InP under high pressures
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R. V. Kasowski E. 1. du Pont de Nemours and Company, Central Research and Development Department, Experimental Station, Wilmington, Delaware 19880-0328 (Received 5 May 1990; accepted 1 May 1992)
The direct energy gaps, Eg, and the indirect gaps at the X point, E(X), of GaAs and AljGai-^As alloys are essentially linear functions of hydrostatic pressure, P. Recent photoluminescence measurements of Tozer et al. for InP under high pressures, however, found that Eg(P) is not quite linear, but bends down slightly at high pressures. Using the first-principles pseudofunction method, we have calculated Eg and E(X) as functions of pressure, as well as the zero-temperature equation of state P(V). Our calculated gap curve for InP, Eg(P), bends down slightly, as found in photoluminescence studies. The slope dEg/dP is 8.8 meV/kbar for small pressures P, and is in good agreement with the experimental value, 8.32 meV/kbar. The observed nonlinearity in the dependence of Eg on pressure for InP is attributed to a large derivative of the bulk modulus with respect to pressure. The calculated bond length, bulk modulus, and critical pressure for a phase transition from the zinc blende to a rocksalt structure, and the unit cell volume change at this phase transition are all in good agreement with the data.
I. INTRODUCTION With the development of diamond-anvil pressure cells, the application of large hydrostatic pressures has proven to be a powerful tool for elucidating the electronic structures of semiconductors. Photoluminescence measurements have been reported for GaAs and Al^Ga^^As alloys under high pressures and reveal that the direct energy gaps, Eg, and the indirect gaps at the X point of the zinc-blende Brillouin zone, E(X), are linear in the hydrostatic pressure P.1-2 However, similar measurements3'4 for InP and Ini_ x Ga^P found that Eg(P) is not quite linear, but bends down slightly with pressure. In this paper we use the first-principles pseudofunction method to obtain Eg(P) for InP, and find that it bends downward slightly at high pressures, as experimentally observed. Then, using the empirical tightbinding formalism of Vogl et al.5 to dissect our computed results, we show that the nonlinearity of Eg(P) for InP is related to the derivative of the bulk modulus with respect to the pressure, B'o: The larger that B'o is, the more Eg(P) bends downward at high pressures. We discuss the differences between GaAs and InP, and explain why Eg(P) appears linear for GaAs but not for InP. II. DETERMINATION OF PRESSURE FROM FIRST-PRINCIPLES CALCULATIONS To calculate the band edges Eg and E(X) as functions of pressure for comparison with data, we employ the pseudofunction method: a first-principles electronic J. Mater. Res., Vol. 7, No. 8, Aug 1992 http://journals.cambridge.org
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structure and total energy (or internal energy) calculational method based on the Hohenburg-Kohn-Sham density functional formalism.6 This method predicts well ground state (i.e., T = 0 K) properties such as total energies and their derivativ
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