Type of presentation: Poster

IT-16-P-2001 Modified Random Walk Algorithm for Monte Carlo Modeling of EBIC and Cathodoluminescence

Priesol J.¹, Šatka A.¹

¹Institute of Electronics and Photonics, Slovak University of Technology, Ilkovičova 3, 812 19 Bratislava, Slovakia

juraj.priesol@stuba.sk

The aim of this contribution is to discuss the results obtained by Monte Carlo (MC) modeling and simulation of the interaction of accelerated primary electrons with semiconductors and semiconductor structures. In electron microscopy practice, MC method is routinely used for quantitative assessment of spatial distribution of energy deposited into the semiconducting material by primary electrons [1], [2], but there is a lack of papers dealing with the MC simulations of consequent diffusion and recombination processes of generated charge carriers [3], [4]. Diffusion of minority carriers has a radical impact on diffusion sensitive methods like electron beam induced current (EBIC) and cathodoluminescence (CL) and therefore it is important to pay a proper attention to it. Due to the complexity of MC simulations, diffusion is usually considered as a random motion of particles according to the random walk algorithm [5], i.e. each generated carrier passes constant distance Δs in random direction constant number of times k. Based on this simple model, three dimensional MC simulations of random diffusion from point source with initial number of N₀ generated carriers were executed. MC simulations reveal non-exponential decrease of the carriers from the point source, which is not in agreement with analytical approximation and it has its origin in erroneous assumption of equal lifetime for each simulated carrier. It has been found out that this discrepancy has only a little effect on CL accuracy whereas it is significant for simulation of EBIC line profiles. To overcome this, a modification of random walk algorithm was proposed, where the value of k was determined using probability density function according to normal statistical distribution. The application of adapted model and its influence on the results of MC simulations of EBIC (Fig. 1) and CL, as well as the comparison of simulation and experiment (Fig. 2) performed on III-N semiconductor structures will be presented and discussed.

References

[1] Joy, D. C.: Monte Carlo modeling for electron microscopy and microanalysis. Oxford University Press, Inc., 1995, 224 pp., ISBN: 0-19-508874-3.
[2] Demers, H. et al, Scanning 33 (2011), p.135–146.
[3] Ledra, M. - Tabet, N., Superlattices and Microstructures 45 (2009), p.444–450.
[4] Doan, Q. T. - El Hdiy, A. - Troyon, M., J. Appl. Phys. 110 (2011), p. 124515.
[5] Pearson, K., Nature, no. 1865, vol. 72, (1905) p. 294.

This work has been supported by the Slovak Research and Development Agency (contract No. APVV-0367-11) and by Slovak Grant Agency (project VEGA No. 1/0921/13).

Fig. 1: Spatial distributions of 10⁵ carriers recombining in GaN sample around the circular Shottky contact with radius r_c = 2500 nm (left) and 150 nm (right) and simulated for electron beam energy E_pe = 5 keV, diffusion length of minority charge carriers L = 196 nm and surface recombination velocity v_s = 0.

Fig. 2: Simulated EBIC line profiles at the circular Schottky contact with radius r_c for different diffusion lengths L of minority carriers at E_pe = 5 keV (left), and EBIC line profiles extracted from EBIC maps measured at reverse polarized Schottky contact formed by tungsten needle set onto the undoped GaN layer (right); fit shows diffusion length ~260nm.