mu uuuu ui iiui imi uui um um iuu mu iuu mui uu uii mi

mu uuuu ui iiui imi uui um um iuu mu iuu mui uu uii mi (12) United States Patent

Parr et al.

(54) HYBRID BANDGAP ENGINEERING FOR SUPER-HE TERO-EPITAXIAL SEMICONDUCTOR MATERIALS, AND PRODUCTSTHEREOF

(75) Inventors: Yeonjoon Park, Yorktown, VA (US); Sang H. Choi, Poquoson, VA (US); Glen C. King, Yorktown, VA (US); James R. Elliott, Yorktown, VA (US)

(73) Assignee: The United States of America as represented by the Administrator of the National Aeronautics and Space Administration, Washington, DC (US)

(*) Notice: Subject to any disclaimer, the term of this patent is extended or adjusted under 35 U.S.C. 154(b) by 933 days.

(21) Appl. No.: 12/254,134

(22) Filed: Oct. 20, 2008

(65) Prior Publication Data

US 2009/0220047 Al Sep. 3, 2009

Related U.S. Application Data

(60) Provisional application No. 60/980,881, filed on Oct. 18, 2007, provisional application No. 60/980,880, filed on Oct. 18, 2007, provisional application No. 60/980,878, filed on Oct. 18, 2007, provisional application No. 60/980,871, filed on Oct. 18, 2007, provisional application No. 60/980,870, filed on Oct. 18, 2007.

(51) Int. Cl. C30B 25118 (2006.01)

(52) U.S. Cl . ................ 117/84; 117/88; 117/89; 117/90; 117/91; 117/92; 117/93; 117/94; 117/101;

117/102; 117/103; 117/104; 117/105; 117/106; 117/107; 117/108

(58) Field of Classification Search .................... 117/84, 117/88-94,101-108,9

See application file for complete search history.

Method-i in real-space (rot X= 6,n=e) R

angle,q

(777) plane —

(220) plane —

Detector angle, 20

(1o) Patent No.: US 8,226,767 B2 (45) Date of Patent: Jul. 24 9 2012

(56) References Cited

U.S. PATENT DOCUMENTS

4,357,183 A 11/1982 Fan et al. 5,205,871 A 4/1993 Godbey et al. 5,394,826 A 3/1995 Ebe et al. 5,667,586 A 9/1997 Ek et al. 5,709,745 A 1/1998 Larkin et al. 5,759,898 A 6/1998 Ek et al.

(Continued)

OTHER PUBLICATIONS

A publication to K. Balakrishnan, et al. entitled "Structural analyses

of MBE grown cubic and hexagonal GaN epilayers by X-ray diffrac-tion," Bulletin of the Electrochemical Laboatory, vol. 60, No. 10, 11, pp. 531-540 (1998).*

(Continued)

Primary Examiner Michael Komakov Assistant Examiner KennethA Bratland, Jr. (74) Attorney, Agent, or Firm Thomas K. McBride, Jr.; Robin W. Edwards

(57) ABSTRACT

"Super-hetero-epitaxial" combinations comprise epitaxial growth of one material on a different material with different crystal structure. Compatible crystal structures may be iden-tified using a "Tri-Unity" system. New bandgap engineering diagrams are provided for each class of combination, based on determination of hybrid lattice constants for the constitu-ent materials in accordance with lattice-matching equations. Using known bandgap figures for previously tested materials, new materials with lattice constants that match desired sub-strates and have the desired bandgap properties may be for-mulated by reference to the diagrams and lattice matching equations. In one embodiment, this analysis makes it possible to formulate new super-hetero-epitaxial semiconductor sys-tems, such as systems based on group IV alloys on c-plane LaF,; group IV alloys on c-plane langasite; Group III-V alloys on c-plane langasite; and group II-VI alloys on c-plane sapphire.

3 Claims, 26 Drawing Sheets

X-ray Source

X-ray propagation direction

Some machines usa symbol psi,W Instead of symbol chi, X

https://ntrs.nasa.gov/search.jsp?R=20120012439 2018-03-27T07:22:30+00:00Z

US 8,226,767 B2

U.S. PATENT DOCUMENTS 2009/0206368 Al 8/2009 Park et al. 2009/0206369 Al 8/2009 Dang et al.

5,769,964 A 6/1998 Charache et al. 2009/0220047 Al 9/2009 Park et al. 5,951,757 A * 9/1999 Dubbelda et al. y 117/102 6,096,389 A 8/2000 Kanai OTHER PUBLICATIONS 6,100,546 A * 8/2000 Major et al . .................. 257/103 6,306,211 BI 10/2001 Takahashi et al. H. Wado, et al. "Epitaxial growth of SiGe on A1203 using Si2H6 gas 6,488,771 B1 12/2002 Powell et al. and Ge solid source molecular beam epitaxy," Journal of Crystal 6,524,935 B1 2/2003 Canaperi et al. Growth, vol. 169, pp. 457-62 (1996).* 6,562,127 BI 5/2003 Kud et al. T.P. Humphreys, et al., "Heteroepitaxial growth and characterization 6,627,809 B1 9/2003 Koga et al. of GaAs on silicon-on sapphire and sapphire substrates", Appl. Phys. 6,653,658 B2 11/2003 Burden Lett., 1989, vol. 54, pp. 1687-1689. 6,784,074 B2 8/2004 Shchukin et al. Nakamura, T. Mukai T, M. Senoh, "High-Power GaN P-N Junction 6,787,793 B2 9/2004 Yoshida Blue-Light-Emitting Diodes", Japanese Journal of Applied Physics 7,247,885 B2 7/2007 Rankin et al. Part 2-Letters 30 (12a): L1998-L2001 Dec. 1, 1991.). 7,341,883 B2 * 3/2008 Park et al . ....................... 438/46 O. Ambacher, "Growth andApplications of Group III-nitrides", Jour- 7,368,335 B2 5/2008 Asami et al. nal of Physics D Applied Physics 31 (20): 2653-2710 Oct. 21, 7,558,371 B2 7/2009 Park et al. 1998.). 7,769,135 B2 8/2010 Park et al. Yeonjoon Park, Michael J, Cich, Rian Zhao, Petra Specht, Eicke R. 7,906,358 B2 3/2011 Park et al. Weber, Eric Stach, Shinji Nozaki, "Analysis of Twin Defects in 8,044,294 B2 10/2011 Park et al. GaAS(I I I)B Moelcular Beam Epitaxy Growth", Journal of Vacuum

2004/0147079 Al 7/2004 Forbes et al. Science and Technology B 18 (3): 1566-1571 May-Jun. 2000.). 2004/0173790 Al 9/2004 Yeo et al. S. SANORPIM E. Talcum, R. Katayama, H. Ichinose, K. Onabe, Y. 2004/0190681 Al 9/2004 Omote Shiraki, "Characterization of MOVPE-grown GaN layers on GaAs 2004/0201022 Al 10/2004 Yamazaki et al. (III)B with a a cubic-GaN (I 11) epitaxial intermediate layer", 2 004/02 144 07 Al 10/2004 Westhoff et al. Physica Status Solidi B-Basic Research 240 (2) : 305-309 Nov. 2003. 2004/0221792 Al 11/2004 Forbes Z. Liliental-Weber, H. Sohn, N. Newman, J. Washburn, "Electron 2006/0163612 Al 7/2006 Kouvetakis et al. Microscopy Characterization of GaN Films Grown by Molecular- 2006/0211221 Al 9/2006 Mand et al. beam Epitaxy on Sapphire and SiC", Journal of Vacuum Science and 2006/0270200 Al 11/2006 Shibata Technology 13 (4): 1578-1581-Jul.-Aug. 1995. 2007/0069195 Al 3/2007 Park et al. Y. Park. G.C. King, S. H. Choi, "Rhombohedral Epitaxy of Cubic 2007/0168130 Al 7/2007 Sherwood et al. SiGe on Trigonal c-plane sapphire", Journal of Crystal Growth 310 2007/0222034 Al* 9/2007 Park et al . ..................... 257/616 (2008) 2724-2731. 2008/0113186 Al 5/2008 Kouvetakis et al. 2008/0257395 Al 10/2008 Jovanovic et al. * cited by examiner

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HYBRID BANDGAP ENGINEERING FOR SUPER-HE TERO-EPITAXIAL

SEMICONDUCTOR MATERIALS, AND PRODUCTSTHEREOF

ORIGIN OF THE INVENTION

This application claims the benefit of the respective filing dates of, and incorporates by reference the entire respective disclosures of, the following commonly assigned U.S. Provi-sional Patent Applications: Ser. No. 60/980,870 filed on Oct. 18, 2007, Ser. No. 60/980,871 filed on Oct. 18, 2007, Ser. No. 60/980,878 filed on Oct. 18, 2007, Ser. No. 60/980,880 filed on Oct. 18, 2007, and Ser. No. 60/980,881 filed on Oct. 18, 2007, each of which contains an overlap of inventive entity with the present application. In addition, this application incorporates by reference the entire disclosures of the follow-ing commonly assigned nonprovisional U.S. patent applica-tions being filed on the same date as the present application: Ser. No. 12/254,017, now U.S. Pat. No. 7,906,358, entitled "EPITAXIAL GROWTH OF CUBIC CRYSTALLINE SEMICONDUCTOR ALLOYS ON BASAL PLANE OF TRIGONAL OR HEXAGONAL CRYSTAL;" Ser. No. 12/254,016, now U.S. Pat. No. 8,044,294, entitled "THER-MOELECTRIC MATERIALS AND DEVICES;" Ser. No. 12/288,379, now U.S. Published Patent Application 2009/ 0206368, entitled "RHOMBOHEDRAL CUBIC SEMI-CONDUCTOR MATERIALS ON TRIGONAL SUB-STRATE WITH SINGLE CRYSTAL PROPERTIES AND DEVICES BASED ON SUCH MATERIALS;" Ser. No. 12/288,380, now U.S. Pat. No. 7,769,135, entitled "X-RAY DIFFRACTION WAFER MAPPING METHOD FOR RHOMBOHEDRAL SUPER-HETERO-EPITAXY;" and Ser. No. 12/254,150, now U.S. Pat. No. 7,558,371, entitled "METHOD OF GENERATING X-RAY DIFFRACTION DATA FOR INTEGRAL DETECTION OF TWIN DEFECTS IN SUPER-HETERO-EPITAXIAL MATERI-ALS;" each one claiming priority to the above-cited provi-sional applications.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of the respective filing dates of and incorporates by reference the entire respective disclosures of, the following commonly assigned U.S. Provi-sional Patent Applications: Ser. No. 60/980,870 filed on Oct. 18, 2007, Ser. No. 60/980,871 filed on Oct. 18, 2007, Ser. No. 60/980,878 filed on Oct. 18, 2007, Ser. No. 60/980,880 filed on Oct. 18, 2007, and Ser. No. 60/980,881 filed on Oct. 18, 2007, each of which contains an overlap of inventive entity with the present application. In addition, this application incorporates by reference the entire disclosures of the follow-ing commonly assigned nonprovisional U.S. patent applica-tions being filed on the same date as the present application: Ser. No. 12/254,017, entitled "EPITAXIAL GROWTH OF CUBIC CRYSTALLINE SEMICONDUCTOR ALLOYS ON BASAL PLANE OF TRIGONAL OR HEXAGONAL CRYSTAL;" Ser. No. 12/254,016, entitled "THERMO-ELECTRIC MATERIALS AND DEVICES;" Ser. No. 12/288,379, entitled "RHOMBOHEDRAL CUBIC SEMI-CONDUCTOR MATERIALS ON TRIGONAL SUB-STRATE WITH SINGLE CRYSTAL PROPERTIES AND DEVICES BASED ON SUCH MATERIALS;" Ser. No. 12/288,380, entitled "X-RAY DIFFRACTION WAFER MAPPING METHOD FOR RHOMBOHEDRAL SUPER-HETERO-EPITAXY; " and Ser. No. 12/254,150, entitled

2 "METHOD OF GENERATING X-RAY DIFFRACTION DATA FOR INTEGRAL DETECTION OF TWIN DEFECTS IN SUPER-HETERO-EPITAXIAL MATERI-ALS;" each one claiming priority to the above-cited provi-

5 sional applications.

BACKGROUND OF THE INVENTION

1. Field of the Invention The present invention is in the fields of solid-state physics

to and semiconductor materials, and more particularly concerns bandgap energy engineering analysis for new semiconductor alloy systems comprising hybrid epitaxial semiconductor crystal structures on heterogeneous substrates, including combinations of cubic, trigonal and hexagonal crystal mate-

15 rials. 2. Description of the Related Art For the last 60 years since the invention of the first transis-

tor by Bardeen, Brattain, and Shockley in 1947, the global microelectronics industry has used diamond structured group

20 IV semiconductor crystals such as silicon (Si) and germa-nium (Ge). Another cubic compound semiconductor crystal structure, i.e. zinc-blende-alpha structure with group III-V and group II-VI, was also utilized by the semiconductor industry for the last 30 years. In the early 1990s, new semi-

25 conductor materials in different crystal structures were intro-duced in the microelectronics industry, including gallium nitride (GaN), aluminum nitride (AIN), and indium nitride (InN) in wurtzite structure. (See S. Nakamura, T. Mukai T, M. Senoh, Japanese Journal OfApplied Physics Part 2-Letters 30

30 (12a): L1998-L2001 Dec. 1, 1991.)

The term "bandgap" generally refers to the energy differ-ence between the top of the valence hand and the bottom of the conduction band of a material, the energy gap that enables electrons to jump from one band to another. "Bandgap engi-neering" is the process of controlling or altering the bandgap

35 of a material by controlling the composition of its constituent semiconductor alloys. Bandgap energy is a fundamental design parameter for semiconductor compositions, and has been particularly important in the design of heterojunction devices, as well as photoelectric devices such as laser diodes

40 and solar cells. The last 60 years of combined global effort in the field has

resulted in a compilation of data showing bandgap energy as a function of the lattice constants associated with various semiconductor alloy compositions, for the diamond, zinc-

45 blende and wurtzite structured materials referred to above. (See, e.g., V. Swaminathan, A. T. Macrander, Materials Aspects of GaAs and InP Based Structures, published by Prentice-Hall, p. 25 (1991); O. Ambacher, Journal of Physics D-Applied Physics 31 (20): 2653-2710 Oct. 21, 1998.)

The present work, including the other disclosures listed 50 above which have been incorporated by reference herein, has

involved development of new semiconductor materials with rhombohedral super-hetero epitaxial structures in various combinations of cubic, trigonal and hexagonal crystalline structures. The methods of determining lattice constants that

55 underlie conventional bandgap engineering approaches translate directly to these new materials. Therefore, there was a need to develop a generalized engineering framework for relating these various crystal combinations, particularly in "super-hetero-epitaxial" combinations (i.e., epitaxial growth

60 of one material on a different material with different crystal structure, and for specifying the bandgap energy engineering applicable to these classes of compositions.

SUMMARY OF THE INVENTION 65

It is an object of the present invention to develop relation-ships of bandgap energy as a function of lattice constants as

US 8,226,767 B2 4

FIG. 9 shows perspective views of three similar planes with a rotation along the <1 l 1> axis of cubic crystal structure.

FIG. 10 is a schematic illustration showing the apparatus of X-ray diffraction method-1 of related disclosures, U.S. patent

5 application Ser. No. 12/254,150, entitled "METHOD OF GENERATING X-RAY DIFFRACTION DATA FOR INTE-GRAL DETECTION OF TWIN DEFECTS IN SUPER-HETERO-EPITAXIAL MATERIALS," and U.S. patent application Ser. No. 12/288,380, entitled "X-RAY DIF-

10 FRACTION WAFER MAPPING METHOD FOR RHOM-BOHEDRAL SUPER-HETERO-EPITAXY," each incorpo-rated herein by reference; both herein referred to as the "XRD disclosures."

FIG. 11 is a schematic illustration showing the apparatus of 15 X-ray diffraction method-2 of the related XRD disclosures.

FIG. 12 is a schematic illustration showing the apparatus of X-ray diffraction method-3 of the related XRD disclosures.

FIG. 13 contains photographs of diamond structured SiGe semiconductor alloy layers grown on c-plane sapphire sub-

20 strate with trigonal space symmetry. FIG. 14 contains graphs showing (Left) XRD normal scan

of polycrystalline sample and (Right) Phi Scan of SiGe {220} peaks from the same sample.

FIG. 15 shows analysis of SiGe {220} Phi Scan from 25 improved sample, (above) Phi Scan of SiGe {220} peaks and

(below) Intensity Plot of Phi-Psi Scan of SiGe {220} peaks. FIG. 16 contains plots showing Phi Scan of SiGe {220}

and sapphire {1-104} peaks: (a) Sample #A37 whole SiGe in Type [B] alignment and (b) Sample #A313 mixture of

30 type [B] and type [A] alignment. FIG. 17 is a plot showing an XRD normal scan of highly

oriented (99.99% in [I 11] direction) SiGe Layer on c-plane sapphire.

FIG. 18 illustrates plots showing Phi Scan of SiGe {220} 35 peaks with a super symmetry breaking, in which the ratio of

majority single crystal:minority twin crystal=92:8. FIG. 19 is a plot of Phi-Psi scan of SiGe {220} peaks also

showing a large symmetry breaking. FIG. 20 is a schematic illustration of the atomic alignment

40 of majority (92% in above sample) single crystal SiGe on c-plane sapphire.

FIG. 21 is a graphic showing super-hetero-epitaxial rela-tionships and validity of twin detection XRD methods for those relationships.

45 FIG. 22 is a schematic illustration showing an example of super-hetero-epitaxy with Tri-Unity relationship: trigonal [0001]—cubic (zinc-blende) [I I I]—hexagonal [0001].

FIG. 23 shows schematic illustrations to be viewed in conjunction with Tables 3 and 4, showing transformed lattice

50 constants (A) of cubic semiconductor crystals and trigonal crystals.

FIG. 24 is a graph showing bandgap energy vs. trans-formed lattice constant (A) for super-hetero-epitaxy in Type [A] Alignment.

55 FIG. 25 is a graph showing bandgap energy vs. transformed lattice constant (A) for super-hetero-epitaxy in Type [B] Alignment.

FIG. 26 is a graph showing bandgap energy vs. trans-formed lattice constant (A) for super-hetero-epitaxy in mixed

60 configuration (trigonal "cubic: Type [B], trigonal "hex-agonal (wurtzite): Type [B], cubic "hexagonal (wurtzite): Type [A]).

3 applicable to super-hetero-epitaxial structures of cubic, trigo-nal and/or hexagonal crystalline materials, and correspond-ing methods of designing super-hetero-epitaxial semiconduc-tor materials based thereon.

It is a further object of the invention to apply the foregoing techniques to formulate useful super-hetero-epitaxial semi-conductor alloys in lattice-matched alignment.

Accordingly, the present invention, drawing on develop-ments in lattice-matching, X-ray diffraction and wafer fabri-cation disclosed in related disclosures which have been incor-porated herein by reference, is a "Tri-Unity" system by which compatible crystal structures may be identified, and provides new bandgap engineering diagrams for each class of combi-nation based on the determination of hybrid lattice constants for the constituent materials in accordance with the lattice-matching equations.

Using known bandgap figures for previously tested mate-rials, new materials with lattice constants that match desired substrates and have the desired bandgap properties may be formulated by reference to the diagrams and lattice matching equations.

In one embodiment, the foregoing analysis makes it pos-sible to formulate new super-hetero-epitaxial semiconductor systems, such as systems based on group IV alloys on c-plane LaF3 ; group IV alloys on c-plane langasite; Group III-V alloys on c-plane langasite; and group II-VI alloys on c-plane sapphire.

Other aspects and advantages of the invention will be apparent from the accompanying drawings, and the detailed description that follows.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present inven-tion and the advantages thereof, reference is now made to the following description taken in conjunction with the accom-panying drawings, wherein like reference numerals represent like parts, in which:

FIG. 1 shows graphs of results from prior studies showing (a) bandgap engineering with diamond (IV) and zinc-blende structures (III-V and II-VI), and (b) bandgap engineering with wurtzite hexagonal structures.

FIG. 2 is a schematic illustration of (a) single crystal, and (b) twinned diamond structure (Si, Ge, and C) with stacking fault.

FIG. 3 is a schematic illustration of (a) single crystal, and (b) twinned zinc-blende structure (group III-V and group II-VI) with stacking fault.

FIG. 4 illustrates perspective views showing crystal struc-ture of unit cells: (a) sapphire (Al2O3), and (b) group IV alloy of Si, Ge, C, and Sn.

FIG. 5 show perspective views of (a) rhombohedral align-ment: <1 I I> direction of cubic crystal aligned with <0001> direction of trigonal substrate, and (b) two possible in-plane azimuthal alignments inside rhombohedral alignment.

FIG. 6 is a schematic illustration showing (a) basal plane of simplified crystal structure of sapphire with trigonal space symmetry and {111 } plane of diamond structure which has trigonal symmetry, (b) Type [A] (lower left) and Type [B] (upper right) atomic alignments; and (c) further detail of Type [B] alignment.

FIG. 7 is a schematic illustration showing fractional (2/3) of Type-A Alignment.

FIG. 8 is a schematic illustration showing "Half of Type [B]" atomic alignments (i) and (ii) at the interface between the 65

{111 } plane of cubic crystal and the basal plane of trigonal crystal.

DETAILED DESCRIPTION

The following is a detailed description of certain embodi-ments of the invention chosen to provide illustrative examples

US 8,226,767 B2 5

6 of how it may preferably be implemented. The scope of the

have previously been published. (SeeYeonj oon Park, Michael

invention is not limited to the specific embodiments

J. Cich, Rian Zhao, Petra Specht, Eicke R. Weber, Eric Stach, described, nor is it limited by any specific implementation, Shinji Nozaki, Journal of Vacuum Science & Technology B composition, embodiment or characterization depicted in the

18 (3): 1566-1571 May-June 2000.) FIGS. 2 and 3 show the

accompanying drawings or stated or described in the inven- 5 twinned diamond structure and zinc-blende structure as a tion summary or the abstract. In addition, it should be noted

result of stacking fault in (I 11) plane. The X-ray character-

that this disclosure describes a number of methods that each

ization of twinning during homo-epitaxy growth on the (I 11) comprise a plurality of steps. Nothing contained in this writ- plane was successfully developed in the cited Park et al. ten description should be understood to imply any necessary publication. That publication noted that the stacking fault in order of steps in such methods, other than as specified by io ZB structure is the same as one monolayer of embedded express claim language. wurtzite structure, as shown in dotted box 302 in FIG. 3(b).

In the ensuing description, the well-known Miller indices

The idea of mixed crystal structures was further investigated notation of lattice planes is used. That is, crystal planes are

by Sanorpim, Shiraki, and others with hexagonal (wurtzite)

designated by numbers within "O", groups of similar planes and later with cubic (zinc-blende) GaN epitaxy on GaAs are designated by numbers within "{ }", direction or length is 15 (111). (See B. S. Sanorpim S, E. Takuma, R. Katayama, H. designated by numbers within "[ ]", and groups of similar

Ichinose, K. Onabe,Y. Shiraki, Physica Status Solidi B-Basic

directions are designated by numbers within "< >". Research 240 (2): 305-309 November 2003.) FIG. 1(a) is a bandgap engineering diagram reflecting a

2) Development of Analysis for Super-Hetero-Epitaxy

previously established and widely accepted mathematical

As developed in an accompanying disclosure that has been diagram with group IV semiconductor materials in cubic 20 incorporated herein by reference (U.S. patent application Ser. diamond structure and group II-V and group II-VI materials

No. 12/288,379, entitled "RHOMBOHEDRAL CUBIC

in cubic zinc-blende structure. FIG. 1(b) is a similar diagram, SEMICONDUCTOR MATERIALS ON TRIGONAL SUB- but for semiconductor materials with wurtzite hexagonal

STRATE WITH SINGLE CRYSTAL PROPERTIES AND

crystal structures. DEVICES BASED ON SUCH MATERIALS"), which we We refer to zinc-blende-alpha structure as zinc-blende 25 shall herein refer to as the "CRYSTAL GROWTH disclo-

(ZB) structure, which is a diatomic variation of diamond

sure", we have investigated the growth of diamond structured structure. Group III-V semiconductor includes gallium ars- group IV alloys on basal plane of trigonal crystals such as enide (GaAs), indium arsenide (InAs), aluminum arsenide c-plane sapphire. FIG. 4 shows the crystal structure of sap- (AlAs), gallium phosphide (GaP) and other combinations phire and diamond structure of group IV alloy made with Si, from these groups in the periodic table. Group II-VI semicon- 30 Ge, C, and Sn. ductor includes zinc selenide (ZnSe), zinc telluride (ZnTe), The primary purpose of the epitaxial trial was to align cadmium sulfide (CdS) and other combinations from those <lll> direction of cubic diamond structure with <0001> groups in the periodic table. The uniform alloys made with

direction of trigonal sapphire substrate. After trials, we found

these groups have unique and different bandgap energy and

that there existed difficulties resulting from the trigonal sym- different average-lattice-constants from the original materi- 35 metry of the <1 l 1> direction of cubic crystals. In many cases, als, as shown in the connecting lines in FIG. 1(a). The aver- the epitaxial layer showed two possible in-plane alignments, aged lattice constant of uniform pseudo alloy was very impor- as shown in the top view in FIG. 5(b). tant to fabrication of defect-free semiconductor devices, The two cubic crystals in FIG. 5(b) are twin crystals rotated while the bandgap energy of group III-V and II-VI materials

by 60° in the {111} plane. High quality semiconductors

determined the wavelength for emitting or absorbing light. 4o require one single crystal structure all across the water. There- For example, dotted line 102 shows that the world's first

fore, if one cubic structure is a desired structure, the other

semiconductor laser diode was built with the almost-lattice- structure becomes a twin (or "double position") defect. How- matched two semiconductor materials, GaAs and AlAs. As ever, the origin and nature of this defect was very different another example, dotted line 104 shows that the alloy of

from the homo-epitaxy case. In the case of homo-epitaxy of

InGaAs can match the lattice constant (see line 106) of InP 45 GaAs (I I I)B, the stacking fault occurs at any place inside substrate and match the bandgap energy of 1.55 micrometer epitaxial layer during the growth, but in the case of rhombo- optical fiber communication wavelength. The most efficient

hedral growth of group IV alloys on c-plane sapphire, the

and reliable fiber communication InGaAs laser diode was stacking fault can occur (1) at the interface and (2) inside the built on dotted line 104 in FIG. 1(a). epitaxial layer. Therefore, the twin defect of rhombohedral

Additional semiconductor materials in wurtzite structure 50 epitaxy on trigonal substrate made for a very different case, that were introduced in the early 1990s were gallium nitride unlike the previous homo-epitaxy study. We found that most (GaN), aluminum nitride (A1N), and indium nitride (InN). of the twin defect came from the interfacial defects rather than Because wurtzite structure has trigonal point symmetry and

internal stacking faults in the middle of epitaxial layer.

hexagonal space symmetry, it could not be merged with cubic

The term "Super-hetero-Epitaxy" is used herein to refer to III-V structure; instead, it formed a separate bandgap diagram 55 the epitaxial growth of one material on a different material as shown in FIG. 1(b). with different crystal structures in order to distinguish it from

The above two bandgap engineering diagrams were built conventional hetero-epitaxy, growth on a different material by many researchers' efforts and it is the engineering sum- with same crystal structure. We may consider the well-known mary of various semiconductor materials science for the last epitaxial growth of GaN and AIN which have hexagonal 60 years of global achievement. 60 space symmetry on c-plane sapphire which has trigonal space

An additional class of bandgap engineering diagrams, for symmetry as one example of super-hetero epitaxy. rhombohedral super-hetero-epitaxy of three different crystal

In another disclosure which has been incorporated herein

structures, cubic (diamond and zinc-blende), trigonal, and

by reference (U.S. patent application Ser. No. 12/254,017, hexagonal crystals will now be established. entitled "EPITAXIAL GROWTH OF GROUP IV CUBIC (1) X-Ray Characterization of Homo-Epitaxy 65 CRYSTALLINE SEMICONDUCTOR ALLOYS ON

As further background, XRD methods for investigating BASAL PLANE OF TRIGONAL OR HEXAGONAL stacking faults and twinning in homo-epitaxial structures

CRYSTAL"), herein referred to as the "LATTICE MATCH-

L,,g,t = =aTri1H- for Type [A] alignment ~ 1)

L,,,t = 3aT,ilH- for Type [B] alignment (2)

1 a lter 4 a for 2/3 of Typ e A alignment (3)

= 3r Tn/H~ Yp [ ]

1-o ger 2 (4)

= 3 aT /H~ for 1/2 of Type [B] alignment

In the related XRD disclosures, (1) integral XRD method ("METHOD OF GENERATING X-RAY DIFFRACTION DATA FOR INTEGRAL DETECTION OF TWIN DEFECTS IN SUPER-HETERO-EPITAXIAL MATERI-ALS") to measure average twin defect concentration with the development of three twin-defect detection X-Ray diffraction techniques and (2) XRD wafer mapping method ("X-RAY DIFFRACTION WAFER MAPPING METHOD FOR RHOMBOHEDRAL SUPER-HETERO-EPITAXY") using {440} peaks to locate twin defect position are used to verify the structure of the fabricated materials, and can also be adapted for nondestructive quality control and wafer selec-tion.

FIG. 9 shows three folded {220} planes of a cubic structure with a rotation along the <1 I I> axis. For diamond structure and zinc-blende structure, {220} planes are a good choice for X-ray diffraction since they have strong diffraction intensity which can be calculated from the structure factor. Other three-folded planes along <1 I I > axis, such as {004}, {113}, {224} and so on, can be used as well, although their X-ray diffrac-tion intensity is not as good as those of the {220} planes. For

US 8,226,767 B2 7

ING disclosure", the development of four lattice-matching equations for rhomohedrally aligned cubic crystals on trigo-nal substrates was represented in a hexagonal coordinate system. In that disclosure, four types of alignment were iden-tified between the cubic and underlying trigonal systems, as shown in FIGS. 6, 7 and 8. These are Type [A] alignment and Type [B] alignment, as shown in FIG. 6(b) (bottom-left and top-right, respectively), and the "fractional alignments," 2/3 of Type [A] alignment (FIGS. 7), and 1/2 of Type [B] alignment (FIG. 8).

The atomic alignment of {111} plane of cubic diamond and zinc-blende structure is shown in FIG. 6 with respect to the basal plane of trigonal lattice of sapphire. In "Type [A]" alignment, the hexagonal ring of atomic sites of { 111 } plane of cubic crystal directly meets the hexagonal ring or atomic sites in trigonal basal plane without any rotations as shown in the lower-left of FIG. 6(b). In "Type [B]" alignment, the hexagonal ring of atomic sites of { 111 } plane of cubic crystal meets the hexagonal ring of atomic sites in trigonal basal plane with 30° rotation, as shown in the upper right of FIG. 6(b). In trigonal symmetry, 30° rotation is the same as 90° rotation.

In addition, there are two more lattice matching conditions with fractional alignment of Type [A] and Type [B], which are referred to as " 2/3 of Type [A]" and " 1/2 of Type [B]" align-ments, as shown in FIGS. 7 and 8, respectively. Fractional " 2/3 of Type [A]" alignment is shown in FIG. 7. Fractional "(/2) of Type [B]" atomic alignments are shown in two sets as (i) and (ii) in FIG. 8.

The corresponding lattice-matching equations (for match-ing the cubic with the underlying trigonal structures in these four cases) are, respectively, as follows:

8 other crystal structures, like Face Centered Cubic (FCC) materials, different planes can be considered with different structure factors.

FIGS. 10, 11, and 12 show the three detailed X-ray diffrac- 5 tion methods reported in the XRD disclosure "METHOD OF

GENERATING X-RAY DIFFRACTION DATA FOR INTE-GRAL DETECTION OF TWIN DEFECTS IN SUPER-HETERO-EPITAXIAL MATERIALS." By measuring three {220} X-ray diffraction peaks in PhiO-scan, a single crys-

io talline cubic material must show only three peaks which are apart from each other by 120°.

The techniques described in the XRD disclosures are not limited to group IV alloys. Cubic crystal includes group IV elements in diamond structure, group III-V and II-VI ele-

15 ments in zinc-blende structure as well as other elements in Body Centered Cubic (BCC) and Face Centered Cubic (FCC) structures. The above four lattice matching equations apply for all these materials. The X-ray diffraction methods of the XRD disclosures may be applied on these lattice matching

20 conditions, on group IV, III-V, II-VI semiconductors, and rhombohedrally-lattice-matched FCC and BCC materials on various trigonal substrates. (3) Grown Samples and Measured Data

As further detailed in the CRYSTAL GROWTH disclo- 25 sure, a series of p-type and n-type SiGe alloy layers were

grown on top of c-plane sapphire which has trigonal space symmetry, as shown in FIG. 13. The X-Ray Diffraction (XRD) analysis of some of the resulting samples is shown in the series of data in FIGS. 14-19.

30 A typical polycrystalline SiGe layer on c-sapphire shows multiple peaks in normal XRD scan data as shown in the left graph of FIG. 14. The SiGe {220} Phi Scan of such a sample often shows that {220} peaks are quite randomly distributed as shown in the right graph of FIG. 14.

35 On the other hand, the highly oriented samples in [111] direction on c-plane sapphire show a very strong SiGe (I 11) peak in the normal XRD scan, and they show a symmetry breaking in the Phi Scan of SiGe {220} peaks as shown in FIG. 15. About 60:40 ratio of symmetry breaking occurred in

4o FIG. 15. The reason for this inequality was that there existed a difference in the formation energy of two diamond crystals which are rotated by 60°.

Phi-psi scan was also developed to compensate any sample-misalignment problem, as shown in the bottom

45 graphic of FIG. 15. The XRD Phi Scan and Phi-psi scan of three-fold inclined planes around the <lll> direction of cubic crystals is referred to as the "Twin Detection XRD Method". This method becomes clearer when the epitaxial layer peaks' phi angles are compared with XRD peaks from

50 the substrate's inclined planes, such as sapphire {1-104} peaks, which are shown as lines 1601-1606 in FIG. 16. A mixture of Type [A] alignment and Type [B] alignment can also occur in some growth conditions, as shown in FIG.16(b).

The highly oriented SiGe layer on c-plane sapphire has an 55 ultra strong (I 11) peak 1701 when it is compared with other

peaks in XRD normal scan, as shown in FIG. 17. About 99.99% of SiGe layer is oriented in [111 ] direction in terms of peak height and peak area, compared with SiGe (113) peak.

The Phi Scan of SiGe {220} peaks show that 92% of layer 60 is the majority single crystal and 8% is the 60° rotated twin

crystal on (I 11) plane as shown in FIG. 18. The super-sym-metry breaking (92:8) shows the existence of a "golden" growth condition, which utilizes the difference of formation energy of two crystals on basal plane of trigonal substrate in

65 trigonal space symmetry group. Phi-psi scan of the same sample also confirms the super

symmetry breaking, as shown in FIG. 19.

US 8,226,767 B2 9

From the above data, the stable majority single-crystalline SiGe crystal on c-plane sapphire forms the atomic alignment as shown in FIG. 20. Three small parallelograms 2001, 2002 and 2003 of SiGe crystal indicate three {100} cubic facet planes surrounding vertical <1 l 1> direction (out of the paper in this diagram.) (4) Tri-Unity Relationship

The extraordinary symmetry breaking (92:89 of highly oriented (99.99% in [I 11] direction) SiGe layer on c-plane sapphire indicates that there exists a golden growth condition to grow single crystalline [I 11] oriented SiGe layer (Cubic) on c-plane sapphire (Trigonal Space Symmetry). Based on these observations, we conclude that there exists a fundamen-tal inter-crystal-structure epitaxial relationship and we refer to it as "Tri-Unity" epitaxial relation because three different crystal structures, cubic (diamond, zinc-blende, FCC, BCC and so on), trigonal (space symmetry), and hexagonal (space symmetry, wurtzite and so on) crystals can be integrated in one continuous epitaxial structure. This relationship is drawn in FIG. 21, along with the corresponding validity of Twin Detection XRD Methods for each type of relation. For those relations for which the Twin Detection XRD Method is appli-cable, it can be used to monitor the epitaxial layers as a non-destructive evaluation tool. It can be used for quality control and selection of prime wafers. The Twin Detection XRD Method can also be used to verity structures and as a key tool in developing unprecedented crystal alloy systems.

In the Tri-Unity diagram of FIG. 21, arrows are drawn from each underlying crystal structure such as substrate to an epi-taxial crystal structure. All three crystal structures satisfy 120° rotational symmetry along cubic [I 11] or trigonal/hex-agonal [0001] axes. However, double position defects can occur ifthe underlying crystal has hexagonal space symmetry including III-N wurtzite crystal structure, because it has addi-tional 60° rotational space symmetry. The epitaxial growth with inevitable double position defect is drawn in dotted arrows 2111 and 2112. The epitaxial growth combinations marked with solid lines 2101, 2102, 2103, and 2104 can avoid double position defects that make twin crystals. The defect-free (no twin crystal) growth in solid line combinations occurs in certain narrow "golden" growth conditions by uti-lizing the difference in the formation energy (as explained at greater length in the CRYSTAL GROWTH disclosure).

As for the dotted epitaxial lines 2111 and 2112, in spite of the interfacial double position defect at the interface, a pos-sibility that a single crystalline layer can be formed by inter-nal stacking faults and domain expansion phenomena in which domain size becomes larger than a wafer size or a region of interest is not excluded. One example of such a domain expansion is the spinodal decomposition.

As for the diatomic and more complex cubic crystals, such as zinc-blendes (GaAs, A1P, and so on), atomic inversion defect such as Ga As vs. As Ga can occur since {111} planes are polarized planes. However, the inversion defects will not be considered here because they are more related with specific stacking sequence.

FIG. 22 shows one example ofrhombohedral super-hetero-epitaxy with a good Tri-Unity epitaxial relationship. Hexago-nal wurtzite structure can repair double position defect by vertical strain of c/2 as shown by Sohn and Lilienthal-Weber et al. (Z. Liliental-Weber, H. Sohn, N. Newman, J. Washburn, Journal of Vacuum Science & Technology B 13 (4): 1578-1581 July-August 1995). Therefore, such a continuous epi-taxial structure can be grown without propagating twin defects in a certain golden growth condition.

10 With the Tri-Unity epitaxial relation, our LATTICE

MATCHING disclosure becomes a special case of [Trigonal (Space Symmetry)-Cubic] and [Hexagonal (Space Symme-try)-Cubic] in FIG. 21.

5 The twin detection XRD methods reported in the XRD disclosures apply to the various epitaxial relations that have circles 2121, 2122, 2123, and 2124 in FIG. 21.

Accordingly, application of twin detection XRD methods to on the epitaxial systems shown in Table 1 is valid:

TABLE 1

Application of twin detection XRD methods on epitaxial systems

15 (1) <111> Cubic Crystal Layer on {0001} Plane of Trigonal

(Space Symmetry) Crystal Material Layer or Substrate (2) <0001> Trigonal Crystal Layer on {111} Plane of Cubic

Crystal Material Layer or Substrate (3) <1I I> Cubic Crystal Layer on {0001} Plane of Hexagonal

(Space Symmetry) Crystal Material Layer or Substrate (4) <0001> Trigonal Crystal Layer on {111} Plane of Hexagonal

20 (Space Symmetry) Crystal Material Layer or Substrate

(5) New Bandgap Engineering for Rhombohedral Super-Het-ero-Epitaxy

25 The transformed lattice constants in Type [A], 2/3 of Type [A], Type [B], and 1/2 or Type [B] alignments are shown in Tables 2 and 3 below and FIG. 23.

TABLE 2 30

Transformed Lattice Constants of Cubic Semiconductor Materials

Group Material A C Type A's a' Eg(eV)

III-V GaAs 5.65 5.65 4.90 1.42 AIAs 5.66 5.66 4.90 2.15

35 InAs 6.06 6.06 5.25 0.35 Gap 5.45 5.45 4.72 2.27 InP 5.87 5.87 5.08 1.34 InSb 6.48 6.48 5.61 0.17 AIP 5.46 5.46 4.73 2.45

IV Si 5.43 5.43 4.70 1.12 40 Ge 5.66 5.66 4.90 0.66

C 3.57 3.57 3.09 5.50 II-VI ZnS 5.42 5.42 4.69 3.60

ZnSe 5.70 5.70 4.94 2.60 CdSe 6.05 6.05 5.24 1.60

45

TABLE 3

Transformed Lattice Constants of Trigonal Crvstals

50 Substrates A C Type [B]'s a"

Sapphire 4.76 12.99 5.49 Calcite 4.99 17.06 5.76 LaF3 7.19 7.37 8.30 Langasite 8.18 5.10 9.44

55 (La3Ga5S10I4)

Because rhombohedral super-hetero-epitaxy uses transformed lattice constant, the bandgap engineering diagrams of bandgap energy vs. lattice constant have to be redrawn. The

60 positions of many diamond group IV and zinc-blende III-V and II-VI semiconductor materials in Type [A] and 2/3 of Type [A] alignment are plotted in FIG. 24 and include a few new possible trigonal (space symmetry) crystal substrates' lines for lattice matching conditions. (As explained in the LAT-

65 TICE MATCHING disclosure, the detailed alloy lines in these diagrams may be further refined inside group IV, group III-V, group II-VI, and group III-nitride areas by taking into

US 8,226,767 B2 11

consideration higher order parameters, such as Bowing parameters and direct-to-indirect bandgap changes.)

Similarly, the same type of bandgap engineering diagrams for Type [B] and 1/2 of Type [B] alignment are shown in FIG. 25.

The most common atomic alignment at interface is a mix-ture of Type [A] and Type [B], including the 2/3 and 1/2 frac-tional variants of these alignments. This frequent common mixed alignment is plotted in FIG. 26. Notice that the trans-formed lattice constant is different from cubic lattice con-stant. The well-known lattice mismatch of 13.7% between GaN and sapphire can be easily shown in this diagram.

Unlike the previous bandgap engineering diagrams in FIG. 1, the rhombohedral super-hetero-epitaxybandgap engineer-ing diagrams in FIGS. 24, 25 and 26 predict unprecedented integrated alloys of different crystal structures in one continu-ous epitaxial structure.

These new bandgap engineering diagrams cover only a subset of possibilities and can be refined with more precise alley lines and expanded by adding more substrates. Never-theless, it its certain that other useful alloys can be formulated by the methods described above and that these bandgap engi-neering diagrams can serve to support the entire global semi-conductor industry as a roadmap for unprecedented super-hetero alloy material systems.

Some of the new materials made possible by the methods described above include the materials listed in Table 4.

TABLE 4

Application of New Bandgap Engineering to <111> Oriented Rhombohedrally Lattice-Matched Semiconductor Alloys

New <1II> Oriented Rhombohedrally Lattice Matched Semiconductor Alloys

(1) Group IV alloys (Si, Ge, C, and Sn) on c-plane LaF3: in half of Type [B] alignment (2) Group IV alloys (Si, Ge, C, and Sn) on c-plane Langasite: in half of Type [B] alignment (3) Group III-V alloys on c-plane Langasite: in half of Type [B] alignment (4) Group II-VI alloys on c-plane Langasite: in half of Type [B] alignment (5) Group III-V alloys on c-plane Sapphire: in Type [B] alignment

Moreover, to the extent that strained InN, InGaN, and AlInN alloys on c-plane LaF 3 substrate can form 2/3 of Type [A] alignment, these could also give low lattice mismatch as shown in FIG. 24.

Thus, it is apparent that the methods and materials described in the present disclosure satisfy the objects of the invention set forth above. In particular, the present invention provides a rhombohedral super-hetero-epitaxy, an unprec-edented hybrid bandgap engineering diagram, and math-ematically-supported new lattice-matching models for deriv-ing transformed lattice constants. The bandgap engineering diagrams summarize individual material-research efforts including novel material development, and also serve and as a long-term roadmap for future material development in accordance with the methods described herein. The invention also uses concurrently filed twin detection XRD methods and the Tri-Unity relationship diagram herein to assist with the rhombohedral super-hetero-epitaxy developments.

The present invention is further discussed inY. Park, G. C. King, S. H. Choi, Rhombohedral epitaxy of cubic SiGe on trigonal c-plane sapphire, Journal of Crystal Growth 310 (2008) 2724-2731, herein incorporated by reference in its entirety.

Although the present invention has been described in detail, it should be understood that various changes, substi-tutions, and alterations may be readily ascertainable by those

12 skilled in the art and may be made herein without departing from the spirit and scope of the present invention as defined by the following claims.

What is claimed as new and desired to be secured by 5 Letters Patent of the United States is:

1. A method for quality control and selection of prime wafers in a rhombohedral, super-hetero epitaxial semicon-ductor material of a continuous epitaxial structure, said mate-rial comprising a substrate having a first crystal structure, and

10 at least one epitaxial layer having a second crystal structure that differs from said first crystal structure, said method com-prising

a) using X-ray diffraction in which the combination of Omega (goniometer angle) and Chi (angle of [111] vec-

15 for relative to the X-ray diffraction reference orienta-tion) parameters, as a function of Theta (Bragg angle) and Beta (interplanar angle of alloy's {111} plane and selected non-perpendicular plane) are selected from the group consisting of (a) Chi=Beta, Omega —Theta; (b) Omega=Theta+Beta, Chi -0; and (c) Omega —Theta-Beta, Chi -0, in order to determine double position defects;

b) wherein said X-ray diffraction method is applied where the correspondence of said first and second crystal struc-tures are within the group consisting of (i)cubic on trigo-

25 nal, (ii) trigonal on cubic, (iii) hexagonal on cubic, and (iv) hexagonal on trigonal (wherein trigonal andhexago-nal refers to space, symmetry).

2. The method of claim 1 applied to super-hetero epitaxial, semiconductor material selected from the group consisting

30 of: a) <1I I> cubic crystal layer on 1000 11 plane of trigonal

crystal material layer or substrate; b) <0001> trigonal crystal layer on {1111 plane of cubic

crystal material layer or substrate; 35 c) <1 11> cubic crystal layer on 1000 11 plane of hexagonal

crystal material layer or substrate; and d) <0001> trigonal crystal layer on {1111 plane of hexago-

nal crystal material layer or substrate. 3. A method for making a rhombohedral, super-hetero

40 epitaxial semiconductor material of a continuous epitaxial structure having a selected bandgap energy comprising depositing on a substrate having a first crystal structure at least one epitaxial layer having a crystal structure that differs from said first crystal structure, said crystal structures each being from among the group consisting of cubic, trigonal

45 (space symmetry) and hexagonal (space symmetry) wherein the first crystal structure and the crystal structure of at least one epitaxial layer are selected to have sufficiently similar transformed lattice constants to form a rhombohedral inter-face and the crystal structure of at least one epitaxial layer is

50 selected to provide the selected bandgap energy, and wherein the correspondence of said first and second crystal structures are within the group consisting of (a) cubic on trigonal, (b) trigonal on cubic, (c) hexagonal on cubic, and (d) hexagonal on trigonal, further comprising performing quality control

55 and selection of prime wafers by using X-ray diffraction in order to determine twin defects, and in which, for such X-ray diffraction, the combination of Omega (goniometer angle) and Chi (angle of {1111 vector relative to the X-ray diffrac-tion reference orientation) parameters, as a function of Theta (Bragg angle) and Beta (interplanar angle of said alloy's

60 11111 plane and selected non-perpendicular plane) are selected from the group consisting of:

i) Chi=Beta, Omega—Theta; ii) Omega=Theta+Beta, Chi -0; and iii) Omega—Theta-Beta, ChiO.

65

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