Hot-electron conduction in ovonic materials Carlo Jacoboni a,⇑ , Enrico Piccinini b,⇑ , Fabrizio Buscemi b , Andrea Cappelli a a Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Istituto Nanoscienze CNR-S3, Università di Modena e Reggio Emilia Via Campi 213/A, I-41125 Modena, Italy b ARCES Research Center, Università di Bologna Via Toffano 2/2, I-40125 Bologna, Italy article info Article history: Available online 13 March 2013 Keywords: Ovonic materials Trap-limited conductivity Phase-change memory abstract Electric conduction in ovonic materials is analyzed with special attention to chalcogenide glasses used for phase-change memories. A general theory is presented based on plausible microscopic assumptions. Electric field, carrier concentration, and electron temperature along the device, as well as diffusion and Poisson self-consistency, are considered. The effect of different ranges of localized levels in the gap is ana- lyzed. The results account for and interpret all main experimental findings in phase-change memory cells. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Ovonic materials feature an electrical switching behavior, i.e., a sudden change in resistivity by several orders of magnitude when a threshold field is reached, that cannot be explained by the standard Mott theory [1,2]. Such a behavior is of great interest for the tech- nology of phase-change memories (PCM) [3], so that in the last decade the study of electron transport in amorphous materials raised renewed interest. Several attempts of interpreting the S-shaped Negative Differ- ential Resistivity (SNDR) of ovonic materials have been proposed in the literature. They rely on different microscopic pictures, rang- ing from the formation of filaments within an amorphous matrix [4–7] to impact ionization [8], or to space-charge accumulation [9]. Recently, transport in chalcogenide glasses was also modeled in terms of a thermally-assisted trap-limited conduction [10,11]. The electron switching is connected to a field effect that either en- hances the carrier concentration in shallow traps [10], or increases the average energy of the trapped carriers [11]. These theories are shortly reviewed in Section 2. In this work, carrier transport in ovonic materials is still inves- tigated by means of trap-limited conduction, but following a hydrodynamic-like approach [12]. Details are reported in Section 3. Unlike the models presented in Refs. [10,11], the energy distribu- tion of the carriers is used to calculate the local carrier concentra- tion and their average energy, as well as the charge and energy fluxes. In the present picture, diffusion effects are explicitly in- cluded, and self-consistency between charge distribution and field is accounted for. These features were instead missing in previous works. We also investigate the switching phenomenon as a function of the energy distribution of the trap levels. Results are reported in Section 4. 2. Available models Several papers on transport in amorphous semiconductors refer to hopping conduction and/or to trap-limited conduction [2]. In the latter case, carriers travel in the band or in extended states above the mobility edge, but are often captured in localized trap states. Such a situation is also referred to as ‘‘reduced mobility’’ (see Fig. 1a) and can be described in two different ways: we may con- sider the total concentration of carriers n 0 with a reduced mobility l, or the reduced concentration n of the carriers actually present in the band moving with the ‘‘free mobility’’ l 0 . The presence of an electric field reduces the height of the barrier to be overcome by the trapped electrons to reach the band, thus increasing the re- duced mobility in one picture, or increasing the concentration of free carriers in the other picture. These two descriptions of the Poole–Frenkel effect are, of course, equivalent. To be precise, the expression ‘‘hopping conduction’’ should strictly refer to the case of carriers jumping from one site to an- other without entering the conduction band. Such transitions may occur if two traps are close enough and the energy barrier be- tween them is not too high. They may consist in a direct tunneling, or may be thermally assisted or thermally activated, as shown in Fig. 1b. If s b is the average free time of an electron in the band before being captured (trapping time), and s t the average time of a trapped electron before being released to the band (escape time), the reduced mobility is easily calculated as l ¼ l 0 s b s b þ s t ð1Þ 0038-1101/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.sse.2013.02.007 ⇑ Corresponding author. E-mail addresses: carlo.jacoboni@unimore.it (C. Jacoboni), enrico.piccinini@ unimore.it (E. Piccinini). Solid-State Electronics 84 (2013) 90–95 Contents lists available at SciVerse ScienceDirect Solid-State Electronics journal homepage: www.elsevier.com/locate/sse