Determination of the collector resistance RCX of bipolar
Determination of the collector resistance RCX of bipolar transistor 5 th European HICUM Workshop N. Kauffmann, C. Raya, F. Pourchon, S. Ortolland, D. Celi STMicroelectronics
Outline HICUM Collector Resistance RCX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 2
HICUM main parameters B E C S RE Emitter (N+) RBX B’’ QJEP IBEP Q CBCX 2 IBCI B’ DS Epitaxy (N) CBCX 1 IT QDC IAVL C’ Buried layer (N+) ISC QJS DTJ S’ CTH CRBI IBEI QJEI IBCI QJCI Base (P+) ISC P QDC RBI PWELL (P+) IBET E’ Sinker (N+) CE 0 X Substrate (P) RCX RSU RTH CSU 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 3
RCX: HICUM External Collector Resistance RCX is a 3 D 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 t. F 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 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 4
Proposed solution for a scalable 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 = r. BL Rsq - Rsq (buried layer sheet resistance) is extracted from test structures - r. BL is computed analytically, function of the transistor geometry E C V = Cst RSK IT IT RBL Buried layer (top view) 6/6/2005 Transistor (cross section) N. Kauffmann - 5 th European HICUM Workshop V = Cst 5
Outline HICUM Collector Resistance RCX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 6
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 A A B C B D RSK LBL WBC LSK Test structure (top view) 6/6/2005 D C WSK RSK RBL Test structure (cross section) N. Kauffmann - 5 th European HICUM Workshop 7
RSK - Sinker Resistance Multi-geometry extraction - RBL = 22. 24 × WBC / (LBL - 1. 00) - RSK = 19. 39 / [WSK × (LSK + 0. 28)] Rsq r. SK = 22. 4 W = 19. 39 W mm 2 1 / RBL 1 / RSK Fit requires effective Sinker and buried layer dimensions LBL = LSK + 0. 8 mm 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop LSK 8
Outline HICUM Collector Resistance RCX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 9
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 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 10
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 : - PC : - V(x, y) Buried layer dimensions Power dissipated in the buried layer Voltage within the buried layer - V(x, y) is obtained by solving Poisson Equation in the Fourier Space 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 11
RBL - Formula (1/3) HX(x) Example : Buried layer with 2 perpendicular contacts (blue) NE = 3 Stripes WE, LE = 0. 2× 0. 8 um 2 HY(y) Equation and solution for V(x, y) Hm and Hn are the Fourier coefficients of H(x) and H(y) 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 12
RBL - Formula (2/3) GX(x) Example : Buried layer with 2 perpendicular contacts (blue) NE = 3 Stripes WE, LE = 0. 2× 0. 8 um 2 GY(y) Solution for RBL Gm and Gn are the Fourier coefficients of G(x) and G(y) 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 13
RBL - Formula (3/3) r. Y Example : Buried layer with 2 perpendicular contacts (blue) NE = 3 Stripes WBL WX L 1/ WBL (LE/ WBL)/12 WE, LE = 0. 2× 0. 8 um 2 WI WX 2 L 1/ WBL L 1 LBL r. X 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 14
RBL – Comparison with numerical results WE, LE = 0. 2× 0. 8 um 2 NE = 3 # terms RBL/ Rsq Error (%) 0 0. 212 60 1 0. 212 60 2 0. 142 6. 96 5 0. 139 5. 08 10 0. 133 0. 72 25 0. 132 0. 08 50 0. 132 0 WE, LE = 0. 2× 10 um 2 NE = 3 # terms RBL/ Rsq Error (%) 0 0. 223 0. 4 1 0. 223 0. 4 2 0. 222 0. 03 5 0. 222 0. 02 10 0. 222 0 25 0. 222 0 50 0. 222 0 M. Schröter: DEVICE, User’s Guide to version 1. 8 – July 2004 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 15
RBL – Results (Potential V) NE = 3 Stripes WE, LE = 0. 2× 0. 8 um 2 2 perpendicular contacts NE = 3 Stripes WE, LE = 0. 2× 10 um 2 2 perpendicular contacts 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 16
RBL – Results (Current) NE = 3 Stripes WE, LE = 0. 2× 0. 8 um 2 2 perpendicular contacts NE = 3 Stripes WE, LE = 0. 2× 10 um 2 2 perpendicular contacts 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 17
RBL – Close-form approximations Kernel Simplification: 3 levels of approximation: Basic (WBL >> LBL only ) Interm. (WBL >> LBL & WBL << LBL) Complex (1 st, 2 nd term exact) Three approximations of the Kernel K: [Complex, Basic and intermediate] vs. exact Fourier series 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 18
Outline HICUM Collector Resistance RCX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 19
RBL : Matlab Form Contact configuration Input geometry Main Window RBL from Fourier Display Features DEVICE 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 20
RSK , Rsq : ICCAP Toolkit Load Files Single extraction Process Data Multi-extraction Statistics 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 21
Outline HICUM Collector Resistance RCX Sinker and contact resistance Buried layer resistance Practical Implementation Conclusion 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 22
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 libraries for full extraction and validation Still, many assumptions need to be carefully checked: - 3 D RCX divided into 2 D RBL and RSK - Approximated boundary conditions with constant voltage - Uniform current injection between stripes, spatially uniform current - Power dissipation approach: effect of current crowding 6/6/2005 N. Kauffmann - 5 th European HICUM Workshop 23
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