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Scaling DC lifetests on GaN HEMT to RF conditions
Microelectronics Reliability 55 (2015) 2499–2504
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/mr
Scaling DC lifetests on GaN HEMT to RF conditions Bruce M. Paine Technology Qualification, Boeing Network and Space Systems, El Segundo CA, USA
a r t i c l e
i n f o
Article history: Received 8 July 2015 Received in revised form 29 August 2015 Accepted 23 September 2015 Available online 3 November 2015 Keywords: Gallium nitride GaN HEMT High-electron mobility transistors (HEMT) Characterization Reliability Life testing
a b s t r a c t The assumptions behind a new lifetesting approach are documented, evaluated, and tested where possible. This approach utilizes “signature parameters” to track individual degradation mechanisms in both DC and RF lifetests, and determines the mean time to failure (MTTF) Arrhenius curves for each mechanism individually, during RF operation. This is important for GaN HEMT because most studies indicate that several mechanisms contribute to its wearout, simultaneously, and this makes it impossible to extrapolate conventional RF wearout curves to other temperatures or longer times. A key assumption is that degradation mechanisms can be identified, and associated with unique signature parameters. A second key assumption is the integrity of degradation mechanisms, whether they occur under steady DC biases, or under oscillating RF biases. This allows us to deduce MTTF's under RF operation from the ratio of degradation rates of the individual mechanisms in DC lifetests, and the rates in RF operation, integrated over the RF waveform. This can be found by means of DC and RF lifetests, monitoring the signature parameters. Then the DC Arrhenius curves can be scaled to the RF conditions. After evaluation of these, and several other assumptions, we find the net uncertainties for one of the GaN HEMT technologies that we used for development of our approach. They amount to — 30%, +100% in MTTF; this is entirely adequate for high-reliability parts evaluation, where a margin of at least 10× (900%) is required. © 2015 The Author. Published by Elsevier Ltd. All rights reserved.
1. Introduction Temperature-accelerated lifetests under DC stress are very useful for studying RF GaN HEMT devices: they allow study of specific degradation mechanisms by setting the biases to emphasize those mechanisms alone, and they are relatively easy to set up, requiring only DC biases and heating. But it is difficult to relate such studies to actual RF operation because the RF gate and drain voltages vary rapidly through large ranges of values, in patterns (i.e. “load lines”) that are not easy to determine accurately [1]. Meanwhile, conventional RF lifetests are difficult to interpret because several mechanisms with different thermal activation energies are likely to be contributing simultaneously. An approach that we have developed [2,3] involves identification of a “signature parameter” for each mechanism, that measures the extent of that mechanism, but is unaffected by the others. It can be monitored in DC lifetests at a bias condition where that mechanism is strong, at various temperatures, to determine the activation energy (Ea), and mean time to failure (MTTF) versus temperature, i.e. the Arrhenius plot. Then it can be monitored further in a brief RF lifetest to find the degradation rate, aRF at one temperature, under the RF conditions of the application, i.e. the same frequency and same degree of output power compression. Then a temperature-independent “scaling factor”, aRF/aDC can be calculated, and used to scale the DC Arrhenius plot to the RF
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.microrel.2015.09.024 0026-2714/© 2015 The Author. Published by Elsevier Ltd. All rights reserved.
conditions. This can be done for each of the operating degradation mechanisms, separately, ultimately giving a series of lines in the Arrhenius plot for RF operation — one for each mechanism. An example is shown in Fig. 1 [3]. This approach is appealing compared to the traditional approach of running a simple RF lifetest with monitoring of an overall performance parameter (e.g. output power, Pout). In the latter, Pout will be affected by all the degradation mechanisms [4], with their different Ea's, and hence not have a well-defined Ea itself, making it impossible to draw a meaningful line on the Arrhenius plot. It is also appealing because it is relatively straightforward to implement. But, like all techniques for reliability estimation, the core arguments involve significant assumptions. In this paper, we document the assumptions, and then present evaluations of them and checks, where possible. This is important because the technique is new, and we need to record the conditions under which it is valid, as well as estimate the uncertainties in its results. We illustrate the process with one of several technologies that we used to develop this technique: a V-band GaN HEMT technology with 0.15 μm gates, vintage 2011. 2. Assumptions and evaluations A key early step is identification of the degradation mechanisms in the technology of interest, and easily-measured parameters (possibly unique to that technology) that scale with each one, and are unaffected by the others. These will then be used to quantify the wearout rates and temperature accelerations in DC and RF lifetests. So a key assumption is:
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B.M. Paine / Microelectronics Reliability 55 (2015) 2499–2504
Fig. 1. Arrhenius plots for the various mechanisms. Note the limiting mechanism for a given application, and the relevant Ea, depend on the temperature of operation. The error bar indicates our estimate for the uncertainty in MTTF. The individual symbols were measured in an RF lifetest, with δ Pout = −1.0 dB as the failure criterion.
Assumption 1. In both DC and RF lifetests, each signature parameter scales only with its degradation mechanism and is not affected by other mechanisms. We were able to achieve this with reasonable confidence, after considerable study with step-stress tests, short lifetests, and physical analysis of degraded parts. Our method for establishing the signature parameters was as follows [2]: A. Define the mechanism, based on all observations (electrical, optical emission, and physical), as well as the literature, and propose a signature parameter. Since our goal is to quantify known mechanisms, and not shed further light on the atomic changes, we adopt definitions that are the most common in recent publications. B. Run step-stresses and short DC lifetests, and see how the parameter varies with biases and observed physical damage, if any. C. See if it has any correlation with the other signature parameters, in stress tests. D. See if it can be extracted from I–V curves, independently of the signatures of any other mechanisms. E. Make a simple physical model for the mechanism and the signature parameter, and see if there are plausible physical arguments for linking the parameter to that mechanism, and no others. But we note that the signature parameters were only good for a limited amount of degradation [2]. Beyond a few 10's % degradation of common DC parameters, or 1 dB drop in RF gain for a single transistor, each mechanism can begin to influence several measureable parameters, and the signature parameters are rapidly “contaminated”. Thus a key limitation of the technique is that it applies only to small degradation. This is quite acceptable for most high-performance applications, where failure is defined as only a small degradation, but may be a problem for a “non-critical” application were failure occurs only after large changes. Step A. The mechanisms and signature parameters found for our example technology are: 1. Electron trapping near the gate: change of threshold voltage (δ Vth). 2. Surface pitting: change of maximum current, i.e. Id for Ig = +5 mA/mm, Vd = 1 V (δ Idmax). 3. Hot electron effects: change of peak transconductance (δ Gmp).
Following the literature on this subject, we use the term “mechanism” to mean the sequence of events that is triggered by the initial phenomenon that we name. Thus by “hot electrons effects” we mean the initial hot electron collisions, plus any subsequent migrations of charges, atoms or atomic bonds. Therefore the thermal activation energy that we measure for a mechanism will be that for the rate-limiting step in the sequence — possibly a diffusion process, and not necessarily the initial phenomenon. These mechanisms and signature parameters are consistent with reports in the literature: electron trapping has been correlated with δ Vth by many authors [5,6,7]; TriQuint and MIT have reported surface pitting, which correlated closely with δ Idmax changes [8,9]; and hot electron intensity, measured with electroluminescence, has been correlated with δ Gmp [5]. Step B. As expected, Vth shifts scaled with gate–drain bias, independent of drain current, and with no damage visible in cross sections. For example the rate increased by a factor of 3 when Vgd was increased from 4 to 25 V, at a constant temperature [3]. This is consistent with charge trapping. The Idmax changes occurred only with large gate–drain biases and significant currents, and these were the only conditions under which surface pitting was observed in cross sections [2]. Finally delta's in Gmp correlated well with electroluminescence intensity (per unit drain current), which is known to scale with the intensity of hot electron concentration [10]. For example, the rate of δ Gmp degradation increased by about 8 ×, as we transitioned from biases at the threshold of visible electroluminescence to the maximum in our scans with Vd up to 12 V [3]. Step C. We looked for correlations between different signature parameters during different operations – initial burn-in, elevatedtemperature lifetest, and unbiased baking: the signature parameters had negligible correlation [2].
Fig. 2. Examples of parameter extraction, illustrating that δ Gmp and δ Vth can be extracted independently.
B.M. Paine / Microelectronics Reliability 55 (2015) 2499–2504
Fig. 3. Example of parameter extraction, illustrating that δ Idmax and δ Gmp can be extracted nearly independently.
Step D. We also looked at how the parameters are extracted from IV curves. Fig. 2(a) shows the process for δ Vth — it can clearly be extracted independently of changes in Gmp. And Fig. 2(b) shows the converse: δ Gmp can be extracted independently of delta's in Vth. Fig. 3 shows that δ Idmax is extracted at Vd = 1.0 V, so it depends mostly on Ron increase, and minimally on Gmp change. Also, since δ Idmax is found for a constant gate current, not gate voltage, it is affected minimally by changes of Vth. Step E. Our physical models are illustrated in Fig. 4. Part (a) shows the situation for Vth and Gmp measurements: when (Vg, Vd) = (~− 2, +10) during measurement of Vth, most of the traps near the gate will be populated with electrons, so Vth is most sensitive to the electron trapping and not the surface pitting. As Vg is swept a little higher, for measurement of Gmp, the depletion under the gate is reduced and current is defined mostly by the depletion in the gate–drain access region, which defines Gmp. In Fig. 4(b), the bias is (Vg, Vd) = (+2, 1), for measurement of Idmax. This sweeps most of the electrons out of traps near
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the gate, so the maximum current is most sensitive to the surface pitting, and much less sensitive to charge trapping. It is useful to consider what happens if this assumption breaks down to a limited extent. Then another mechanism would contribute to the signature parameter, i.e. it is “contaminated”. This is unlikely in a DC lifetest, because it will have been conducted in a bias zone where the mechanism of interest is strong and others are not. But it is possible in RF lifetest because the waveform passes through a wide range of biases, and all mechanisms will be active. We observe that different degradation mechanisms will usually move a parameter in the same direction. (For example both surface pitting and hot electron effects reduce Idss, and both electron trapping and hot electrons increase Ron.) So in the RF lifetest, the contamination would probably make a signature parameter reach the failure criterion before the mechanism has really reached failure. Therefore the error is probably towards shorter MTTF, which is conservative. Thus we assign a larger uncertainty on the positive direction, for our final estimate for MTTF. In our example technology, we assigned an uncertainty of −5, +10% for Assumption 1. The second key assumption is that the mechanisms themselves remain the same, whether we study them with DC or RF lifetests. Assumption 2. During RF operation, the only degradation mechanisms that occur are those that were observed at various biases in DC lifetesting. In other words, the RF operation does not trigger new mechanisms with new Ea's, as illustrated in Fig. 5. This is likely to hold for small degradations, because individual mechanisms tend to initiate in different physical locations in the FETs. But even if Mechanism X “catalyzes” or “neutralizes” Mechanism Y to a new fixed rate, without changing either of the mechanisms, or the Ea's, the scaling factor will measure the change and our approach is still valid. However if Mechanism X and Mechanism Y interact to form a new Mechanism Z with new Ea, our assumption fails. But we note that if this happens, the result is more likely to be a “catalysis”, i.e. faster degradation, not slower degradation. Therefore the predicted MTTF will again be conservative. Our estimated uncertainties were −5, +10%. A test for this assumption is to extend the RF lifetesting to two or more temperatures. (Only one temperature is needed for the basic technique.) Then one can extract Ea's for the various mechanisms, and compare them with those measured in the DC lifetests. If a new value appears, it may be an indicator of a new mechanism. We attempted this test on our example technology, and the results are shown in Table 1. We found close agreement in the Ea's for 2 signature parameters, but the uncertainties were significant so we cannot rule out small changes. For the third signature parameter (δ Vth), the results do not conflict but the uncertainties are larger still. Next we come to the scaling factor: we want it to be constant, and to relate the DC lifetests to the actual RF operation. Assumption 3. The scaling factor is a constant, independent of temperature. For a given mechanism, δ Sig:Para: ¼ aXX : e−Ea=kT : time;
Fig. 4. Examples of models for degraded devices, with the effects of (a) Vth and Gmp, and (b) Idmax characterizations. The biases used for each tend to minimize effects of the other, so each signature parameter has minimal influence from other mechanisms.
for both DC and RF stresses, and scaling factor = aDC / aRF. Now aDC is the rate of the mechanism in a DC lifetest, which is constant for small degradation. And aRF is the rate in the RF lifetest, which is the integral of the rates at all the points around the loadline. This also is fixed, as long as the loadline does not change. This requires that Pin be adjusted for each new temperature so the degree of output power compression is unchanged. We assigned an uncertainty of ±10% for this assumption. This approach can be checked by conducting temperature-dependent physics-based RF modeling, but this is beyond the scope of the present study.
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Fig. 5. Assumption 2 indicates the above scenario will not happen. In other words, while the DC lifetests yield the various Ea's for the degradation mechanisms, there will not be a new mechanism occurring under RF drive that has a different Ea.
Assumption 4. The RF lifetest has the same degree of stress as the application. Again, this is achieved by ensuring Pin is adjusted so the output power compression is unchanged. And we assigned a further uncertainty of ±10%. Finally we come to practical aspects of lifetesting. Assumption 5. We can estimate the DC failure criteria, equivalent to δ Pout = −1 dB. For our example technology we used a “first principles” model, and assigned uncertainty of ± 10%. More realistic models could improve on this substantially. For a power FET, an estimate for maximum power is [11]: Pout ¼ Idmax ðVdmax –Vknee Þ=8
ð1Þ
where the variables are defined in Fig. 6(a). We observe that Vdmax and Vknee do not change significantly in operation, compared to Idmax [10]. Now if the Gm curve is approximated as shown in the transfer curves of Fig. 6(b), we can approximate Idmax and Idss as: Idmax ¼ Idss þ Gma Vgon and Idss ¼ −Gmb Vth Thus Pout ¼ const: Gma Vgon −Gmb Vth
ð2Þ
Conducting partial differentiation with respect to the various signature variables, we get δ Vth associated with a δ Pout (in dB) due to Vth effects only, indicated by “δ Pout(in dB)|Vth”: δ Vth ¼
Gma Vgon −Gmb Vth Gmb
(
1−alog
δPout ðin dBÞjVth
ð3Þ
10
This is achieved by conducting all analysis with the linear parts of the drift curves, and ignoring any subsequent saturation. A hint of saturation before reaching the failure criterion was noted in the RF lifetests [3]. Since saturation slows down the degradation, this is very conservative position, and we assign an uncertainty of −0, +50%. Assumption 7. Signature parameters measured with slow millisecond pulsing are sufficient to characterize the degradation mechanisms. In other words we assume there are no fast trap mechanisms that add to the changes in the signature parameters, but have dissipated before we can do our slow millisecond pulsed I–V characterizations. It is important to check for this. We conducted microsecond pulsed I–V characterizations of all our signature parameters and found that only δ Idmax was significantly different — by up to 2 × larger in magnitude. Therefore we added microsecond pulsed characterizations for δ Idmax only [12]. Once this was done, the assigned uncertainty was insignificant.
3. Results We summarize the assumptions implicit in our lifetest approach, and the uncertainties that we assigned for our example technology, as follows: 1. Signature parameters are pure: −5, +10%.
Table 1 Thermal activation energies. Para
DC Ea
RF Ea
δ Gmp δ Vth δ Idmax
1.10 ± 0.2 0.52 ± 0.2 0.78 ± 0.2
0.93 ± 0.2 0.81 ± 0.3a 0.81 ± 0.2
Noisy measurement.
Assumption 6. The Arrhenius law holds for drift curves, and they do not “saturate” with time.
)!
and similar formulae for δ Gmb, δ Vgon, δ Gma and δ Idmax. Note that we include δ Gmb and δ Vgon because they are independent effects from
a
the degradation, but they are not necessarily signature parameters for any other mechanisms. As reported in [2], we conducted a check on these calculations as illustrated schematically in Fig. 7. For a single-stage amplifier, we measured the Pout degradation in a lifetest, with RF power meters: − 3.6 dB. We also measured the degradation of DC parameters, and used our model to convert these to drops in RF power. Their sum came to −3.8 dB, which gives us confidence that the model is approximately correct, and we have not overlooked a major degradation mechanism, and supports our estimate of 10% uncertainty.
2. 3. 4. 5. 6. 7.
No interference of degradation mechanisms: −5, +10%. Scaling factor independent of temperature: ±10%. RF lifetest represents application: ±10%. DC failure criteria are accurate: ±10%. No saturation with time: −0, +50%. Sufficiently fast pulsing: 0%.
B.M. Paine / Microelectronics Reliability 55 (2015) 2499–2504
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Fig. 6. Approximations for first-principles calculation of delta's in signature parameters that give failure of Pout (eg. drop of 1 dB). (a) Idealized load line on the Vd–Id plane of the FET, showing parameter definitions. (b) Transfer curves (ie. Gm and Id versus Vg for Vd = 10 V), showing approximations for Gm in two Vg regions: Gmb for Vth to 0 V; Gma for 0 to Vgon.
To these we add some uncertainties that are common to all lifetesting: 8. Statistical uncertainty in measured rates: ±30%. 9. Uncertainty in absolute temperatures: ±10%. Adding in quadrature (assuming the effects are independent and random), and rounding, we find the net uncertainty in MTTF is −35, +100%. These are indicated by the error bar drawn in Fig. 1, which shows the MTTF curves for our example technology. These uncertainties apply at temperatures from 200 to 350 °C; the figures become gradually larger outside this range. Such uncertainties are not much different from those one would estimate in a typical conventional lifetest with similar quantities of parts. Also, they are entirely adequate for high-reliability parts evaluation, where a margin of at least 10 × (900%) is required. The
MTTF that we predict (~105 h at channel temperature of 150 °C) was reasonable for 2011 when our example parts were fabricated, but we can expect substantial improvements with more-recent process revisions. We estimated that the results are conservative by up to a factor of 2×. We checked this by conducting a 2-temperature lifetest on our example parts, and using δ Pout = −1.0 dB as the failure criterion. The results are plotted as individual symbols in Fig. 1. We see that the MTTF's are longer by factors ranging from 0.2 to 4; this appears consistent with our estimate, on average. The individual symbols in Fig. 1 are probably accurate for those temperatures, but as we argued in the introduction, extrapolation of pure RF lifetest data like this to other temperatures is impossible. In this example it would have predicted MTTF's that are erroneously long at lower operating temperatures, and completely ignored the possible effects of the electron trapping mechanism.
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B.M. Paine / Microelectronics Reliability 55 (2015) 2499–2504
the RF stress, but a further DC lifetest will generally be required. This is a lifetest at the DC bias that is present when there is no RF, with measurement of the degradation rates of the various mechanisms (bi). Then for each mechanism, at a given temperature, the net rate is ai = f · bi + (1 − f) · aiRF, where aiRF is the RF rate found in our technique (described in the introduction), and MTTFi = Ci / ai, where Ci is the failure criterion for mechanism i. The thermal activation energies are known from the DC lifetests in our technique. Thus a plot analogous to Fig. 1 can be constructed. Acknowledgments
Fig. 7. Procedure for checking model estimates of δ Pout's due to degradation of various DC parameters. Model predictions are summed and compared with the δ Pout measured with an RF power meter.
4. Conclusion We evaluated the assumptions behind a new lifetest technique involving signature parameters to track individual degradation mechanisms. We found that they are reasonable, and the associated uncertainties are comparable to those found in conventional lifetests. We showed that for some of the basic assumptions of our technique to apply, the failure criteria must be relatively small: δ Pout = −1 dB, or δ Idmax = − 10%. So the technique is suitable for high-performance parts, but may not be appropriate for non-critical parts that can change by a large margin before jeopardizing the system. There remains the question of whether a signature parameter can be found for all degradation mechanisms. As the technology improves and basic mechanisms are eliminated, it will undoubtedly become difficult, requiring sophisticated characterizations such as cross sectioning, μs pulsing, capacitance–voltage measurement, or optical emission spectrometry. Also, some mechanisms may appear simply as sudden failures, and it may be impractical to detect any precursor changes. In this case the signature parameter may be simply catastrophic failure, and both RF and DC lifetests must take most specimens to failure. Then the analysis can follow our procedure, but in terms of MTTF's, and not degradation rates. If a mechanism is not accelerated by elevated temperature, then another accelerant must be found, e.g. voltage or humidity, just as in any lifetesting. Finally we note that if a device operates for some fraction of the time (f) under DC bias, without RF signals, then our technique still applies for
This work was supported by a Technology Investigation Agreement between the Air Force Research Laboratory, contract # FA8650-11-21187 (Lois Kehias), and the Boeing Network and Space Systems Internal Research and Development program (Remy Hiramoto). References [1] J. Joh, J.A. del Alamo, U. Chowdhury, J.L. Jimenez, Correlation between RF and DC reliability in GaN high electron mobility transistors, Proc. JEDEC Workshop on Reliability of Compound Semiconductors 2008, pp. 185–194. [2] B.M. Paine, S.R. Polmanter, V.T. Ng, N.T. Kubota, C.R. Ignacio, Degradation rate for surface pitting in GaN HEMT, Proceedings of the IEEE International Reliability Physics Symposium, Monterey, CA, USA, 2015 (paper CD.1). [3] B.M. Paine, S.R. Polmanter, V.T. Ng, N.T. Kubota, C.R. Ignacio, Lifetesting GaN HEMTs with multiple degradation mechanisms, IEEE Trans. Device Mater. Reliab. (2015) (in press). [4] J. Joh, J.A. del Alamo, RF power degradation of GaN high electron mobility transistors, Proc. IEEE Intl. Electron Devices Mtg, 2010 (paper 20.2). [5] E. Zanoni, G. Meneghesso, G. Verzellesi, F. Danesin, M. Meneghini, F. Rampazzo, A. Tazzoli, F. Zanon, A review of failure modes and mechanisms of GaN-based HEMTs, Proc. of the IEEE International Electron Devices Meeting 2007, pp. 381–384. [6] M. Meneghini, N. Ronchi, A. Stocco, G. Meneghesso, U.K. Mishra, Y. Pei, E. Zanoni, Investigation of trapping and hot-electron effects in GaN HEMTs by means of a combined electrooptical method, IEEE Trans. Electron Devices 58 (2011) 2996–3002. [7] M. Caesar, M. Dammann, V. Polyakov, P. Waltereit, W. Bronner, M. Baeumler, R. Quay, M. Mikulla, O. Ambacher, Generation of traps in AlGaN/GaN HEMTs during RF-and DC-stress test, IEEE International Reliability Physics Symposium, CD.6, 2012. [8] S.Y. Park, C. Floresca, U. Chowdhury, J.L. Jimenez, C. Lee, E. Beam, P. Saunier, T. Balistreri, M.J. Kim, Physical degradation of GaN HEMT devices under high drain bias reliability testing, Microelectron. Reliab. 49 (2009) 478–483. [9] P. Makaram, J. Joh, J.A. del Alamo, T. Palacios, C.V. Thompson, Evolution of structural defects associated with electrical degradation in AlGaN/GaN high electron mobility transistors, Appl. Phys. Lett. 96 (2010) 233509. [10] G. Meneghesso, G. Verzellesi, F. Danesin, F. Rampazzo, F. Zanon, A. Tazzoli, M. Meneghini, E. Zanoni, Reliability of GaN high-electron-mobility transistors: state of the art and perspectives, IEEE Trans. Device Mater. Reliab. 8 (2008) 332–343. [11] P. Ladbrooke, MMIC Design: GaAs FETs and HEMTs, Artech House, Norwood MA, 1989. [12] B. M. Paine, S. R. Polmanter, V. T. Ng, N. T. Kubota, and C. R. Ignacio, Fast-Pulsed Characterization of Wearout in GaN HEMTs, unpublished.
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/mr
Scaling DC lifetests on GaN HEMT to RF conditions Bruce M. Paine Technology Qualification, Boeing Network and Space Systems, El Segundo CA, USA
a r t i c l e
i n f o
Article history: Received 8 July 2015 Received in revised form 29 August 2015 Accepted 23 September 2015 Available online 3 November 2015 Keywords: Gallium nitride GaN HEMT High-electron mobility transistors (HEMT) Characterization Reliability Life testing
a b s t r a c t The assumptions behind a new lifetesting approach are documented, evaluated, and tested where possible. This approach utilizes “signature parameters” to track individual degradation mechanisms in both DC and RF lifetests, and determines the mean time to failure (MTTF) Arrhenius curves for each mechanism individually, during RF operation. This is important for GaN HEMT because most studies indicate that several mechanisms contribute to its wearout, simultaneously, and this makes it impossible to extrapolate conventional RF wearout curves to other temperatures or longer times. A key assumption is that degradation mechanisms can be identified, and associated with unique signature parameters. A second key assumption is the integrity of degradation mechanisms, whether they occur under steady DC biases, or under oscillating RF biases. This allows us to deduce MTTF's under RF operation from the ratio of degradation rates of the individual mechanisms in DC lifetests, and the rates in RF operation, integrated over the RF waveform. This can be found by means of DC and RF lifetests, monitoring the signature parameters. Then the DC Arrhenius curves can be scaled to the RF conditions. After evaluation of these, and several other assumptions, we find the net uncertainties for one of the GaN HEMT technologies that we used for development of our approach. They amount to — 30%, +100% in MTTF; this is entirely adequate for high-reliability parts evaluation, where a margin of at least 10× (900%) is required. © 2015 The Author. Published by Elsevier Ltd. All rights reserved.
1. Introduction Temperature-accelerated lifetests under DC stress are very useful for studying RF GaN HEMT devices: they allow study of specific degradation mechanisms by setting the biases to emphasize those mechanisms alone, and they are relatively easy to set up, requiring only DC biases and heating. But it is difficult to relate such studies to actual RF operation because the RF gate and drain voltages vary rapidly through large ranges of values, in patterns (i.e. “load lines”) that are not easy to determine accurately [1]. Meanwhile, conventional RF lifetests are difficult to interpret because several mechanisms with different thermal activation energies are likely to be contributing simultaneously. An approach that we have developed [2,3] involves identification of a “signature parameter” for each mechanism, that measures the extent of that mechanism, but is unaffected by the others. It can be monitored in DC lifetests at a bias condition where that mechanism is strong, at various temperatures, to determine the activation energy (Ea), and mean time to failure (MTTF) versus temperature, i.e. the Arrhenius plot. Then it can be monitored further in a brief RF lifetest to find the degradation rate, aRF at one temperature, under the RF conditions of the application, i.e. the same frequency and same degree of output power compression. Then a temperature-independent “scaling factor”, aRF/aDC can be calculated, and used to scale the DC Arrhenius plot to the RF
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.microrel.2015.09.024 0026-2714/© 2015 The Author. Published by Elsevier Ltd. All rights reserved.
conditions. This can be done for each of the operating degradation mechanisms, separately, ultimately giving a series of lines in the Arrhenius plot for RF operation — one for each mechanism. An example is shown in Fig. 1 [3]. This approach is appealing compared to the traditional approach of running a simple RF lifetest with monitoring of an overall performance parameter (e.g. output power, Pout). In the latter, Pout will be affected by all the degradation mechanisms [4], with their different Ea's, and hence not have a well-defined Ea itself, making it impossible to draw a meaningful line on the Arrhenius plot. It is also appealing because it is relatively straightforward to implement. But, like all techniques for reliability estimation, the core arguments involve significant assumptions. In this paper, we document the assumptions, and then present evaluations of them and checks, where possible. This is important because the technique is new, and we need to record the conditions under which it is valid, as well as estimate the uncertainties in its results. We illustrate the process with one of several technologies that we used to develop this technique: a V-band GaN HEMT technology with 0.15 μm gates, vintage 2011. 2. Assumptions and evaluations A key early step is identification of the degradation mechanisms in the technology of interest, and easily-measured parameters (possibly unique to that technology) that scale with each one, and are unaffected by the others. These will then be used to quantify the wearout rates and temperature accelerations in DC and RF lifetests. So a key assumption is:
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B.M. Paine / Microelectronics Reliability 55 (2015) 2499–2504
Fig. 1. Arrhenius plots for the various mechanisms. Note the limiting mechanism for a given application, and the relevant Ea, depend on the temperature of operation. The error bar indicates our estimate for the uncertainty in MTTF. The individual symbols were measured in an RF lifetest, with δ Pout = −1.0 dB as the failure criterion.
Assumption 1. In both DC and RF lifetests, each signature parameter scales only with its degradation mechanism and is not affected by other mechanisms. We were able to achieve this with reasonable confidence, after considerable study with step-stress tests, short lifetests, and physical analysis of degraded parts. Our method for establishing the signature parameters was as follows [2]: A. Define the mechanism, based on all observations (electrical, optical emission, and physical), as well as the literature, and propose a signature parameter. Since our goal is to quantify known mechanisms, and not shed further light on the atomic changes, we adopt definitions that are the most common in recent publications. B. Run step-stresses and short DC lifetests, and see how the parameter varies with biases and observed physical damage, if any. C. See if it has any correlation with the other signature parameters, in stress tests. D. See if it can be extracted from I–V curves, independently of the signatures of any other mechanisms. E. Make a simple physical model for the mechanism and the signature parameter, and see if there are plausible physical arguments for linking the parameter to that mechanism, and no others. But we note that the signature parameters were only good for a limited amount of degradation [2]. Beyond a few 10's % degradation of common DC parameters, or 1 dB drop in RF gain for a single transistor, each mechanism can begin to influence several measureable parameters, and the signature parameters are rapidly “contaminated”. Thus a key limitation of the technique is that it applies only to small degradation. This is quite acceptable for most high-performance applications, where failure is defined as only a small degradation, but may be a problem for a “non-critical” application were failure occurs only after large changes. Step A. The mechanisms and signature parameters found for our example technology are: 1. Electron trapping near the gate: change of threshold voltage (δ Vth). 2. Surface pitting: change of maximum current, i.e. Id for Ig = +5 mA/mm, Vd = 1 V (δ Idmax). 3. Hot electron effects: change of peak transconductance (δ Gmp).
Following the literature on this subject, we use the term “mechanism” to mean the sequence of events that is triggered by the initial phenomenon that we name. Thus by “hot electrons effects” we mean the initial hot electron collisions, plus any subsequent migrations of charges, atoms or atomic bonds. Therefore the thermal activation energy that we measure for a mechanism will be that for the rate-limiting step in the sequence — possibly a diffusion process, and not necessarily the initial phenomenon. These mechanisms and signature parameters are consistent with reports in the literature: electron trapping has been correlated with δ Vth by many authors [5,6,7]; TriQuint and MIT have reported surface pitting, which correlated closely with δ Idmax changes [8,9]; and hot electron intensity, measured with electroluminescence, has been correlated with δ Gmp [5]. Step B. As expected, Vth shifts scaled with gate–drain bias, independent of drain current, and with no damage visible in cross sections. For example the rate increased by a factor of 3 when Vgd was increased from 4 to 25 V, at a constant temperature [3]. This is consistent with charge trapping. The Idmax changes occurred only with large gate–drain biases and significant currents, and these were the only conditions under which surface pitting was observed in cross sections [2]. Finally delta's in Gmp correlated well with electroluminescence intensity (per unit drain current), which is known to scale with the intensity of hot electron concentration [10]. For example, the rate of δ Gmp degradation increased by about 8 ×, as we transitioned from biases at the threshold of visible electroluminescence to the maximum in our scans with Vd up to 12 V [3]. Step C. We looked for correlations between different signature parameters during different operations – initial burn-in, elevatedtemperature lifetest, and unbiased baking: the signature parameters had negligible correlation [2].
Fig. 2. Examples of parameter extraction, illustrating that δ Gmp and δ Vth can be extracted independently.
B.M. Paine / Microelectronics Reliability 55 (2015) 2499–2504
Fig. 3. Example of parameter extraction, illustrating that δ Idmax and δ Gmp can be extracted nearly independently.
Step D. We also looked at how the parameters are extracted from IV curves. Fig. 2(a) shows the process for δ Vth — it can clearly be extracted independently of changes in Gmp. And Fig. 2(b) shows the converse: δ Gmp can be extracted independently of delta's in Vth. Fig. 3 shows that δ Idmax is extracted at Vd = 1.0 V, so it depends mostly on Ron increase, and minimally on Gmp change. Also, since δ Idmax is found for a constant gate current, not gate voltage, it is affected minimally by changes of Vth. Step E. Our physical models are illustrated in Fig. 4. Part (a) shows the situation for Vth and Gmp measurements: when (Vg, Vd) = (~− 2, +10) during measurement of Vth, most of the traps near the gate will be populated with electrons, so Vth is most sensitive to the electron trapping and not the surface pitting. As Vg is swept a little higher, for measurement of Gmp, the depletion under the gate is reduced and current is defined mostly by the depletion in the gate–drain access region, which defines Gmp. In Fig. 4(b), the bias is (Vg, Vd) = (+2, 1), for measurement of Idmax. This sweeps most of the electrons out of traps near
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the gate, so the maximum current is most sensitive to the surface pitting, and much less sensitive to charge trapping. It is useful to consider what happens if this assumption breaks down to a limited extent. Then another mechanism would contribute to the signature parameter, i.e. it is “contaminated”. This is unlikely in a DC lifetest, because it will have been conducted in a bias zone where the mechanism of interest is strong and others are not. But it is possible in RF lifetest because the waveform passes through a wide range of biases, and all mechanisms will be active. We observe that different degradation mechanisms will usually move a parameter in the same direction. (For example both surface pitting and hot electron effects reduce Idss, and both electron trapping and hot electrons increase Ron.) So in the RF lifetest, the contamination would probably make a signature parameter reach the failure criterion before the mechanism has really reached failure. Therefore the error is probably towards shorter MTTF, which is conservative. Thus we assign a larger uncertainty on the positive direction, for our final estimate for MTTF. In our example technology, we assigned an uncertainty of −5, +10% for Assumption 1. The second key assumption is that the mechanisms themselves remain the same, whether we study them with DC or RF lifetests. Assumption 2. During RF operation, the only degradation mechanisms that occur are those that were observed at various biases in DC lifetesting. In other words, the RF operation does not trigger new mechanisms with new Ea's, as illustrated in Fig. 5. This is likely to hold for small degradations, because individual mechanisms tend to initiate in different physical locations in the FETs. But even if Mechanism X “catalyzes” or “neutralizes” Mechanism Y to a new fixed rate, without changing either of the mechanisms, or the Ea's, the scaling factor will measure the change and our approach is still valid. However if Mechanism X and Mechanism Y interact to form a new Mechanism Z with new Ea, our assumption fails. But we note that if this happens, the result is more likely to be a “catalysis”, i.e. faster degradation, not slower degradation. Therefore the predicted MTTF will again be conservative. Our estimated uncertainties were −5, +10%. A test for this assumption is to extend the RF lifetesting to two or more temperatures. (Only one temperature is needed for the basic technique.) Then one can extract Ea's for the various mechanisms, and compare them with those measured in the DC lifetests. If a new value appears, it may be an indicator of a new mechanism. We attempted this test on our example technology, and the results are shown in Table 1. We found close agreement in the Ea's for 2 signature parameters, but the uncertainties were significant so we cannot rule out small changes. For the third signature parameter (δ Vth), the results do not conflict but the uncertainties are larger still. Next we come to the scaling factor: we want it to be constant, and to relate the DC lifetests to the actual RF operation. Assumption 3. The scaling factor is a constant, independent of temperature. For a given mechanism, δ Sig:Para: ¼ aXX : e−Ea=kT : time;
Fig. 4. Examples of models for degraded devices, with the effects of (a) Vth and Gmp, and (b) Idmax characterizations. The biases used for each tend to minimize effects of the other, so each signature parameter has minimal influence from other mechanisms.
for both DC and RF stresses, and scaling factor = aDC / aRF. Now aDC is the rate of the mechanism in a DC lifetest, which is constant for small degradation. And aRF is the rate in the RF lifetest, which is the integral of the rates at all the points around the loadline. This also is fixed, as long as the loadline does not change. This requires that Pin be adjusted for each new temperature so the degree of output power compression is unchanged. We assigned an uncertainty of ±10% for this assumption. This approach can be checked by conducting temperature-dependent physics-based RF modeling, but this is beyond the scope of the present study.
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Fig. 5. Assumption 2 indicates the above scenario will not happen. In other words, while the DC lifetests yield the various Ea's for the degradation mechanisms, there will not be a new mechanism occurring under RF drive that has a different Ea.
Assumption 4. The RF lifetest has the same degree of stress as the application. Again, this is achieved by ensuring Pin is adjusted so the output power compression is unchanged. And we assigned a further uncertainty of ±10%. Finally we come to practical aspects of lifetesting. Assumption 5. We can estimate the DC failure criteria, equivalent to δ Pout = −1 dB. For our example technology we used a “first principles” model, and assigned uncertainty of ± 10%. More realistic models could improve on this substantially. For a power FET, an estimate for maximum power is [11]: Pout ¼ Idmax ðVdmax –Vknee Þ=8
ð1Þ
where the variables are defined in Fig. 6(a). We observe that Vdmax and Vknee do not change significantly in operation, compared to Idmax [10]. Now if the Gm curve is approximated as shown in the transfer curves of Fig. 6(b), we can approximate Idmax and Idss as: Idmax ¼ Idss þ Gma Vgon and Idss ¼ −Gmb Vth Thus Pout ¼ const: Gma Vgon −Gmb Vth
ð2Þ
Conducting partial differentiation with respect to the various signature variables, we get δ Vth associated with a δ Pout (in dB) due to Vth effects only, indicated by “δ Pout(in dB)|Vth”: δ Vth ¼
Gma Vgon −Gmb Vth Gmb
(
1−alog
δPout ðin dBÞjVth
ð3Þ
10
This is achieved by conducting all analysis with the linear parts of the drift curves, and ignoring any subsequent saturation. A hint of saturation before reaching the failure criterion was noted in the RF lifetests [3]. Since saturation slows down the degradation, this is very conservative position, and we assign an uncertainty of −0, +50%. Assumption 7. Signature parameters measured with slow millisecond pulsing are sufficient to characterize the degradation mechanisms. In other words we assume there are no fast trap mechanisms that add to the changes in the signature parameters, but have dissipated before we can do our slow millisecond pulsed I–V characterizations. It is important to check for this. We conducted microsecond pulsed I–V characterizations of all our signature parameters and found that only δ Idmax was significantly different — by up to 2 × larger in magnitude. Therefore we added microsecond pulsed characterizations for δ Idmax only [12]. Once this was done, the assigned uncertainty was insignificant.
3. Results We summarize the assumptions implicit in our lifetest approach, and the uncertainties that we assigned for our example technology, as follows: 1. Signature parameters are pure: −5, +10%.
Table 1 Thermal activation energies. Para
DC Ea
RF Ea
δ Gmp δ Vth δ Idmax
1.10 ± 0.2 0.52 ± 0.2 0.78 ± 0.2
0.93 ± 0.2 0.81 ± 0.3a 0.81 ± 0.2
Noisy measurement.
Assumption 6. The Arrhenius law holds for drift curves, and they do not “saturate” with time.
)!
and similar formulae for δ Gmb, δ Vgon, δ Gma and δ Idmax. Note that we include δ Gmb and δ Vgon because they are independent effects from
a
the degradation, but they are not necessarily signature parameters for any other mechanisms. As reported in [2], we conducted a check on these calculations as illustrated schematically in Fig. 7. For a single-stage amplifier, we measured the Pout degradation in a lifetest, with RF power meters: − 3.6 dB. We also measured the degradation of DC parameters, and used our model to convert these to drops in RF power. Their sum came to −3.8 dB, which gives us confidence that the model is approximately correct, and we have not overlooked a major degradation mechanism, and supports our estimate of 10% uncertainty.
2. 3. 4. 5. 6. 7.
No interference of degradation mechanisms: −5, +10%. Scaling factor independent of temperature: ±10%. RF lifetest represents application: ±10%. DC failure criteria are accurate: ±10%. No saturation with time: −0, +50%. Sufficiently fast pulsing: 0%.
B.M. Paine / Microelectronics Reliability 55 (2015) 2499–2504
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Fig. 6. Approximations for first-principles calculation of delta's in signature parameters that give failure of Pout (eg. drop of 1 dB). (a) Idealized load line on the Vd–Id plane of the FET, showing parameter definitions. (b) Transfer curves (ie. Gm and Id versus Vg for Vd = 10 V), showing approximations for Gm in two Vg regions: Gmb for Vth to 0 V; Gma for 0 to Vgon.
To these we add some uncertainties that are common to all lifetesting: 8. Statistical uncertainty in measured rates: ±30%. 9. Uncertainty in absolute temperatures: ±10%. Adding in quadrature (assuming the effects are independent and random), and rounding, we find the net uncertainty in MTTF is −35, +100%. These are indicated by the error bar drawn in Fig. 1, which shows the MTTF curves for our example technology. These uncertainties apply at temperatures from 200 to 350 °C; the figures become gradually larger outside this range. Such uncertainties are not much different from those one would estimate in a typical conventional lifetest with similar quantities of parts. Also, they are entirely adequate for high-reliability parts evaluation, where a margin of at least 10 × (900%) is required. The
MTTF that we predict (~105 h at channel temperature of 150 °C) was reasonable for 2011 when our example parts were fabricated, but we can expect substantial improvements with more-recent process revisions. We estimated that the results are conservative by up to a factor of 2×. We checked this by conducting a 2-temperature lifetest on our example parts, and using δ Pout = −1.0 dB as the failure criterion. The results are plotted as individual symbols in Fig. 1. We see that the MTTF's are longer by factors ranging from 0.2 to 4; this appears consistent with our estimate, on average. The individual symbols in Fig. 1 are probably accurate for those temperatures, but as we argued in the introduction, extrapolation of pure RF lifetest data like this to other temperatures is impossible. In this example it would have predicted MTTF's that are erroneously long at lower operating temperatures, and completely ignored the possible effects of the electron trapping mechanism.
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the RF stress, but a further DC lifetest will generally be required. This is a lifetest at the DC bias that is present when there is no RF, with measurement of the degradation rates of the various mechanisms (bi). Then for each mechanism, at a given temperature, the net rate is ai = f · bi + (1 − f) · aiRF, where aiRF is the RF rate found in our technique (described in the introduction), and MTTFi = Ci / ai, where Ci is the failure criterion for mechanism i. The thermal activation energies are known from the DC lifetests in our technique. Thus a plot analogous to Fig. 1 can be constructed. Acknowledgments
Fig. 7. Procedure for checking model estimates of δ Pout's due to degradation of various DC parameters. Model predictions are summed and compared with the δ Pout measured with an RF power meter.
4. Conclusion We evaluated the assumptions behind a new lifetest technique involving signature parameters to track individual degradation mechanisms. We found that they are reasonable, and the associated uncertainties are comparable to those found in conventional lifetests. We showed that for some of the basic assumptions of our technique to apply, the failure criteria must be relatively small: δ Pout = −1 dB, or δ Idmax = − 10%. So the technique is suitable for high-performance parts, but may not be appropriate for non-critical parts that can change by a large margin before jeopardizing the system. There remains the question of whether a signature parameter can be found for all degradation mechanisms. As the technology improves and basic mechanisms are eliminated, it will undoubtedly become difficult, requiring sophisticated characterizations such as cross sectioning, μs pulsing, capacitance–voltage measurement, or optical emission spectrometry. Also, some mechanisms may appear simply as sudden failures, and it may be impractical to detect any precursor changes. In this case the signature parameter may be simply catastrophic failure, and both RF and DC lifetests must take most specimens to failure. Then the analysis can follow our procedure, but in terms of MTTF's, and not degradation rates. If a mechanism is not accelerated by elevated temperature, then another accelerant must be found, e.g. voltage or humidity, just as in any lifetesting. Finally we note that if a device operates for some fraction of the time (f) under DC bias, without RF signals, then our technique still applies for
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