Is the power-law model applicable beyond the direct tunneling regime?
Introduction
After in the late 1970s the quality of silicon dioxide dielectrics was optimized with respect to interface state density and impurities, long term reliability aspects came into the focus of the MOSFET development. At that time two competing models were developed, which both proposed that the electric oxide field is the root cause of the dielectric degradation. On the one hand, the so called linear E model [1], [2] is based on the field induced thermo-chemical breakage of Si–Si bonds, acting as defects in the SiO2 network [3]. The model is developed for thick SiO2 and describes a large fraction of experimental data very well. Furthermore the mechanism may also be relevant for all other polar bonded dielectrics. On the other hand, the inverse E model proposed a current driven degradation with a Fowler–Nordheim dominated tunneling current in SiO2 layers [4]. For this model experimental evidence was also reported. The physical understanding of the inverse E model was completed by the introduction of the anode hole-injection mechanism in 1993 [5]. Many theoretical and experimental studies were carried out to solve the controversy and to unify both models, i.e. to clarify the validity range and the transition region of the two models [6], [7]. For thin oxides it was shown few years ago, that no longer the electric field but the gate voltage and the leakage current are the driving force for degradation [8]. In addition, the voltage dependence of the dielectric breakdown was found to be power-law like rather than exponential [9]. This so called power-law model is experimentally well confirmed for silicon dioxide (and oxynitrides) with a thickness below 3 nm corresponding to a gate voltage for typical constant voltage tests below 3.5 V, i.e. in the direct tunneling regime.
For process qualification it is crucial to determine the valid model that describes the dielectric degradation in a time frame experimentally not assessable. The rather conservative linear E model may result in a too pessimistic assessment, whereas the validity of the very progressive inverse E model is generally not demonstrated at use voltage. The power-law model, resulting in a voltage acceleration in-between the two other models, may allow progressive down scaling of the dielectric thickness while considering reliability aspects. The exact physical origin of this model is still under discussion [10], [11]. One of the basic requirements is that there is no energy dissipation of the tunneling charges within the dielectric layer. For silicon oxide (and oxynitrides) this is true in the direct tunneling regime, which results in the upper limit given above (3 nm, 3.5 V), but this is also satisfied in the elastic Fowler–Nordheim range, which extends to about 8 V. The focus of this work is a detailed study of the voltage acceleration of dielectric breakdown exactly in the voltage range of 3.5–8 V. The question, which should be answered, is, whether there are mechanisms which coincidentally result in a power-law like behavior in the experimentally accessible voltage range and what the consequences would be for reliability assessment based on such measurements.
Section snippets
Experimental
A variety of n-channel MOSFETs were investigated, with a dielectric thickness from about 3.0 to 12 nm and n-type poly Si as gate material. Most of the samples are from state of the art DRAM technologies and few from logic processes, mainly for comparison. Thus the data represent pure and nitrided oxides. The time-dependent dielectric breakdown (TDDB) measurements were performed with constant voltage stress (CVS) on wafer and package level, to cover a wide range in breakdown times. The breakdown
Results and discussion
In Fig. 1 the result of typical CVS measurements for n-MOSFET structures with a gate oxide thickness of 6.1 nm are shown. To distinguish between the different possible voltage acceleration models extensive wafer level measurements were done up to a breakdown time of t63 = 10,000 s. Different models were fit to these wafer level data. Additional long-term, package-level measurements match the power-law model (tBD ∼ V−n) and not the exponential relation described by linear V: tBD ∼ exp(−gV) or inverse V
Summary
The measurements confirm that even in the elastic Fowler–Nordheim range the voltage and not the thickness (or field) is the crucial parameter for the change in breakdown mechanism. The detailed analysis demonstrates that besides statistical issues the recently reported impact of back end of line anneals on the voltage acceleration behavior of time-dependent dielectric breakdown and even the change in tunneling mechanism from direct to elastic Fowler–Nordheim may complicate the determination of
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