Physica B 302–303 (2001) 123–134 Intrinsic limitations to the doping of wide-gap semiconductors W. Walukiewicz* Materials Sciences Division, Lawrence Berkeley National Laboratory, MS 2-200, 1 Cyclotron Rd. Berkeley, CA 94720, USA Abstract Doping limits in semiconductors are discussed in terms of the amphoteric defect model (ADM). It is shown that the maximum free electron or hole concentration that can be achieved by doping is an intrinsic property of a given semiconductor and is fully determined by the location of the semiconductor band edges with respect to a common energy reference, the Fermi level stabilization energy. The ADM provides a simple phenomenological rule that explains experimentally observed trends in free carrier saturation in a variety of semiconductor materials and their alloys. The predictions of a large enhancement of the maximum electron concentration in III–N–V alloys have been recently confirmed by experiment. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Compound semiconductors; Native defects; Doping 1. Introduction the stability of dopant and compositional profiles are becoming key issues for many of the new It has been realized early on that many of the devices. large variety of semiconductor materials are The past several years have witnessed specta- difficult to dope. The problem has been especially cular progress in the development of a new severe in wide-bandgap semiconductors where in generation of short wavelength optoelectronic many instances n- or p-type doping cannot be devices based on group III nitrides [4–6] and achieved at all, significantly limiting the range of wide-gap II–VI semiconductors [7,8]. In both cases applications of these materials [1–3]. These doping this progress was made possible through the limitations have become even more important in discovery of more efficient ways to activate new, emerging device technologies that put strin- acceptor impurities in these material systems. gent demands on nanoscale control of electronic Despite this progress, the high resistance of p-type and structural properties of semiconductor mate- layers is still a major hurdle in the development rials. Such devices require the preparation of small of the devices requiring high current injection size structures with very high doping levels and levels. abrupt doping and composition profiles. The limits There have been numerous attempts to under- of the maximum doping levels and the question of stand the maximum doping limits in semiconduc- tors. Most of these were aimed at explaining limitations imposed on a specific dopant in a *Tel.: +1-510-486-5329; fax: +1-510-486-5530. E-mail address: w [email protected] specific semiconductor. Thus, it has been argued (W. Walukiewicz). that in the case of amphoteric impurities in III–V 0921-4526/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0921-4526(01)00417-3 124 W. Walukiewicz / Physica B 302–303 (2001) 123–134 compounds, doping is limited by the impurities In this paper, the saturation of the free carrier occupying both acceptor and donor sites, com- concentration in semiconductors obtained through pensating each other. Redistribution of impurities doping will be discussed in terms of the ampho- can also lead to limitations of the maximum teric defect model (ADM). In recent years, the doping level in the materials with impurity model has been successfully applied to numerous diffusion strongly depending on the Fermi energy doping related phenomena in semiconductors. It [3]. Formation of new stable solid phases involving has been used to explain doping induced suppres- dopant atoms can be a severe limitation in sion of dislocation formation [15] as well as achieving high doping levels. This limitation impurity segregation [16,17] and interdiffusion depends on the chemical identity of the dopants [18] in semiconductor superlattices. We will show and the host lattice elements and may be critical in that the ADM provides a simple phenomenologi- the cases where only a limited number of potential cal rule capable of predicting trends in the doping dopants is available [9]. behavior of a large variety of semiconductor Passivation of donor and acceptor impurities by systems. highly mobile impurities is another major mechan- ism limiting the electrical activity of dopants. Hydrogen, lithium and copper are known to 2. Amphoteric defect model passivate intentionally introduced dopants in semiconductors. Hydrogen has been an especially All point defects and dopants can be divided extensively studied impurity as it is a commonly into two classes: delocalized, shallow dopants and used element in most semiconductor processing highly localized defects and dopants. Shallow techniques and in all the growth techniques hydrogenic donors and acceptors belong to the involving metalorganic precursors [10]. In some first class. Their wave functions are delocalized cases hydrogen can be removed during a post- and formed mostly out of the states close to the growth annealing. Magnesium doped p-type GaN conduction band minimum or the valence band is frequently obtained by thermal annealing of maximum. As a result the energy levels of these MOCVD grown, hydrogen passivated films dopants are intimately associated with the respec- [11,12]. However in other instances, as in the case tive band edges, conduction band for donors and of N doped ZnSe, hydrogen is too tightly bound to the valence band for acceptors. In general the the N acceptors and cannot be removed by a energy levels will follow the respective band edges thermal annealing [13]. when the locations of the edges change due to Over the last few years a considerable effort has external perturbation such as hydrostatic pressure been directed towards overcoming the doping or changing alloy composition. limits. For example it has been proposed that In contrast, wave functions of highly localized one can enhance incorporation of electrically defects or dopants cannot be associated with any active centers by co-doping with donors and specific band structure extremum. They are rather acceptors. It has been argued, based on theoretical formed from all the extended states in the Brillouin calculations that because of the reductions of the zone with the largest contribution coming from the lattice relaxation and Madelung energies forma- regions of large density of states in the conduction tion energies of proper donor acceptor complexes and the valence band. Consequently the energy can be lower than the formation energy of isolated levels of such defects or dopants are insensitive to dopant species [13]. Some preliminary experimen- the location of the low density of states at the tal results indicate that indeed the co-doping conduction and valence band edges. For example, method has produced p-type ZnO that cannot be it has been shown that transition metal impurities achieved by any other method [14]. Further studies with their highly localized d shells belong to this are needed to fully understand the issues of poor class of dopants [19,20]. The insensitivity of the reproducibility of the results obtained by the co- transition metal energy levels to the position of doping method. local band extrema has led to the concept of using W. Walukiewicz / Physica B 302–303 (2001) 123–134 125 these levels as energy references to determine the level [29]. This is a clear indication that the native band offsets in III–V and II–VI compounds [20] defect states determining the electrical character- and the band edge deformation potentials in GaAs istics of heavily damaged materials are of highly and InP [21]. localized nature. As can be seen in Fig. 1 the Compelling evidence for the localized nature of location of the stabilized Fermi energy in heavily native defects has been provided by studies of damaged III–V semiconductors is in good agree- semiconductor materials heavily damaged with ment with the Fermi level pinning position high gamma rays or electrons [22–28]. It has been observed at metal/semiconductor interfaces [30]. found that for sufficiently high damage density, This finding strongly supports the assertion that i.e., when the properties of the material are fully the same defects are responsible for the stabiliza- controlled by native defects, the Fermi energy tion of the Fermi energy in both cases. stabilizes at a certain energy and becomes insensi- The mechanism explaining the defect induced tive to further damage. The location of this Fermi stabilization of the Fermi energy is based on the level stabilization energy, EFS, does not depend on concept of amphoteric native defects. The stabili- the type or the doping level of the original material zation of the Fermi energy can be understood if we and therefore is considered to be an intrinsic assume that the type of defects formed during high property of a given material. As is shown in Fig. 1 energy particle irradiation or metal deposition on the Fermi level stabilization energies for different the semiconductor surface depends on the location III–V semiconductors line up across semiconduc- of the Fermi energy with respect to EFS. For Fermi tor interfaces and are located approximately at a energy EF > EFS ðEF5EFSÞ acceptor-like (donor- constant energy of about 4.9 eV below the vacuum like) defects are predominantly formed resulting in a shift of the Fermi energy towards EFS. Conse- quently, the condition EF ¼ EFS is defined as the situation where the donor and acceptor like defects are incorporated at such rates that they perfectly compensate each other leaving the Fermi energy unchanged. Such an amphoteric behavior of simple native defects is supported by theoretical calculations that show that depending on the location of the Fermi energy vacancy like defects can acquire either negative or positive charge acting as acceptors or donors, respectively. In the case of GaAs it was shown that both gallium and arsenic vacancies can undergo amphoteric transforma- tions [31].