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Band Parameters for III–V Compound Semiconductors and Their Alloys

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Band Parameters for III–V Compound Semiconductors and Their Alloys Band parameters for III–V compound semiconductors and their alloys Cite as: Journal of Applied Physics 89, 5815 (2001); https://doi.org/10.1063/1.1368156 Submitted: 04 October 2000 . Accepted: 14 February 2001 . Published Online: 07 June 2001 I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan ARTICLES YOU MAY BE INTERESTED IN Detailed Balance Limit of Efficiency of p-n Junction Solar Cells Journal of Applied Physics 32, 510 (1961); https://doi.org/10.1063/1.1736034 First-principles calculations for defects and impurities: Applications to III-nitrides Journal of Applied Physics 95, 3851 (2004); https://doi.org/10.1063/1.1682673 Two dimensional electron gases induced by spontaneous and piezoelectric polarization in undoped and doped AlGaN/GaN heterostructures Journal of Applied Physics 87, 334 (2000); https://doi.org/10.1063/1.371866 Journal of Applied Physics 89, 5815 (2001); https://doi.org/10.1063/1.1368156 89, 5815 © 2001 American Institute of Physics. JOURNAL OF APPLIED PHYSICS VOLUME 89, NUMBER 11 1 JUNE 2001 APPLIED PHYSICS REVIEW Band parameters for III–V compound semiconductors and their alloys I. Vurgaftmana) and J. R. Meyer Code 5613, Naval Research Laboratory, Washington, DC 20375 L. R. Ram-Mohan Worcester Polytechnic Institute, Worcester, Massachusetts 01609 ͑Received 4 October 2000; accepted for publication 14 February 2001͒ We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other. © 2001 American Institute of Physics. ͓DOI: 10.1063/1.1368156͔ TABLE OF CONTENTS K.AlN................................... 5835 L. InN.................................... 5836 I. Introduction................................ 5816 IV. Ternary alloys............................. 5837 II. Relation to band structure theory and general A. Arsenides............................... 5838 considerations.............................. 5817 1. AlGaAs............................. 5838 A. Multiband k"P method.................... 5817 2. GaInAs.............................. 5839 1. Zinc blende materials.................. 5818 3. AlInAs.............................. 5840 2. Nitrides with wurtzite structure.......... 5819 B. Phosphides.............................. 5840 3. Strain in heterostructures............... 5821 1. GaInP............................... 5840 4. Piezoelectric effect in III–V 2. AlInP............................... 5841 semiconductors....................... 5821 3. AlGaP.............................. 5841 5. Band structure in layered C. Antimonides............................. 5842 heterostructures....................... 5822 1. GaInSb.............................. 5842 B. Relation of k"P to other band structure 2. AlInSb.............................. 5842 models................................. 5822 3. AlGaSb............................. 5843 1. Empirical tight binding model........... 5822 D. Arsenides antimonides.................... 5843 2. Effective bond orbital model............ 5823 1. GaAsSb............................. 5843 3. Empirical pseudopotential model......... 5823 2. InAsSb.............................. 5844 III. Binary compounds......................... 5823 3. AlAsSb.............................. 5844 A.GaAs.................................. 5823 E. Arsenides phosphides..................... 5844 B. AlAs................................... 5824 1. GaAsP.............................. 5844 C. InAs................................... 5826 2. InAsP............................... 5845 D.GaP................................... 5827 3. AlAsP............................... 5846 E. AlP.................................... 5828 F. Phosphides antimonides................... 5846 F. InP.................................... 5828 1. GaPSb.............................. 5846 G.GaSb.................................. 5829 2. InPSb............................... 5846 H.AlSb................................... 5830 3. AlPSb............................... 5846 I. InSb................................... 5831 G. Nitrides................................ 5846 J. GaN................................... 5832 1. GaInN.............................. 5846 1. Wurtzite GaN........................ 5832 2. AlGaN.............................. 5847 2. Zinc blende GaN...................... 5834 3. AlInN............................... 5847 0021-8979/2001/89(11)/5815/61/$18.005815 © 2001 American Institute of Physics 5816 J. Appl. Phys., Vol. 89, No. 11, 1 June 2001 Appl. Phys. Rev.: Vurgaftman, Meyer, and Ram-Mohan 4. GaAsN.............................. 5848 To fully exploit this flexibility, one clearly needs a reli- 5.GaPN............................... 5849 able and up-to-date band parameter database for input to the 6.InPN................................ 5849 electronic structure calculations and device simulations. 7. InAsN............................... 5849 However, after many years Volume 17 of the Landolt– V. Quaternary alloys........................... 5849 Bornstein series1 remains the most frequently quoted source A. Lattice matched to GaAs.................. 5850 of III–V band parameters. Although that work contains 1. AlGaInP............................. 5850 much of the required data for a broad range of materials, it is 2. GaInAsP............................. 5850 nearly 20 yr old, lacks detailed descriptions of many of the 3. AlGaInAs............................ 5851 important III–V alloys, and contains no information at all on 4. GaInAsN............................ 5851 the crucial band offset alignments for heterostructures. A B. Lattice matched to InP.................... 5851 popular compilation by Casey and Panish2 covers the band 1. GaInAsP............................. 5851 gaps for all III–V non-nitride binary materials and 12 ternary 2. AlGaInAs............................ 5852 alloys, but the rapid progress in growth and characterization 3. GaInAsSb............................ 5852 of many of those materials taking place since its publication C. Lattice matched to InAs................... 5852 in 1978 has decreased its usefulness. While a number of 1. GaInAsSb............................ 5852 recent books and reviews on individual material systems are 2. AlGaAsSb........................... 5853 available,3–10 they are not necessarily complete or mutually 3. InAsSbP............................. 5853 consistent. A useful recent compilation of band structure pa- D. Lattice matched to GaSb................... 5853 rameters by Levinshtein et al.11 does not contain in-depth 1. GaInAsSb............................ 5853 information on aluminum-containing elemental semiconduc- 2. AlGaAsSb........................... 5854 tors, is often based on a limited number of original sources, E. Other substrates.......................... 5854 and considers only six ternary and two quaternary alloys. 1. AlGaAsP............................ 5854 The objective of the present work is to fill the gap in the F. Nitride quaternaries....................... 5854 existing literature by providing a comprehensive and mutu- VI. Heterostructure band offsets.................. 5854 ally consistent source of the latest band parameters for all of A. GaAs/AlAs.............................. 5855 the common III–V zinc blende and wurtzite semiconductors B. GaInAs/AlInAs/InP....................... 5856 ͑GaAs, AlAs, InAs, GaP, AlP, InP, GaSb, AlSb, InSb, GaN, C. Strained InAs/GaAs/InP and related AlN, and InN͒ and their ternary and quaternary alloys. The ternaries................................ 5856 reviewed parameters are the most critical for band structure D. GaInP/AlInP/GaAs....................... 5857 calculations, the most commonly measured and calculated, E. GaPandAlP............................ 5858 and often the most controversial. They include: ͑1͒ direct and F. GaSb/InAs/AlSb......................... 5858 indirect energy gaps and their temperature dependences; ͑2͒ G. GaSb/InSb and InAs/InP................... 5860 spin-orbit splitting; ͑3͒ crystal-field splitting for nitrides; ͑4͒ H. Quaternaries............................. 5861 electron effective mass; ͑5͒ Luttinger parameters and split- I. GaN, InN, and AlN....................... 5861 ͑ ͒ off hole mass; 6 interband matrix element E P and the as- VII. Summary................................ 5862 sociated F parameter which accounts for remote-band effects in eight-band k"P theory; ͑7͒ conduction and valence band deformation potentials that account for strain effects in I. INTRODUCTION pseudomorphic thin layers; and ͑8͒ band offsets on an abso- lute scale which allows the band alignments between any At present, III–V compound semiconductors provide the combination of materials to be determined. All parameter materials basis for a number of well-established commercial sets
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