A Self Consistent Joint Extraction of t 0 and RCX for HICUM

1. A Self Consistent Joint Extraction of t0 and RCX for HICUM 6th European Hicum Workshop 12-13 June 05, ATMEL in Heilbronn Zoltan Huszka austriamicrosystems AG

2. Purpose • Proposal for a new t0 & RCX extraction • Demonstration of the results • Lowlights and Highlights

3. Outline • Former RCX extraction methods • Overview of the existing t0extraction methods • Theory of joint extraction for both parameters • Extraction procedure • Extraction results • Summary

4. A Few Known RCX Extraction Methods • Forced beta (Logan_1971) • DIsub (Berkner_1994) • Solution of Parasitic pnp (Paasschens_2001) • Special test structures (Schroeter_1991) • Modified forced beta (Wu_2004) • 2D numerical calculations (Kaufmann_ 2005)

5. t0 Extraction Methods • Corrected Inverse FT vs. VT/Ic (Schroeter_1991) • Refined Inverse FT vs. VT/Ic (Ardouin_2001) • Inverse FT vs. 1/gm (Malorny_2002) • 3-variate linear regression (Fregonese_2006)

6. Existing Concept of t0 Extraction t0 is the zero intercept for infinite Ic • Key model parameters must be formerly known • Correct magnitude of RCX is critical • Internal collector time constant is omitted • The formula is approximative only

7. A Novel Concept • Extract intrinsic FT of block#1 with nonzero rci • Apply result to HICUM

8. Block Transformations (1) Unilateralized (UL) two-port parameters: Consequently: With : Dividing :

9. Block Transformations (2) Starting from the outside: RELATION OF RAW AND INTRINSIC UL BETA The intrinsic transistor has a single pole ac beta:

10. Determining RCX RCX can be expressed from the first equation Unknown in numerator will be obtained by regression

11. Determining the Time Constants (1) Canceling RCX yields the regression equation with variables The zero intercept allows for the computation of RCX

12. Determining the Time Constants (2) can be computed by deembedding raw data with the known RCX. The coefficients with the time constants are obtained by regression from Quadratic for and then regression povides t0 gives correct transit time in full bias range

13. Example: main regression The high linearity is confirming the concept

14. Example: Averaging RCX RCX of a short (Le=0.8um) and a long (Le=24um) device

15. Example: RCX from parasitic PNP A perfect fit to measurements

16. Example: RF and DC Comparision Only a part of RCX is in the Isub current path The difference may be particularly critical for HICUM!

17. Example: Time constants (1) Transit time of unilateralized Block#3

18. Example: Time constants (2) Intrinsic and collector time constants from quadratic

19. Example: Extraction of t0 Raw and intrinsic low current transit times

20. Lowlights • The method mines data from the full depth of the model: high quality low noise RF data is reqired • The quadratic may provide complex roots at higher biases: not critical since a few points are enough for t0 regression

21. Highlights • The method is unprecedented as to jointly extract RBX with the intrinsic low-bias time constant • No former model parameters are needed • Self-consistency is insured by using one single data • HICUM preference is met by extracting critical parameters from RF measurements • The firm theoretical basis may provide confidence in customers and modeling engineers Correct transit times in full bias range from one single raw s-parameter set!

22. Suggestion to the Model Developers • Revive the discussion of the low-bias collector time constant in the model documentation • Advise a proper way how to merge the collector time-constant in the present model structure

23. Acknowledgement The author is grateful to Dr. Bishwanat Senapati for the careful measurement of the samples and designing the setup & codes for a noiseless substrate current acquisition.