Comparison of the results of optical and electrophysical measurements of free electron density in <i>n</i>-GaAs samples doped with tellurium
A theoretical model has been developed that allows one to determine free electron density in <i>n</i>-GaAs from the characteristic points on far-infrared reflection spectra. It was shown that, in this case, it is necessary to take into account the plasmon-phonon coupling (otherwise, the electron density is overestimated). The calculated dependence of electron density, <i>N</i><sub>opt</sub>, on the characteristic wave number, ν<sub>+</sub>, which is described by a second degree polynomial, has been obtained.Twenty-five tellurium-doped gallium arsenide samples were used to measure the electron density in two ways: according to traditional four-contact Hall method (Van der Pauw method) and using the optical method we developed (measurements were carried out at room temperature). Based on the experimental results, the dependence was constructed of the electron density values obtained from the Hall data, <i>N</i><sub>Hall</sub>, on the electron density obtained by the optical method, <i>N</i><sub>opt</sub>. It is shown that this dependence is described by linear function. It is established that the data of optical and electrophysical measurements coincide if the electron density is <i>N</i><sub>eq</sub> = 1.07 ⋅ 10<sup>18</sup> cm<sup>-3</sup>, for lower values of the Hall density <i>N</i><sub>Hall</sub> < <i>N</i><sub>opt</sub>, and for large values <i>N</i><sub>Hall</sub> > <i>N</i><sub>opt</sub>. A qualitative model is proposed to explain the results. It has been suggested that tellurium atoms bind to vacancies of arsenic into complexes, as a result of which the electron density decreases. On the surface of the crystal, the concentration of arsenic vacancies is lower and, therefore, the condition <i>N</i><sub>opt</sub> > <i>N</i><sub>Hall</sub> should be satisfied. As the doping level increases, more and more tellurium atoms remain electrically active, so electron density in the volume begins to prevail over the surface one. However, with a further increase in the doping level, the ratio <i>N</i><sub>Hall</sub>/<i>N</i><sub>opt</sub> again decreases, tending to unity. This, probably, is due to the fact that the rate of decomposition of the complexes “tellurium atom + arsenic vacancy” decreases with increasing doping level.