Solid State Communications, Vol.55,No.4, pp.327-331, 1985. 0038-1098/85 $3.00 + .00 Printed in Great Britain. Pergamon Press Ltd. DEPENDENCE OF THE DIRECT ENERGY GAP OF GaP ON HYDROSTATIC PRESSURE S. Ves +, K. StrOssner, Chul Koo Kim*, and Manuel Cardona Max-Planck-Institut fur FestkSrperforschung, Heisenbergstrasse I, D-7000 Stuttgart 80, Federal Republic of Germany Received: April 17, 1985, by Manuel Cardona The dependence of the direct gap of GaP (r~ + r~) on hydrostatic pres- sure P up to 23 GPa is reported. The pressures were applied with a diamond anvil cell and measured using the ruby fluorescence technique. At 22.1 ± 0.3 GPa the material undergoes a transition to a phase opaque in the visible. The energy gap E0(eV) = 2.76+9.7×10-'P-35×10-~P 2 (P in GPa) exhibits a sublinear dependence on P. The dependence of E 0 on the relative change of lattice constant (Aa/a0) is more linear but still remains sublinear to a larger extent than for other tetrahedral semi- conductors measured (Ge, GaAs, InP). The subllnearity found for GaP is well reproduced by band structure calculations based on a local empiri- cal pseudopotential. We also report the calculated linear and quadratic shifts of the E~ and the indirect gaps with Aa/a0. INTRODUCTION The experimental investigation of the dependence of optical gaps in semiconductors on hydrostatic pressure P was the object of considerable interest some 25 years ago. ~ The results were instrumental in the symmetry assignment of the corresponding electronic transitions. Those days, however, the pres- sures were limited to values below -I GPa. The advent of the diamond anvil cell and the ruby manometer 2 made possible optical trans- mission measurements up to nearly-hydrostatlc pressures above 25 GPa. 2-s At these pressures most tetrahedral semiconductors undergo phase transitions, often into metallic phases. With the exception of the I-VII compounds the mate- rials become strongly opaque to visible and near ir radiation and transmission measure- ments can no longer be performed. In the low pressure range (<I GPa) opti- cal gaps of semiconductors shift linearly with P. When measured in the range of the diamond anvil cell, however, non-llnear, usually sub- linear, variations are seen. '-s These subll- near dependences on P are partly due to the "equation of state": the lattice constant a varies sublinearly with P. When plotted vs. Aa/ao, the relative change in a, they become considerably more linear. Actually, according to a recent measurement based on modulation spectroscopy (photoreflectance) ' and a theore- tical equation of state', the dependence of the lowest gap of GaAs, labelled Eo, may even be suprallnear. 8 It is of interest to compare the linear and quadratic coefficients of the dependence of gaps on Aa/a o with theoretical calculations. The linear coefficients are related to electron one-phonon coupling con- stants while the quadratic coefficients con- +On leave from Aristotle University of Thessaloniki, First Laboratory of Physics, Thessaloniki, Greece *Alexander yon Humboldt Fellow. On leave from Yonsel University, Dept. of Physics, Seoul 120, Korea rain Information on electron two-phonon inter- action. ~° For most of the materials investi- gated so far the lowest absorption edge is go: a direct edge between the top of the valence band (r,5) and the bottom of the conduction band (F,). In the case of germanium there is a weak indirect edge slightly below E o. We dis- cuss here GaP, a material with an indirect edge (rl5 ÷ At) at 2.2 eV, well below E o (2.75 eV), I~ a situation somewhat similar to that of AISb.'' In spite of the strong contribution of indirect transitions at the E o photon energy we are able to identify Eo in the absorption spectrum of a 5pm thick sample placed in the diamond anvil cell and to follow it up to P > 10 OPa. EXPERIMENT High-pressure optical absorption measure- ments to 20 GPa were performed in a gasketed diamond anvil cell. 2 The GaP sample, which was chemically polished down to a thickness of -5 pm and broken into sufficiently small pieces measuring about 100 um across, was inserted into the hole of the cell resting flat on the lower diamond, together with several ruby chips needed for the measurement of the pres- sure. The samples used originated from two different ingots. One was oriented in a (111) surface while the other had a (110)-orlenta- tion. The results obtained for both types of samples, one of them p-type and the other n-type, were identified. As a pressure trans- mitting fluid a 4:1 mixture of methanol and ethanol was used. The pressure was measured to within ±0.1 GPa up to -10 GPa and within ~0.3 GPa beyond, by using the standard ruby fluo- rescence technique. 12 The absorption coeffi- cient was obtained by normalizing the trans- mission through the sample to the transmission through a clear area next to the sample. The size of the beam must therefore be smaller than that of the sample (-100 um diameter). This was achieved by illumina'ting a 100 pm aperture with a Xe 75-W high pressure lamp which in turn was imaged on the sample through 327