Role of Electron—Phonon Interaction and Peripheral Phonons in the Lattice Thermal Conductivity of Doped Semiconductor at Low Temperatures. Application to Phosphorus-Doped Germanium†

The role of the electron—phonon scattering and the peripheral phonons are studied by calculating the lattice thermal conductivity of phosphorous doped Ge in the temperature range 1 to 5 K. The temperature and the carrier concentration dependences of the reduced Fermi potential (η*) and of the density of states effective mass (m*) of electrons are also studied at low temperatures. The entire study is made using the Ziman expression of the electron—phonon scattering relaxation rate and the Callaway integral of the lattice thermal conductivity. The contribution of the peripheral phonons in the total phonon conductivity of the P-doped Ge is also studied. A good agreement is found between the calculated and experimental value of the phonon conductivity for five different samples of P-doped Ge having different carrier concentrations of 1.2 × 1017 to 1.1 × × 1018 cm−3 in the entire temperature range 1 to 5 K. The analytical expressions are also obtained for the phonon conductivity of the doped semiconductor in the low temperature approximation. Die Rolle der Elektron—Phonon-Streuung und der auseren Phononen werden durch die Berechnung der thermischen Gitterleitfahigkeit von Phosphor-dotiertem Ge im Temperaturbereich von 1 bis 5 K untersucht. Die Abhangigkeiten des reduzierten Fermipotentials (η*) und der effektiven Masse der Zustandsdichte (m*) von der Temperatur und der Ladungstragerkonzentration werden bei tiefen Temperaturen ebenfalls untersucht. In der gesamten Behandlung wird durchweg der Zimansche Ausdruck far die Relaxationsrate der Elektron—Phononstreuung sowie das Callaway-Integral fur die thermische Gitterleitfahigkeit benutzt. Der Beitrag der auseren Phononen zur gesamten Phononenleitfahigkeit von P-dotiertem Ge wird ebenfalls untersucht. Es wird gute Ubereinstimmung zwischen den berechneten und experimentellen Werten der Phononenleitfahigkeit von funf verschiedenen Proben von P-dotiertem Ge mit unterschiedlichen Ladungstragerkonzentrationen von 1,2 × 1017 bis 1,1 × 1018 cm−3 im gesamten Temperaturbereich von 1 bis 5 K gefunden. Fur die Phononenleitfahigkeit der dotierten Halbleiter werden analytische Ausdrucke in der Tieftemperaturnaherung erhalten.

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