Fig. 16.9 Comparison of solution time for the electrical-only, electrothermal, and electrothermomechanical simulations in FLOORS

compressive strain as shown in Fig. 16.8. Figure 16.9 compares the increase in simulation time with increase in domains. It takes about twice as long to run an electrothermal simulation than just an electrical simulation and about six times as long to complete an electrothermomechanical simulation.

16.3FLOORS Example: Oxide Degradation Under Radiation

16.3.1 Introduction

In device modeling, SiO2, or any oxide, is usually treated as an ideal insulator – no mobile or fixed charges exist in the oxide, and the electric field or electrostatic potential drop across the inside of the oxide, as determined by Poisson’s equation with charge ¼ 0, is constant. The electrostatic potentials on either side of the insulator, i.e., in the gate and semiconductor, are the boundary conditions for full solution of the problem.

One-way oxide degradation occurs when charge is generated in or injected into the oxide, or onto the oxide/semiconductor interface [17]. Ionizing radiation is one such environmental phenomenon that is energetic enough to create charge, in the form of electron–hole pairs, across even the 9-eV bandgap of SiO2. These electrons and holes are known to interact with oxygen vacancy complexes and hydrogenous species present in the oxide, eventually leading to fixed charge centers (deep hole traps) [18, 19] and interface trap buildup [20, 21]. To numerically account for this charge transport and defect interactions, SiO2 can no longer be treated as a homogeneous insulator. Instead, SiO2 is treated as a wide-bandgap semiconductor;

drift-diffusion equations are specified in the oxide, using appropriate values of diffusivity and mobility for each mobile particle being simulated in the oxide. The concentrations of preexisting neutral defects, such as oxygen vacancies (Vo) and hydrogenated oxygen vacancies (VoH), will probably not be known and will have to be estimated to fit resultant changes in device characteristics. Similarly, the concentration of molecular hydrogen (H2) may have to be estimated.

16.3.2 The Problem

Consider an MOS capacitor that has been irradiated by Co-60 gamma rays to a total dose of 30 krad and at a dose rate of 26 rad(SiO2)/s [22]. Experimental evidence suggests that many of the holes that are generated by the radiation are captured in “deep traps,” close to the interface, and that protons, liberated from the oxide as a result of irradiation, are responsible for interface trap buildup [23, 24]. Theoretical, quantum mechanical, first principles calculations on the molecular scale suggest that reactions 12 and 13 are feasible in thermally grown SiO2 at room temperature [25]:

First (16.12), a hole (h+) can be captured on an oxygen vacancy (Vo) with a 0.0- eV energy barrier (Ef0). This hole is in a deep trap, since 4.5 eV (Er0) is halfway into the SiO2 bandgap. Holes in this trap will probably not be able to get enough thermal energy (kBT) at room temperature to escape. Once the oxygen vacancy has captured a hole, it may “crack” molecular hydrogen (H2), which can be left over in SiO2 interstitial regions from processing steps involving H2, forming a hydrogenated oxygen vacancy (VoH) and a free proton (H+) in the process.

First principles calculations also suggest that hydrogenated oxygen vacancies, formed during processing steps, prior to irradiation, also capture holes with a 0.0-eV barrier (16.14) and that once these precursors have captured a hole, protons may be released directly:

It is possible to test whether these mechanisms can quantitatively explain the effects observed by experiment using FLOORS. The next section describes how.