Electrical and Optical Properties of Crystalline Black Phosphorus

Abstract

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^{$\frac{3}{2}$})⁻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.