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**Unformatted text preview: **MOSFET Scaling Device scaling: Simplified design goals/guidelines for shrinking device dimensions to achieve density and performance gains, and power duction in VLSI. reduction in VLSI. Issues: Short-channel effect, Power density, Switching delay, Reliability. The principle of constant-field scaling lies in scaling the device voltages and the device dimensions (both horizontal nd vertical) by the same factor ) such that the electric 2/22/2010 1 and vertical) by the same factor, ( > 1), such that the electric field remains unchanged . Rules of Constant Field Scaling MOSFET Device and Circuit Parameters Multiplicative Factor ( > 1) caling evice imensions / Scaling assumptions Device dimensions ( t ox , L , W , x j ) Doping concentration ( N a , N d ) Voltage ( V ) 1/ 1/ Derived scaling Electric field ( E ) 1 behavior of device parameters Carrier velocity ( v ) Depletion layer width ( W d ) Capacitance ( C = A / t ) 1 1/ 1/ Inversion layer charge density ( Q i ) Current, drift ( I ) Channel resistance ( R ch ) 1 1/ 1 Derived scaling behavior of circuit parameters Circuit delay time ( CV / I ) Power dissipation per circuit ( P VI ) Power-delay product per circuit ( P ) ircuit density ( / 1/ 1/ 2 1/ 3 2 2/22/2010 2 Circuit density ( 1/ A ) Power density ( P / A ) 1 Scaling of Depletion Width W V qN D si bi dd a = + 2 ( ) Maximum drain depletion width: or nd For N a N a and V dd V dd / , W D W D / if V dd >> bi . W qN S si bi a = 2 However, the source depletion width, is indep. of V d and only scales as W W / . dd S S Furthermore, the maximum gate depletion width, cales even less than 1/ W kT N n q N dm si a i a 2 4 = ln( / ) 2/22/2010 3 scales even less than 1/ . Generalized Scaling Allows electric field to scale up by ( E E ) while the device dimensions scale down by , e voltage scales by i.e., voltage scales by / ( V ( / ) V ). More flexible than constant-field scaling, ut has reliability and power concerns but has reliability and power concerns. To keep Poissons equation invariant under the p q transformation, ( x , y ) ( x , y )/ and /( / ) within the depletion region: 2 2 ( / ) ( / ) qN N a should be scaled to ( ) N a . 2 2 ( ) ( / ) ( ) ( / ) x y q a si + = 2/22/2010 4 Constant Voltage Scaling Special case of = in generalized scaling: The only mathematically correct scaling as far as 2D Poisson eq. and boundary conditions are concerned. N a 2 N a , kT N n 4 ln( / ) therefore, the maximum depletion width, scales down by . oth the short hannel ll ff W q N dm si a i a 2 = ( ) t ox L W t dm ox + 24 2 3 / Both the short-channel V t roll-off, and the threshold voltage, V W V e t dm bi bi ds = + ( ) V V qN V C t f b B si a B bs ox = + + + 2 2 2 ( ) remain unchanged for constant-voltage scaling....

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