Fabio Bernardini

Spontaneous polarization and piezoelectric constants of III-V nitrides

The spontaneous polarization, dynamical Born charges, and piezoelectric constants of the III-V nitrides AlN, GaN, and InN are studied ab initio using the Berry-phase approach to polarization in solids. The piezoelectric constants are found to be up to ten times larger than in conventional III-V and II-VI semiconductor compounds, and comparable to those of ZnO. Further properties at variance with those of conventional III-V compounds are the sign of the piezoelectric constants ~positive as in II-VI compounds! and the very large spontaneous polarization. @S0163-1829~97!51740-1# In this paper we report an ab initio study of the spontaneous polarization, piezoelectric constants, and dynamical charges of the III-V nitride semiconductors AlN, GaN, and InN. 1 This class of polarization-related properties is of obvious importance for the study of nitride-based piezodevices 2 and multilayer structures. In particular, knowledge of these properties allows an insightful treatment of the polarization ~and ensuing electric fields! in strained and polarized nitride junctions and superlattices under any strain condition, as discussed elsewhere. 3 From the present study, one of the first applications of the modern theory of polarization in solids 4,5 to real and ‘‘difficult’’ materials of technological interest, the nitrides emerge as highly unusual III-V materials, resembling II-VI oxides and in some respects ferroelectric perovskites. The results we report here are of special interest in view of the scarcity of the data ~both experimental and theoretical! available at present for the nitrides. In the absence of external fields, the total macroscopic polarization P of a solid is the sum of the spontaneous polarization P eq in the equilibrium structure, and of the straininduced or piezoelectric polarization dP. In the linear regime, the piezoelectric polarization is related to the strain e by

Pyroelectric properties of Al(In)GaN/GaN hetero- and quantum well structures

The macroscopic nonlinear pyroelectric polarization of wurtzite AlxGa1-xN, InxGa1-xN and AlxIn1-xN ternary compounds (large spontaneous polarization and piezoelectric coupling) dramatically affects the optical and electrical properties of multilayered Al(In)GaN/GaN hetero-, nanostructures and devices, due to the huge built-in electrostatic fields and bound interface charges caused by gradients in polarization at surfaces and heterointerfaces. Models of polarization-induced effects in GaN-based devices so far have assumed that polarization in ternary nitride alloys can be calculated by a linear interpolation between the limiting values of the binary compounds. We present theoretical and experimental evidence that the macroscopic polarization in nitride alloys is a nonlinear function of strain and composition. We have applied these results to interpret experimental data obtained in a number of InGaN/GaN quantum wells?(QWs) as well as AlInN/GaN and AlGaN/GaN transistor structures. We find that the discrepancies between experiment and ab initio theory present so far are almost completely eliminated for the AlGaN/GaN-based heterostructures when the nonlinearity of polarization is accounted for. The realization of undoped lattice-matched AlInN/GaN heterostructures further allows us to prove the existence of a gradient in spontaneous polarization by the experimental observation of two-dimensional electron gases?(2DEGs). The confinement of 2DEGs in InGaN/GaN QWs in combination with the measured Stark shift of excitonic recombination is used to determine the polarization-induced electric fields in nanostructures. To facilitate inclusion of the predicted nonlinear polarization in future simulations, we give an explicit prescription to calculate polarization-induced electric fields and bound interface charges for arbitrary composition in each of the ternary III-N alloys. In addition, the theoretical and experimental results presented here allow a detailed comparison of the predicted electric fields and bound interface charges with the measured Stark shift and the sheet carrier concentration of polarization-induced 2DEGs. This comparison provides an insight into the reliability of the calculated nonlinear piezoelectric and spontaneous polarization of group III nitride ternary alloys.

Evidence for nonlinear macroscopic polarization in III–V nitride alloy heterostructures

We provide explicit rules to calculate the nonlinear polarization for nitride alloys of arbitrary composition, and hence, the bound sheet charge induced by polarization discontinuity at the interfaces between different alloy and binary (epi)layers. We then present experimental results and simulations of polarization-related quantities in selected nitride-alloy-based heterostructure systems. The agreement of experiment and simulation, also in comparison to previous approaches, strongly suggests that the macroscopic polarization of nitride alloys is indeed nonlinear as a function of composition.

EFFECTS OF MACROSCOPIC POLARIZATION IN III-V NITRIDE MULTIPLE QUANTUM WELLS

Huge built-in electric fields have been predicted to exist in wurtzite III-V nitrides thin films and multilayers. Such fields originate from heterointerface discontinuities of the macroscopic bulk polarization of the nitrides. Here we discuss the background theory, the role of spontaneous polarization in this context, and the practical implications of built-in polarization fields in nitride nanostructures. To support our arguments, we present detailed self-consistent tight-binding simulations of typical nitride quantum well structures in which polarization effects are dominant.

First-principles prediction of structure, energetics, formation enthalpy, elastic constants, polarization, and piezoelectric constants of AlN, GaN, and InN: Comparison of local and gradient-corrected density-functional theory

A number of diverse bulk properties of the zinc-blende and wurtzite III-V nitrides AlN, GaN, and InN, are predicted from first principles within density-functional theory using the plane-wave ultrasoft pseudopotential method, within both the local density approximation (LDA) and generalized gradient approximation (GGA) to the exchange-correlation functional. Besides structure and cohesion, we study formation enthalpies (a key ingredient in predicting defect solubilities and surface stability), spontaneous polarizations and piezoelectric constants (central parameters for nanostructure modeling), and elastic constants. Our study bears out the relative merits of the two density-functional approaches in describing diverse properties of the III-V nitrides (and of the parent species

Spontaneous versus Piezoelectric Polarization in III–V Nitrides: Conceptual Aspects and Practical Consequences

{\mathrm{N}}_{2},

Nonlinear macroscopic polarization in III-V nitride alloys

Al, Ga, and In). None of the two schemes gives entirely successful results. However, the GGA associated with the multiprojector ultrasoft pseudopotential method slightly outperforms the LDA overall as to lattice parameters, cohesive energies, and formation enthalpies of wurtzite nitrides. This is relevant to the study of properties such as polarization, vibrational frequencies, elastic constants, nonstochiometric substitution, and absorption. A major exception is the formation enthalpy of InN, which is underestimated by the GGA (\ensuremath{\sim}0 vs -0.2 eV).

Free-carrier screening of polarization fields in wurtzite GaN/InGaN laser structures

Macroscopic polarization plays a major role in determining the optical and electrical properties of nitride nanostructures via polarization-induced built-in electrostatic fields. While currently fashionable, this field of endeavour is still by far in its early infancy. Here we contribute some clarifications on the conceptual issues involved in determining built-in fields in III–V nitride nanostructures, sorting out in particular the roles of spontaneous and piezoelectric polarization.

Polarization-Based Calculation of the Dielectric Tensor of Polar Crystals

We study the dependence of macroscopic polarization on composition and strain in wurtzite III-V nitride ternary alloys using ab initio density-functional techniques. The spontaneous polarization is characterized by a large bowing, strongly dependent on the alloy microscopic structure. The bowing is due to the different response of the bulk binaries to hydrostatic pressure and to internal strain effects (bond alternation). Disorder effects are instead minor. Deviations from parabolicity (simple bowing) are of order 10% in the most extreme case of AlInN alloys, much less at all other compositions. Piezoelectric polarization is also strongly nonlinear. At variance with the spontaneous component, this behavior is independent of microscopic alloy structure or disorder effects, and due entirely to the nonlinear strain dependence of the bulk piezoelectric response. It is thus possible to predict the piezoelectric polarization for any alloy composition using the piezoelectricity of the parent binaries.

Accurate calculation of polarization-related quantities in semiconductors

The free-carrier screening of macroscopic polarization fields in wurtzite GaN/InGaN quantum well lasers is investigated via a self-consistent tight-binding approach. We show that the high carrier concentrations found experimentally in nitride laser structures effectively screen the built-in spontaneous and piezoelectricpolarization fields, thus inducing a “field-free” band profile. Our results explain some heretofore puzzling experimental data on nitride lasers, such as the unusually high lasing excitation thresholds and emission blue shifts for increasing excitation levels.