Computationally Efficient Method to Include Metal-Metal Interface Resistance in Semiconductor Device Modeling
Publication Date: 2015-Feb-12
The IP.com Prior Art Database
An efficient method and system to include metal-metal interafce resisvity in semiconductor device modelling.
The emergence of Middle-of-Line (MOL) and Back-End-of-Line (BEOL) interconnect structures as significant performance limiters, is one well known consequence of aggressive pitch scaling. The advent of copper supported continued scaling by containing the growing resistivity problem associated with shrinking interconnect dimensions, but also drove the need for barrier layers to prevent its diffusion into adjacent silicon and dielectric materials. Interconnect vias, for example, contain interfaces associated with nanoscale level metal films such as Copper, Tantalum and Tantalum-Nitride, through which current flows and for which the resistance has become an increasingly important performance component in aggressively scaled technology nodes (14 nm and beyond). Engineering via structures to simultaneously satisfy resistance and reliability targets is expensive if accomplished only through experimental means, which makes simulation approaches very attractive as a means to reduce cost and development time. Toward this end, continuum-based simulation approaches to quantifying the relationship between proposed designs (e.g., materials, topology) and their electrical performance implications (e.g, R-C delay), have yielded useful guidance but fail to accurately capture increasingly important material interface effects. Conventional “bulk resistance” formulae are inadequate to model via resistance, the interface components in particular. In this work we invoked a “quantized resistance” methodology , and showed that a significant part of via resistance derives from the Ta/TaN interface. A simple closed-form analytical expression was derived for interface resistance in terms of known bulk material properties. The effects of a discrete number of grain boundaries on resistance were accounted for through the simple mapping of a polycrystalline film solution to the n-metal interface problem. Implementation of the model in the context of a continuum device simulator (i.e., a multi-scale approach) has been prototyped, which greatly broadens the scope of problems which can be evaluated toward optimization of interconnect structures.
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Computationally Efficient Method to Include Metal - Semiconductor Device Modeling
-Metal Interface Resistance in
Metal Interface Resistance in
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As shown in Fig. 1 (a), the methods uses an analytical expression to calculate metal-metal interface resistance, while simulating device characteristic in a TCAD simulator. As mentioned "bulk resistivity" formula is not valid anymore for small length scale structure as shown in Fig. 1 (b). In addition, while calculating interface resistance, the method uses a look up table for various parameters it needed as input. Furthermore, this algorithm also includes the self-heating effect where the device operates in elevated temperature conditions. The method also provides an algorithm to calibrate analytical expression for thickness/temperature dependent resistivity using self consistent numerical simulation. Fig. 1(b) shows a typical via structure, where small length metals (Ta,TaN) are barrier layers- where this methodology/algorithms is applicable.
A generalized algorithm can be used used to calculate the interface resistance for any metal-metal interface depending on their thickness as shown in Figure. 2 below
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In an embodiment, it uses "Landauer quantized conductance" formalism for resistance if its length is smaller than the bulk mean free path. In doing so, it uses an novel and unique methodology to calculate the number of modes of transmission in terms of bulk resistivity, which is, otherwise computationally expensive to calculate. The interface resistivity method it use is
In this method, for a combination of multiple small metallic films, the Eq.1 can be extended easily to multiple interface problem with appropriate modes of transport and transmission coefficients. For an example, for two barrier material of small thickness, the interface resistivity is
The method uses the Transmission coefficient (T in Eq. 1 and in Eq. 2) of carriers from one metal to another at the interface. For an ideal interface, this transmission coefficient comes from the mode mismatch of two metals. Nevertheless, it can act as a calibration parameter in TCAD simulator and any non-ideality of the interface can be absorbed into this transmission coefficient factor. For ideal case, the method calculates the transmission coefficient using...