved-surface regions are concave- shaped where said first lattice constant is greater than said second lattice constant. 2. An epitaxial layer as claimed in claim 1 wherein the epitaxial layer disposed on each point on each curved-surface region has a thickness greater than the radius of curvature at such point multiplied by the abso- lute value of the difference between said first lattice constant and said second lattice constant and divided by said first lattice constant. 3. An epitaxial layer composed of materials belonging to the cubic crystal system disposed on a plu- rality of curved-surface regions of a substrate; charac¬ terized in that: said epitaxial layer has a first lattice constant on a first side of said epitaxial layer, said first side of said epitaxial layer being adjacent to said substrate, and a second lattice constant on the side of said epitaxial layer opposite to said first side; said first lattice constant differs from said second lattice constant; and said curved-surface regions are concave- shaped and said first lattice constant is greater than said second lattice constant. 4. An epitaxial layer as claimed in claim 3 wherein the epitaxial layer disposed on each point on each curved-surface region has a thickness greater than the radius of curvature at such point multiplied by the abso¬ lute value of the difference between said first lattice constant and said second lattice constant and divided by said first lattice constant. 5. An epitaxial layer composed of materials ■ belonging to the cubic crystal system disposed on a plu¬ rality of curved-surface regions of a substrate; charac¬ terized in that: said epitaxial layer has a first lattice constant on a first side of said epitaxial layer, said first side of said epitaxial layer being adjacent to said substrate, and a second lattice constant on the side of said epitaxial layer opposite to said first side; said first lattice constant differs from said second lattice constant; and said curved-surface regions are convex-shaped and said first lattice constant is less than said second lattice constant. 6. An epitaxial layer as claimed in claim 5 wherein the epitaxial layer disposed on each point on each curved-surface region has a thickness greater than the radius of curvature at such point multiplied by the abso¬ lute value of the difference between said first lattice constant and said second lattice constant and divided by said first lattice constant.

Inventors: COOK MELVIN S, COOK, MELVIN, S.
Applicants: HOLOBEAM, HOLOBEAM, INC.
Application year: 1986
Main classification: H01L21
IPC codes: H01L21