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Computing transit time components from a regional analysis: A practical implementation

Computing transit time components from a regional analysis: A practical implementation. 6 th European HICUM Workshop June 12,13, 2006 - Heilbronn N. Kauffmann. Introduction. The regional approach

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Computing transit time components from a regional analysis: A practical implementation

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  1. Computing transit time components from a regional analysis:A practical implementation 6th European HICUM Workshop June 12,13, 2006 - Heilbronn N. Kauffmann

  2. Introduction • The regional approach • Bipolar transistor divided into neutral (WE, WB , WC) and SCR (WBE , WBC ) regions • Detection of an hole injection layer (WI) in the collector • Decomposition based on DC and quasi-static analysis, in 1D only • Transit time components computed from the above decomposition: TF = TE + TBE + TB + TBC + TC • Importance of the regional approach • Educational purpose, better understanding of bipolar physics • Device optimization • First order model parameters extraction • Practical Test • Database of 1D NPN SiGe simulations • DEVICE Simulator (Drift-Diffusion only) • Regional data computed and checked for all members of the database • Note : 1D simulation only available so far (no 2D/3D effects) and S Node not Available N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  3. WE NE NC NB WC WB NEPI WEPI WTBL Introduction • Simulation database : validation of the regional approach • 2 case studies : • Low / Medium injection : VBE = 0.8 V, VBC =0 V • High injection : VBE = 0.9 V, VBC =0 V • Examples of computed regional data used in these slides: • NEPI = { 1.1016, 2.1016, 5.1016, 1.1017 } N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  4. Outline • Introduction • Regional approach • Examples • Conclusion N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  5. Regional Approach - Definitions • Transit times • TF : Forward transit time (BC Short) • TR : Reverse transit time (BE Short) • TFF : Total transit time from CE Short, = 1 / (2p FT) • Transit time components • TE : Transit time of minority carriers in the neutral emitter • TBE : Transit time of minority carriers in the BE SCR • TB : Transit time of minority carriers in the neutral base and BC SCR (electrons) • TC : Transit time of minority carriers in the neutral collector and BC SCR (holes) • TBC : Recharging time of the BC SCR (transport of majority carriers – electrons) • Charges • Qm : Minority charge Qm= { QN if |QN| < |QP| , QP otherwise } • QC : Uncompensated charge QC = QP - QN N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  6. Regional Approach - Overview QP = SQP(x) N(x), P(x) QN(x), QP(x) DC Analysis NA(x), ND(x) TF = (QmE+QmB+QmC+QcC) / gmF CBE = QcE Forward QUAS-E Analysis gmF, dn(x), dp(x) TE = (QmE-QmEB) / gmF dqN(x), dqP(x) TBE = (QmEB+QmBE) / gmF TB = (QmB-QmBE) / gmF TFF = SdqP / gm FT = 1 / 2p TFF TBC = QcC / gmF TC = QmC / gmF CE Short WB WE, WBE WC, WBC , WI QUAS-B Analysis gm, dn(x), dp(x) dqN(x), dqP(x) Reverse TR = (SQm+QcE) / gmR QUAS-C Analysis gmR, dn(x), dp(x) dqN(x), dqP(x) CBC = QcC N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  7. E E B B C C Regional Approach (Low injection) • Quasi-static analysis: dVE = -1 (dVBE = 1) induces : • Change in charge density : dQp and dQn • Change in current (Forward transconductance): gmF = 7.0259 mS / um2 un • Minority charge dQm = min (dQn , dQp ) , • Uncompensated charge dQC = dQp - dQn N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  8. Regional Approach (Low injection) • Regional analysis : transistor divided in elementary regions [xi xi+1] where dQN>dQP or dQN>dQP • Decomposition in minority (Qm) and uncompensated (QC) carriers • Use of DC metallurgical junctions to separate the 3 regions N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  9. Regional Approach (Low injection) • BE Space-Charge-Region analysis : • From quasi-static analysis[dVE = -1 ] • Limits defined at 50 % of the transferred uncompensated charge 50%(Qp-QpC) 50%(Qp-QpC) QpC QmEB QmBE 50%Qn 50%Qn E B E B N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  10. Regional Approach (Low injection) • BC Space-Charge-Region analysis : • From quasi-static analysis[dVC = -1 ] • Limits defined at 50 % of the transferred uncompensated charge B C B C 0.0729 < 0.0800 : No injection layer N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  11. Regional Approach (Low injection) • Computations : CBE = 9.5 fF /um2 C = dQC / dVBE t = dQ / gmF Transit times Widths N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  12. E E B B C C Regional Approach (High injection) • Quasi-static analysis: dVE = -1 (dVBE = 1) induces : • Change in charge density : dQp and dQn • Change in current (Forward transconductance): gmF = 12.4907 mS / um2 • Minority charge dQm = min (dQn , dQp ) , • Uncompensated charge dQC = dQp - dQn N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  13. Regional Approach (High injection) • Regional analysis : transistor divided in elementary regions [xi xi+1] where dQN>dQP or dQN>dQP • Decomposition in minority (Qm) and uncompensated (QC) carriers • Use of DC metallurgical junctions to separate the 3 regions Injection layer N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  14. Regional Approach (High injection) • BE Space-Charge-Region analysis : • From quasi-static analysis[dVE = -1 ] • Limits defined at 50 % of the transferred uncompensated charge 50%(Qp-QpC) 50%(Qp-QpC) 50%Qn 50%Qn QpC QmEB QmBE E B E B N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  15. Regional Approach (High injection) • BC Space-Charge-Region analysis : • From quasi-static analysis[dVC = -1 ] • Limits defined at 50 % of the transferred uncompensated charge QmBC B C B C 0.4597 > 0.0800 : Injection layer N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  16. Regional Approach (High injection) • Computations : CBE = 7.49 fF /um2 C = dQC / dVBE t = dQ / gmF Transit times Widths N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  17. Outline • Introduction • Regional approach • Examples • Conclusion N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  18. WBE vs. VBE • Plot of WBE vs. VBE in the Off (Left) and Forward (Right) region WBE is also compared to the theoretical width of the CBE capacitance assuming it is a pure plate capacitance. Conclusion : Very good match when operating at low current injection. However, either WBE or CBE are underestimated in the high injection region. N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  19. 0.2 um 0.28 um 0.43 um 0.54 um WBC vs. IC @ VBC=-2 V • Plot of WBC vs. IC for NEPI = { 1.1016, 2.1016, 5.1016, 1.1017 } The simulated DC electric field of the current operating point (red dot) is plotted in the right figure, allowing a crude evaluation of the BC SCR width. WBC appears to be very close to the width of the BC SCR defined by the electric field. The maximum value of WBC is 0.55 mm, close from the theory (WBC≈ WEPI) Note that when the doping concentration of the epitaxy layer is very low, WBC does not enter the buried layer and its value is therefore shorter than what is estimated by the electric field. N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  20. WBC vs. IC @ VBC=-0.5 V • Plot of WBC vs. IC for NEPI = { 1.1016, 2.1016, 5.1016, 1.1017 } B C At VBC = -0.5 V, WBC does not behave as expected by the theory, going down to a value close to 0 for some points or ‘glitches’. In the right figure, the uncompensated carriers of the BC region are plotted while going through one of this glitch (moving red dot) . At some point, the electronic charge in the BC SCR splits, generating two peaks at the boundaries of the epitaxy layer. The splitting of the charge is most likely induced by the Ge concentration at the BC interface. N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  21. B C WBC vs. IC @ VBC=0.4 V • Plot of WBC vs. IC for NEPI = { 1.1016, 2.1016, 5.1016, 1.1017 } B C At VBC = 0.4 V, the BC SCR must vanish as the transfer current increases (quasi-saturation region). As expected, WBC decreases with IC , going down to a small but non-zero value: 30 nm. In the right figure, the uncompensated carriers of the BC region are plotted at the minimum of WBC (red dot) . Both boundaries of the BC SCR are probably not optimal, due to the shape of the peaks N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  22. WI vs. IC • Plot of WI vs. IC for NEPI = 1.1016 (left) & 1.1017 (right) and VBC = {-2V, -1V, -0.5V, 0V, 0.2V, 0.4V, 0.6V} The injection width WI behaves as expected: WI = 0 before the high-injection regime starts and then increases sharply up to a maximum value close to WEPI. When the doping of the epitaxy is high (right figure), the curves at VBC<0 are affected by the avalanche current. The shape of the WI curves is strongly technology dependant, although it is only modeled by the HICUM parameter Ick (The HICUM parameter ahc is not supposed to have a physical meaning) . N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  23. Transit times • Transit times vs. IC @ VBC = -0.5 V (Left) & VBC = 0.4 V(Right) The transit-time components are plotted vs. IC for two different values of VBC and NEPI = 1.1016 cm-3. In both cases, TBC is the major contribution to TF at low injection due to the very wide BC SCR. TBE is entirely responsible of the increase in TF at very low injection but decreases sharply with IC. However, it remains greater than TE in the high injection region leading to a possible overestimation of WBE . As expected TB and TC become predominant at very high injection. N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  24. Outline • Introduction • Regional approach • Examples • Conclusion N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

  25. Conclusion • Regional Approach implementation • Bipolar transistor structure divided in neutral and SCR regions using DC & quasi-static information • Region assignment based on quasi-static data and DC metallurgical boundaries • Definition of SCR Boundaries : 50% of the SCR quasi-static electron / hole charge displaced • So far, no transit time component for BC SCR minority carriers – majority carriers only • Test & qualitative results • Database of 1D TCAD simulations of NPN-SiGe transistors – DEVICE Simulator used (Drift/diffusion) • Very smooth and robust results over the entire database • Results physically consistent : Transit times, region widths behave as expected • Quantitative results • Quasi-static charge distribution probably affected by Ge content leading to more complex peak structures • Results are usually very good but in some cases, they may not be fully optimal. • AC simulations required to validate the variations of the BE and BC capacitances with IC • Perspectives • Extraction of a first order set of HICUM parameters • 2D extension, S node N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006

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