Keynote speakers

Opportunities for GSI are governed by a hierarchy of limits whose five levels can be codified as: fundamental, material, device, circuit and system. This constructive methodology is extended here by elucidating the impact on GSI of random dopant atom placement in the channel region of a MOSFET and random interconnect placement in binary logic networks. Random microscopic fluctuations in the number and location of dopant atoms in the channel depletion region of a MOSFET induce stochastic variations in device parameters such as threshold voltage, subthreshold swing and drain current. The standard deviations of these parameter distributions increase as device dimensions are scaled down. These increases in combination with concurrent upward scaling of the number of MOSFETs per chip cause a rapid escalation of the maximum deviations of MOSFET parameter values for the ensemble of devices within a given die. At some value of maximum deviation of threshold voltage, for example, faulty operation of logic circuits ensues. The effective channel doping concentration F(na), the threshold voltage F(Vts), the subthreshold swing F(S), and the drain current F(Idsat) distribution density functions for a MOSFET with a nominally uniform channel doping profile have been determined. Calculations of the standard and maximum deviations of threshold voltage, Vt , across the technology generations projected by the US National Technology Roadmap for Semiconductors (NTRS) indicate alarmingly large 4589% maximum deviations of threshold voltage for the NTRS 2010 or 0.07mm generation of chips. For more than three decades, Rent’s rule has proven to be a useful empirical relationship between the number of logic gates in a block, Ng , and the number of signal input/output interconnects, Ni/o , of the block. The form of the relationship is Ni/o =3D K(Ng)p, where K and p are= empirical constants. Rent’s rule has been applied recursively to a square array of logic gates for the purpose of deriving the complete stochastic wire length distribution of the array including local, semi-global and global interconnects. For an array of 34.4 million gates assumed to be implemented with 0.1 micron or 2007 generation technology in a die area of 1100 mm2, this distribution density function is typically described by values of K in the range of 4 and p in the range of 0.6. The chip includes approximately 107 wires less than three gate pitches in length and a single wire 6,700 gate pitches in length. About 93% of the wires are less than 25 gate pitches in length and consume only 23% of the total interconnect length on the chip. Interconnects longer than 220 gate pitches constitute 50% of the wiring demand, but only 1.1% of the number of interconnects, which underscores the importance of working with a complete wiring distribution including all global wiring in preparing a priori estimates of chip wiring demand.