Electronic and optoelectronic devices all depend on semiconductor doping. For instance, adding small amounts of phosphorus turns silicon (Si) into a conductor for electrons (n-type), and adding small amounts of boron turns Si into a hole conductor (p-type). Light-emitting devices require the ability to dope material as both n-type and p-type, so that electrons and holes can be injected and transported to the active layer, where they recombine and emit light. Such ambipolar doping has been a longstanding problem in the wide-band-gap semiconductors that are used in short-wavelength light emitters (green, blue, or UV).
Figure 1. (a) Schematic of a shallow effective-mass acceptor, which gives rise to a valence-band (VB) derived state (indicated by the dotted red line) that is easily ionized, making it an efficient dopant. (b) In contrast, a deep acceptor gives rise to a state (indicated by the solid red line) far from the valence band and conduction band (CB) that is usually difficult to ionize, making it an inefficient dopant.
In gallium nitride (GaN), n-type doping is straightforward, and can be achieved by adding elements such as silicon or germanium. However, p-type doping is still imperfect.1 Intriguingly, magnesium (Mg) is the only impurity that can produce p-type GaN, and it suffers from significant limitations. Mg has a much larger ionization energy (∼200meV) than typical shallow acceptors in conventional semiconductors: see Figure 1(a). Therefore, high concentrations of Mg impurities are required to achieve hole concentrations that are just satisfactory for device operation. In addition, high-temperature post-growth annealing is necessary to activate Mg acceptors, which are passivated by hydrogen in typical growth processes.2
Optical spectroscopy, which is often used to characterize doped semiconductors, has produced puzzling results that are difficult to reconcile with shallow-acceptor behavior. If Mg acts as a true shallow acceptor, it would give rise to a sharp photoluminescence peak close to the band-gap energy. Yet Mg-doped GaN exhibits two main photoluminescence signals: a peak in the UV, at 3.27eV, and a blue luminescence peak near 2.8eV.3 The UV signal has been attributed to a transition from the conduction band to the ‘shallow’ Mg acceptor, and the blue peak to a transition from an unknown deep center to the Mg acceptor. These assignments, however, conflict with the behavior observed during post-growth heat treatments performed to activate Mg acceptors: annealing causes a decrease in UV and an increase in blue emission.
Using state-of-the-art first-principles calculations, we have recently unraveled this behavior.4 Standard calculations based on density functional theory suffer from the ‘band-gap problem,’ in which the band gaps of semiconductors are severely underestimated. This shortcoming makes quantitative prediction of the properties of defects and dopants very difficult. To overcome this problem, we have employed a hybrid functional,5 which improves the description of exchange interactions and properly describes the experimental band gap. In the process, it also correctly predicts the electronic and optical properties of defects and dopants in semiconductors.
Our calculations show that the Mg acceptor exhibits a dual character: electrically behaving like a shallow dopant but optically like a deep acceptor.4 Figure 1 illustrates the difference: a shallow effective-mass acceptor gives rise to a valence-band-derived state that is highly delocalized (spread out over a large number of atoms). Such an acceptor is easily ionized by capturing a valence-band electron, characterized by an ionization energy determined by the hydrogenic model within the effective-mass approximation.6 In contrast, a deep acceptor gives rise to a state in the gap that is separated from the valence band and is spatially localized: see Figure 1(b). It typically requires a much higher ionization energy, making it ineffective as a doping source. Such deep impurities often trigger large relaxations of the surrounding semiconductor host atoms, which in turn give rise to luminescence signals at energies much smaller than would be expected based on the position of the electrical level in the band gap.
Figure 2. Magnesium (Mg) in gallium nitride (GaN) exhibits behavior characteristic of a ‘deep center.’ Its electrical level (solid line) lies close enough to the valence band of GaN to generate a modest concentration of holes, but in optical experiments (dashed line and blue arrow) a deep level is observed. The model on the right shows the large atomic displacements that occur when a hole (spin density illustrated by the yellow isosurface) is trapped on the MgGa acceptor, giving rise to a neutral charge state.
Our results show that Mg exhibits the key features of a deep center: large lattice relaxations occur in the neutral charge state, corresponding to a hole being trapped in a highly localized state. Concomitantly, broad deep-level luminescence appears around 2.8eV, i.e., at an energy well below that expected for a shallow impurity in GaN: see Figure 2. The isolated Mg acceptor therefore explains the blue luminescence observed in Mg-doped GaN. In spite of this overall character as a deep center, the electrical level associated with Mg occurs fortuitously relatively close to the valence band, with an ionization energy that is small enough to allow for adequate p-type doping. As to the UV signal, we propose it originates from the Mg-H complex that is present in as-grown GaN. This assignment is consistent with the decrease of the signal observed upon annealing, which breaks up the Mg-H complexes.
We have also explored the properties of Mg acceptors in aluminum nitride (AlN) and indium nitride (InN), other important members of the nitride semiconductor family. The ability to alloy the nitride semiconductors is one of their key features, and allows for light emission that spans from the IR into the UV. AlN has a large band gap (6.2eV) and can be alloyed with GaN to extend light emission to even shorter wavelengths, whereas InN has a much smaller band gap (0.7eV). We observe that the behavior of the Mg acceptor is intimately tied to the character of the valence bands of the nitrides, with deeper and flatter valence bands promoting localization. AlN has the deepest valence band on an absolute energy scale7 and the largest hole effective mass. Consequently, we find that the Mg acceptor has the highest ionization energy in AlN (780meV), exhibiting a highly localized character. On the other hand, InN has the highest-lying valence band and smallest hole mass. For InN we find no hole localization, and Mg acts as a true shallow acceptor, with the smallest ionization energy among the nitrides.
In summary, we have shown that the only efficient acceptor in nitride semiconductors actually exhibits key features of a deep center, giving rise to broad, blue luminescence. Altogether, these results can explain a large number of puzzling experimental observations, and may pave the way toward improvements in p-type doping in this key material for solid-state lighting. We are now studying the properties of other acceptor dopants, as well as alternative methods for improving hole transport in nitrides.
This research was supported by the National Science Foundation and by the University of California, Santa Barbara, Solid State Lighting and Energy Center.
John L. Lyons, Anderson Janotti, Chris G. Van de Walle
University of California, Santa Barbara
Santa Barbara, CA
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