Impact of Charge Transitions at Atomic Defect Sites on Electronic Device Performance

4.2 Charge trapping in monolayer tungsten diselenide (1L-WSe${}_2$)

For the study in [237], a WSe${}_2$ film with native point defects was transferred onto a back-gate stack of 25 nm Al${}_2$O${}_3$ on sputter-deposited Pt/TiN on p${}^{++}$-Si substrate. An RTN signal in $I_{\mathrm{DS}}$ was observed in these devices when a negative back gate voltage was applied at low temperatures ($T=15$ K), where fast nuclear tunneling dominates the charge transitions. At room temperature, energy supplied by phonons allows for overcoming the classical barrier for charge trapping as described by the NMP model (see Section 2.1.4). Consequently, defects in the oxide also become electrically active and the distinct RTN traces disappear, as multiple RTN traces, associated with different defects, superimpose. This underscores the importance of fabricating ultra-scaled devices to observe and investigate the RTN phenomenon. technology computer aided design (TCAD) simulations confirmed that these RTN traces originate from hole trapping at fast defects in the substrate, as oxide defects freeze out at low temperatures. Furthermore, TCAD suggested that the responsible defects have a trap energy of approximately 100 meV or less above the VBM and a $E_{\mathrm{Relax}}$ smaller than 150 meV. To explore the atomic origin of these phenomena, DFT calculations were carried out, which will be described in the following.

4.2.1 Defect types

The 2D film studied in [237] has a crystalline 2H-WSe${}_2$ structure with several point defects, including Se vacancies ($V_{\mathrm{Se}}$), antisite defects with Se substituting W (${\mathrm{Se}}_{\mathrm{W}}$) and W substituting Se (${\mathrm{W}}_{\mathrm{Se}}$), as well as W vacancies ($V_{\mathrm{W}}$). These defect types have already been identified as the most abundant in monolayer WSe${}_2$ [238].

In this thesis, the hole trapping properties of ${\mathrm{Se}}_{\mathrm{W}}$ and $V_{\mathrm{W}}$ are investigated. Both defect types are possible candidates for causing the detected RTN signal via hole trapping and detrapping at the defect site. While $V_{\mathrm{Se}}$ can form in WSe${}_2$, this defect type does not offer a possible state for hole trapping, as a hole cannot localize at the $V_{\mathrm{Se}}$ defect but rather creates a delocalized state inside the valence band in accordance with [239]. Therefore, the $V_{\mathrm{Se}}$ will not be considered as a potential hole trap in the following.

Defect calculations were carried out in a monolayer WSe${}_2$ supercell containing 432 atoms with 40 Å of vacuum perpendicular to the monolayer to minimize spurious interactions with periodic images. More details about the computational setup for the DFT calculations can be found in Appendix E. Monolayers containing one single defect were structurally relaxed with DFT in both their neutral and positive charge state. The $V_{\mathrm{W}}$ consists of a single missing W atom in the WSe${}_2$ lattice as shown in Fig. 4.19 for the relaxed atomic defect structures, both neutral (a) and positively charged (b).

The electronic wave functions of the localized defect orbitals are depicted for an isovalue of 0.05 e/Å${}^3$. Hereby, blue bubbles represent the HOMO of the neutral structure, while red bubbles depict the LUMO of the positively charged system. For the neutral $V_{\mathrm{W}}$, the HOMO is concentrated at the Se atoms surrounding the vacancy. When a hole is added to the system, it localizes at these Se atoms, following atomic relaxations.

The second investigated defect type ${\mathrm{Se}}_{\mathrm{W}}$ is stable when the Se moves away from the W lattice position and stabilizes in the center of four adjacent Se atoms near the defect site as shown in Fig. 4.20.

The HOMO of the neutral structure is localized around several W of the defect site. An added hole localizes at the W atoms around the defect site, following small atomic relaxations.

NMP characterization

Both defect types, $V_{\mathrm{W}}$ and the ${\mathrm{Se}}_{\mathrm{W}}$, introduce unoccupied and occupied Kohn–Sham (KS) states in the WSe${}_2$ band gap, which can host up to two electrons in opposite spin states as shown in Fig. 4.21(a).

The occupied KS levels are closely above the VBM, indicating that these defects can potentially be classified as shallow hole traps, and might therefore be responsible for generating the RTN signal measured in the device. To confirm this assumption, the thermodynamic CTLs of both defect types are calculated for single hole trapping are given in Table 4.4 and are depicted in Fig. 4.21(b). Compared to the KS levels of a defect, which are directly obtained from DFT calculations of a fixed atomic configuration, the CTL also accounts for the energy change of the system upon charge trapping due to atomic relaxations as described in Section 2.1.3. Thus, CTLs can be related to experimentally detected trap levels. Finite size corrections of the total energy compensating for electrostatic potential offsets and spurious interactions due to periodic boundary conditions in charged supercells were carried out using the CoFFEE code [240], which implements the FNV correction scheme (see Section 2.2.1) for 2D systems. The KS states and CTLs of both defect types are shown in the context of the electronic band gap of a WSe${}_2$ monolayer.

Furthermore, the relaxation energies for hole capture ($E_{\mathrm{Relax}}^{0/+1}$) and emission ($E_{\mathrm{Relax}}^{+1/0}$) at the defect sites as described in Section 2.1.3 and the configuration coordinate change $\mathrm{\Delta }Q$ as described in Section 2.1.2 were calculated. The results are presented in Table 4.4.

For both the $V_{\mathrm{W}}$ and the ${\mathrm{Se}}_{\mathrm{W}}$, the hole trap level lies closely above the VBM of the pristine bulk, with only small relaxation energies for hole capture as well as for hole emission. Both defect types can therefore be classified as hole traps and have trapping and relaxation energies close to those of the TCAD predictions as presented in [237]. Therefore, it is concluded that both $V_{\mathrm{W}}$ and the ${\mathrm{Se}}_{\mathrm{W}}$ are probable defect candidates to explain the RTN signal detected in the investigated devices.