Dot size effects of nanocrystalline germanium on charging dynamics of memory devices
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NANO EXPRESS
Open Access
Dot size effects of nanocrystalline germanium on charging dynamics of memory devices Ling-Feng Mao
Abstract The dot size of nanocrystalline germanium (NC Ge) which impacts on the charging dynamics of memory devices has been theoretically investigated. The calculations demonstrate that the charge stored in the NC Ge layer and the charging current at a given oxide voltage depend on the dot size especially on a few nanometers. They have also been found to obey the tendency of initial increase, then saturation, and lastly, decrease with increasing dot size at any given charging time, which is caused by a compromise between the effects of the lowest conduction states and the capacitance of NC Ge layer on the tunneling. The experimental data from literature have also been used to compare and validate the theoretical analysis. Keywords: Quantum size, Nanocrystalline, Tunneling, Memory devices PACS: 85.30.Tv, 85.35.-p, 73.63.-b
Background Memory structures based on Ge nanocrystals (NCs) have received much attention for the next-generation nonvolatile memory devices due to their extended scalability and improved memory performance [1-7]. There are numerous ways of synthesizing Ge NCs. The mean diameter (d) of nanocrystalline germanium (NC Ge) using molecular beam epitaxy is uniquely controlled by the nominal thickness (of the deposited amorphous Ge according to the law d ≈ Kt with K ~ 7 using molecular beam epitaxy [1,2]. Comparison of electron and hole charge dynamics in NC Ge flash memories has been discussed in [3]. As we know, the crystal size of semiconductor less than 100 nm can lead to a larger band gap and a change in dielectric constant. In the former work [8,9], the effect of silicon grain size on the performance of thin-film transistors has been studied. To explore NC Ge in a memory device, it is worthy to study how the crystal size of NC Ge on charging dynamics works. Methods Theory
The energy of the highest valence state (Ev) and the energy of the lowest conduction state (Ec) for spherical NCs of Correspondence: [email protected] Institute of Intelligent Structure and System, School of Urban Rail Transportation, Soochow University, Suzhou 215006, China
diameter d (given in nanometer) are given by the following expression [3] Ec ðd Þ ¼ Ec ð1Þ þ Ev ðd Þ ¼ Ev ð1Þ
d2
11863:7 ðmeVÞ þ 2:391d þ 4:252
15143:8 ðmeVÞ: d 2 þ 6:465d þ 2:546
ð1Þ ð2Þ
The mean diameter (d) of Ge NCs is uniquely controlled by the nominal thickness (t) of the deposited amorphous Ge using molecular beam epitaxy according to the law [1,2] d ≈ Kt
ð3Þ
where K ~ 7 uses molecular beam epitaxy. The average density of Ge NCs according to the law [1,2] is DNC ≈ 6 103 =t 2 :
ð4Þ
Note that the Ge NCs have a truncated spherical form and present an aspect ratio (height over diameter) of about 0.8 [1,2]. Thus the filling factor that is the ratio of area of Ge NCs to the total area can be obtained as 2 6 103 d f ¼ π ¼ 0:2309: ð5Þ t2 2
© 2013 Mao; licensee Springer. This is an Open Access article distr
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