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Single Event Upsets in Digital VLSI Circuits EYES Summer Internship Program 2007 University of New Mexico Vinay Jain Dr. Payman Zarkesh-Ha Final Year Undergraduate Assistant Professor ECE Indian Institute of Technology Kanpur University of New Mexico

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Acknowledgements

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Outline Introduction Soft-Spot Analysis Inverter Model proposed Simulation Results Extension of the Model

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Introduction Origin Soft errors, Single Event Transients (SET) and Single Event Upsets (SEU) Techniques to reduce SET propagation Softness of a node Particle Strike in CMOS Digital VLSI circuits. SET and SEU Origin of Soft errors: cosmic neutrons and α- particles

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Soft-Spot Analysis Timing Masking Factor, T N Tendency of a node to allow noise in particular time window Computed using time delays and sensitive window durations of various gates in the path Logic Masking Factor, L N Likelihood for noise at a node to logically reach the storage element Computed using probability of nodes in the path to acquire certain states Electrical Masking Factor, E N Ability of a node to allow noise propagation with enough strength Computed from the characteristics of Noise Rejection Curves Overall Softness, S N S N = T N *L N *E N

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Noise Rejection Curves Noise Rejection Curves for an inverter and its effects as Load and Size of the inverter is varied

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Inverter Model Proposed Model proposed is- replacement of MOS transistors with constant current sources the DC value of which is the average drain currents of the transistors

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A. Velocity Saturation Effects in short channel MOSFETs υ = μ.E / (1 + E / E C ), E < E C = υ SAT, E > E C where E C = 2 υ SAT / μ V DSATn = V GTn / (1 + V GTn / E Cn. L n ) for short channel (small L n ) saturates to V DSATn = E Cn. L n as V GTn is increased = V GTn, long channel (large L n )

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I DSATn = υ SATn.C ox.W n.( V GTn -V DSATn ) = υ SATn.C ox.W n.(V GTn ) 2 / (V GTn + E Cn. L n ) ~ υ SATn. C ox.W n.(V GTn ) for small channel MOSFETs (small L n ) ~ υ SATn. C ox.W n.(V GTn ) 2 / E Cn. L n for long channel MOSFETs (large L n )

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B. Voltage Transfer Characteristic Voltage Transfer Characteristic for an Inverter (INVx1) Noise can propagate only when input pulse has magnitude greater than V m

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C. Average Current Model I D V DS characteristic for an inverter (INVx1) for gate Voltage greater than V m I N =(I Dn ) avg = I DSATn (1 + λ n (V DD + V m )/ 2) I N = C n *. I DSATn where C n * = 1 + λ n (V DD + V m )/ 2

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I P = (I Dp ) avg = [ (I P1 /2). + {(I P1 +I P2 )/2}.(V DD – V m – ) ] / (V DD – V m ) = I DSATp.(1 + λ p (V DD - V m )/ 2 – /(2.(V DD - V m )) ) Thus, I P = C p *. I DSATp where C p * = 1 + λ p (V DD - V m )/ 2 – /(2.(V DD - V m )) = V DSATp at V G = (V DD + V m )/ 2 I P1 = I DSATp. (1+λ p. ) I P2 = I DSATp. (1+λ p.(V DD - V m ))

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Thus, we have I N = C n *I DSATn & I P = C p *I DSATp where both C n * & C p * are constants and close to unity. We can now calculate T C as the minimum duration required for a noise pulse of height V C volts, to propagate through the inverter as T C = C L.(V DD - V m )/(I N - I P ) with V G = V C The above equation gives a relation between T C and V C as a function of only Gate size (W and L) of p-MOS and n-MOS.

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Simulation Results Noise Rejection Curves comparison for INVx2 (Load = 200fF) Time taken for simulation by matlab = 0.077 sec Time taken for simulation by Tspice = 4.45 sec Mean %error = 4.68% Noise Rejection Curves comparison for INVx1 (Load = 200fF) Time taken for simulation by matlab = 0.074 sec Time taken for simulation by Tspice = 4.48 sec Mean %error = 11.59%

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Noise Rejection Curves comparison for INVx8 (Load = 200fF) Time taken for simulation by matlab = 0.069 sec Time taken for simulation by Tspice = 4.42 sec Mean %error = 17.65% Noise Rejection Curves comparison for INVx4 (Load = 200fF) Time taken for simulation by matlab = 0.074 sec Time taken for simulation by Tspice = 4.61 sec Mean %error = 6.70%

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Extension of the model Modeling of NAND gates for easy computation of Noise Rejection Curves

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Modeling of NOR gates for easy computation of Noise Rejection Curves

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Noise Rejection Curves comparison for NANDx1 (Load = 200fF) Time taken for simulation by matlab = 0.078 sec Time taken for simulation by Tspice = 5.05 sec Mean %error = 30.16% Noise Rejection Curves comparison for NORx1 (Load = 200fF) Time taken for simulation by matlab = 0.076 sec Time taken for simulation by Tspice = 5.09 sec Mean %error = 9.23%

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References [1]C. Zhao, X. Bai, S. Dey, “A scalable soft spot analysis methodology for compound noise effects in nano-meter circuits,” DAC’04, pp. 894-899, June 2004. [2]C. Zhao, S. Dey, “Improving transient error tolerance of digital VLSI circuits using RObustness COmpiler (ROCO),” International Symposium on Quality Electronic Design, ISQED’06 [3]C.G. Sodini, P. Ko, J. Moll, “The effect of high fields on MOS device and circuit performance,” IEEE transactions on Electron Devices, October 1984, pp.1386- 1393 [4] J. M. Rabaey, A. Chandrakasan, B. Nikolic, “Digital Integrated Circuits,” Second edition, 2003

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Thank You

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