ABSTRACT
CONTENTS 14.1 Introduction ...................................................................................................................... 400 14.2 Interface States ................................................................................................................. 401 14.3 Oxide Charges .................................................................................................................. 404 14.4 Measurement Issues ........................................................................................................ 405 14.5 Characterization of Relaxation....................................................................................... 405
14.5.1 Functional Form of the Universal Relaxation Function ................................ 407 14.6 Characterization of MSM Data ...................................................................................... 408
14.6.1 Influence of Measurement-Delay on the Power-Law Parameters............... 410 14.7 Modeling of NBTI............................................................................................................ 411
14.7.1 Reaction-Diffusion Models ................................................................................ 413 14.7.1.1 Standard RD Model ............................................................................ 413 14.7.1.2 Pre-RD Regime .................................................................................... 415 14.7.1.3 Relaxation as Predicted by the RD Model....................................... 416
14.7.2 Extended Classical RD Models ......................................................................... 417 14.7.2.1 Two-Region RD Model....................................................................... 418 14.7.2.2 Two-Interface RD Model.................................................................... 418 14.7.2.3 Explicit H-H2 Conversion RD Model .............................................. 419 14.7.2.4 Vanderbilt Model ................................................................................ 420
14.7.3 Final Notes on RD Models ................................................................................ 421 14.7.4 Dispersive NBTI Models.................................................................................... 421
14.7.4.1 Reaction-Dispersive-Diffusion (RDD) Models ............................... 421 14.7.4.2 Dispersive Pre-RD Regime................................................................. 425 14.7.4.3 Relaxation as Predicted by the RDD Models .................................. 426 14.7.4.4 Dispersive-Rate Coefficients .............................................................. 427 14.7.4.5 Simple Dispersive Hole Trapping Model ........................................ 429 14.7.4.6 Detailed Dispersive Hole Trapping Model ..................................... 431
14.7.5 Multiple Mechanisms ......................................................................................... 432 14.8 Conclusions....................................................................................................................... 432 References.................................................................................................................................... 433
Negative bias temperature instability (NBTI) has been known for 40 years [1] and is attracting an ever growing industrial and scientific attention as one of the most important reliability issues in modern complementary metal-oxide semiconductor (CMOS) technology. It affects mostly p-metal-oxide-semiconductor field-effect transistors (pMOSFETs) at elevated temperatures with a large negative voltage applied to the gate. While the typical NBT setup requires the other terminals to be grounded, an application of a larger voltage at the drain creates interesting mixed patterns with hot-carrier degradation (HCI) and a large voltage at the bulk contact can be used to investigate the dependence of NBTI on hot or cold holes. Altogether, as a result of this stress condition, a shift in the threshold voltage is observed [2,3]. In addition to this threshold voltage shift, other crucial transistor parameters degrade as well, such as the drain current, the transconductance, the subthreshold slope, the gate capacitance, and the mobility [2,3]. The evolution of the threshold voltage during stress is commonly described by a power
law of the form:
DVth(t) ¼ A(T,Eox) tn, (14:1)
with the prefactor A strongly depending on the temperature and the electric field. The actual dependencies of the power-law exponent n are still not fully clarified with some groups [4,5] reporting a temperature-and technology-independent value around n 0.15, while recent publications show considerably smaller values [6,7]. Alternatively, some groups have reported a log-like dependency [6,8,9], for instance of the form:
DVth(t) ¼ A(T,Eox) log (1þ t=t), (14:2)
at least at early times. A typical scenario is depicted in Figure 14.1 where the same data are shown once on a lin-log and on a log-log plot. Depending on the accuracy of the initial threshold voltage determination or, in that example, the initial drain current in the linear regime, different interpretations seem possible [6]. The detailed microscopic physics behind NBTI are not yet fully understood [10-14] but
the creation of interface states seems to be a universally acknowledged feature of NBTI [2,15]. A growing number of recent publications, however, attribute at least a part of the degradation to positive charge generation in the oxide bulk [11,13,16,17]. Possible positive charges that have been suggested include holes trapped in either preexisting traps [11,16] or in traps generated by the hydrogen species released during the creation of the interface states [13]. Other potential contributions to a threshold voltage shift like mobile charges are com-
monly assumed to be negligible for NBTI [2] and the total threshold voltage shift is thus given by
DVth(t) ¼ DQit(t)þ DQox(t)Cox , (14:3)
with DQit and DQox being the effective charges due to interface and oxide states and Cox the gate capacitance per area. The fundamental problem in the context of NBTI is given by the fact that the degradation
created during the stress phase begins to recover immediately once the stress is removed. This makes the classic measurement technique where the stress is interrupted during the
extraction of the threshold voltage problematic [9,18]. In particular, the value of the extracted power-law exponent depends significantly on the delay introduced during the measurement [5,14,19]. Experimental results obtained with delayed measurements show a linear increase of the exponent with temperature [5,8,14] with values around 0.2-0.3. In contrast, temperature-independent exponents in the range 0.07-0.2 have been extracted from recent delay-free measurements [4,6,20]. Of particular interest is the question related to the origin of this extremely fast relaxation
[9,14,21]. While some authors assume that hole trapping is negligible and both degradation as well as relaxation are determined by the temporal change of the interface state density and an associated back-and forth-diffusion of hydrogen [5], others acknowledge at least partial importance of trapped charges [6,8,13,22]. In the latter case it has been assumed that trapped charges either form the fast component of NBTI relaxation superimposed onto some interface defect relaxation [6,22] or are solely responsible for any recovery while created interface defects do not recover at all [8,13].
