Information on carrier diffusion length is necessary to optimize electronic and optoelectronic devices constructed of graphene. Photoelectromagnetic (PEM) investigations are a known method of determining this parameter in semiconductors. The aim of this paper is to present applicability of contactless PEM method in investigations of graphene. When a graphene sample is illuminated by a circular spot of radiation, free electrons and holes are photogenerated in the illuminated spot and diffuse in all directions in the layer. In external magnetic field perpendicular to graphene surface the diffusing carriers are deflected by Lorentz force and the circulating PEM current flows. Under amplitude-modulated illumination of a sample the PEM current varies, and consequently the changing magnetic flux, caused by it, can induce a measurable voltage in suitably placed pick-up coils. The PEM signal depends on external magnetic field and on the gradient of concentrations of photogenerated carriers. It increases with the photogeneration rate, i.e., with illumination intensity and quantum coefficient of photogeneration of free carriers. PEM signal is also dependent on the carrier diffusion length, which is proportional to the square root of carrier mobility multiplied by their lifetime. As the carrier mobility in graphene is high, it is possible to measure PEM signal even in case of very short carrier lifetimes.
Theoretical calculations provide conclusion that there are at least three possible methods of using contactless PEM investigations for determining carrier parameters in graphene. Knowledge of inductive coupling between PEM current and the used pick-up coils is not necessary in these methods. They are based on fitting of experimental results with theoretical dependence of measured signal on the following experimental variables: external magnetic field, frequency of illumination chopping, and profile of laser beam incident upon a sample (changed e.g. by using refractive beam shaper). We present comparison of the results obtained for graphene films deposited on different substrates.
The presented contactless and nondestructive PEM method of investigations is suitable for rapid and simple inspection of graphene. It enables to avoid possible contaminations of the sample during contact preparation, as well as the difficulties in preparation of contacts. We anticipate our paper to be a starting point for mapping the recombination non-uniformity in graphene samples by scanning them with a light probe and performing the contactless PEM measurements.
This work was supported by the National Science Centre (Poland) project no. DEC-2012/05/B/ST7/01198.