Dislocation-independent mobility in lattice-mismatched epitaxy: application to GaN D.C. Look a, * , C.E. Stutz b , R.J. Molnar c , K. Saarinen d , Z. Liliental-Weber e a Semiconductor Research Center, Wright State University, Dayton, OH 45435, USA b Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA c Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA 02173, USA d Laboratory of Physics, Helsinki University of Technology, FIN-02015 HUT, Finland e Materials Science Div., Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Received 21 December 2000; accepted 26 December 2000 by M. Cardona Abstract Lattice-mismatched epitaxy produces a high concentration of dislocations (N dis ) in the interface region, and this region is often highly conductive, due to donor (N D ) decoration of the dislocations. Here we show that a simple postulate, N D  aN dis =c; where c is the lattice constant and a a constant of order 1±2, predicts a nearly constant low-temperature mobility, independent of N dis . This prediction is experimentally veri®ed in GaN grown on Al 2 O 3 , and is also applied to other mismatched systems. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Interfaces; B. Epitaxy; C. Dislocations PACS: 73.61.Ey; 73.40.Kp; 61.72.Lk Lattice-mismatched epitaxial growth (e.g. GaAs on Si, ZnO on Al 2 O 3 , or GaN on Al 2 O 3 ) is of high technological importance, and thus has been widely studied in the past two decades. The principal problem encountered in this growth is a high dislocation density N dis in a narrow region between the substrate (e.g. Al 2 O 3 ) and epilayer (e.g. GaN); moreover, these dislocations can promote impurity diffusion (so-called `pipe diffusion'), leading to a clustering of the impurities around the dislocations (`Cottrell atmosphere'). If these impurities are donor-like (e.g. Si Ga in GaAs, Al Zn in ZnO, or O N in GaN), then a thin, degenerate, donor-impurity band can form in the substrate/layer interface region. Since degenerate electrons are temperature-independent, they can dominate the low-temperature (low-T ) electrical properties, because the non-degenerate bulk electrons will freeze out on their parent donors [1,2]. We have observed this degenerate interface region in every single sample of a group of 31 GaN layers grown on Al 2 O 3 by the hydride vapor-phase epitaxial (HVPE) method, at three different laboratories. As expected, the low-T values of sheet electron concentration n s varied widely, from 3 £ 10 14 to 5 £ 10 16 cm 22 ; however, a very surprising ®nding is that most (27) of the samples have mobilities (m s) tightly clustered around a value of 52 cm 2 /V s, while the remaining few (4) all have m s of about 30 cm 2 /V s. To explain these `magic mobilities', we ®rst develop the general scattering theory for degenerate electrons at low T, and then apply a simple postulate: N D  aN dis =c; where N D is the donor concentra- tion, c the appropriate lattice constant, and a a constant of order 1±2. Recent theoretical [3±5] and experimental [5±7] studies have shown that edge-dislocation cores in n-GaN are negatively charged, most likely due to Ga vacancy (V Ga ) acceptors along each of the cores, a distance c apart (5.185 A Ê ). Thus, a may be thought of as the average number of donor atoms decorating each dislocation-core lattice site. From independent measurements, we show that the interface acceptors involve V Ga , as expected from the theoretical arguments, and that the donors are O. We also apply the magic-mobility concept to other systems which involve large dislocation densities. Scattering theory for low-T, degenerate electrons is straightforward because: (1) n is simply related to the Hall Solid State Communications 117 (2001) 571±575 0038-1098/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S0038-1098(01)00010-2 PERGAMON www.elsevier.com/locate/ssc * Corresponding author. Tel.: 11-937-255-1725; fax: 11-937- 255-3374. E-mail address: david.look@wpafb.af.mil (D.C. Look).