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465045 Charge Transport Model to Predict Intrinsic Reliability for Dielectric Materials in Integrated Circuits

The charge transport model is based on electron conduction and defect/trap formation in the dielectric, and uses Poisson’s equation to calculate the potential distribution, continuity equations for mobile and trapped electrons, and a defect reaction equation [3]. The mobile carrier concentration injected into the dielectric depends on the probability of the electrons to overcome the energy barrier from the Fermi level of the metal electrode to the conduction band of the dielectric, known as Schottky emission [4]. Failure originates from the interaction of high energy electrons with the dielectric matrix. The electrons gain energy due to the applied electric field, and lose energy to the matrix through collisions with defects or other constituents of the dielectric [5]. The energy released during the collisions becomes available to generate additional defects, and the mobile electrons become trapped within the dielectric by these defects. As the defect concentration increases over time, the probability for trapped electrons to tunnel from trap-to-trap through the dielectric increases. This trap-assisted tunneling is quickly accelerated once a critical defect concentration is reached [6]. The emptying of traps due to tunneling electrons enhances the local field at the cathode. This causes an increase in the injection of electrons, and further increases defect generation. This is known as positive feedback, or feed-forward, failure [7], and is the cause for the abrupt increase in current seen at failure. The charge transport model is one-dimensional and is solved by numerical methods using COMSOL® software. All of the parameters used in the model have some theoretical basis, are material properties of the dielectric, or are experimental conditions.

Current and failure data was obtained from several sources in literature for low-k SiCOH [8, 9] and high-k SiN [10] dielectrics. Both materials are commonly found in integrated circuits. Similar tests were also conducted at GLOBALFOUNDRIES on low-k SiCOH materials. Model parameters were set based on the dielectric material (dielectric constant, thickness, etc.) and experimental conditions (temperature). The boundary condition for the voltage at the cathode was altered to match the test type (constant voltage or voltage ramp) for each data set. The model reproduces the current as a function of time for constant voltage tests, capturing the current decay at early stress times and the subsequent current increase due to defect generation. Current vs. voltage curves are also reproduced for voltage ramp tests. For both test types, the rapid increase in current observed at failure is reproduced by the model. Experimentally, a large jump in current is defined as the breakdown point, and this method was also used in our simulations to determine the time-to-failure as a function of the applied electric field for high voltage testing. The model is then used predictively to determine device failure times at low voltages, or near operating conditions. These low-voltage predictions are compared to the most commonly used empirical models for dielectric reliability. Finally, simulations are also run altering key parameters, such as the dielectric constant or thickness, in order to hypothesize how these parameters can affect device reliability.

References

[1] Chen, F., C. Graas, M. Shinosky, K. Zhao, S. Narasimha, X.H. Liu, and C. Tian. 2015. “Breakdown Data Generation and in-Die Deconvolution Methodology to Address BEOL and MOL Dielectric Breakdown Challenges.” *Microelectronics Reliability* 55 (12, Part B): 2727–47.

[2] McPherson, J. W. 2012. “Time Dependent Dielectric Breakdown Physics – Models Revisited.” *Microelectronics Reliability* 52 (9–10): 1753–60.

[3] Ogden, S.P., J. Borja, J.L. Plawsky, T.-M. Lu, K.B. Yeap, and W.N. Gill. 2015. “Charge Transport Model to Predict Intrinsic Reliability for Dielectric Materials.” *Journal of Applied Physics* 118 (12): 124102.

[4] Yeap, K. B., T. Shen, G. W. Zhang, S. F. Yap, B. Holt, A. Gondal, S. Choi, S. L. Liew, W. Yao, and P. Justison. 2015. “Impact of Electrode Surface Modulation on Time-Dependent Dielectric Breakdown.” In *Reliability Physics Symposium (IRPS), 2015 IEEE International*, 2A.1.1–2A.1.5.

[5] Canright, G. S., and G. D. Mahan. 1987. “Time-Dependent Theory of Hot Electrons Using the Discrete Boltzmann Equation.” *Physical Review B* 36 (2): 1025–31.

[6] Lombardo, S., J. H. Stathis, and B. P. Linder. 2003. “Breakdown Transients in Ultrathin Gate Oxides: Transition in the Degradation Rate.” *Physical Review Letters* 90 (16): 167601.

[7] Chen, I. C., S. Holland, and C. Hut. 1985. “A Quantitative Physical Model for Time-Dependent Breakdown in SiO2.” In *Reliability Physics Symposium, 1985. 23rd Annual*, 24–31.

[8] Chery, E., X. Federspiel, D. Roy, F. Volpi, and J. -M. Chaix. 2013. “Identification of the (√E + 1/E)-Dependence of Porous Low-K Time Dependent Dielectric Breakdown Using over One Year Long Package Level Tests.” *Microelectronic Engineering*, Insulating Films on Semiconductors 2013, 109 (September): 90–93.

[9] Croes, K., C. Wu, D. Kocaay, Y. Li, Ph Roussel, J. Bömmels, and Zs. Tőkei. 2015. “Current Understanding of BEOL TDDB Lifetime Models.” *ECS Journal of Solid State Science and Technology* 4 (1): N3094–97.

[10] Allers, K. -H. 2004. “Prediction of Dielectric Reliability from I–V Characteristics: Poole–Frenkel Conduction Mechanism Leading to √E Model for Silicon Nitride MIM Capacitor.” *Microelectronics Reliability* 44 (3): 411–23.

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