Electrical and Optical Properties of Crystalline Black Phosphorus

Polycrystalline black phosphorus has been produced by the Bridgman method of combined temperature and pressure and found to be p type with room-temperature resistivity around one Ω-cm, in agreement with the observations of previous workers. From 300° to 700°K, the resistivity can be fitted by an expression ρ_av=4.6×10^-3 exp(0.35/2kT) Ω-cm, and the Hall data by (ReT^3/2)^-1 = constant exp(-0.34/2kT). The product Rσ can be represented in this temperature range by (Rσ)_av = 9×10⁵T^-1.4 cm²/V-sec. The deviation from this law toward lower mobility observed by Keyes from 250° to 350°K does not occur in these samples. The resistivity continues to rise even near liquid-helium temperature, and maxima in the Hall coefficient occur between 24° and 30°K. The low-temperature Rσ products also exhibit maxima, and the magnitude of this product is small near liquid-helium temperature. Although these characteristics are consistent with two-band conduction, the relative appearance of the two sets of maxima is not consistent with a prediction of the simplest two-band theory. An optical absorption edge is found in the 2- to 6-μ region and its temperature dependence yields dW/dT = 2.8×10^-4 eV/deg. A sharp absorption peak observed near 21 μ moves to longer wavelengths with increasing temperature at a rate dW/dT = -2×10^-6 eV/deg. At helium temperature the ac photoconductive response is substantially flat from one to 20 μ. At nitrogen temperature the response is peaked between 4 and 5 μ, while at room temperature a peak is observed in the same wave-length range but the sensitivity is considerably less.