A UNIFIED COMPUTATIONAL APPROACH TO OXIDE AGING PROCESSES Harold P. Hjalmarson, Peter A. Schultz, Duane J. Bowman, and Daniel M. Fleetwood Sandia National Laboratories, Albuquerque, NM 87111

ABSTRACT

In this paper we describe a unified, hierarchical computational approach to aging and relia- bility problems caused by materials changes in the oxide layers of Si-based microelectronic devices. We apply this method to a particular low-dose-rate radiation effects problem.

INTRODUCTION

The oxide Si02 is both an electrical insulator and a protective coating for Si-based micro- electronics devices. This oxide has been an ongoing source of technical problems involving defects, radiation effects, and degradation. [l] Defects are intrinsic to the oxide because the thermal growth process produces a non-crystalline, amorphous oxide. The main defects are oxygen vacancies and P b centers which are Si dangling bonds at the Si/SiOz interface. [2] Both types of defects have been srtensively studied.

The main radiation problems are due to holes which can become trapped to form charged defects, and the generation of interface traps via the interaction of hydrogen related species at the Si/SiO2 interface. The resultant trapped charge can alter the device properties. For example, it can change the turn-on voltage of a transistor.

Recently, a low-dose-rate radiation problem has been identified in certain types of devices such as bipolar transistors in linear integrated circuits used in spacecraft, satellite, and weapons applications. [3-71 This is a problem which may take years to develop and thus we classify it as an aging problem. Studies have shown that for these devices a given total ionizing radiation dose is more harmful if the radiation rate is reduced to a level which is much lower than that used for baseline testing. [3]

The low-dose-rate problem seems to occur in the passivation or field oxides covering the emitter-base junction in lateral or substrate bipolar transistors. [&lo] Device modeling has shown that increased net positive oxide-trap charge may lead to increased surface recom- bination in the base of a transistor. [SI In turn, this affects the transistor gain, an effect consistent with the measured modification of the device characteristics. However, the phys- ical mechanism responsible for the buildup of excess trapped positive charge at low dose rates is not clear.

The absence of a clearcut mechanism leads to time-consuming and expensive testing. Because of the slowness of the radiation exposure, a comprehensive test of a component can take up to six months or more to complete.

APPROACH TO THE PROBLEM

The essence of the computational problem is to compute the radiation generated trapped charge, compute the effect of this charge on the performance of microelectronic devices such as transistors, and compute the effect of device performance on the circuit performance. Our approach to these problems is an integrated, multiple level approach illustrated in Fig.

DISC LA1 M ER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

Figure 1: Shows the computational approach.

1. This approach takes into account the fact that the aging problem has multiple length and time scales; these will be described in more detail. Furthermore, the problem has incomplete information which must be taken into account in a pragmatic way. The approach we have crafted couples or links a variety of computational tools. As can be seen in the figure, our approach involves several levels ranging kom the microscopic to the circuit level and a different computational tool is used for each level. The essence of the physics problem and the need for levels of approach will now be discussed.

The computation of the trapped charge requires solving a set of equations governing electrons and holes in semiconductors, the semiconductor transport equations. [ll, 121 The governing equations for electron density n(r, t ) and hole density p ( r , t ) as a function of position r and time t are the continuity equations:

In these equations, Jn(r, t ) and Jp(r, t ) are, respectively, the electron and hole current densities and &,(r, t ) and Rp(rl t ) are generation-recombination terms for electron and holes, respectively.

A prototypical contribution to the generation-recombination term arises from hole t r a p ping. This process can be written as a reaction

T + p * T p

involving traps T and trapped holes Tp, and it leads to a generation-recombination term

in terms of rate constants kf and IC,. A series of equations with terms of this form need to be solved to compute response to ionizing radiation. [12]

A computational approach to an aging problem is more challenging. One aspect of the challenge can be seen by considering the trapping reaction, Eq. (2). In an aging problem, the total concentration of traps can also become timevarying on a slow time scale. This leads to new equations which are similar to those which would govern the preparation and processing of the oxide. More challenging is the fact that the time scales of these new equations is vastly different than that of the transport equations. For example, the electrons and holes can be captured in lo-% but the aging process of interest may take place in 108 s. This leads to equations with multiple time scales; such equations are called ’stif€’ and they require special solution techniques. [13]

Another aspect of the problem is incomplete information. The best and most studied phenomena are those which take place rapidly during transient radiation studies. These processes certainly need to be considered in the reactions. However, the more important reactions for this problem are those which take place slowly and these have not been well- studied. Thus it is likely that some of the information characterizing the trap reactions during device aging is incomplete.

The problem of incomplete information led us to work on this problem on both a con- tinuum and a microscopic level as shown in the lower left of Fig. 1. The continuum level involves the solution of the semiconductor transport and kinetic equations as a function of time and radiation dose for a given set of processing conditions. These equations are solved using software REO (Radiation EEects in Oxides). For the initial calculations, the parameters are either obtained from the literature [12] or estimated. The initial series of continuum calculations were done to explore which mechanisms have the potential to explain the low-dose-rate effect. These calculations led to insight about candidate mechanisms such as the hydrogen de-passivation mechanism described in this paper. However, many of the quantities which govern the reaction rates are not m l l known and this fact stimulated a series of more microscopic calculations, electronic structure calculations of defect energies.

The electronic structure calculations are performed using QUEST, software which uses density functional theory to compute the total energy of defects in the SiO:!. [14] Two types of calculations are important for the reaction rates. First, the equilibrium energy of the various defects such the E’ center is needed to define the steady state or equilibrium defect densities using REO. Second, the transition state or barrier energy is needed to compute the rate of the defect reactions to be used in REO. At this time, the second set of calculations has not been undertaken. Instead, the rates are estimated by approximating the relevant partition functions. [15]

Given the trapped charge as a function of time, another set of calculations is needed to define the device response. These device level calculations use the information from the continuum level calculations to compute the device response. We use PISCES for these calculations. [16] In this level the semiconductor transport equations are solved for particular devices such as bipolar transistors and they take into account the trapped charge in the oxide and at the interface.

Finally, to draw conclusions about circuit performance, SPICE is us d to compute the electrical performance of a circuit consisting of transistors, resistors, capacitors and other components. [17] For these calculations, the information from the PISCES calculations is conveyed in a physics-based transistor model. [18)

APPLICATION TO THE LOW-DOSERATE PROBLEM

Several candidate mechanisms can be postulated to explain the low dose rate effect. The nonlinear nature of many of the defect reactions leads to this conclusion. To understand this point, consider the reaction shown in &. (2). If the trap density were constant, then this reaction would be linear. If all such reactions were linear, there would be no true dose rate effects. However, if the trap density [T] also varies due to atomic migration, then the reaction becomes non-linear and it has the potential to contribute to a dose rate effect. Perhaps the most simple reaction which yields a dose rate effect is the reaction of an electron and a hole to form an exciton, a neutral hydrogen-like entity. The formation of excitons is more prevalent at high dose rates because the reaction is bi-molecular. Thus, if these excitons were to recombine without generating trapped charge, then this reaction would lead to reduced charge trapping at high dose rate, consistent with the experimental situation.

Several reactions are included in the simulations. These were all chosen for their role in controlling the density of Pb and E' centers, the main defects which play a role in radiation- induced trapped charge. In addition, reactions involving hydrogen were also included be- cause it has been implicated both in passivating and creating defects in SiOz. [2,19-211

The importance of hydrogen in passivating &centers led us to formulate a mechanism in which de-passivation of traps leads to a low-de ra t e effect. The essence of this mechanism is contained in the reactions

which govern the densities of holes (p), neutral hydrogen (p), neutral, un-passivated traps (To), trapped holes (Tp'), passivated traps (THO), and molecular hydrogen ( H i ) . The first

High dose-rate case

Free holes

Trapped hole H-passivated trap

Low dose-rate case

3 - l f 9 Figure 2: Schematic showing the de-passivation mechanism.

two reactions are stimulated by the well-known role of H in passivating &enters. [2,19] At dose rates comparable with the hydrogen release rate (reverse reaction of 4), additional un-passivated traps are created at a rate comparable with the hole capture rate (forward reaction of 6). The de-passivation reaction is slow, which leads to a dose rate effect at low dose rates. However, at high dose rates, holes are captured only at the initially un-passivated traps. This mechanism is illustrated in Fig. 2.

The predicted net charge of the de-passivation mechanism is shown in Fig. 3. For this calculation, [p] E 3 . 3 ~ 1 0 ~ ' ~ m - ~ , [THO] G 1013, and the mide thickness is 1 pm. [15] By inspection, this mechanism predicts a low dose rate effect which is in qualitative agreement with the experimental observations. [3-7,221 However, the observed crass-over occurs at somewhat higher dose rates; for this reason, we are revising the kinetic parameters of this mechanism as well as considering other contributions to the effect. [15]

A series of cal- culations concerning this defect reaction and similar reactions are underway. The kinetics are sensitive to defect formation energies which are not very well known. Thus QUEST cal- culations are being undertaken to com- pute the key defect formation energies to further examine whether this mech- anism may contribute to the low dose rate

"""7

io5 10" 10" i o 2 i o 1 ioo io' io2 Dose rate [rad(Si)/secJ

problem. Figure 3 Shows the trapped charge dependence on dose rate for the hydrogen de-passivation mechanism.

CONCLUSIONS

We have described a computational approach to oxide aging problems in which multiple time and distance scales are incorporated by using several linked computational methods. The approach is illustrated by discussing a mechanism which may contribute to the problem of low-doserate radiation effects in bipolar devices.

ACKNOWLEDGMENTS

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DEAC0494AL85000.

REFERENCES

[l] E. H. Nicollian and J. R Brews, MOS Physics and Technology (Wiley, New York, 1982).

[2] P. M. Lenahan and J. J. F. Conley, J. Vu. Sci. Tech. B 16, 2134 (1998).

[3] E. W. Enlow et d., IEEE Trans. Nucl. Sci. NS-38, 1342 (1991).

[4] R. N. Nowli et al., in Proceedings 1991 IEEE Bipolar Circuits and Technology Meeting (IEEE, NY, 1991), pp. 174-177.

[5] A. H. Johnston, B. G. Rax, and C. I. Lee, IEEE Trans. Nucl. Sci. 42, 1650 (1995).

[SI A. H. Johnston, C. I. Lee, and B. G. Rax, IEEE Trans. Nucl. Sci. 43,3049 (1996).

[7] R. L. Pease et al., IEEE Trans. Nucl. Sci. 44, 1981 (1997).

[SI D.. M. Schmidt et al., BEE Trans. Nucl. Sci. 42, 1541 (1995).

[9] R. D. Schrimpf et al., IEEE Trans. Nucl. Sci. 42, 1641 (1995).

[lo] D. M. Fleetwood et al., IEEE Trans. Nucl. Sci. 43, 2537 (1996).

[ll] S. M. Sze, Physics of Semiconductor Dewices (J. Wiley and Sons, New York, 1981).

[12] R. Sokel and R. C. Hughes, J. Appl. Phys. 53, 7414 (1982).

[13] C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, hc., Englewood Cliffs, NJ, 1971).

[14] Developed and written by M. P. Sears and P. A. Schultz at Sandia National Laboratories, Albuquerque, NM 87185.

[15] H. P. Hjalmarson (unpublished).

[16] M. R. Pinto, C. S.Ra.fFerty, and R. W. Dutton, Technical report, Stanford Electronics Laboratories, Stanford University (unpublished).

[17] L. W. Nagel, Technical Report No. Memorandum No. EmM520, Electronic Research Laboratory, College of Engineering, University of California, Berkeley (unpublished).

[18] T. A. Fjeldly, T. Ytterdal, and M. Shur, Introduction to Device Modeling and Circuit Simulation (John Wiley and Sons, hc., New York, NY, 1998).

[19] R. E. Stahlbush, A. H. Edwards, D. L. Griscom, and B. J. Mrstik, J. Appl. Phys. 73, 658 (1993).

[20] K. L. Brower, Phys. Rev. B 38, 9657 (1988).

[21] K. L. Brower, Phys. Rev. B 42, 3444 (1990).

[22] S. C. Witczak et al., IEEE Trans. Nucl. Sci. 44, 1989 (1997).