Why short wires scale but long wires dont
Why short wires scale, but long wires don’t Stephen Felix Alpha Technology Compaq Computer Corporation Shrewsbury, Massachusetts Shubu Mukherjee VSSAD, Alpha Technology Compaq Computer Corporation Shrewsbury, Massachusetts Disclaimer: We don’t discuss repeaters in this talk Better answers
Resistance of Wires (R) L current flow t W R = L / (t W), = resistivity Better answers Slide 2
Capacitance of Wires (C) W t v h Metal Layer 3 wire X Metal Layer 2 Metal Layer 1 Clateral = L t / h, Cvertical = L W / v Ctotal for wire X = 2 * Clateral + 2 * Cvertica Better answers Slide 3
Wire Delay L t R= L/ current flow(t W) C = 2 * ( L t / h + L W W Delay of Short Wires C, assuming constant drive Delay of Long Wires RC What’s a long wire? • intrinsic RC delay of wire significant fraction of gate delay 4 Better • >answers 0. 3 - 0. 7 mm in. Slide 0. 125 technology, depends on
Scaling Equation: example R L / (t W) u Let f = scaling factor u l u typically, f = 0. 7 every generation Let f. R = scaling factor of R f. R = f / f, constant, if t = constant (past) l f R = f / (f * f) = 1 / f, if t scales as f (future) l – Better answers resistance increases! Slide 5
Wire Delay Scaling in the Past L t R= L/ current flow(t W) C = 2 * ( L t / h + L W / W Assume: t & v = constant Delay of short wires C Clateral + Cvertical • Clateral constant, Cvertical scales as f 2 • if Clateral = 0, delay reduces by f 2 ~ 50% • if Clateral = Cvertical, delay reduces by [ 1 - (1 + f 2) / (1 + 1)] ~ 25% Delay of long wires RC • Better RC scales as C, because R is constant, ~ Slide 6 answers 25 - 50%
Wire Scaling in the Future Key Assumption Violated: t & v NOT constants New Assumption: all dimensions scale the same wa t W W L PAST t FUTURE Better answers Slide 7
Wire Delay Scaling in the Future L t current flow R = L / (t W) C = 2 * ( L t / h + L W / v) W Delay of short wires C delay reduces by (1 - f) 30% every generation Delay of long wires RC delay constant in every generation, because L, W, t, & h scale in the Better answers same way Slide 8
Conclusions u Past l l u Future l l u delay on a short wire reduces by 25 - 50% per generation delay on a long wire reduces by 25 - 50% per generation delay on a short wire reduces by 30% per generation delay on a long wire is constant Many “short wires” become “long wires” in next generation l intrinsic & constant RC appears relatively higher compared to faster gates Better answers Slide 9
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