1. INTEGRATED CIRCUITS Dr. Esam Yosry Lec. #8

2. VLSI Components in CMOS Technology  Introduction  Resistor Design  Capacitor Design  Inductor Design  MOSFETs (CMOS)  BJTs  BiCMOS

3. Introduction ( Chip Fabrication Cycle)

4. Resistor Design Assume we have a sheet of material of thickness t and width W, then A = W t Next assume that L = W ; which means that we have a square, then the resistance becomes the sheet resistance per square (Ω/□). Material technological parameters

5. Resistor Design The fabrication house supplies the designer with the values of the sheet resistance R □. R □ resistance of one square of the fabricated silicon layer. The engineer designs for the number of squares to be put in series or in parallel to get the needed resistance.

6. Resistor Design Sheet Resistance Counting Squares End Contacts Bends (Corners) RR 3R  R  /3 End contact = 0.3 to 0.4  (0.35  is typical) Corner = 0.65  CC=dxd 2dx2d

7. Resistor Design Example If R □ = 100 Ω/□, and the resistance needed is 200 Ω, then two squares are added in series. If the resistance needed is 50 Ω, then two squares must be put in parallel. n squares in series R= n R □ n squares in parallel R= R □ /n The sheet resistance of the diffused layer from 10 to 200 Ω (100kΩ?!)

8. Equivalent Resistance of End Contacts R= body resistance (nR  ) + end contacts resistance (2x0.35R  ) + corners resistance (n c x0.65R  ) + metal/Si contact resistance R C (usually very low) End contact = 0.35  CC=dxd 2dx2d

9. Resistor’s Accuracy Absolute Accuracy Matching Accuracy *Resistors are usually made from polysilicon * Inaccuracy comes from poly line edge-shift during processing (PR dimensional change, lateral etching, UV diffraction,…etc) *As inaccuracy is almost the same in the two resistors matching accuracy is very high

10. Absolute Accuracy R nominal = n R  =(nL/L) R  = (length/width) R  Include line-edge shift of   L R = (length   L / L   L) R   (length / L   L) R  = (length/L)(1  +  L/L) R  = (length/width) R  )(1  +  L/L) = R nominal (1  +  L/L)  L/L = 1 to 5 % R= nR  n squares L Length>>width

11. Matching Accuracy R1 = R1 nominal (1  +  L/L) R2 = R2 nominal (1  +  L/L) R1 / R2 = R1 nominal / R2 nominal Accurate VLSI designs should depend on resistance ratio rather than on absolute resistance n2 squares R1= n1R  n1 squares R2=n2 R  Matching resistors is feasible in ICs but accurate resistors are hard to obtain

12. How to Increase Absolute Accuracy ? Use rounded corners (since errors on corner squares are high) Use straight lines with metallic interconnects (to eliminate any corner effect) Use dummy features (to reduce over etching - see explaination)

13. Rounded Corners Current density is more uniformly distributed in rounded corners than in square corners Perfectly rounded shapes are sometimes not supported by Si foundries 45 o are accepted by most layout tools and Si foundries

14. Straight Poly Lines with Metallic Interconnects End contacts should have the lowest contact resistance Color Code for Masks: Red: Polysilicon Blue: Metalic interconnect Black: Contact cut

15. Dummy Poly Features The dummy shapes around the main body of the resistor makes the lateral etching equal allover the poly edges. Knowing the etching rate, the etching time is optimized to etch just the necessary volume of poly. Without dummy features With dummy features

16. How to Increase Matching Accuracy? Use pairs with common centroid (to reduce the effect of technological parameter spread also called gradient) R1 R2 dummy

17. Comparison of the Chip Area required for Serpentine Resistor Geometries Versus Multiple Straight Resistors

18. Capacitors Between two polys C nominal =  A / T ox Poly I Poly II Oxide dielectric const.,  r = 4 Upper poly II area Oxide thickness between poly I and Poly II

19. Capacitor’s Accuracy Absolute Accuracy Matching Accuracy * Inaccuracy comes from poly line edge-shift during processing (PR dimensional change, lateral etching, UV diffraction,…etc) *As inaccuracy is almost the same in the two caps matching accuracy is very high if of the same perimeter-to-area ratio

20. Absolute Accuracy A nominal = a x b (dashed line) A = A nominal -  x P  is the edge-shift P is the nominal perimeter = 2(a + b) Absolute Cap Error =  C/C=  A/A=-  x P/A (A is nominal) Error is proportional to the perimeter-to-area ratio Never use large perimeter features (like zigzags) a b

21. Matching Accuracy Cap ratio Error =  C1/  C2 = [C1 x  x P1/A1]/ [C2 x  x P2/A2] For matched caps C1=C2 (nominal and real values) P1/A1 = P2/A2 makes  C1=  C2 for matched real values

22. On Chip Inductors Square (hollow) Octagonal (hollow) Series resistance R s Parasitic cap C s Substrate Conductivity Losses R p Q=3 to 10 at 1 GHz Equivalent Circuit

23. Equivalent Circuit Elements C s = cap to substrate Substrate eddy current loss Substrate displacement current loss RpRp R s = series resistance

24. Substrate Resistivity Effect No substrate current loss Low cap (series caps) High self resonance frequency No substrate current loss Large cap Low inductance

25. Multi-Layer Inductors Series resistance increases linearly with number of turns while L increases quadratically, hence Q is improved L up to 60 nH

26. Bond Wire Inductors 1 nH / mm L = 3 to 4 nH, Q = 40 to 50 but poor reproducibility High pad and pin caps reduces the self-resonance frequency Not suitable for mass production

27. 3-D Inductors High L (up to 15 nH). High Q (30 - 50) Good reproducibility Large pad caps

28. Thanks Many thanks to Prof. Hany Fikry and Prof Wael Fikry for their useful materials that help me to prepare this presentation.