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A New Physics-Based Model for Understanding Single-Event Gate Rupture in Linear Devices Nicholas Boruta, Member, IEEE, Gary K. Lum, Senior Member, IEEE, Hugh O’Donnell, Member, IEEE, L. Robinette, Marty R. Shaneyfelt, Senior Member, IEEE, and Jim R. Schwank, Fellow, IEEE

Abstract—This paper presents a new physics-based model for understanding the basic mechanism of single-event gate rupture (SEGR) in analog devices. This model accounts for the different competing physics mechanisms, such as carrier drift, diffusion, recombination in the drift diffusion, and Poisson’s equations, to explain the dependence of SEGR on biasing voltage, cross section, and critical electric field strength. Hence, the model provides a more accurate method of understanding and predicting the breakdown of oxides from heavy-ion strikes. Index Terms—Dielectric breakdown, heavy ion, linear devices, oxide breakdown, single-event gate rupture (SEGR).

I. INTRODUCTION

D

ESTRUCTIVE single-event gate rupture (SEGR) has been studied in a number of devices [1]–[6]. SEGR has been observed in analog devices as a result of high voltage across oxide capacitors [7], [8]. In a previous paper [9], the susceptibility to SEGR of a number of linear devices considered for use in space applications was shown. Under certain biasing conditions or angle of incidence with heavy ions, SEGR has been observed at a linear energy transfer (LET) as low as 26.6 MeV-cm /mg under standard operating conditions. Catastrophic failure due to some types of single-event effects (SEEs) may be prevented, e.g., cycling the power can be used to mitigate SEE-induced latchup, whereas SEGR failures are always catastrophic. SEGR failures are difficult to mitigate using system-level hardening approaches. This is because capacitors in linear circuits are integrated into the chip, are always charged when power is supplied to the chip, and do not require additional current to rupture. Therefore, it is important for a designer to understand the limitations of linear devices in space systems. If a device is determined to be sensitive to SEGR, the system designer may be constrained to lower the supply voltage, change the duty cycle, use redundancy, or select another device. With the availability of predictive models for SEGR, system designers can rapidly explore design options for system hardness.

Manuscript received July 17, 2001. This work was supported under CRADA SC96/01443W between Sandia, a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy under Contract DE-AC04-94AL85000, and Lockheed Martin Space Systems Company. N. Boruta, G. K. Lum, H. O’Donnell, and L. Robinette are with Lockheed Martin Space Systems Company, Sunnyvale, CA 94088 USA. M. R. Shaneyfelt and J. R. Schwank are with Sandia National Laboratories, Albuquerque, NM 87185 USA. Publisher Item Identifier S 0018-9499(01)10670-2.

Wrobel et al. [1] developed an empirical model for SEGR in tunneling oxides for nonvolatile memories, Titus et al. [3] created one for power MOSFETs, and Sexton et al. [4] developed a model for 5- to 100-nm gate oxides. These empirical models do not take into account the different competing mechanisms, such as carrier drift, diffusion, recombination, and impact ionization due to high fields in the oxide for charge generation, trapping, and transport in oxides. In this paper, we describe a physics-based model that takes into account these competing mechanisms to better understand the mechanisms and to more accurately predict SEGR. The drift-diffusion and Poisson’s equations are solved, taking into account electron and hole drift, diffusion, and recombination. Data taken on OP27EJ operational amplifiers and capacitors were used to validate the new model. II. EXPERIMENTAL DETAILS SEGR testing was conducted at Brookhaven National Laboratory’s tandem Van de Graaff accelerator with heavy ions ranging in LET between 27 and 82 MeV-cm /mg. In this study, OP27EJ operational amplifiers from Analog Devices, Lot Date Code T9736, N33472, were exposed at normal incidence and biased in a common circuit configuration used in space applications [9]. Capacitors in the OP27EJ have aluminum gates over a highly n-doped region. Because the integrated capacitors that were in the OP27EJ are buffered by internal circuitry, it was difficult to monitor the exact voltages across the capacitors. The voltages across the capacitors were measured in the laboratory with microprobes. There is a 4 V difference between the power-supply voltage and the exact voltage across the capacitor measured by the microprobes at supply voltages of 8 V. It rises linearly to a 5.4 V difference at 22 V, i.e., at 12 V the difference was 4.5 V. The oxide thickness of the capacitors was determined to be 56 nm based on microprobe and capacitance voltage (CV) measurements. State-of-the-art capacitors can have oxide thickness down to 20 nm. To confirm our OP27EJ results, Sandia National Laboratories provided isolated capacitors of similar oxide thickness, 64.8 nm. The ions used included gold, iodine, bromine, silver, and nickel. Their energies and LET are shown in Table I. Two regions of interest were measured for each ion species: 1) the supply voltages at which SEGR was first observed and 2) the saturated cross section where the measured cross section appears to approach the area of the suspected capacitor, i.e., 10 cm . In the former case, at cross sections below 10 cm , high fluxes between 10 and 10 ions/(cm -s) were used, while in the latter case, at cross sections greater than 10 cm , low

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TABLE I A COMPARISON OF THE ELECTRIC FIELD AT THE SEGR THRESHOLD BETWEEN THE OP27EJ CAPACITOR AND THE SINGLE CAPACITORS FROM SANDIA NATIONAL LABORATORIES (SNL)

Fig. 1. SEGR cross section versus supply voltage of the OP27 with gold ions at normal incidence.

fluxes between 1 and 100 ions/(cm -s) were used. To accurately determine the fluence when an SEGR event occurred, the beam was electronically turned off when the output slammed to the negative supply rail. In addition, the size of the aperture in the beam monitoring system was increased to control within 20% the uniformity of the beam. When an OP27EJ fails, the induced currents are not as large as the change observed at the output. For this reason, the output voltage was used as the trigger signal to turn off the beam. Current monitors, Tektronix CT-2 (5 mV/mA), were used to capture the negative and positive supply currents. The supply voltages for the OP27EJ devices were incremented in 0.25 to 0.5 V steps near the SEGR threshold. Figs. 1–3 show the SEGR cross sections as a function of supply voltage for gold, bromine, iodine, and silver ions, respectively. Fig. 1 illustrates a measured SEGR cross section curve versus the delta external supply voltage for OP27EJ devices. The delta supply voltage is the total voltage across the OP27EJ devices, i.e., the sum of the magnitudes of the positive and negative supply voltages. SEGR was measured for devices irradiated with Au ions at normal incidence. Gold ions have an LET of 82 MeV-cm /mg. Within experimental uncertainty, the saturation cross section is equal to the area of the suspected capacitor (identified as C3) in the OP27EJ (10 cm ). The supply voltages at which SEGR occurred is 12 V. A schematic diagram of the OP27 and the location of C3 are

Fig. 2. SEGR cross section versus supply voltage with bromine ions at normal incidence of the OP27.

Fig. 3.

SEGR cross section versus supply voltage with silver and iodine ions.

given in [9]. By microprobing, isolating the shorted capacitor, and using scanning electron microscopy, we were able to locate the rupture in C3. More than 100 OP27 devices have been tested showing a consistent failure mode of the output dropping to the negative supply rail. A time response of the failure signature is shown in [9]. The area of C3 is 1.2 10 cm or about 3.3% of the area of the entire die. From CV measurement, the oxide

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thickness of the capacitors in the OP27EJ was 56 nm and from microprobing, the voltage across the suspected capacitor was V) V. This corresponded to an electric field of ( 3.48 MV/cm. As the ion LET is lowered, the SEGR supply voltage threshold increases. This is illustrated in Fig. 2, which is a plot of the SEGR cross section versus the delta external supply voltage for the OP27EJ devices irradiated with Br ions at normal incidence. The Br ions have an LET of 36.7 MeV-cm /mg. Although we could not irradiate devices at high enough supply voltages to get the saturation cross section (without causing electrical breakdown of the capacitors), the data suggest that the saturation cross section for Br ions also will be close to the area of the capacitors. For Br ions, the supply voltage threshold is 40 V. Fig. 3 is plot of the SEGR cross section versus the delta external supply voltage for the OP27EJ devices irradiated with I and Ag ions at normal incidence. The LETs of I and Ag ions are 59.4 and 45.9 MeV-cm /mg, respectively. The results of Fig. 3 are qualitatively similar to the results of Figs. 1 and 2. The SEGR supply threshold voltages for I and Ag ions are 29 and 31 V, respectively. The Sandia capacitors were biased with an HP4145B semiconductor parameter analyzer at voltages between 20 and 40 V. The voltages were incremented in 1 V steps. Data on Sandia capacitors are also presented in Table I. At SEGR threshold, the electric field across the capacitor varies from 3.78 MV/cm for Au ions to 6.79 MV/cm for Ni ions. These data agree very well with the electric field at SEGR threshold for the OP27EJ devices. III. MODEL AND DISCUSSION As an ion traverses an oxide, a thin cylindrical region of electron–hole pairs is created in the oxide. Fig. 4 illustrates the generation of electron–hole pairs in the oxide following an ion strike. This figure shows a capacitor biased by an external voltage supply with the gate at positive potential and the silicon substrate at negative potential. Both electrons and holes are generated in a narrow column in the oxide immediately after passage of the ion. The time for an ion to traverse through the oxide is very short 0.3 ps. The electron–hole charge density can be as high as 10 C/cm along the center of the track and falls off very rapidly with radius. Fig. 5 shows the specific curve from Katz and Kobetich [10] for the radial energy density deposited . This is the in quartz for an ion with a velocity velocity for a Au ion with an LET 82 MeVcm /mg. There is a separate (see [10]) Katz and Kobetich curve (normalized to atomic number) for each ion velocity. Since we know the LET for each ion and we assume that the electron–hole charge density follows these radial energy density curves, then by scaling the respective curve to the LET, we can determine the total number of electron–hole pairs generated in the oxide (i.e., quartz) by each traversing ion. This then allows us to calculate the radial carrier charge density deposited in the oxide. Once created, the holes are essentially immobile (for the duration of the SEGR event) due to their very low diffusivity (6.5 10 cm /s) and hole mobility (10 cm /V-s) [11]. The electrons, on the other

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Fig. 4. Illustration of the generation of electron–hole pairs in an oxide by a heavy-ion strike.

Fig. 5. The energy dose in quartz (energy per gram per effective charge) as a function of radius t (g/cm ).

hand, are much more mobile due to their much higher values of mobility (20 cm /V-s) and diffusivity (0.261 cm /s). They are free to move by diffusion and drift in both the radial and axial directions, but the diffusion in the radial direction is self-limiting because any radial charge separation induces a radial restoring electric field. The ion energy does not change appreciably across the 56-nm oxide thickness, so the axial (i.e., -direction) carrier density can be assumed to be uniform. To simplify the analysis, we need to compare the relative importance of the axial and radial carrier dynamics. We will show that the axial flux density for electrons drifting due to an axial external applied field is much greater than the radial diffusion or radial drift. The electron motion is then dominated by the axial drift and radial motion is insignificant during this drift time. The net effect is the removal of electrons at the positive (metal) electrode by drift leaving a cylindrical track of positive charge that is highly peaked at the center of the ion path. In addition, columnar electron–hole recombination reduces the hole density but a sufficient number of holes survive recombination to create a large in the dielectric. This internal field internal electric field to provide a net local then adds to the external applied field field capable of breaking down the oxide. We now discuss the modeling in more detail. The different competing mechanisms (carrier drift, diffusion, and recombination as well as possible impact ionization due to high fields in the oxide) are described by three equations: the electron and

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Fig. 7. Calculated electric field E in oxide showing rapid rise near each surface and largest value near oxide/Si-substrate interface. Fig. 6. Modeling of the buildup of the electric field strength versus time from the passage of an ion.

hole drift-diffusion equations (1) and (2) and Poisson’s equation (3) (1) (2) (3) where and are the electron and hole densities, respectively, is the electron–hole recombination coefficient, is the electron–hole impact ionization coefficient, is the effective is the hole–electron hole–electron mobility in oxide, and diffusivity [11]. In these equations, is the total electric field. (due to It is composed of the sum of the internal field and axial components) and the constant both radial applied across the capacitor. So the complete external field . The external field points axially from the metal top gate toward the field oxide/silicon interface. Fig. 6 shows the calculated time development of the axial in 60-nm oxide component of the total oxide field due to the net positive charge from heavy ions when a fixed external 24-V supply voltage is applied across the oxide. No recombination is taken into account here. The total oxide field s to reach its maxrises extremely fast, taking less than 10 imum. The buildup of the maximum electric field (the net axial field along the center of the cylindrical pipe) is comparable to the time it takes for the electrons to be swept out of the oxide. Also, as the ion LET increases, the maximum value of the electric field increases, because more charge is deposited in the exceeds eioxide. When the net axial local field ther the local defect-related breakdown field or the dielectric for the capacitor, the dielectric begins to breakdown field rupture. The minimum external field that provides this condi[4]. As will be shown tion is then defined as the critical field below, the electric field in the oxide varies along the length of the oxide, reaching a maximum near the silicon-substrate/oxide

interface. The initial breakdown thus occurs near the negative (silicon-substrate) electrode of the capacitor where the total internal oxide electric field reaches its maximum magnitude. If the breakdown is not associated with defects in the oxide, electrons may be injected into this high field region by Fowler–Nordheim tunneling from the negative silicon electrode and continue the breakdown process by additional charge creation due to impact ionization. An example of how the electric field varies along the length of the oxide due to a highly peaked positive charge density is shown in Fig. 7, where we have also added the external due to the supply. The net field is a superposition of field both fields, and the curve shows that the maximum is located at the oxide–silicon interface. The curve was calculated for an 82 MeV-cm /mg Au ion traversing a capacitor with a 60-nm ) of 3.5 MV/cm applied oxide and an external field (equal to across the capacitor. An interesting observation is that the magnitude of the field rapidly rises near the ends of the cylinder. This is due to the highly peaked nature of the charge density and is quite different from the linear increase expected for a uniformly charged cylinder. Equations (1)–(3) were solved in the following way. Because the holes are effectively trapped in the oxide (on the time scale to initiate breakdown), only the recombination term survives in (2). For electrons, a numerical estimate of the diffusion and drift terms in (1) shows that radial diffusion is at least one order of magnitude smaller than the drift term along the axis of the column. This is shown in Fig. 8, where we plot the ratio of the axial drift flux density to the radial diffusion flux density at time s. The initial radial diffusion flux density is determined by the gradient of the initial electron charge density obtained by fitting to the curve in Fig. 5 for an 82 MeV-cm /mg Au ion with . At later times, this ratio can only become a velocity of larger since the electron charge density gradient decreases with time. The initial gradient of the axial electron charge density is zero. Since the radial diffusion is very small compared to the axial drift, we are then justified in taking out the diffusion term in (1). The radial drift terms in (1) can also be ignored because radial electric fields are nonzero only when there is substantial radial diffusion and we have just shown that radial diffusion can be ignored. We do not take into account the impact ionization

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Fig. 8. Ratio of initial drift/diffusion current densities showing that carrier dynamics is mainly due to drift and not diffusion.

terms since impact ionization is primarily important at fields greater than 7 MV/cm. From Fig. 7, we see this might occur in a very limited region within 4 nm of the oxide/silicon interface. So finally, only the recombination term and constant external drift term are retained in (1). We then see that the axial SEGR mechanism is controlled by the axial electron drift with the internal electric field determined by the density of surviving holes after recombination once the electrons have completely drifted out of the oxide. Using a two-step calculation, we first determine the radial density for zero axial drift. The second step then calculates the -dependence of the density due to drift. For the first step, with the above simplifications, the electron and hole radial density for s are governed by the following simple equations: the first 10 (4) (5) where and depend only on the radius and time and and are the initial electron and hole distributions, respectively. The solutions to (4) and (5) are readily found to be (6)

(7)

and are not equal. Because we are for the case where interested in the case where the electron and hole initial charge

Fig. 9. Dependence of critical voltage on the intrinsic oxide breakdown voltage.

densities are equal, the solutions for the case are obtained by . The result is taking the limit (8)

is the initial electron–hole charge density. For the In (8), second step, we calculate the time dependence of the maximum ) by noting that a internal axial electric field in the oxide ( net positively charged region due to the trapped holes gets uncovered starting near the silicon/oxide surface as the electrons . We indrift toward the metal/poly gate with drift velocity in (8) over the drift time tegrate the hole charge density to obtain the field produced on the axis at the cylinder at the surface. We can then use the hole density time development exin (8) to obtain the density as a function of and pression by replacing the time variable with its equivalent , where is the distance that the positive region boundary has . A more actraveled in the time at a drift velocity of curate treatment would entail solving the axial diffusion/drift dynamics fully, but our approximate treatment still contains the essential physics. We now make the very simple and general asis equal to the sumption that the dielectric breakdown field sum of the external critical field and the internally generated . This alaxial oxide field due to the ion, i.e., and lows us to derive an expression relating the critical field the recombination coefficient where the value of the maximum (located at the oxide interface) is given by the integral. In is the capacitor oxide (9), shown at the bottom of the page, thickness and is the effective electron mobility in the oxide. . Note that Our aim is to solve (9) for the critical field is both inside and outside of the integral, and so the solution to (9) needs to be performed numerically. Fig. 9 shows the critical (i.e., ) versus (oxide breakdown) values voltage

(9)

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for bromine, nickel, and iodine for 60-nm oxide. These curves in (9) for different oxide breakwere obtained by solving for down fields . The figure shows how one might use (9) to determine the critical voltage for an ion in a 60-nm oxide when the values oxide breakdown field is known. The useful range of is between 10 and 16 MV/cm. Once we know the recombination coefficient and the oxide breakdown value, then the critical voltage for 60-nm oxides can be obtained from the curves. The first step in modeling the SEGR event is to obtain a value for the recombination coefficient . This value can be determined by using the experimental SEGR data for Au ions at an LET of 82 MeV-cm /mg and the oxide thickness of 56 nm. To determine the value for , we use a) an initial electron–hole denbased on the radial energy density curves sity distribution given in Katz [10], b) the experimentally determined intrinsic of 12.2 MV/cm, and c) the measured oxide breakdown field for Au. Fig. 1 shows the measured SEGR cross critical field section curves as a function of supply voltage for gold ions at normal incidence with a LET of 82 MeV-cm /mg. The gold ion data shows a knee in the cross section with a pronounced threshold at a supply voltage of 12 V and a saturation cross section that equals the area (1.2 10 cm ) of the capacitor C3 that was shown to be the site of SEGR in the OP27 [9]. Based on these data, the critical field for this device is 3.5 MV/cm (19.5 V over 56 nm—namely, 24 V minus 4.5 V due to the voltage drop through the circuitry. A curve of the actual voltages across the capacitor for different supply voltages was obtained by microprobing. Using these parameters, we calculate cm /s for the recombination coefficient. Fig. 10 shows the on the value of recombinadependence of the internal field tion coefficient . From this figure, one can see that the internal field generated by the ions has its strongest dependence on between 10 and 10 cm /s. Different recombination rates will strongly influence the critical field for this range of recombination coefficients. Fixing the value for the recombination coefficient at 2.3 10 cm /s based on the gold ion, the critical electric field for other ions was determined from (9). The results are shown in Fig. 11. This figure shows both measured and predicted values for the critical field versus LET for several ions. Solving , for iodine (LET MeV-cm /mg), we get (9) for MeV-cm /mg), we get 4.4 MV/cm; for bromine (LET MeV-cm /mg), we 6.4 MV/cm; and for nickel (LET get 7.8 MV/cm. Fig. 11 shows excellent agreement between the predicted and measured values. Hence, the measured values tend to validate our model for SEGR, and our model can be for other ions. Assuming that used to accurately predict the empirically determined recombination coefficient is the same for other devices, one should be able to predict (without additional heavy-ion testing) the sensitivity of other analog devices to SEGR. A critical comment that needs to be made is not associated concerning (9) is that it is valid only when with process-induced defects. We need to determine whether our model can predict the critical fields for oxides of different thickness. We have used a 56-nm oxide to fix the value for . Using this same value in (9), we can create a set for and varying the value of curves for various oxide thicknesses. Fig. 12 shows the of

IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 48, NO. 6, DECEMBER 2001

Fig. 10. Rapid decrease in maximum oxide field as a function of the electron– hole recombination rate increases.

Fig. 11. The dependence of critical field on LET for OP27 ICs. The experimental results are compared to predicted values using our model.

Fig. 12.

Comparison between our model and experimental data.

experimental data for 45-nm oxide data from Wrobel [1] and 50-nm oxides from Wheatley [12], compared with predicted values from (9). As can be seen, the data fit quite well with the possible exception of the 45-nm data point for Au at an LET of 82 MeV-cm /mg. The reason it appears lower than ex(obpected is not clear. On the whole, for tained from 56-nm oxides), (9) predicts good values for for oxide thicknesses down to 45 nm. We have also used the

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18-nm data from Sexton [13]. A comparison between the predicted values from (9) and the experimental 18-nm data shows a substantial difference. A careful look at Fig. 4 in Sexton [13] shows that the critical field for their 18-nm data almost coincides with the 45-nm data from Wrobel in spite of the fact that the for the 18-nm oxide is 2.5 MV/cm higher breakdown field than for the 45-nm data. If the data are correct, then this indicates the possibility that ion-induced breakdown in thinner oxides may be due to different mechanisms than for thicker oxides. Thinner oxides typically have higher intrinsic breakdown fields, and we would expect that the critical fields would then be correspondingly higher as well. However, this scaling is not exact because Fowler–Nordheim electron injection becomes important for thinner oxides, and this has not been accounted for in our model. Additionally, trapping dynamics as well as impact ionization have been ignored altogether in our model but in fact may play a larger role for thinner oxides than we suspect. Another reason for the observed discrepancy may be that the recombination coefficient is process dependent. It is clear that the comparison data were taken on entirely different kinds of test structures. Wheatley’s test structures were DMOS power transistors, Wrobel’s were n-poly/Al gate capacitors, and Sexton used Al gate test capacitors. To determine the process dependence for would require a careful set of experiments showing how the recombination coefficient changes with various process parameters. A comparison of our model for SEGR with other models in the literature is of some interest. Our model explicitly depends on the generation of a large electrical field as a by-product of the positive charges immobilized in the oxide. This field in conjunction with the applied external field creates a net field in the oxide large enough to reach the oxide breakdown value. In our model, we concern ourselves with the initiation event for oxide breakdown. Further events that lead to catastrophic destruction of the metal or poly gate or the underlying silicon are not our main interest. We chose the oxide electric field as the primary physical parameter in our model because it is a well-defined physical quantity and its value can be directly compared with the intrinsic oxide breakdown field. Most of the models in the literature begin with a discussion of the currents that flow along the plasma pipe created by the heavy ion path. Wrobel’s [1] discussion centers on the power dissipated by current flowing through the metal/oxide/silicon plasma pipe. His primary mechanism is the thermal modulation of the oxide resistivity. The oxide resistivity reduction by 15 orders of magnitude allows high currents to flow, dissipating the energy required to destroy the structure. Wheatley [12] describes a voltage drop due to excess carriers that locally weakens the space charge region below the oxide of a vertical power MOSFET permitting “dangerously large voltage to form across the oxide.” If accumulation of excess charges along the Si–SiO interface is sufficiently large, then the image field induced across the oxide can exceed a critical field. Wheatley , develops an empirical expression relating the critical field the breakdown field , and the LET

LET

(10)

where is a fitting parameter determined from the measured data. The physical basis for the parameter is not given. Sexton [4] attempts to give a physical meaning to . He analyzes the effects of two currents components—1) injected current from the anode due to applied field across the oxide and 2) current by the carrier pair creation from the heavy ion—and derives an expression for (11) describes transport due to applied field injection, where describes transport of carriers generated by heavy ion, is the electron density from high field injection, and comes LET. Because in general from the assumption that most of the parameter values in this expression are not known, this still requires one to simply use as a fitting parameter to measured data. It is interesting to observe that our model allows us to give a clear and simple physical interpretation for as follows. We . By a simple algebraic start with the expression exercise, we can rewrite this expression as LET LET

(12)

so that, comparing (12) with (10), we find that LET

(13)

The fitting parameter can then be interpreted as the ratio between the critical field and the internal oxide field (due to the positive charges) multiplied by the LET. Of course, this interpretation requires that the product of these factors be a conand can be calculated because stant. The two fields we know , , and the LET, so it is possible to evaluate a numerical value for the parameter from first principles. For exMeVcm /mg, ample, if we use the Au ion values of LET MV/cm, and MV/cm, . then we get IV. CONCLUSIONS We have developed a new physics-based model to understand SEGR in capacitors by analyzing the detailed physics expected during the passage of a heavy ion through an oxide dielectric. The oxide field produced by the uncompensated holes is a very sensitive function of the detailed carrier dynamics for both holes and electrons. We have been able to derive an expression relating the critical field to the oxide breakdown and the carrier recombination coefficient. This expression can be used to accurately predict the critical field for all other ions once we have calculated the recombination coefficient for a single test ion. Experiments were performed to verify the model, and the measured results show good agreement with the model. We showed new evidence that the saturated SEGR cross section of the OP27EJ at an LET of 82 MeV-cm /mg is close to the area of the failed capacitor, suggesting that SEGR breakdown occurs

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at the electric field strength of the dielectric. The buildup of the electric field strength from an ion track in conjunction with the externally applied bias approaches the dielectric breakdown threshold. We find that our model agrees well with the experimental results for oxide thickness between 56 and 45 nm but that for available data at 18 nm, the model does not predict the critical field well. For thinner oxides, other mechanisms (e.g., Fowler–Nordheim tunneling) appear to play a role, and we have not taken this source of electron injection in account in our current model. It would be very interesting to solve (1) with both the diffusion and impact ionization terms explicitly taken into account as well as adding Fowler–Nordheim carrier injection to the model. This would obviously necessitate a numerical solution of the equations. In all, this model shows that most of the important physics for SEGR events in capacitors can be understood on the basis of straightforward electrostatics and carrier dynamics. Ion-initiated oxide breakdown is really an extension of ordinary oxide breakdown with the ion-induced carrier dynamics taken into account. ACKNOWLEDGMENT N. Boruta would like to acknowledge useful discussions about the model with A. Crichton and J. Baker. REFERENCES [1] T. F. Wrobel, “On heavy ion induced hard-errors in dielectric structures,” IEEE Trans Nucl. Sci., vol. NS-34, pp. 1262–1268, 1987. [2] G. M. Swift and R. Katz, “An experimental survey of heavy ion induced dielectric rupture in actel field programmable gate arrays (FPGA’s),” IEEE Trans. Nucl. Sci., vol. 43, pp. 967–972, 1996.

[3] J. L. Titus, C. F. Wheatley, D. I. Burton, I. Mouret, M. Allenspach, J. Brews, R. Schrimpf, and K. Galloway, “Impact of oxide thickness on SEGR failure in vertical power MOSFETs; Development of a semi-empirical expression,” IEEE Trans. Nucl. Sci., vol. 42, pp. 1928–1934, 1995. [4] F. W. Sexton, D. M. Fleetwood, M. R. Shaneyfelt, P. E. Dodd, G. L. Hash, L. P. Schanwald, R. A. Loemker, K. S. Krisch, M. L. Green, B. E. Weir, and P. J. Silverman, “Precursor ion damage and angular dependence of single event gate rupture in thin oxides,” IEEE Trans. Nucl. Sci., vol. 45, pp. 2509–2518, 1998. [5] A. H. Johnston, G. M. Swift, T. Miyahira, and L. D. Edmonds, “Breakdown of gate oxides during irradiation with heavy ions,” IEEE Trans. Nucl. Sci., vol. 45, pp. 2500–2508, 1998. [6] I. Mouret, P. Calvel, M. Allenspach, J. L. Titus, C. F. Wheatley, K. A. LaBel, M.-C. Calvet, R. D. Schrimpf, and K. F. Galloway, “Measurement of a cross-section for single-event gate rupture in power MOSFET’s,” IEEE Electron Device Lett., vol. 17, pp. 163–165, Apr. 1996. [7] P. T. McDonald, B. G. Henson, and W. J. Stapor, “Destructive failure of OP470/OP471 operational amplifiers due to breakdown of gate oxides during space radiation performance qualification,” in Proc. 2000 HEART/GOMAC Dig., vol. 25, 2000, pp. 336–339. [8] M. V. O’Bryan, K. A. LaBel, R. A. Reed, J. W. Howard, J. L. Barth, C. M. Seidleck, P. W. Marshall, C. J. Marshall, H. S. Kim, D. K. Hawkins, M. A. Carts, and K. E. Forslund, “Recent radiation damage and single event effect results for microelectronics,” in Proc. 1999 IEEE Radiation Effects Data Workshop, 1999. [9] G. K. Lum, H. O’Donnell, and N. Boruta, “The impact of single event gate rupture in linear devices,” IEEE Trans. Nucl. Sci., vol. 47, pp. 2373–2379, Dec. 2000. [10] R. Katz and Kobetich, “Formation of etchable tracks in dielectrics,” Phys. Rev., vol. 170, pp. 401–405, 1968. [11] T. M. Oldham, “Charge generation and recombination in silicon dioxide from heavy charged particles,” HDL-TR-1985 Harry Diamond Labs, June 10, 1985. [12] C. F. Wheatley, J. L. Titus, and D. I. Burton, “Single-event gate rupture in vertical power MOSFETs: An original empirical expression,” IEEE Trans. Nucl. Sci., vol. 41, pp. 2152–2159, Dec. 1994. [13] F. W. Sexton, D. M. Fleetwood, M. R. Shaneyfelt, P. E. Dodd, and G. L. Hash, “Single event gate rupture in thin gate oxides,” IEEE Trans. Nucl. Sci., vol. 44, pp. 2345–2352, Dec. 1997.

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A New Physics-Based Model for Understanding Single-Event Gate Rupture in Linear Devices Nicholas Boruta, Member, IEEE, Gary K. Lum, Senior Member, IEEE, Hugh O’Donnell, Member, IEEE, L. Robinette, Marty R. Shaneyfelt, Senior Member, IEEE, and Jim R. Schwank, Fellow, IEEE

Abstract—This paper presents a new physics-based model for understanding the basic mechanism of single-event gate rupture (SEGR) in analog devices. This model accounts for the different competing physics mechanisms, such as carrier drift, diffusion, recombination in the drift diffusion, and Poisson’s equations, to explain the dependence of SEGR on biasing voltage, cross section, and critical electric field strength. Hence, the model provides a more accurate method of understanding and predicting the breakdown of oxides from heavy-ion strikes. Index Terms—Dielectric breakdown, heavy ion, linear devices, oxide breakdown, single-event gate rupture (SEGR).

I. INTRODUCTION

D

ESTRUCTIVE single-event gate rupture (SEGR) has been studied in a number of devices [1]–[6]. SEGR has been observed in analog devices as a result of high voltage across oxide capacitors [7], [8]. In a previous paper [9], the susceptibility to SEGR of a number of linear devices considered for use in space applications was shown. Under certain biasing conditions or angle of incidence with heavy ions, SEGR has been observed at a linear energy transfer (LET) as low as 26.6 MeV-cm /mg under standard operating conditions. Catastrophic failure due to some types of single-event effects (SEEs) may be prevented, e.g., cycling the power can be used to mitigate SEE-induced latchup, whereas SEGR failures are always catastrophic. SEGR failures are difficult to mitigate using system-level hardening approaches. This is because capacitors in linear circuits are integrated into the chip, are always charged when power is supplied to the chip, and do not require additional current to rupture. Therefore, it is important for a designer to understand the limitations of linear devices in space systems. If a device is determined to be sensitive to SEGR, the system designer may be constrained to lower the supply voltage, change the duty cycle, use redundancy, or select another device. With the availability of predictive models for SEGR, system designers can rapidly explore design options for system hardness.

Manuscript received July 17, 2001. This work was supported under CRADA SC96/01443W between Sandia, a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy under Contract DE-AC04-94AL85000, and Lockheed Martin Space Systems Company. N. Boruta, G. K. Lum, H. O’Donnell, and L. Robinette are with Lockheed Martin Space Systems Company, Sunnyvale, CA 94088 USA. M. R. Shaneyfelt and J. R. Schwank are with Sandia National Laboratories, Albuquerque, NM 87185 USA. Publisher Item Identifier S 0018-9499(01)10670-2.

Wrobel et al. [1] developed an empirical model for SEGR in tunneling oxides for nonvolatile memories, Titus et al. [3] created one for power MOSFETs, and Sexton et al. [4] developed a model for 5- to 100-nm gate oxides. These empirical models do not take into account the different competing mechanisms, such as carrier drift, diffusion, recombination, and impact ionization due to high fields in the oxide for charge generation, trapping, and transport in oxides. In this paper, we describe a physics-based model that takes into account these competing mechanisms to better understand the mechanisms and to more accurately predict SEGR. The drift-diffusion and Poisson’s equations are solved, taking into account electron and hole drift, diffusion, and recombination. Data taken on OP27EJ operational amplifiers and capacitors were used to validate the new model. II. EXPERIMENTAL DETAILS SEGR testing was conducted at Brookhaven National Laboratory’s tandem Van de Graaff accelerator with heavy ions ranging in LET between 27 and 82 MeV-cm /mg. In this study, OP27EJ operational amplifiers from Analog Devices, Lot Date Code T9736, N33472, were exposed at normal incidence and biased in a common circuit configuration used in space applications [9]. Capacitors in the OP27EJ have aluminum gates over a highly n-doped region. Because the integrated capacitors that were in the OP27EJ are buffered by internal circuitry, it was difficult to monitor the exact voltages across the capacitors. The voltages across the capacitors were measured in the laboratory with microprobes. There is a 4 V difference between the power-supply voltage and the exact voltage across the capacitor measured by the microprobes at supply voltages of 8 V. It rises linearly to a 5.4 V difference at 22 V, i.e., at 12 V the difference was 4.5 V. The oxide thickness of the capacitors was determined to be 56 nm based on microprobe and capacitance voltage (CV) measurements. State-of-the-art capacitors can have oxide thickness down to 20 nm. To confirm our OP27EJ results, Sandia National Laboratories provided isolated capacitors of similar oxide thickness, 64.8 nm. The ions used included gold, iodine, bromine, silver, and nickel. Their energies and LET are shown in Table I. Two regions of interest were measured for each ion species: 1) the supply voltages at which SEGR was first observed and 2) the saturated cross section where the measured cross section appears to approach the area of the suspected capacitor, i.e., 10 cm . In the former case, at cross sections below 10 cm , high fluxes between 10 and 10 ions/(cm -s) were used, while in the latter case, at cross sections greater than 10 cm , low

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TABLE I A COMPARISON OF THE ELECTRIC FIELD AT THE SEGR THRESHOLD BETWEEN THE OP27EJ CAPACITOR AND THE SINGLE CAPACITORS FROM SANDIA NATIONAL LABORATORIES (SNL)

Fig. 1. SEGR cross section versus supply voltage of the OP27 with gold ions at normal incidence.

fluxes between 1 and 100 ions/(cm -s) were used. To accurately determine the fluence when an SEGR event occurred, the beam was electronically turned off when the output slammed to the negative supply rail. In addition, the size of the aperture in the beam monitoring system was increased to control within 20% the uniformity of the beam. When an OP27EJ fails, the induced currents are not as large as the change observed at the output. For this reason, the output voltage was used as the trigger signal to turn off the beam. Current monitors, Tektronix CT-2 (5 mV/mA), were used to capture the negative and positive supply currents. The supply voltages for the OP27EJ devices were incremented in 0.25 to 0.5 V steps near the SEGR threshold. Figs. 1–3 show the SEGR cross sections as a function of supply voltage for gold, bromine, iodine, and silver ions, respectively. Fig. 1 illustrates a measured SEGR cross section curve versus the delta external supply voltage for OP27EJ devices. The delta supply voltage is the total voltage across the OP27EJ devices, i.e., the sum of the magnitudes of the positive and negative supply voltages. SEGR was measured for devices irradiated with Au ions at normal incidence. Gold ions have an LET of 82 MeV-cm /mg. Within experimental uncertainty, the saturation cross section is equal to the area of the suspected capacitor (identified as C3) in the OP27EJ (10 cm ). The supply voltages at which SEGR occurred is 12 V. A schematic diagram of the OP27 and the location of C3 are

Fig. 2. SEGR cross section versus supply voltage with bromine ions at normal incidence of the OP27.

Fig. 3.

SEGR cross section versus supply voltage with silver and iodine ions.

given in [9]. By microprobing, isolating the shorted capacitor, and using scanning electron microscopy, we were able to locate the rupture in C3. More than 100 OP27 devices have been tested showing a consistent failure mode of the output dropping to the negative supply rail. A time response of the failure signature is shown in [9]. The area of C3 is 1.2 10 cm or about 3.3% of the area of the entire die. From CV measurement, the oxide

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thickness of the capacitors in the OP27EJ was 56 nm and from microprobing, the voltage across the suspected capacitor was V) V. This corresponded to an electric field of ( 3.48 MV/cm. As the ion LET is lowered, the SEGR supply voltage threshold increases. This is illustrated in Fig. 2, which is a plot of the SEGR cross section versus the delta external supply voltage for the OP27EJ devices irradiated with Br ions at normal incidence. The Br ions have an LET of 36.7 MeV-cm /mg. Although we could not irradiate devices at high enough supply voltages to get the saturation cross section (without causing electrical breakdown of the capacitors), the data suggest that the saturation cross section for Br ions also will be close to the area of the capacitors. For Br ions, the supply voltage threshold is 40 V. Fig. 3 is plot of the SEGR cross section versus the delta external supply voltage for the OP27EJ devices irradiated with I and Ag ions at normal incidence. The LETs of I and Ag ions are 59.4 and 45.9 MeV-cm /mg, respectively. The results of Fig. 3 are qualitatively similar to the results of Figs. 1 and 2. The SEGR supply threshold voltages for I and Ag ions are 29 and 31 V, respectively. The Sandia capacitors were biased with an HP4145B semiconductor parameter analyzer at voltages between 20 and 40 V. The voltages were incremented in 1 V steps. Data on Sandia capacitors are also presented in Table I. At SEGR threshold, the electric field across the capacitor varies from 3.78 MV/cm for Au ions to 6.79 MV/cm for Ni ions. These data agree very well with the electric field at SEGR threshold for the OP27EJ devices. III. MODEL AND DISCUSSION As an ion traverses an oxide, a thin cylindrical region of electron–hole pairs is created in the oxide. Fig. 4 illustrates the generation of electron–hole pairs in the oxide following an ion strike. This figure shows a capacitor biased by an external voltage supply with the gate at positive potential and the silicon substrate at negative potential. Both electrons and holes are generated in a narrow column in the oxide immediately after passage of the ion. The time for an ion to traverse through the oxide is very short 0.3 ps. The electron–hole charge density can be as high as 10 C/cm along the center of the track and falls off very rapidly with radius. Fig. 5 shows the specific curve from Katz and Kobetich [10] for the radial energy density deposited . This is the in quartz for an ion with a velocity velocity for a Au ion with an LET 82 MeVcm /mg. There is a separate (see [10]) Katz and Kobetich curve (normalized to atomic number) for each ion velocity. Since we know the LET for each ion and we assume that the electron–hole charge density follows these radial energy density curves, then by scaling the respective curve to the LET, we can determine the total number of electron–hole pairs generated in the oxide (i.e., quartz) by each traversing ion. This then allows us to calculate the radial carrier charge density deposited in the oxide. Once created, the holes are essentially immobile (for the duration of the SEGR event) due to their very low diffusivity (6.5 10 cm /s) and hole mobility (10 cm /V-s) [11]. The electrons, on the other

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Fig. 4. Illustration of the generation of electron–hole pairs in an oxide by a heavy-ion strike.

Fig. 5. The energy dose in quartz (energy per gram per effective charge) as a function of radius t (g/cm ).

hand, are much more mobile due to their much higher values of mobility (20 cm /V-s) and diffusivity (0.261 cm /s). They are free to move by diffusion and drift in both the radial and axial directions, but the diffusion in the radial direction is self-limiting because any radial charge separation induces a radial restoring electric field. The ion energy does not change appreciably across the 56-nm oxide thickness, so the axial (i.e., -direction) carrier density can be assumed to be uniform. To simplify the analysis, we need to compare the relative importance of the axial and radial carrier dynamics. We will show that the axial flux density for electrons drifting due to an axial external applied field is much greater than the radial diffusion or radial drift. The electron motion is then dominated by the axial drift and radial motion is insignificant during this drift time. The net effect is the removal of electrons at the positive (metal) electrode by drift leaving a cylindrical track of positive charge that is highly peaked at the center of the ion path. In addition, columnar electron–hole recombination reduces the hole density but a sufficient number of holes survive recombination to create a large in the dielectric. This internal field internal electric field to provide a net local then adds to the external applied field field capable of breaking down the oxide. We now discuss the modeling in more detail. The different competing mechanisms (carrier drift, diffusion, and recombination as well as possible impact ionization due to high fields in the oxide) are described by three equations: the electron and

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Fig. 7. Calculated electric field E in oxide showing rapid rise near each surface and largest value near oxide/Si-substrate interface. Fig. 6. Modeling of the buildup of the electric field strength versus time from the passage of an ion.

hole drift-diffusion equations (1) and (2) and Poisson’s equation (3) (1) (2) (3) where and are the electron and hole densities, respectively, is the electron–hole recombination coefficient, is the electron–hole impact ionization coefficient, is the effective is the hole–electron hole–electron mobility in oxide, and diffusivity [11]. In these equations, is the total electric field. (due to It is composed of the sum of the internal field and axial components) and the constant both radial applied across the capacitor. So the complete external field . The external field points axially from the metal top gate toward the field oxide/silicon interface. Fig. 6 shows the calculated time development of the axial in 60-nm oxide component of the total oxide field due to the net positive charge from heavy ions when a fixed external 24-V supply voltage is applied across the oxide. No recombination is taken into account here. The total oxide field s to reach its maxrises extremely fast, taking less than 10 imum. The buildup of the maximum electric field (the net axial field along the center of the cylindrical pipe) is comparable to the time it takes for the electrons to be swept out of the oxide. Also, as the ion LET increases, the maximum value of the electric field increases, because more charge is deposited in the exceeds eioxide. When the net axial local field ther the local defect-related breakdown field or the dielectric for the capacitor, the dielectric begins to breakdown field rupture. The minimum external field that provides this condi[4]. As will be shown tion is then defined as the critical field below, the electric field in the oxide varies along the length of the oxide, reaching a maximum near the silicon-substrate/oxide

interface. The initial breakdown thus occurs near the negative (silicon-substrate) electrode of the capacitor where the total internal oxide electric field reaches its maximum magnitude. If the breakdown is not associated with defects in the oxide, electrons may be injected into this high field region by Fowler–Nordheim tunneling from the negative silicon electrode and continue the breakdown process by additional charge creation due to impact ionization. An example of how the electric field varies along the length of the oxide due to a highly peaked positive charge density is shown in Fig. 7, where we have also added the external due to the supply. The net field is a superposition of field both fields, and the curve shows that the maximum is located at the oxide–silicon interface. The curve was calculated for an 82 MeV-cm /mg Au ion traversing a capacitor with a 60-nm ) of 3.5 MV/cm applied oxide and an external field (equal to across the capacitor. An interesting observation is that the magnitude of the field rapidly rises near the ends of the cylinder. This is due to the highly peaked nature of the charge density and is quite different from the linear increase expected for a uniformly charged cylinder. Equations (1)–(3) were solved in the following way. Because the holes are effectively trapped in the oxide (on the time scale to initiate breakdown), only the recombination term survives in (2). For electrons, a numerical estimate of the diffusion and drift terms in (1) shows that radial diffusion is at least one order of magnitude smaller than the drift term along the axis of the column. This is shown in Fig. 8, where we plot the ratio of the axial drift flux density to the radial diffusion flux density at time s. The initial radial diffusion flux density is determined by the gradient of the initial electron charge density obtained by fitting to the curve in Fig. 5 for an 82 MeV-cm /mg Au ion with . At later times, this ratio can only become a velocity of larger since the electron charge density gradient decreases with time. The initial gradient of the axial electron charge density is zero. Since the radial diffusion is very small compared to the axial drift, we are then justified in taking out the diffusion term in (1). The radial drift terms in (1) can also be ignored because radial electric fields are nonzero only when there is substantial radial diffusion and we have just shown that radial diffusion can be ignored. We do not take into account the impact ionization

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Fig. 8. Ratio of initial drift/diffusion current densities showing that carrier dynamics is mainly due to drift and not diffusion.

terms since impact ionization is primarily important at fields greater than 7 MV/cm. From Fig. 7, we see this might occur in a very limited region within 4 nm of the oxide/silicon interface. So finally, only the recombination term and constant external drift term are retained in (1). We then see that the axial SEGR mechanism is controlled by the axial electron drift with the internal electric field determined by the density of surviving holes after recombination once the electrons have completely drifted out of the oxide. Using a two-step calculation, we first determine the radial density for zero axial drift. The second step then calculates the -dependence of the density due to drift. For the first step, with the above simplifications, the electron and hole radial density for s are governed by the following simple equations: the first 10 (4) (5) where and depend only on the radius and time and and are the initial electron and hole distributions, respectively. The solutions to (4) and (5) are readily found to be (6)

(7)

and are not equal. Because we are for the case where interested in the case where the electron and hole initial charge

Fig. 9. Dependence of critical voltage on the intrinsic oxide breakdown voltage.

densities are equal, the solutions for the case are obtained by . The result is taking the limit (8)

is the initial electron–hole charge density. For the In (8), second step, we calculate the time dependence of the maximum ) by noting that a internal axial electric field in the oxide ( net positively charged region due to the trapped holes gets uncovered starting near the silicon/oxide surface as the electrons . We indrift toward the metal/poly gate with drift velocity in (8) over the drift time tegrate the hole charge density to obtain the field produced on the axis at the cylinder at the surface. We can then use the hole density time development exin (8) to obtain the density as a function of and pression by replacing the time variable with its equivalent , where is the distance that the positive region boundary has . A more actraveled in the time at a drift velocity of curate treatment would entail solving the axial diffusion/drift dynamics fully, but our approximate treatment still contains the essential physics. We now make the very simple and general asis equal to the sumption that the dielectric breakdown field sum of the external critical field and the internally generated . This alaxial oxide field due to the ion, i.e., and lows us to derive an expression relating the critical field the recombination coefficient where the value of the maximum (located at the oxide interface) is given by the integral. In is the capacitor oxide (9), shown at the bottom of the page, thickness and is the effective electron mobility in the oxide. . Note that Our aim is to solve (9) for the critical field is both inside and outside of the integral, and so the solution to (9) needs to be performed numerically. Fig. 9 shows the critical (i.e., ) versus (oxide breakdown) values voltage

(9)

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for bromine, nickel, and iodine for 60-nm oxide. These curves in (9) for different oxide breakwere obtained by solving for down fields . The figure shows how one might use (9) to determine the critical voltage for an ion in a 60-nm oxide when the values oxide breakdown field is known. The useful range of is between 10 and 16 MV/cm. Once we know the recombination coefficient and the oxide breakdown value, then the critical voltage for 60-nm oxides can be obtained from the curves. The first step in modeling the SEGR event is to obtain a value for the recombination coefficient . This value can be determined by using the experimental SEGR data for Au ions at an LET of 82 MeV-cm /mg and the oxide thickness of 56 nm. To determine the value for , we use a) an initial electron–hole denbased on the radial energy density curves sity distribution given in Katz [10], b) the experimentally determined intrinsic of 12.2 MV/cm, and c) the measured oxide breakdown field for Au. Fig. 1 shows the measured SEGR cross critical field section curves as a function of supply voltage for gold ions at normal incidence with a LET of 82 MeV-cm /mg. The gold ion data shows a knee in the cross section with a pronounced threshold at a supply voltage of 12 V and a saturation cross section that equals the area (1.2 10 cm ) of the capacitor C3 that was shown to be the site of SEGR in the OP27 [9]. Based on these data, the critical field for this device is 3.5 MV/cm (19.5 V over 56 nm—namely, 24 V minus 4.5 V due to the voltage drop through the circuitry. A curve of the actual voltages across the capacitor for different supply voltages was obtained by microprobing. Using these parameters, we calculate cm /s for the recombination coefficient. Fig. 10 shows the on the value of recombinadependence of the internal field tion coefficient . From this figure, one can see that the internal field generated by the ions has its strongest dependence on between 10 and 10 cm /s. Different recombination rates will strongly influence the critical field for this range of recombination coefficients. Fixing the value for the recombination coefficient at 2.3 10 cm /s based on the gold ion, the critical electric field for other ions was determined from (9). The results are shown in Fig. 11. This figure shows both measured and predicted values for the critical field versus LET for several ions. Solving , for iodine (LET MeV-cm /mg), we get (9) for MeV-cm /mg), we get 4.4 MV/cm; for bromine (LET MeV-cm /mg), we 6.4 MV/cm; and for nickel (LET get 7.8 MV/cm. Fig. 11 shows excellent agreement between the predicted and measured values. Hence, the measured values tend to validate our model for SEGR, and our model can be for other ions. Assuming that used to accurately predict the empirically determined recombination coefficient is the same for other devices, one should be able to predict (without additional heavy-ion testing) the sensitivity of other analog devices to SEGR. A critical comment that needs to be made is not associated concerning (9) is that it is valid only when with process-induced defects. We need to determine whether our model can predict the critical fields for oxides of different thickness. We have used a 56-nm oxide to fix the value for . Using this same value in (9), we can create a set for and varying the value of curves for various oxide thicknesses. Fig. 12 shows the of

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Fig. 10. Rapid decrease in maximum oxide field as a function of the electron– hole recombination rate increases.

Fig. 11. The dependence of critical field on LET for OP27 ICs. The experimental results are compared to predicted values using our model.

Fig. 12.

Comparison between our model and experimental data.

experimental data for 45-nm oxide data from Wrobel [1] and 50-nm oxides from Wheatley [12], compared with predicted values from (9). As can be seen, the data fit quite well with the possible exception of the 45-nm data point for Au at an LET of 82 MeV-cm /mg. The reason it appears lower than ex(obpected is not clear. On the whole, for tained from 56-nm oxides), (9) predicts good values for for oxide thicknesses down to 45 nm. We have also used the

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18-nm data from Sexton [13]. A comparison between the predicted values from (9) and the experimental 18-nm data shows a substantial difference. A careful look at Fig. 4 in Sexton [13] shows that the critical field for their 18-nm data almost coincides with the 45-nm data from Wrobel in spite of the fact that the for the 18-nm oxide is 2.5 MV/cm higher breakdown field than for the 45-nm data. If the data are correct, then this indicates the possibility that ion-induced breakdown in thinner oxides may be due to different mechanisms than for thicker oxides. Thinner oxides typically have higher intrinsic breakdown fields, and we would expect that the critical fields would then be correspondingly higher as well. However, this scaling is not exact because Fowler–Nordheim electron injection becomes important for thinner oxides, and this has not been accounted for in our model. Additionally, trapping dynamics as well as impact ionization have been ignored altogether in our model but in fact may play a larger role for thinner oxides than we suspect. Another reason for the observed discrepancy may be that the recombination coefficient is process dependent. It is clear that the comparison data were taken on entirely different kinds of test structures. Wheatley’s test structures were DMOS power transistors, Wrobel’s were n-poly/Al gate capacitors, and Sexton used Al gate test capacitors. To determine the process dependence for would require a careful set of experiments showing how the recombination coefficient changes with various process parameters. A comparison of our model for SEGR with other models in the literature is of some interest. Our model explicitly depends on the generation of a large electrical field as a by-product of the positive charges immobilized in the oxide. This field in conjunction with the applied external field creates a net field in the oxide large enough to reach the oxide breakdown value. In our model, we concern ourselves with the initiation event for oxide breakdown. Further events that lead to catastrophic destruction of the metal or poly gate or the underlying silicon are not our main interest. We chose the oxide electric field as the primary physical parameter in our model because it is a well-defined physical quantity and its value can be directly compared with the intrinsic oxide breakdown field. Most of the models in the literature begin with a discussion of the currents that flow along the plasma pipe created by the heavy ion path. Wrobel’s [1] discussion centers on the power dissipated by current flowing through the metal/oxide/silicon plasma pipe. His primary mechanism is the thermal modulation of the oxide resistivity. The oxide resistivity reduction by 15 orders of magnitude allows high currents to flow, dissipating the energy required to destroy the structure. Wheatley [12] describes a voltage drop due to excess carriers that locally weakens the space charge region below the oxide of a vertical power MOSFET permitting “dangerously large voltage to form across the oxide.” If accumulation of excess charges along the Si–SiO interface is sufficiently large, then the image field induced across the oxide can exceed a critical field. Wheatley , develops an empirical expression relating the critical field the breakdown field , and the LET

LET

(10)

where is a fitting parameter determined from the measured data. The physical basis for the parameter is not given. Sexton [4] attempts to give a physical meaning to . He analyzes the effects of two currents components—1) injected current from the anode due to applied field across the oxide and 2) current by the carrier pair creation from the heavy ion—and derives an expression for (11) describes transport due to applied field injection, where describes transport of carriers generated by heavy ion, is the electron density from high field injection, and comes LET. Because in general from the assumption that most of the parameter values in this expression are not known, this still requires one to simply use as a fitting parameter to measured data. It is interesting to observe that our model allows us to give a clear and simple physical interpretation for as follows. We . By a simple algebraic start with the expression exercise, we can rewrite this expression as LET LET

(12)

so that, comparing (12) with (10), we find that LET

(13)

The fitting parameter can then be interpreted as the ratio between the critical field and the internal oxide field (due to the positive charges) multiplied by the LET. Of course, this interpretation requires that the product of these factors be a conand can be calculated because stant. The two fields we know , , and the LET, so it is possible to evaluate a numerical value for the parameter from first principles. For exMeVcm /mg, ample, if we use the Au ion values of LET MV/cm, and MV/cm, . then we get IV. CONCLUSIONS We have developed a new physics-based model to understand SEGR in capacitors by analyzing the detailed physics expected during the passage of a heavy ion through an oxide dielectric. The oxide field produced by the uncompensated holes is a very sensitive function of the detailed carrier dynamics for both holes and electrons. We have been able to derive an expression relating the critical field to the oxide breakdown and the carrier recombination coefficient. This expression can be used to accurately predict the critical field for all other ions once we have calculated the recombination coefficient for a single test ion. Experiments were performed to verify the model, and the measured results show good agreement with the model. We showed new evidence that the saturated SEGR cross section of the OP27EJ at an LET of 82 MeV-cm /mg is close to the area of the failed capacitor, suggesting that SEGR breakdown occurs

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at the electric field strength of the dielectric. The buildup of the electric field strength from an ion track in conjunction with the externally applied bias approaches the dielectric breakdown threshold. We find that our model agrees well with the experimental results for oxide thickness between 56 and 45 nm but that for available data at 18 nm, the model does not predict the critical field well. For thinner oxides, other mechanisms (e.g., Fowler–Nordheim tunneling) appear to play a role, and we have not taken this source of electron injection in account in our current model. It would be very interesting to solve (1) with both the diffusion and impact ionization terms explicitly taken into account as well as adding Fowler–Nordheim carrier injection to the model. This would obviously necessitate a numerical solution of the equations. In all, this model shows that most of the important physics for SEGR events in capacitors can be understood on the basis of straightforward electrostatics and carrier dynamics. Ion-initiated oxide breakdown is really an extension of ordinary oxide breakdown with the ion-induced carrier dynamics taken into account. ACKNOWLEDGMENT N. Boruta would like to acknowledge useful discussions about the model with A. Crichton and J. Baker. REFERENCES [1] T. F. Wrobel, “On heavy ion induced hard-errors in dielectric structures,” IEEE Trans Nucl. Sci., vol. NS-34, pp. 1262–1268, 1987. [2] G. M. Swift and R. Katz, “An experimental survey of heavy ion induced dielectric rupture in actel field programmable gate arrays (FPGA’s),” IEEE Trans. Nucl. Sci., vol. 43, pp. 967–972, 1996.

[3] J. L. Titus, C. F. Wheatley, D. I. Burton, I. Mouret, M. Allenspach, J. Brews, R. Schrimpf, and K. Galloway, “Impact of oxide thickness on SEGR failure in vertical power MOSFETs; Development of a semi-empirical expression,” IEEE Trans. Nucl. Sci., vol. 42, pp. 1928–1934, 1995. [4] F. W. Sexton, D. M. Fleetwood, M. R. Shaneyfelt, P. E. Dodd, G. L. Hash, L. P. Schanwald, R. A. Loemker, K. S. Krisch, M. L. Green, B. E. Weir, and P. J. Silverman, “Precursor ion damage and angular dependence of single event gate rupture in thin oxides,” IEEE Trans. Nucl. Sci., vol. 45, pp. 2509–2518, 1998. [5] A. H. Johnston, G. M. Swift, T. Miyahira, and L. D. Edmonds, “Breakdown of gate oxides during irradiation with heavy ions,” IEEE Trans. Nucl. Sci., vol. 45, pp. 2500–2508, 1998. [6] I. Mouret, P. Calvel, M. Allenspach, J. L. Titus, C. F. Wheatley, K. A. LaBel, M.-C. Calvet, R. D. Schrimpf, and K. F. Galloway, “Measurement of a cross-section for single-event gate rupture in power MOSFET’s,” IEEE Electron Device Lett., vol. 17, pp. 163–165, Apr. 1996. [7] P. T. McDonald, B. G. Henson, and W. J. Stapor, “Destructive failure of OP470/OP471 operational amplifiers due to breakdown of gate oxides during space radiation performance qualification,” in Proc. 2000 HEART/GOMAC Dig., vol. 25, 2000, pp. 336–339. [8] M. V. O’Bryan, K. A. LaBel, R. A. Reed, J. W. Howard, J. L. Barth, C. M. Seidleck, P. W. Marshall, C. J. Marshall, H. S. Kim, D. K. Hawkins, M. A. Carts, and K. E. Forslund, “Recent radiation damage and single event effect results for microelectronics,” in Proc. 1999 IEEE Radiation Effects Data Workshop, 1999. [9] G. K. Lum, H. O’Donnell, and N. Boruta, “The impact of single event gate rupture in linear devices,” IEEE Trans. Nucl. Sci., vol. 47, pp. 2373–2379, Dec. 2000. [10] R. Katz and Kobetich, “Formation of etchable tracks in dielectrics,” Phys. Rev., vol. 170, pp. 401–405, 1968. [11] T. M. Oldham, “Charge generation and recombination in silicon dioxide from heavy charged particles,” HDL-TR-1985 Harry Diamond Labs, June 10, 1985. [12] C. F. Wheatley, J. L. Titus, and D. I. Burton, “Single-event gate rupture in vertical power MOSFETs: An original empirical expression,” IEEE Trans. Nucl. Sci., vol. 41, pp. 2152–2159, Dec. 1994. [13] F. W. Sexton, D. M. Fleetwood, M. R. Shaneyfelt, P. E. Dodd, and G. L. Hash, “Single event gate rupture in thin gate oxides,” IEEE Trans. Nucl. Sci., vol. 44, pp. 2345–2352, Dec. 1997.