Abstract
The total ionizing dose (TID) effect is one of the main causes of the performance degradation/failure of semiconductor devices under high-energy γ-ray irradiation. In special, the concentration of doubly-hydrogenated oxygen vacancy (a case study of ) in the oxide layer seriously exacerbates the TID effect. Therefore, we developed a dynamic model of mobile particles and fixed defects by solving the rate equations and Poisson’s equation simultaneously, to reveal the contribution and influence mechanisms of on the TID effect of MOS devices. We found that can directly and indirectly promote the formation of and , respectively, which can increase the electric field near the Si/SiO2 interface and reduce the threshold voltage of silicon MOS devices accordingly. Controlling with a concentration below 1014 cm−3 can suppress the adverse TID effects. The results are much helpful for analyzing the microscopic mechanisms of the TID effect and designing new MOS devices with high radiation-hardening.
Introduction
More and more new semiconductor materials are widely used as the core electronic components of sensors, detectors, radar and so on. In extreme service environments, semiconductor devices are inevitably affected by harsh radiation effects. All kinds of high-energy particles will cause serious ionization or displacement damage to semiconductors, then lead to the degradation/failure of the electrical performance of semiconductor devices, and pose adverse effects on the safety and lifetime of the entire electronic systems (Benton and Benton, 2001).
As early as 1964, Hughes and Giroux conducted a preliminary study (Hughes and Giroux, 1964) on the performance degradation of semiconductor devices (MOS) under the total ionizing dose (TID). They found that TID-induced performance degradation is due to the additional charge generated in the oxide layer (SiO2) rather than on the surface. In subsequent decades, a large number of experimental studies of ionizing irradiation showed that the key mechanism of the performance degradation induced by the TID is the formation of oxide charged defects (Not) in the gate oxide region (Hughes, 1965a; Hughes, 1965b; Kooi, 1965; Zaininger, 1966). Therefore, identification of neutral defects in SiO2 before irradiation and exploration of the evolution of charged defects after irradiation are the basis for studying the TID effect of MOS devices.
In 1956, Robert used electron paramagnetic resonance (EPR) for the first time to measure radiation-induced defects in crystalline or amorphous SiO2 (Weeks, 1963) and found two basic types of oxygen vacancies in SiO2, including deep () and shallow () level defects. In the 1980s, these methods have been used to study possible chemical reactions and free radical formation in thermal oxides of MOS devices during irradiation (Blöchl, 2000). Several kinds of defects that existed in the oxide layer before and after irradiation were thus determined. The existing initial defects in the oxide layer (SiO2) of the device before irradiation include oxygen vacancy ( and ), singly-hydrogenated oxygen vacancy ( and ) and doubly-hydrogenated oxygen vacancy ( and ) defects (Conley and Lenahan, 1993; Walle and Tuttle, 2000). Whereas, after irradiation, defects generated in the oxide layer of the device are mainly oxide charged defects (, , , , and ) (Lenahan and Dressendorfer, 1984).
The pre-existing concentration of defects in SiO2 is still known little. Density functional theory (DFT) calculations suggest that relative concentrations of different pre-existing trap species, and order of magnitude estimates of the actual concentration of defects have been suggested by etch-back experiments of irradiated oxides (Devine et al., 1993). It is found that the initial concentration of doubly-hydrogenated oxygen vacancy before irradiation is relatively high, while its charged concentration after irradiation is the lowest among the oxide charged defects (Rowsey et al., 2011a). In the process of ionizing irradiation, the evolution process of doubly-hydrogenated oxygen vacancy and its specific contribution to the TID effect are still unclear. It is thus urgent to establish a dynamic model of the TID effect that includes the dynamic of doubly-hydrogenated oxygen vacancy to reveal their influence mechanism.
In this paper, a one-dimensional (1-D) dynamics model of mobile particles and fixed defects in the oxide layer (SiO2) of typical silicon MOS devices is developed to systematically study the influence of doubly-hydrogenated oxygen vacancy on the TID effect. This work provides theoretical guidance by controlling the concentration of doubly-hydrogenated oxygen vacancy for the radiation-hardening-by-design (RHBD) techniques of semiconductor devices.
Simulation methods
Dynamics model
The model framework is shown in Figure 1. First, the initial distribution of defects can be determined by EPR measurements (Lenahan and Conley, 1998; Lu et al., 2002). The reaction events and rate coefficients between mobile particles and defects are mainly given by the DFT calculations (Rowsey et al., 2011a; Rowsey et al., 2011b). Then, with this information, the continuity equations of mobile particles and fixed defects can be described based on the rate theory. In addition, the Poisson equation is established to determine the spatial electric field distribution. Finally, the finite difference method is employed to solve the ordinary differential equations (ODEs). The evolution and distribution of oxide charged defects and electric fields can thus be obtained by this model.
FIGURE 1
Continuity equation
The continuity Eq. 1 in Figure 1, where represents the concentration of particle i at a certain position at a certain time. and represent the generation (only for electron/hole) and reaction (with other defects) rates of the particle i, respectively. represents the mobility of mobile charged particles, represents the diffusion coefficients of mobile particles, and E represents the electric field.
The generation rate of e-h pairs induced by ionizing irradiation is given as follows (Oldham, 2000),where G0 represents the density of e-h pairs per unit ionizing dose, Y is the survival rate of the e-h pairs after initial recombination, which is set to be 0.01 for SiO2 under γ-ray irradiation (Shaneyfelt et al., 1991), and R is the dose rate (rad/s).
The reaction rates of mobile particles with fixed defects are determined by the rate theory, which is proportional to the reactant concentrations. Comprehensively considering all reaction events, the total reaction rate of the particle i is given by (Xu et al., 2018),where the j, m and n are termed as the other reactants, and the α and β represent the forward and reverse reaction rate coefficients, respectively.
Since the fixed defect is immobile and has no additional generation, the continuity equation includes only the reaction term (), given in Eq. 4. For the continuity equation of mobile particles, the drift-diffusion term should be considered. Especially for electrons/holes, the generation term () should also be introduced, given in Eq. 1.
Reaction events and coefficients
Since deep- and shallow-level defects cannot be transformed into each other, we only consider the dynamics of deep-level defects (, and ) in the model. This simplification will not affect the purpose of exploring the influence of doubly-hydrogenated oxygen vacancy on the TID effect.
For oxygen vacancy (), singly-hydrogenated oxygen vacancy () and doubly-hydrogenated oxygen vacancy () formed during high-temperature processing steps (Hughart et al., 2009; Tuttle et al., 2010), first principles results indicate that the initial concentration of defects are approximately 1015 cm−3, 1014 cm−3 and 1016 cm−3, respectively (Rowsey et al., 2011a; Rowsey et al., 2011b). All three first capture a hole to form positively charged defects, then split hydrogen molecular (H2) to release a proton (H+), directly release a H+, can directly release a H+ or directly dissociate into H2 (Hughart et al., 2012). All three of these charged defects can also capture electrons as the recombination center (Rowsey et al., 2011a; Xu et al., 2018). The above chemical reaction and rate coefficients are given in Table 1.
TABLE 1
| Chemical reaction | ||
|---|---|---|
| 1.03 × 10−13 | 1.26 × 10−62 | |
| 1.92 × 10−19 | 1.03 × 10−19 | |
| 1.97 × 10−14 | 3.21 × 10−138 | |
| 1.03 × 10−13 | 1.26 × 10−62 | |
| 5.04 × 10−22 | 8.21 × 10−37 | |
| 2.06 × 10−7 | 5.07 × 10−113 | |
| 1.03 × 10−13 | 4.16 × 103 | |
| 3.81×105 | 1.03 × 10−19 | |
| 1.90 × 105 | 4.02 × 10−21 | |
| 2.06 × 10−7 | 3.21 × 10−138 |
Chemical reaction and rate coefficients (Bunson et al., 2000; Rowsey et al., 2012; Patrick et al., 2015; Sharov et al., 2022).
The accumulation of the charged defects results in the formation of a built-in electric field in the oxide layer. The electric field can be solved by Poisson’s equation as below (Esqueda et al., 2012; Jafari et al., 2015),where, is the total charge density in the oxide layer, is the relative permittivity of SiO2, and is the permittivity in a vacuum.
An important parameter is the density of Not, with units of cm−2, which can be integrated from the distribution of each oxide charged defect as (Esqueda et al., 2011),where Lox is the thickness of the oxide layer, and x refers to the distance from the Gate.
Numerical method
The finite difference method with a uniform spatial grid is adopted for solving the partial differential equations (PDEs). Here the lsoda solver of the C version (Whitbeck, 1991) is employed to solve the corresponding ODEs. The key to using the finite difference method to solve the above time and space related problems is the setting of appropriate initial values and boundary conditions. The initial concentration of charged defects and charged particles is set to 0. In the 1-D model, there are two boundaries of Gate/SiO2 and Si/SiO2 in contact with the SiO2 layer. The mobile particles can flow freely at both boundaries, so the first kind of boundary conditions are adopted. In addition, we specify that the electrostatic potential is continuous at all boundaries (Xu et al., 2018).
Results and discussions
This section presents the evolution and distribution of defects in the SiO2 layer of an NPN-type MOS capacitor (Lox = 200 nm) irradiated by γ-rays of uniformly for the whole SiO2 layer (Esqueda et al., 2011). The mobility of electrons and holes in SiO2 are 20 and (Hughart et al., 2011), respectively. The diffusion coefficients of H2 and H+ in SiO2 are 10−9 and , respectively (Rowsey et al., 2011b).
Validation and verification
The simulated density of oxide charged defects (Not) is compared with the experimental ones (Tuttle et al., 2010) to verify our model. Figure 2 shows the time evolution of the density of Not, under the time of with the dose rate of 20 rad/s at 300 K. The Capacitance-Gate voltage curves of the irradiated devices under three different TIDs were measured to determine the average densities of Not. Typically, Not increase gradually with irradiation time and tend to saturation. The simulation results are consistent with the experimental ones well. The little differences may be caused by the model approximations and measurement errors. Thus, our model should be reasonable enough for simulating the TID effect.
FIGURE 2
The influence of on and
In the following, we studied the key factors of the oxide charged defects for the TID effect, such as their composition, distribution and evolution. Figure 3A shows the distributions of different oxide charged defects under the TID of 10 krad with the dose rate of 10 rad/s at 300 K. is the main component of the oxide charged defects, while the initial density of is the highest in the oxide layer. We also simulated the evolutions of and under the dose rate of 10 rad/s at 300 K. As shown in Figure 3B, the densities of and decrease with increasing TID. This means that formed by the hole capture of will not exist stably but continue to be dissociated. Thus, has the lowest density, while can promote the formation of and .
FIGURE 3
Also as shown in Figure 3A, with increasing the distance from the Gate, the densities of and slowly increase in the oxide layer but decrease at the boundaries, because the reaction particles (holes) of flow out at the boundaries, the density of holes decrease near the Si/SiO2 interface. With increasing the distance from the Gate, the density of first increase and then decrease, and rise again near (about 30 nm) the Si/SiO2 boundary. In the first rise range, the reaction of capturing holes is dominant, but they are unstable and dissociate easily. So in the latter range, the reaction releasing H+/H2 forms or is dominant.
As given above, promote the formation of and . However, through what transformation mechanism does promote the generation of and , we further explored the transformation mechanism that promotes the generation of and . We simulated the densities of , and as a function of TID with and without , under the TID of 10 krad with the dose rate of 10 rad/s at room temperature. As shown in Figure 4A, with , the density of increases with increasing TID, and approaches to saturation. Thus, there are other channels that can produce or . As shown in Figure 4B, without , the density of is constant, which means there’s no other reaction to form or . Compare Figures 4A,B, the density of with is always higher than that without , and the increase up to 30% when the TID is 10 krad. Therefore, the increase of only comes from through , and the reason why the increase of becomes slow is that the density of decreases with increasing TID. In addition, the density of with is almost no different from that without during the ionizing process, while the density of with is obviously higher than that without . Therefore, the directly promotes the formation of through releasing H2.
FIGURE 4
We also simulated the densities of , and as a function of TID with and without , under the TID of 10 krad with the dose rate of 10 rad/s at room temperature. As shown in Figure 5A, with , the density of increases with increasing TID, and the growth rate is gradually slow, which is similar to the evolution of . It also means that there are other channels that can produce . As shown in Figure 5B, without , the density of is constant that means there’s no other reaction to form or . Compare Figures 5A,B, the density of with is always higher than that without , and the increment is up to 6 times when the TID is 10 krad. Thus, the increase only comes from though , with the density increases slowly due to the decreases of with increasing TID. In addition, the density of decreases with increasing TID without , for the is constantly transformed into during the ionizing process. The density of increases from 0 to 3.0 krad and then decreases with increasing TID with . The increases because the rate at which is converted to is higher than the rate at which is converted to during the ionizing process. The decrease of from 3.0 to 10.0 krad is due to that convert to faster than convert to . The density of with is always higher than that without , and the density of decreases with increasing TID without . Therefore, the directly promotes the formation of through releasing H+, then promotes the formation of through capturing holes.
FIGURE 5
It has been known that the TID effect of devices is closely related to the electric field near the Si/SiO2 interface () of the oxide layer, which can be simply described as follows,
According to Eq. 8, when the gate voltage (), the thickness () and the permittivity () of oxide layer are fixed, the relationship of with the total charge density () follows . Changing the concentration of corresponds to changing the after irradiation. As shown in Figure 6, we simulated the with increasing the concentration of () under the TID of 10 krad with the dose rate of 10 rad/s at 300 K. We found that, does not change with before irradiation. After irradiation, when is lower than about 1014 cm−3, almost does not change with the increase of , but when is higher than about 1015 cm−3, increases rapidly with increasing , following . This means that is mainly contributed by when less than about 1014 cm−3 and is affected by over about 1015 cm−3. at 1016 cm−3 of is about 1.7 times as high as at 1014 cm−3 of . This means that when the concentration of is lower than that of about 1014 cm−3, has almost no influence on the TID effect, while when the concentration of is higher than 1015 cm−3, has a more obvious influence on the TID effect. The results show that the irradiation resistance of the device can be improved by controlling the concentration of below 1014 cm−3 when fabricating the oxide layer of the MOS device. Although the quantitative relationship between the density of and cannot be given in current experiments, it has important guiding significance for future experimental development and device anti-radiation design.
FIGURE 6
Conclusion
In summary, is the main component of the oxide charged defects, and the contribution of is crucial, high concentration of can intensify the TID effect of MOS devices. The can directly promote the formation of , and first promotes the formation of , then indirectly promotes the formation of . with concentration higher than 1014 cm−3 can enhance the negative TID effect. This finding provides a new idea that controlling in the oxide layer with concentration below 1014 cm−3 are more conducive to the design of anti-irradiation to the TID effect.
Statements
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.
Author contributions
GL: Methodology, Software, Data Curation, Formal analysis, Writing—Original Draft. JL: Methodology, Formal analysis, Software, Writing—Review and; Editing. QZ: Writing—Review and; Editing. YL: Formal analysis, Writing—Review and; Editing, Funding acquisition.
Funding
This work was supported by the National Natural Science Foundation of China (Grant No. 11975018), the National MCF Energy R&D Program (Grant No. 2018YEF0308100), and the Outstanding member of Youth Innovation Promotion Association CAS (Grant No. Y202087). Some of the calculations were performed at the Center for Computational Science of CASHIPS, the ScGrid of Supercomputing Center, and the Computer Network Information Center of the Chinese Academy of Sciences. This research work was also supported by the Tianhe-2JK computing time award of the Beijing Computational Science Research Center (CSRC).
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
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Summary
Keywords
total ionizing dose effect, dynamic modeling, doubly-hydrogenated oxygen vacancy, microscopic mechanism, MOS devices
Citation
Lu G, Liu J, Zheng Q and Li Y (2022) Influence of doubly-hydrogenated oxygen vacancy on the TID effect of MOS devices. Front. Mater. 9:1010049. doi: 10.3389/fmats.2022.1010049
Received
02 August 2022
Accepted
07 September 2022
Published
28 September 2022
Volume
9 - 2022
Edited by
Weiliang Wang, Sun Yat-sen University, China
Reviewed by
Zexiang Deng, Guilin University of Aerospace Technology, China
Haiming Huang, Guangzhou University, China
Updates
Copyright
© 2022 Lu, Liu, Zheng and Li.
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*Correspondence: Yonggang Li, ygli@theory.issp.ac.cn
This article was submitted to Computational Materials Science, a section of the journal Frontiers in Materials
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.