Charging behavior of MNOS and SONOS memory structures with embedded semiconductor nanocrystals - Computer simulation
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Charging behavior of MNOS and SONOS memory structures with embedded semiconductor nanocrystals - Computer simulation K. Z. Molnár1, P. Turmezei1, and Zs. J. Horváth1,2 1 Óbuda University, Kandó Kálmán Faculty of Electrical Engineering, Institute of Microelectronics and Technology, Budapest,Tavaszmező u. 15-17, H-1084 Hungary 2 Hungarian Academy of Sciences, Research Centre for Natural Sciences, Institute for Technical Physics and Materials Science, Budapest, P.O. Box 49, H-1525 Hungary
ABSTRACT The effects of the oxide and nitride thicknesses and of the presence of semiconductor nanocrystals are studied on the charging behaviour of MNOS and SONOS non-volatile memory structures by the calculation of electron and hole tunnelling probability into the nanocrystals or to the nitride conduction or valence band, respectively, and by the simulation of memory hysteresis behaviour. The results are discussed in terms of the actual shape of potential barrier yielding different tunnelling current mechanisms. It is concluded for both MNOS and SONOS structures that the optimal tunnel oxide thickness for the charging behaviour is about 2 nm. Low nitride thickness decreases the efficiency of the injected charge due to its loss via the blocking layer, yielding narrower memory window. The presence of nanocrystals enhances the charge injection resulting in the better performance, but for the structures with thin tunnel oxide layer (below 3-4 nm) only, and if the nanocrystals are located close to the Si substrate at the oxide/nitride interface. The results of simulations are in agreement with the experimental results obtained in MNOS structures with Si or Ge nanocrystals. INTRODUCTION It was obtained in our recent works that the presence of Si or Ge nanocrytals (NCs) enhanced the charge injection properties of MNOS (metal-nitride-oxide-silicon) structures [1-3]. For better understanding the experimental results, the tunnelling probability of electrons and holes into the nanocrystals and to the conduction or valence band of the nitride layer, respectively, has been calculated for MNOS structures with and without NCs [4] using WKB approximation [5]. Using these probabilities the actual memory hysteresis characteristics were simulated to understand the role of NCs and the effect of layer thicknesses [6]. In this paper the results of calculations are briefly analysed and discussed. Although the calculations have been performed for MNOS structures, the obtained dependences are valid for SONOS (silicon-oxidenitride-oxide-silicon) structures as well, as the presence of a capping oxide layer does not influence on the charge injection directly. THEORY On the basis of WKB approximation [5], the tunneling probability of an electron through a potential barrier with an arbitrary shape can be expressed as
A25
P
§ · x ¨ 2 2 ¸ exp¨ ³ 2m * [U ( x ) E ]dx ¸ ! ¨ ¸ x1 © ¹ § ·½ x ¨ 2 2 ¸° ° 1 * 1 exp 2 [ ( ) ] m U x E dx ® ¨ ¸¾ ³ 4 ! ¨ ¸° ° x1 © ¹¿ ¯
2
(1)
where P is the tunneling probability, x1 and x2 are the coordinates, where the ele
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