Enhanced low-flux sensitivity (ELFS) effect of neutron-induced displacement damage in bipolar devices: physical mechanism and parametric model

TL;DR

This paper investigates the physical mechanism behind the enhanced low-flux sensitivity (ELFS) effect in neutron-induced damage in bipolar devices, proposing a defect cluster annealing model that accurately reproduces experimental observations.

Contribution

A new defect cluster annealing model is developed to explain ELFS, improving understanding of neutron damage effects in bipolar devices.

Findings

The model reproduces experimental ELFS behavior accurately.

The key parameter is the ratio of Si interstitials captured by defect clusters.

The model predicts nonsensitive regions at low and high fluxes.

Abstract

Similar to the enhanced low-dose-rate sensitivity (ELDRS) effect of ionization damage, an enhanced low-flux senstivity (ELFS) effect has been reported in ions/neutron irradiation on n-type silicon or PNP transistors. However, the existing mechanism and simulation dominated by the diffusion dynamics give much higher transition flux than the experimental observations. In this work, we develop a new model based on the annealing of defect clusters for the ELFS effect. Simulations considering Si-interstitial-mediated inter-cluster interactions during their annealing processes successfully reproduce the ELFS effect. The ratio of Si interstitials captured by defect clusters to those dissipating off on the sample edges or re-merging into the bulk is found as the key parameter dominating the enhancement factor (EF) of the ELFS effect. We also establish a compact parametric model based on the mechanism, which is found to provide a good quantitative description of the experimental results. The model predicts the existence of nonsensitive regions at sufficiently low and high fluxes as well as a non-trivial fluence and temperature dependence of the enhancement factor.

Tables

Table 1. Table 1 : Parameter list

Parameters

GLPNP

Equations

$$I+V\to \varnothing ,$$

$$I+V_2\to V,$$

$$V+V\to V_2,$$

$$V+O\to VO,$$

$$\frac{\partial [X]}{\partial t}=D_X\frac{{\partial }^2[X]}{\partial X^2}-U_X+G_X,$$

$$m{I}_{cls}\to (m-1)I_{cls}+I,$$

$$m{V}_{cls}+I\to (m-1)V_{cls},$$

$$V+m{V}_{cls}\to (m+1)V_{cls},$$

Full text

I Introduction

Displacement damage (DD) in irradiated Si bipolar devices causes the degradation of electronic properties of the systems. In most operational amplifiers and comparators, the degradation of the input bias current ($I_{iB}$) is usually the most sensitive parameters. The most sensitive components with respect to the degradation of $I_{iB}$ are the input-stage bipolar junction transistors (BJTs)  Pease1996; Barnaby1999; Barnaby2001; Barnaby2002. Numerous reports Srour2003; Srour2013 have studied various DD effects and the underlying mechanisms are attributed to the formation of several defect structures including point defects and small clustersBracht1998; Cowern1999, rod like ({311}) defects Li1998; Eaglesham1994, and dislocations Li1998; Boninelli2006. These defects change the recombination rate of charge carriers in the base region of the transistors and may also cause donor/acceptor compensation, which remarkably influence the electronic properties of BJTs. In the experiments of heavy ions implantation with high fluence ($>1\times 10^{12}~{}\text{cm}^{-2}$) and high flux ($>1\times 10^{10}~{}\text{cm}^{-2}\text{s}^{-1}$), the more densed particle bombardment is found to enhance the DD at higher irradiation flux Holland1985; Haynes1991. For the situations of lower fluence ($<1\times 10^{10}~{}\text{cm}^{-2}$) and flux ($1\times 10^{7}\text{-}2\times 10^{10}~{}\text{cm}^{-2}\text{s}^{-1}$), there are also reports saying that the DD can decrease with increasing flux Svensson1995; Svensson1997.

Neutron induces the highest NIEL/IEL ratio among the particles, where NIEL and IEL stand for non-ionizing energy loss and ionization energy loss, respectively. However, the study of the flux dependence of neutron-induced DD is rarely seen. There are suspicions of the presence of the flux effect of neutron iradiations, based on considerations as follows.

1. Different from the heavy ions with MeV energies, the neutron impacts normally do not generate a prominent long trace of defects; Instead, the damage clusters are smaller and more localized in space.
2. The average distance between the adjacent impacts for neutron irradiation is huge, which is larger than $1\mu m$ even at a total fluence of $1\times 10^{12}~{}\text{cm}^{-2}$. The experimental observations show that there is rarely defect clusters with radius larger than $5~{}nm$ Donnelly2003; Narayan1981; Jencic1995, thus the direct overlap among clusters is less possible. Estimated by Gossick’s theory Gossick1959; Curtis1973, the maximum range of the influence of the electric potential distorted by a single cluster is hardly larger than $1~{}\mu m$. Therefore, it is naturally to see the effects of neutron irradiations as the accumulated events of single-particle incidence, thus the DD is thought to unlikly show flux effects. Actually, results supporting that there is no flux effect has been reported zontar1999.

To clarify the influence of the flux on the neutron induced DD in silicon bipolar devices, very recently, we did low equivalent fluence ($1\times 10^{10}~{}\text{cm}^{-2}$) and various flux ($5\times 10^{5}-5\times 10^{6}~{}\text{cm}^{-2}\text{s}^{-1}$) neutron irradiation experiments on bipolar analogy circuits and BJTs Zhang2019. In contrast to the results of heavy ion bombardment results of high fluence, our experiments have shown evident enhanced low flux sensitivity (ELFS) effects of the DD in both integrated circuits and discrete transistors. To identify the dominate mechanisms, the characteristic time of different possible processes of DD were estimated and compared with the experimental conditions. It is found that, the mechanisms responsible for the flux dependence arise in the processes of short-term annealing, i.e. the interactions among sequential impacts influence the formation of the stable damage. Some previous research suggest that the flux dependent results come from the interactions among defect clusters whose reaction rates are limited by the diffusion of Si interstitials Hallen1991; Svensson1993; Svensson1997. However, there are nonnegligible discrepancy of the transition flux between the calculated results and the experimental observations. The transitions flux derived from simulations are much higher than the experimental results which will be discussed in the main body of this paper.

In this work, we investigate the reasons and propose a defect clusters’ self-annealing limited model and a parametric model for the ELFS effect of neutron-induced DD. The proposed model considers the cluster nature of the neutron-induced displacement defects and suggest the reactions of inter clusters are limited by the reordering processes of each cluster. To test the mechanisms, numerical simulations are performed. The charged states of defects and the mobility enhancement effect of mobile particles promoted by exchanging charge carriers with the environment are also considered BarYam1984(1); BarYam1984(2); Car1984. The simulated results show qualitatively agreements with the experimental observations and predict an inverse S-shaped flux dependence. Further analyses of the mechanisms of the flux effects leads to the construction of an analytical model. The modeling results show good quantitative agreements with the experimental results and predict that the DD depends on not only the flux but also on the total fluence and irradiation temperature.

The paper is organized as following. In Sec. II, the experimental results are simply shown. In Sec. III, the conventional model Hallen1991; Svensson1993; Svensson1997 and simulated results are given. The discrepancy between the simulated results and the experimental observations are discussed and the reasons are attributed to the formation of metastable defect complexes. A modified model is demonstrated in Sec. IV, by which the simulated results show better agreement with the experimental results. In Sec. IV.3, we analysis the mechanisms of the flux effect and show that a retarded recombination mechanisms during the annealing process of defect clusters dominates the effect. Based on the mechanisms, a compact parametric model is proposed in Sec. LABEL:sec:Parametricmodel. The model gives analytical solutions of DD with respect to the irradiation flux, fluence and temperature. Some modifications that may need to be made in future are discussed in Sec. LABEL:sec:discussion. Conclusions are gathered in Sec. LABEL:sec:conclusion.

II Experimental results overview

The detailed characteristics of the experimental results have been analysed in details in one of our previous papersZhang2019, here we just briefly explain the settings of the experiments and emphasis the key characteristics of the results of the flux effects.

Two kinds of operational amplifier, LM324N and LM124 produced by Texas Instruments, and a kind of gate lateral PNP (GLPNP) BJTs are used as the research objects. In LM324N and LM124, the input bias currents are most sensitive to the base currents of their input-stage PNP BJTs. The configuration of the GLPNP BJT is illustrated in Fig. 1. Neutron irradiations were performed at the Chinese Fast Burst Reactor-II (CFBR-II) of Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics. The reactor provides a controlled 1MeV equivalent neutron irradiation. All samples were irradiated to a total fluence of $1\times 10^{10}~{}\text{cm}^{-2}$ at room temperature, at flux varying between $5\times 10^{5}~{}\text{cm}^{-2}\text{s}^{-1}$ and $5\times 10^{6}~{}\text{cm}^{-2}\text{s}^{-1}$. During the irradiation, all pins are shorted and grounded.

The increased $I_{iB}$ of LM324N and LM124 circuits are shown as the red and blue curves in Fig. 2. The solid symbols represent the mean values of sample splits containing 5 parts and the error bars show the standard deviations of the currents. Explicit increase of the input bias currents are observed on all samples of both types of circuits. More importantly, the results show apparent divergence among splits exposed at different flux rates. As shown in the figure, when the flux decreases from $5\times 10^{6}~{}\text{cm}^{-2}\text{s}^{-1}$ to $5\times 10^{5}~{}\text{cm}^{-2}\text{s}^{-1}$, for LM324N, the mean value of the excess input bias currents increase monotonously from $0.33~{}nA$ to $1.35~{}nA$. For LM124, the mean value of the excess input bias currents increase monotonously from $1~{}nA$ to $1.7~{}nA$. The explicit divergence of $\Delta I_{iB}$ reveals an ELFS effect of neutron-induced DD. The increase of the base currents ($I_{B}$) of GLPNP BJTs irradiated to $1\times 10^{10}~{}\text{cm}^{-2}$ fluence is plotted in Fig. 2 by the green curve. The results show that, when the flux decrease from $5\times 10^{6}~{}\text{cm}^{-2}\text{s}^{-1}$ to $5\times 10^{5}~{}\text{cm}^{-2}\text{s}^{-1}$, the mean value of the excess base currents increase monotonously from $0.5~{}nA$ to $1.3~{}nA$. TCAD simulations confirmed that $\Delta I_{B}$ shows a linear dependence on the concentration of the defects in silicon bulk (see Appendix. LABEL:app:TCAD and Fig. LABEL:fig:GLPNP_Ib). Hence, the defect concentraiton follows a similar flux effect as the input bias current or base current. To investigate the mechanism and characteristics of the effects, numerical simulations of defects generation have been developed.

III Results of the diffusion dynamics limited model

III.1 Model details

Typical deep-level transient spectroscopy (DLTS) measurement have suggested main (electrically active) defects in silicon induced in DD; they are vacancy, $V$, divacancy, $V_{2}$, vacancy-oxygen complex, $VO$, vacancy-impurity complex, $VP$ and their charged states Irmscher1984; Su1990; Monakhov2002; Fleming2007; Vines2009; Fleming2010.

To capture the main characteristics of the damage, we did one dimensional (1D) simulation of the evolution of the defects. The simulation method is similar to the one used by Hallén et al Hallen1991. Further here, we also take into account the influence of the charge states of the defects and the charge-promoted hopping of interstitials Baraff1984; BarYam1984(1); BarYam1984(2); Car1984; Maroudas1993. In the model, the defects of $I$, $V$, $V_{2}$, $O$, $VO$, and their charged states are considered. The model is rooted on a bimolecular reaction framework and the reactions among the defects are listed as follows:

[TABLE]

where the subscript $I$ indicates an interstitial particle. The concentration of a particular defect or carrier is determined by

[TABLE]

where $[X]$ is the density of the ingredient $X$, $D_{X}$ is the diffusion coefficients, $U_{X}$ and $G_{X}$ are the consumption and generation rate of species $X$, respectively. The transitions among charged states of the above defects are described through the capture and excitation of the charge carriers Lutz1999, and the system is thought to be charge neutral as a whole during the simulation. The model may not cover all possible reactions as we focus primarily on the reactions having the most prominent influence to the evolution of the displacement defects. The values of the parameters are chosen from Table 1 in Ref. Myers2008.

The length of the simulated region is defined through a comparison with the experimental configurations. In our experiments, the total fluence is $1\times 10^{10}~{}\text{cm}^{-2}$, which results in an average distance of the order of $1um$ between collision cascades. (The generation of a single defect cluster and the results of several impacts are illustrated in Fig. 3.) Thus in the 1D approach, the simulated length is set to be $12um$ with total number of impacts equals to 6. Slight larger margins are left on both edges to relieve the perturbations from the boundary conditions; the vacancy and interstitial concentrations are set to be zero at both edges. The consequence of each impact particle is treated as newly generated vacancies and interstitials, which distribute uniformly in a $50\AA$ width region and have a concentration of $1\times 10^{18}~{}\text{cm}^{-3}$. The impacts are distributed randomly in the simulated region and are separated in time with a constant interval $\Delta t$.

III.2 Simulation results and its discrepancy from the experimental results

Simulated results for silicon is shown in Fig. 4. In the pristine silicon, the solid defects obtained are mainly $V_{2}$ and $VO$. It can be seen from Fig. 4 (a) and (b) that the concentrations of $V_{2}$ and $VO$ is higher at low flux irradiation (large $\Delta t$) than the values at high flux irradiation (small $\Delta t$). The dependence of the integrated concentration of defects on incident flux is plotted in Fig. 4(c). The results show that, when a transition flux, $\Phi_{t}$, of values of $\sim 10^{11}\text{-}10^{14}~{}\text{cm}^{-2}\text{s}^{-1}$, the integrated number of defects exhibit a clear ELFS effect. The conversion between $\Phi_{t}$ and $\Delta t$ is given in Appendix. LABEL:app:fluxcalculation.

However, in our experiments, the neutron flux is between $5\times 10^{5}$ and $5\times 10^{6}~{}\text{cm}^{-2}~{}\text{s}^{-1}$. Hence, there is a big discrepancy of transition flux between the experiments and the simulations. Even for the extreme cases, i.e., the income particles is not neutron but heavy ions whose energy depositions are more efficient (assuming that every incoming ion can collide with lattice atoms), the value of $\Phi_{t}$ is no less than $10^{9}\text{-}10^{11}~{}cm^{-2}s^{-1}$. This value is still much larger than the fluxes observed in the experiments. This contrast might be one of the reasons that, as claimed in the previous paper Hallen1991, this simulation is only a qualitative support to the experiments and more sophisticated models are required.

III.3 Reasons for the conflicts

The conflicts between the simulation and experiments stem from the simplifications in the previous models. In the previous models, the generation processes of defects are treated as reactions among discrete vacancies, interstitials and impurities in crystalline structures. However, inside the core of each collision cascade the initial defects have high concentrations and the amorphous nature of the regions should not be avoided. In other words, beside discrete defects, more complicated structures containing several interstitial and/or vacancy-related defects are generated. As mentioned in Ref. Pelaz1999, after Si implantation, the interstitials and vacancies survive recombinations are mostly stored in metastable and immobile clusters ($I_{cls}$ and $V_{cls}$). The metastable structures of interstitial and vacancy-related complexes are also used in the simulations of Ref. Bragado2013; Bragado2008. The presence of the intermediate products is also supported by the comparison of characteristic time between defects diffusing and annealing processes. Assuming Langevin dynamics is still valid, the rates of the recombination/annealing process are limited by the mobilities of the defects and proportional to the concentrations of the reactants. In our systems, the mobility of the Si interstitial is approximately $10^{-6}\text{-}10^{-4}\text{cm}^{2}/\text{s}$. The expected time for a Si interstitial to drift over $50nm$ (which is the approximated size of one damage cascade) is $10^{-7}\text{-}10^{-5}s$, which is much faster than all observed annealing results after particles implantation Sander1966; Srour1970; Srour1972; Srour1973. From the above considerations, within a damage cluster containing high concentration of defects, the rates of the annealing processes are likely to be dominated by the dissolutions of the defect complexes. (Also, the interstitials injected from outside the clusters assist the annealing.) To take into account these considerations and achieve better simulating results, a modified model containing clustered defects are proposed.

IV The clusters reordering dynamics limited model

IV.1 Model details

The impact of the incoming particle on Si can create isolated and clustered defects, and the ratio of the clusters to isolated defects depends on the energies of the primary knock-on atoms (PKAs) Srour2003; Srour2013. Simulations have shown that a decent amount of defect clusters are generated once the energy of PKA surpasses a threshold of several keV Wood1980. Though for simplicity, in many analysis, the clusters are treated as highly concentrated isolated vacancies, divacancies and interstatials, e.g. $V$, $V_{2}$ and $I$ Myers2008; Hallen1991; Li2014; Fleming2008; Monakhov2002(1), the amorphization of the region cause the traditional definitions of vacancies and interstitials making less sense. Moreover, there is no restrict criteria distinguishing isolated defects and amorphous region, and in many cases the amorphization of a region of the material is simply defined by containing defects of concentration overcoming a certain threshold value Bragado2013. Our particle transport and reaction simulations for 1 MeV incident neutrons performed by GENT4 show that most PKAs have energies overcoming a few tens or hundreds keV, see Appendix LABEL:app:GENT4. The following molecular dynamic calculations identify regions containing high concentrations of clustered defects, which are constructed within several tens of picoseconds after the impact of a PKA atom, see Fig. 3(a)-(d). The defects of high concentrations can form more complicated defect structures as described in the last paragraph of Chapter. III.3 (e.g. $I_{cls}$, $V_{cls}$, etc.).

The annealing of these defects are different from the annealing of the isolated interstitials and vacancies of high mobilities. The reasons are as follows.

1. The properties of the isolated defects derived in crystalline solid are no more valid in the core of the damage cascades;
2. the annealing processes are dominated by the internal reordering mechanisms of the defect complexes. An evidence is the extraordinary different annealing time of Si samples bombarded with $1.4~{}\text{MeV}$ electrons and fission neutrons Srour1970; Srour1972; Srour1973. In the experiments, the electron irradiated samples anneal to one-third of their initial damage within $10^{-2}\text{-}10^{0}~{}\text{s}$, while the neutron irradiated samples take much more time, approximately $10^{3}~{}\text{s}$, to reach the similar results. The annealing curves are also different. The electrons are generally considered to introduce discrete defects distributed throughout the samples, while the high energy neutrons cause a mass of defect clusters. Thus the comparisons imply the different annealing processes of the two defect structures. However importantly, the characteristic annealing time of the neutron irradiated damage coincide with that we observed in experiments ($\sim 10^{3}~{}s$, see Chap. III.2 and Appendix LABEL:app:GENT4). The accordance implies that ELFS effects are results of the interactions among the annealing of defect clusters, instead of the simple drift-recombinations of discrete defects. From these considerations, the problem of the strange characteristic time of simulations in the previous work can be relieved.

Based on the above analyses and the explanations in the last chapter, a modified model is proposed. In this model, the collision cascade from an incoming neutron is considered to result in complicated defect complexes. The annealing of the damage is dominated by the reordering of these defect clusters. The interactions among the clusters are mediated through the particles emitted during the reordering processes. To explore the primary features of the mechanisms, numerical simulations of the basic components and reactions have been constructed. In the calculations, the defect clusters are defined as a region containing spatially overlapped immovable interstitial and vacancy-related defects, $I_{cls}$ and $V_{cls}$. The results of each collision cascade of incoming neutron are simulated by a defect cluster spanning $50\AA$ in width containing $1\times 10^{18}~{}\text{cm}^{-3}$ interstitial and vacancy-related defects. The reordering processes are simulated through the spontaneous decomposition of the interstitial-related components $I_{cls}$ (emission of Si interstitials) and the following recombinations of the mobile Si interstitials ($I$) and vacancy-related components ($V_{cls}$). The decomposition rate is determined by Arrhenius equation $v_{d}Exp(-\frac{E_{d}}{k_{B}T})$, and the energy barrier $E_{d}$ and the velocity constant $v_{d}$ are chosen to be $E_{d}=0.2~{}eV$ and $v_{d}=10^{13}/\text{s}$ Watkins1965. The primary reactions in the models are listed below:

[TABLE]

where $m$ is a counting number.

IV.2 Simulation results

Results of the simulations are shown in Fig. 5. The region of calculation is $12~{}\mu m$ width and $6$ successive impacts are used. The time interval $\Delta t$ varies from $10^{1}~{}s$ to $10^{4}~{}s$. The configurations designed in the 1D simulation is to best mimic the real 3D experimental configurations, as described in Chap. III.1.

In Fig. 5(a), the concentrations of vacancy related defects are higher at lower flux irradiation (big $\Delta t$) than at higher flux irradiation (small $\Delta t$). The integrated numbers of defects are plotted in Fig. 5(b) as a function of the flux. An inverse S-shaped curve is derived, which contains two near-flat plateaus at low and high flux edges and a fast changing region in the middle. The results are similar to those given by the discrete defects model (Fig. 4(c) in Chap. III), but have remarkably lower sensitive flux region (or larger $\Delta t$). The transition flux show better agreements with the experimental results. It explains the experiences that why we only observe explicit ELFS effects for neutrons bombardment at low flux ($<10^{7}~{}\text{cm}^{-2}\text{s}^{-1}$). The model also predicts a saturation of DD for very low flux irradiations. Though many merits the model possesses, more sophisticated models are still required and the concerns will be discussed in Chap. LABEL:sec:discussion.

IV.3 Mechanisms for the neutron-induced ELFS effect

The way how the flux rate effects stem from the interactions between defect clusters is illustrated in Fig. 6. For low flux irradiations, the time intervals $\Delta t$ between the sequent impacts of incoming neutrons are large. Before the following impacts happen, the defect cluster in an impact has enough time to anneal. During the processes, the metastable structures decompose and emit mobile particles (mainly Si interstitials), which can traverse towards the edges and be absorbed by the surface or re-merge/disappear somewhere in the lattice Cowern1999(2); Jung2004; Jung2004; Agarwal1997; Vuong2000 (see Fig. 6(a)). Thus the damage cascades of subsequent impacts do not feel the influence of the previous impacts. While for high flux irradiations, the time intervals between the sequent impacts are small, and are not enough for the annealing of each isolated defect cluster. In this limit, the particles ejected from the previously created defect clusters gain increased possibilities to encounter the subsequent defect clusters before disappearing (see Fig. 6(b)). The effect enhances the efficiency of the reordering processes of the defect clusters, which results in a reduced number of defects. This is the experimentally observed ELFS effect.