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Determination of the collector resistance R CX of bipolar transistor

Determination of the collector resistance R CX of bipolar transistor. 5 th European HICUM Workshop. N. Kauffmann, C. Raya, F. Pourchon, S. Ortolland, D. Celi. Outline. HICUM Collector Resistance R CX Sinker and contact resistance Buried layer resistance Practical Implementation

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Determination of the collector resistance R CX of bipolar transistor

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

  2. Outline • HICUM Collector Resistance RCX • Sinker and contact resistance • Buried layer resistance • Practical Implementation • Conclusion N. Kauffmann - 5th European HICUM Workshop

  3. RE CE0X E’ IBET QDC RBI RBX IT B’’ QJEP IBEP B’ IBEI QJEI CBCX2 IBCI IBCI QJCI QDS QDC CRBI CBCX1 IAVL C’ ISC ISC QJS RCX DTJ RSU S’ CTH RTH P CSU HICUM main parameters B E C S Emitter (N+) Sinker (N+) PWELL (P+) Base (P+) Epitaxy (N) Buried layer (N+) Substrate (P) N. Kauffmann - 5th European HICUM Workshop

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

  5. Proposed solution for a scalable RCX • RCX is divided in two components: RCX = RBL+ RSK • RSK(sinker + contact resistance) is extracted using test structures • RBL(buried layer resistance) is extracted / obtained from analytical formulas • The buried layer sheet resistance is uniform: RBL = rBL Rsq • Rsq(buried layer sheet resistance) is extracted from test structures • rBL is computed analytically, function of the transistor geometry C E V = Cst RSK IT IT RBL V = Cst Buried layer (top view) Transistor (cross section) N. Kauffmann - 5th European HICUM Workshop

  6. Outline • HICUM Collector Resistance RCX • Sinker and contact resistance • Buried layer resistance • Practical Implementation • Conclusion N. Kauffmann - 5th European HICUM Workshop

  7. RSK - Sinker Resistance • Test structure: Buried layer with 4 sinker wells ( A B C D ) of dimensions LSK× WSK • RBL = VBC / IAD • RSK= [ VBC/IBC –(1– WSK/ WBC) × RBL] / 2 • New test structure will use real transistors with 2 separate collector contacts D A B C B C D A RSK RSK RSK RSK WBC LBL LSK RBL WSK Test structure (top view) Test structure (cross section) N. Kauffmann - 5th European HICUM Workshop

  8. RSK - Sinker Resistance • Multi-geometry extraction • RBL = 22.24 × WBC / (LBL - 1.00) Rsq = 22.4 W • RSK= 19.39 / [WSK × (LSK + 0.28)] rSK = 19.39Wmm2 • Fit requires effective Sinker and buried layer dimensions 1 / RSK 1 / RBL LBL = LSK + 0.8 mm LSK N. Kauffmann - 5th European HICUM Workshop

  9. Outline • HICUM Collector Resistance RCX • Sinker and contact resistance • Buried layer resistance • Practical Implementation • Conclusion N. Kauffmann - 5th European HICUM Workshop

  10. RBL - Buried Layer Resistance • 7 contact configurations investigated, any number NE of emitter stripes • Emitter stripes parallel to contacts • Emitter stripes perpendicular to contacts • Surrounding and U-Shaped collectors N. Kauffmann - 5th European HICUM Workshop

  11. RBL - Principle and main assumptions: • Main assumptions: • The collector current IC is uniformly distributed among the NE 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: • WBL, LBL : Buried layer dimensions • PC : 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 N. Kauffmann - 5th European HICUM Workshop

  12. RBL - Formula (1/3) HX(x) • Example : Buried layer with 2 perpendicular contacts (blue) NE = 3 Stripes WE, LE = 0.2×0.8 um2 HY(y) • Equation and solution for V(x,y) Hm and Hn are the Fourier coefficients of H(x) and H(y) N. Kauffmann - 5th European HICUM Workshop

  13. RBL - Formula (2/3) GX(x) • Example : Buried layer with 2 perpendicular contacts (blue) NE = 3 Stripes WE, LE = 0.2×0.8 um2 GY(y) • Solution for RBL Gm and Gn are the Fourier coefficients of G(x) and G(y) N. Kauffmann - 5th European HICUM Workshop

  14. RBL - Formula (3/3) rY • Example : Buried layer with 2 perpendicular contacts (blue) L1/ WBL NE = 3 Stripes WBL (LE/ WBL)/12 WE, LE = 0.2×0.8 um2 WI WX WX2 L1/ WBL LBL L1 rX N. Kauffmann - 5th European HICUM Workshop

  15. RBL – Comparison with numerical results NE = 3 WE, LE = 0.2×0.8 um2 NE = 3 WE, LE = 0.2×10 um2 M. Schröter: DEVICE, User’s Guide to version 1.8 – July 2004 N. Kauffmann - 5th European HICUM Workshop

  16. RBL – Results (Potential V) NE = 3 Stripes WE, LE = 0.2×0.8 um2 2 perpendicular contacts NE = 3 Stripes WE, LE = 0.2×10 um2 2 perpendicular contacts N. Kauffmann - 5th European HICUM Workshop

  17. RBL – Results (Current) NE = 3 Stripes WE, LE = 0.2×0.8 um2 2 perpendicular contacts NE = 3 Stripes WE, LE = 0.2×10 um2 2 perpendicular contacts N. Kauffmann - 5th European HICUM Workshop

  18. RBL – Close-form approximations • Kernel Simplification: • 3 levels of approximation: Basic (WBL >> LBL only ) Interm. (WBL >> LBL &WBL << LBL) Complex (1st, 2nd term exact) Three approximations of the Kernel K: [Complex, Basic and intermediate] vs. exact Fourier series N. Kauffmann - 5th European HICUM Workshop

  19. Outline • HICUM Collector Resistance RCX • Sinker and contact resistance • Buried layer resistance • Practical Implementation • Conclusion N. Kauffmann - 5th European HICUM Workshop

  20. RBL : Matlab Form Contact configuration Input geometry RBL from Fourier Main Window Display Features DEVICE N. Kauffmann - 5th European HICUM Workshop

  21. RSK , Rsq : ICCAP Toolkit Load Files Single extraction Process Data Multi-extraction Statistics N. Kauffmann - 5th European HICUM Workshop

  22. Outline • HICUM Collector Resistance RCX • Sinker and contact resistance • Buried layer resistance • Practical Implementation • Conclusion N. Kauffmann - 5th European HICUM Workshop

  23. Conclusion • Scalable RCX available using both extraction and analytical methods • RSK Rsq, resistances are extracted from test structure • RBL 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 librariesfor full extraction and validation • Still, many assumptions need to be carefully checked: • 3D RCX divided into 2D RBL and RSK • Approximated boundary conditions with constant voltage • Uniform current injection between stripes, spatially uniform current • Power dissipation approach: effect of current crowding N. Kauffmann - 5th European HICUM Workshop

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