EE 241 Class Project Substrate Noise Current Injected by Digital IP Cores Stefano Zanella Mentor: Luca Carloni

2 Outline n Introduction n Background n Noise Spectrum n Standard Cells Characterization n Circuit Characterization n Summary

3 Introduction IP2 IP1 Substrate Isub n Digital IPs may inject considerable amount of noise into analog IPs through the common substrate u Example: fast switching digital IP connected to an antenna n Process variations are important in DSM n No tools for circuit level injection analysis under process variations are available today

4 Principles of substrate Injection n Impact Ionization n Capacitive Coupling n Gate Induced Drain Leakage n Photon Induced Current (PIC) n Diode Leakage Current V PIC Hot e- Cell signature GIDL

5 State of the Art - SUBWAVE n Only one methodology: SUBWAVE [Charbon et al, TCAD 3/99] n Hypotheses u 2 signatures per gate (H-L, L-H) u No dependence on load and input slope n No explicit formulae for the spectrum n No statistical variations

6 Why the Process Variations n Identically designed devices always behave in a different way n Causes: u Systematic variations: F Mask misalignments F Optical aberrations u Random Variations F Diffusion lengths F Doping profiles

7 Noise Spectrum n Allow to check the influence on the analog part n Depends upon: u process variations F two identical circuits have slightly different spectra u input sequence F might be necessary to average different inputs n The substrate might behave as a filter!

8 n Hypotheses: u Linear substrate F Can be modeled as filter u Equipotential substrate in the noise source (not really necessary) => cell signatures sum up n Spectrum: u Fourier transform of the injected current u Can be estimated with moment matching techniques Spectrum Evaluation

9 How to Estimate I B (f) n Mac-Laurin: n It can be proved that a n can be calculated starting from the moments n moments? n Thus, if we are able to calculate m n we can derive the

10 Circuit Characterization t IBIB i B,1 i B,2 i B,3 n Each transition must be characterized n Each cell injects current during each transition.

11 How to calculate I B Event driven simulation n The n-th moment of I B is linear combination of the first n moments of the i B n Only the moments of each transition need to be stored Switching activity

12 How to calculate I B Event driven simulation Std. cells models (i B moments) Moments of I B n The n-th moment of I B is linear combination of the first n moments of the i B n Only the moments of each transition need to be stored

13 Signature Characterization time (ns) Injected current (  A) Approximation of the Substrate Current Injected by a Multiplexer Approx. SPICE n Multiplexer 2:1 n Moments derived from SPICE simulation n 15 moments n Very good approximation n Must improve convergence

14 Does it work? n Convergence: u Time domain: easy prove of uniform convergence of i B (t) if Legendre Orthogonal Polynomials are used u Does I B (t) converge? F Yes, Uniformly. n Error: u Parseval Theorem: rms error is the same for I B (t) and I B (f) -> easy to prove u Bounded? Likely to be….

15 Process Variations n No variations: moments are numbers n Variations: moments are random variables  Must express m n as function of the process (electrical) parameters (V TH, T OX,  L,  W …) u Must avoid monte-carlo methods (time consuming) => use RSM n The spectrum can be expressed as function of the process parameters

16 Ongoing Work n Characterization of a counter: u 50 gates u 350 nm technology n Manually ran event-driven simulation (no standard cell models are yet available) n Manually characterizing the injection of the cells (automatic tool to be installed soon). No process parameters yet taken into account n Implementing in Matlab all the necessary routines

17 Future Work n Application to a relevant number of standard benchmarks n Bound the error n Statistically characterize the process variations at cell level n Statistically characterize the spectrum (explicit formula) => allows easy design optimization n Extend the methodology to non equipotential substrates (use multi-port networks theory)

18 Summary n An analytical technique to derive substrate injected current spectrum has been developed n No explicit storage of signatures is required n Process variations effects will be taken into account n Defined a cell/circuit level characterization technique n Characterization more expensive than usual n Provide a fast information to the designers n Better IP reuse enabled