On the Differences between Ultra-fast NBTI Measurements and Reaction-Diffusion Theory *A.E. Islam, S. Mahapatra 1 , S. Deora 1 , V. D. Maheta 1 , and M.A. Alam *Email: aeislam@ieee.org , Phone: 765-532-6514, Fax: 765-494-6441 Department of ECE, Purdue University, West Lafayette, IN 47906, USA; 1 CEN and Department of EE, IIT Bombay, India Abstract Reaction-Diffusion (R-D) theory, well-known to successfully explain most features of NBTI stress, is perceived to fail in explaining NBTI recovery. Several efforts have been made to understand differences between NBTI relaxation measured using ultra-fast methods and that predicted by R-D theory. Many alternative theories have also been proposed to explain ultra-fast NBTI relaxation, although their ability in predicting features of NBTI stress remains questionable. In this work, a hole-trap/interface-trap (N HT /N IT ) separation framework (Fig. 1a) is used to demonstrate that N IT relaxes slower compared to overall NBTI and this N IT relaxation is consistent with R-D theory. The framework also explains, perhaps for the first time, the observed impacts of nitrogen, stress-time, temperature, frequency, duty cycle, etc. on NBTI degradation. In sum, together with N HT , the R-D model governing N IT is shown to explain NBTI stress and recovery features in nitrided gate oxide p-MOSFETs. 1. Introduction Recent introduction of ultra-fast NBTI measurements [1-3] have inspired a number of studies [1,2,4-6] to understand the gap between NBTI theory and experiment. Among all NBTI theories, the R-D model explains many experimental signatures for p-MOSFETs having lightly nitrided oxides [7- 9] including stress-phase time exponent, activation energy, field acceleration, frequency independence, etc. However, recent reports of ultra-fast NBTI relaxation that initiates at ~μs time-scale is inconsistent with N IT dynamics, predicted by the R-D model (Fig. 1b), where H-H 2 conversion takes place at poly-Si/dielectric interface and long-term diffusion of H 2 occurs in poly-Si [10]. This inconsistency has raised questions regarding the general validity of the R-D theory [1,2,4,5]. The purpose of this work is to perform NBTI stress/relaxation experiments using an ultra-fast on-the-fly (UF-OTF) setup [3] on p-MOSFETs with nitrided dielectric, and to show that the theory-experiment gap in explaining ΔV T relaxation can be bridged, if one accounts for the respective relaxation dynamics of its components: ΔV HT (due to ΔN HT ) and ΔV IT (due to ΔN IT ). A ΔV HT /ΔV IT separation scheme (Figs. 1-4; which was previously used in NBTI stress phase [6]) can explain the difference between start of overall NBTI relaxation (t REC,start ~μs) and N IT relaxation (t NIT,start ~sec) (Figs. 5-7). This framework not only anticipates the duty-cycle/frequency dependencies of AC NBTI stress (Fig. 8), but also establishes the AC NBTI dependencies on nitrogen content (%N), temperature (T), and stress time (t STS ). 2. Non-universality of NBTI relaxation Several studies [1,4,5,11] on NBTI have reported the universality of log-t relaxation, with t REC,start (start of ~5% NBTI relaxation) of ~ μs (Fig. 1b). However, our measurements on p-MOSFETs having a variety of nitrided dielectric (Fig. 1c and [12-14]) using UF-OTF demonstrate that fractional NBTI relaxation depends on %N of the dielectric, as well as on the difference between stress and recovery voltages (V STS -V REC ). As shown in Fig. 1c, t REC,start is larger (~ms) for low %N and smaller (V STS -V REC ), very clearly indicating the non-universal nature of NBTI recovery. This is due to the existence of different (N HT and N IT ) species during stress [6, 14], with very different respective relaxation dynamics during recovery. Therefore, isolation of N IT and N HT is essential, before R-D theory (that governs N IT ΔV T Time Stress Relaxation ΔV IT ΔV HT ~ 5% t REC,start t NIT,start (1a) 10 -12 10 -9 10 -6 10 -3 10 0 0.00 0.25 0.50 0.75 1.00 0 V V REC -1.3V Meas. V STS /V REC (V) t STS UFV -2.2/0 10 5 UF-OTF -2.3/-1.3 10 3 ΔV T (t REC )/ΔV T (t STS ) t REC /t STS R-D Theory (1b) t REC,start 10 -6 10 -4 10 -2 10 0 10 2 10 4 0.00 0.25 0.50 0.75 1.00 t STS =1000s V STS / V REC (V) -2.3 / -1.8 -2.3 / -1.3 t REC [sec] ΔV T (t REC )/ΔV T (t STS ) Open: Low %N Crossed: High %N (1c) Fig. 1: (a) ΔVT due to NBTI stress recovers once the stress is removed (solid line). On nitrided transistors, ΔVT can be attributed to: interfacial traps (ΔVIT, dotted line) and pre-existing hole traps (ΔVHT, dashed line) with respective time-dynamics. (b) tREC,start in ultra-fast VT (UFV) measurement [1], at VREC ~ 0, commences ~5 decades earlier in time compared to the prediction of H-H2 R-D theory. Our UF-OTF measurement at VREC ~ -1.3V shows similar relaxation trend. (c) Though tREC,start is considered to be ~ µs in several reports [4,5,11], UF-OTF measurements on nitrided transistors, at different VREC, demonstrate that tREC,start depends on %N and (VSTS – VREC). In general, tREC,start ranges from µs to ms and is smaller in the presence of higher %N and for larger (VSTS – VREC).