First-Principles Study of Defect Levels Caused by Transition Metal Atoms in Silicon Nitride for Non-Volatile Memory Applications
Authors: Agrawal Rahul , Kobayashi Kiyoteru 
Published: December 2020

The silicon nitride-based charge trap memory architecture has been considered as one of the promising solutions for high-bit-density three-dimensional NAND-type flash memories [1]. In this architecture, electrons and holes are trapped by point defects distributed in silicon nitride. This phenomenon induces a shift of the threshold voltage of memory transistors and is applied to store data. Recently, multi-level cell technology has been introduced in NAND-type flash memories to increase the bit density, which has needed to enlarge the threshold voltage shift [2]. Thus, the increase in the density of the point defects which can generate deep trap levels in silicon nitride is demanded to realize the high-bit-density flash memories. In the present work, we investigate the energy levels caused by transition metal (Ti, V, or Mn) defects in silicon nitride using first-principles calculations.
Amorphous silicon nitride film has been used as the charge trap layer in flash memories. The hexagonal β-Si3N4 crystalline phase is believed to have similar local structures as amorphous silicon nitride [3]. Therefore, to discuss the realistic nature of transition metal atoms in silicon nitride, a 168-atom supercell was formed by expanding a unit cell of β-Si3N4 phase in a 2x2x3 matrix on a-axis, b-axis, and c-axis, respectively. The structure optimization and self-consistent field (SCF) calculations were performed using Advance/PHASE ver. 3.5 software. The generalized-gradient approximation with the PBE functional was used for the exchange-correlation energy of electrons. The kinetic energy cutoffs for wavefunctions were 40, 52, 64, 76, and 88 Ry and those for charge density were 400, 520, 640, 760, and 880 Ry in the calculations. 2x2x4 k-points sampling in the Monkhorst-Pack grid was used to perform SCF calculations.
The behavior of transition metal atoms in semiconductors and dielectrics has been widely studied. Shibata et al. explained the behavior of transition metal atoms in silicon nitride using density-functional theory (DFT) calculations in terms of formation energies [4]. However, there are few reports on the energy levels generated by transition metal atoms in silicon nitride. In the present work, the density of states (DOS) of electrons in four supercell structures of Si72N96, Si71N96Mn, Si71N96V, and Si71N96Ti have been investigated. The calculations with the conditions mentioned earlier have been performed on the supercells, where a transition metal atom (Ti, V, or Mn) was substituted for a Si atom.
Figure 1(a) shows total DOS calculated for the supercell Si71N96Mn. We can see five different defect levels of energy 1.59, 1.91, 2.03, 3.00, and 3.12 eV below the bottom of the conduction band. From Atomic Layer DOS (ALDOS) calculation results, we have found that all five trap levels are mainly localized at the Mn atom. Some of these trap levels would be able to behave as deep electron trap levels.
Total DOS calculated for the supercell Si71N96V is shown in Fig. 1(b). Similar to the Si71N96Mn, five different defect levels appeared. However, three levels close to the bottom of the conduction band in Si71N96V are shallower in energy as compared to those in Si71N96Mn. Electrons trapped by these shallow levels might be easily emitted to the conduction band. The emission of electrons from the defect levels would degrade the retention characteristics of flash memories. We also calculated total DOS for the supercell Si71N96Ti. No defect levels appeared in the forbidden gap of Si71N96Ti.
In conclusion, we have performed the DFT calculations to investigate the defect levels generated by transition metal atoms (Ti, V, or Mn) in silicon nitride. The substitution of a Si atom with a Mn atom generated deep defect levels in the forbidden gap. Some of the defect levels can be expected to behave as deep trap levels for electrons. The doping of silicon nitride with Mn atoms would have potential for enhancing the carrier trapping properties of the silicon nitride charge trap layer. Further experimental studies would be needed to validate the effectiveness of doping of silicon nitride with Mn atoms to the enhancement of the charge trapping properties in flash memories.
We would like to show our gratitude to K. Niisato, Y. Ota and T. Inushima for sharing their pearls of wisdom with us during the course of this research. This work was partly supported by JSPS KAKENHI Grant Number JP18K04244.
[1] S. Inaba, 2018 IEEE Inte. Memory Workshop, Kyoto, 1 (2018).
[2] K. Parat et al., 2018 IEEE Inter. Electron Devices Meeting, San Francisco, 2.1.1 (2018).
[3] L. E. Hintzsche et al., Physical Review B., 86, 235204 (2012).
[4] D. Shibata et al., ECS Transactions, 64(11), 229 (2014).

Figure 1