1. STMicroelectronics Determination of the collector resistance R CX of bipolar transistor N. Kauffmann, C. Raya, F. Pourchon, S. Ortolland, D. Celi 5 th European HICUM Workshop

2. N. Kauffmann - 5 th European HICUM Workshop 2/23 6/6/2005 Outline HICUM Collector Resistance R CX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion

3. N. Kauffmann - 5 th European HICUM Workshop 3/23 6/6/2005 HICUM main parameters Emitter (N+) Buried layer (N+) Epitaxy (N) Base (P+) Substrate (P) Sinker (N+) PWELL (P+) BCES C SU R SU Q JS S’S’ I SC Q DS RERE RCXRCX RBXRBX C BCX 1 C E0 X B’’ R BI C RBI I BET I BEP I BCI Q JEP C BCX2 TJTJ C TH R TH P I AVL C’ E’ ITIT B’ Q DC I BCI Q JCI I BEI Q JEI

4. N. Kauffmann - 5 th European HICUM Workshop 4/23 6/6/2005 R CX : HICUM External Collector Resistance R CX is a 3D resistance, which includes -Sinker and Contact resistance -Buried layer resistance only (but not epi resistance) R CX is an important parameter: -Set the internal Collector voltage (C’ node) -Affect the extraction of the highly critical  F and all high injection model parameters Main issues: -Difficult to extract. No efficient method so far -Poor R CX extraction makes HICUM model not scalable Objective: -Determine a scalable expression for R CX

5. N. Kauffmann - 5 th European HICUM Workshop 5/23 6/6/2005 Proposed solution for a scalable R CX C R SK R BL E R CX is divided in two components: R CX = R BL + R SK -R SK (sinker + contact resistance) is extracted using test structures -R BL (buried layer resistance) is extracted / obtained from analytical formulas The buried layer sheet resistance is uniform: R BL = r BL R sq -R sq (buried layer sheet resistance) is extracted from test structures -r BL is computed analytically, function of the transistor geometry V = Cst Buried layer (top view)Transistor (cross section) ITIT ITIT

6. N. Kauffmann - 5 th European HICUM Workshop 6/23 6/6/2005 Outline HICUM Collector Resistance R CX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion

7. N. Kauffmann - 5 th European HICUM Workshop 7/23 6/6/2005 Test structure: Buried layer with 4 sinker wells ( A B C D ) of dimensions L SK × W SK -R BL = V BC / I AD -R SK = [ V BC /I BC – (1 – W SK / W BC ) × R BL ] / 2 New test structure will use real transistors with 2 separate collector contacts R SK - Sinker Resistance D R SK R BL Test structure (top view)Test structure (cross section) A BCD R SK W BC L SK ABC W SK R SK L BL

8. N. Kauffmann - 5 th European HICUM Workshop 8/23 6/6/2005 Multi-geometry extraction -R BL = 22.24 × W BC / (L BL - 1.00)R sq = 22.4  -R SK = 19.39 / [W SK × (L SK + 0.28)]  SK = 19.39   m 2 Fit requires effective Sinker and buried layer dimensions R SK - Sinker Resistance 1 / R BL L BL = L SK + 0.8  m L SK 1 / R SK

9. N. Kauffmann - 5 th European HICUM Workshop 9/23 6/6/2005 Outline HICUM Collector Resistance R CX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion

10. N. Kauffmann - 5 th European HICUM Workshop 10/23 6/6/2005 R BL - Buried Layer Resistance 7 contact configurations investigated, any number N E of emitter stripes Emitter stripes parallel to contacts Emitter stripes perpendicular to contacts Surrounding and U-Shaped collectors

11. N. Kauffmann - 5 th European HICUM Workshop 11/23 6/6/2005 R BL - Principle and main assumptions: Main assumptions: -The collector current I C is uniformly distributed among the N E emitter stripes -The current density is assumed to be constant within each stripe -Each sinker is replaced by a reference plan of constant voltage -The buried layer sheet resistance is assumed to be constant Power dissipation approach: -W BL, L BL :Buried layer dimensions -P C : Power dissipated in the buried layer -V(x,y)Voltage within the buried layer -V(x,y) is obtained by solving Poisson Equation in the Fourier Space

12. N. Kauffmann - 5 th European HICUM Workshop 12/23 6/6/2005 R BL - Formula (1/3) Example : Buried layer with 2 perpendicular contacts (blue) H m and H n are the Fourier coefficients of H(x) and H(y) Equation and solution for V(x,y) N E = 3 Stripes W E, L E = 0.2×0.8 um 2 H X (x) H Y (y)

13. N. Kauffmann - 5 th European HICUM Workshop 13/23 6/6/2005 R BL - Formula (2/3) Example : Buried layer with 2 perpendicular contacts (blue) G m and G n are the Fourier coefficients of G(x) and G(y) Solution for R BL N E = 3 Stripes W E, L E = 0.2×0.8 um 2 G Y (y) G X (x)

14. N. Kauffmann - 5 th European HICUM Workshop 14/23 6/6/2005 R BL - Formula (3/3) Example : Buried layer with 2 perpendicular contacts (blue) N E = 3 Stripes W E, L E = 0.2×0.8 um 2 W X2 WXWX WIWI L1L1 L 1 / W BL (L E / W BL )/12 rXrX rYrY L BL W BL

15. N. Kauffmann - 5 th European HICUM Workshop 15/23 6/6/2005 R BL – Comparison with numerical results M. Schröter: DEVICE, User’s Guide to version 1.8 – July 2004 # termsR BL / RsqError (%) 00.21260 10.21260 20.1426.96 50.1395.08 100.1330.72 250.1320.08 500.1320 # termsR BL / RsqError (%) 00.2230.4 10.2230.4 20.2220.03 50.2220.02 100.2220 250.2220 500.2220 W E, L E = 0.2×0.8 um 2 W E, L E = 0.2×10 um 2 N E = 3

16. N. Kauffmann - 5 th European HICUM Workshop 16/23 6/6/2005 R BL – Results (Potential V) N E = 3 Stripes W E, L E = 0.2×0.8 um 2 N E = 3 Stripes W E, L E = 0.2×10 um 2 2 perpendicular contacts

17. N. Kauffmann - 5 th European HICUM Workshop 17/23 6/6/2005 R BL – Results (Current) N E = 3 Stripes W E, L E = 0.2×0.8 um 2 N E = 3 Stripes W E, L E = 0.2×10 um 2 2 perpendicular contacts

18. N. Kauffmann - 5 th European HICUM Workshop 18/23 6/6/2005 R BL – Close-form approximations Three approximations of the Kernel K: [Complex, Basic and intermediate] vs. exact Fourier series Kernel Simplification: 3 levels of approximation: Basic ( W BL >> L BL only ) Interm. ( W BL >> L BL & W BL << L BL ) Complex ( 1 st, 2 nd term exact )

19. N. Kauffmann - 5 th European HICUM Workshop 19/23 6/6/2005 Outline HICUM Collector Resistance R CX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion

20. N. Kauffmann - 5 th European HICUM Workshop 20/23 6/6/2005 R BL : Matlab Form Contact configuration Input geometry R BL from Fourier Display Features DEVICE Main Window

21. N. Kauffmann - 5 th European HICUM Workshop 21/23 6/6/2005 R SK, R sq : ICCAP Toolkit Load Files Single extraction Process Data Multi-extraction Statistics

22. N. Kauffmann - 5 th European HICUM Workshop 22/23 6/6/2005 Outline HICUM Collector Resistance R CX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion

23. N. Kauffmann - 5 th European HICUM Workshop 23/23 6/6/2005 Conclusion Scalable R CX available using both extraction and analytical methods -R SK R sq, resistances are extracted from test structure -R BL computed from analytical formulas for 7 contact configurations Practical implementation with Matlab and ICCAP -New, more accurate test structures coming soon -Formulas to be implemented in model libraries for full extraction and validation Still, many assumptions need to be carefully checked: -3D R CX divided into 2D R BL and R SK -Approximated boundary conditions with constant voltage -Uniform current injection between stripes, spatially uniform current -Power dissipation approach: effect of current crowding