Next: 3.4.1 Comparison of Different Transport Module Realizations Up: 3. Defect Creation Previous: 3.3.2 WCC of High-Voltage Devices
As outlined in Section 1.5, the employed physical model for hot-carrier degradation includes three main sub-tasks: the carrier transport module, a module describing interface state generation and a module for the simulation of the degraded devices. The presented carrier transport module of the model is based on the solution of the BTE (Section 2.6) by means of a full-band MC device simulator MONJU [154]. However, Monte-Carlo simulations are time consuming and their substitution by faster simplified schemes - such as hydrodynamic (Section 2.2) and drift-diffusion (Section 2.3) models - for Boltzmann transport equation solving appears very attractive, see e.g. [168]. There is a considerable amount of papers (see e.g. [169,96,97]) devoted to the comparison between different transport schemes and showing that HD and DD models fail to properly describe hot carriers in the case of a channel length less than 0.1um. A detailed analysis of results obtained with MC, HD and DD approaches to the BTE solution was performed in [169] confirming that HD and DD schemes may be applicable for channel lengths longer than 0.1um. The developed HCD model has been verified using MOSFETs with a channel length longer than 0.5um, see Section 3.2. In these long-channel devices the SP-mechanism plays the dominant role. The SP-mechanism is triggered by the "hottest" carriers, i.e. is defined by the high-energy tail of the DF. As a consequence, the HCD model for this case will be the most sensitive to the chosen transport scheme. Therefore, it appears mandatory to investigate whether simplified treatments of carrier transport may be successfully employed in the model to substitute the time-consuming Monte-Carlo method. Thus, this Section aims to compare different (i.e. based on MC, HD and DD methods) realizations of the HCD model.
To verify these model versions, three 5V n-MOSFETs of the same architecture (Figure 3.2) were employed, differing only in channel lengths (Lch = 0.5, 1.2 and 2.0um as in Section 3.2). Devices were stressed at a gate voltage of Vgs = 2.0V and a drain voltage of Vds = 6.25V at 25oC. In the first approach, the DF is obtained by solving the BTE with the Monte-Carlo method. In the second version, only the average energy is taken from the MC solution in order to emulate the solution of an hydrodynamic transport model. The energy profile ⟨E⟩(x) is then used to approximate the carrier DF as a function of position as it is normally done in energy transport based physical models described by
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(3.18) |
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(3.19) |