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

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn  The regional approach Bipolar transistor divided into neutral (W E, W B, W C ) and SCR (W BE, W BC ) regions Detection of an hole injection layer (W I ) in the collector Decomposition based on DC and quasi-static analysis, in 1D only Transit time components computed from the above decomposition: T F = T E + T BE + T B + T BC + T C  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 Introduction

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Introduction WCWC W EPI W TBL WBWB WEWE NCNC N EPI NBNB NENE Region x i (nm)x i+1 (nm)N (cm -3 ) E B C-EPI C-TBL C-BL  Simulation database : validation of the regional approach 2 case studies :  Low / Medium injection : V BE = 0.8 V, V BC = 0 V  High injection : V BE = 0.9 V, V BC = 0 V Examples of computed regional data used in these slides: N EPI = { , , , }

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

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Regional Approach - Definitions 1.Transit times T F : Forward transit time (BC Short) T R : Reverse transit time (BE Short) T FF : Total transit time from CE Short, = 1 / (2  F T ) 2.Transit time components T E : Transit time of minority carriers in the neutral emitter T BE : Transit time of minority carriers in the BE SCR T B : Transit time of minority carriers in the neutral base and BC SCR (electrons) T C : Transit time of minority carriers in the neutral collector and BC SCR (holes) T BC : Recharging time of the BC SCR (transport of majority carriers – electrons) 3.Charges Q m : Minority charge Q m = { Q N if |Q N | < |Q P |, Q P otherwise } Q C : Uncompensated charge Q C = Q P - Q N

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Regional Approach - Overview DC Analysis QUAS-E Analysis gm F, dn(x), dp(x) QUAS-B Analysis gm, dn(x), dp(x) QUAS-C Analysis gm R, dn(x), dp(x) Regional analysis : Qm = min(qp,qn), Qc = (qp-qn) EX MIN X MAX Qm E Qc E BX MIN X MAX Qm B Qc B CX MIN X MAX Qm C Qc C Regional analysis : Qm = min(qp,qn), Qc = (qp-qn) EX MIN X MAX Qm E Qc E BX MIN X MAX Qm B Qc B CX MIN X MAX Qm C Qc C BE SCR analysis : BEX MIN X MAX Qm EB Qm BE BC SCR analysis : BCX MIN X MAX Qm BC Qm CB W E, W BE W C, W BC, W I WBWB T F = (Qm E +Qm B +Qm C +Qc C ) / gm F T E = (Qm E -Qm EB ) / gm F T BE = (Qm EB +Qm BE ) / gm F T BC = Qc C / gm F T B = (Qm B -Qm BE ) / gm F T C = Qm C / gm F C BE = Qc E C BC = Qc C T R = (  Qm+Qc E ) / gm R dq N (x), dq P (x) T FF =  dq P / gm F T = 1 / 2  T FF N A (x), N D (x) N(x), P(x)Q N (x), Q P (x) Q P =  Q P (x) Forward Reverse CE Short

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Quasi-static analysis: dV E = -1 (dV BE = 1 ) induces : Change in charge density : dQ p and dQ n Change in current (Forward transconductance) : gm F = mS / um 2 Regional Approach (Low injection) Minority charge dQ m = min (dQ n, dQ p ), Uncompensated charge dQ C = dQ p - dQ n EBCEBC un

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Regional analysis : transistor divided in elementary regions [x i x i+1 ] where dQ N >dQ P or dQ N >dQ P Decomposition in minority (Q m ) and uncompensated (Q C ) carriers Use of DC metallurgical junctions to separate the 3 regions Regional Approach (Low injection) Region Maj x i (um)x i+1 (um)dQ p (fC)dQ n (fC)dQ m (fC)dQ C (fC) 1 (E)N (B)P (C)N (C)N

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn BE Space-Charge-Region analysis : From quasi-static analysis [ dV E = -1 ] Limits defined at 50 % of the transferred uncompensated charge Regional Approach (Low injection) Region x i (um)x i+1 (um)Qm EB (fC)Qm BE (fC) BE %Q n 50%(Q p -Q pC ) 50%Q n Q pC 50%(Q p -Q pC ) Qm BE Qm EB EB EB

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn BC Space-Charge-Region analysis : From quasi-static analysis [ dV C = -1 ] Limits defined at 50 % of the transferred uncompensated charge Regional Approach (Low injection) Region x i (um)x i+1 (um)Qm BC (fC)Qm CB (fC) BC < : No injection layer BC BC

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Regional Approach (Low injection) C = dQ C / dV BE  = dQ / gm F 5.Computations : Region x i (um) x i+1 (um)  Q m (fC)  Q C (fC) E B C Region x i (um)x i+1 (um)Qm EB (fC)Qm BE (fC) BE Region x i (um)x i+1 (um)Qm BC (fC)Qm CB (fC) BC Region x i (um)x i+1 (um)  Q m (fC)  Q C (fC)  ps  E BE B BC C Total W E (um)W BE (um)W B (um)W I (um)W BC (um)W C (um) Transit times Widths C BE = 9.5 fF /um 2

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Quasi-static analysis: dV E = -1 (dV BE = 1 ) induces : Change in charge density : dQ p and dQ n Change in current (Forward transconductance) : gm F = mS / um 2 Regional Approach (High injection) Minority charge dQ m = min (dQ n, dQ p ), Uncompensated charge dQ C = dQ p - dQ n EBCEBC

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Regional analysis : transistor divided in elementary regions [x i x i+1 ] where dQ N >dQ P or dQ N >dQ P Decomposition in minority (Q m ) and uncompensated (Q C ) carriers Use of DC metallurgical junctions to separate the 3 regions Regional Approach (High injection) Region Maj x i (um)x i+1 (um)dQ p (fC)dQ n (fC)dQ m (fC)dQ C (fC) 1 (E)N (B)P (B)N (B)P (C)N (C)P (C)N (C)N (C)N Injection layer

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn BE Space-Charge-Region analysis : From quasi-static analysis [ dV E = -1 ] Limits defined at 50 % of the transferred uncompensated charge Regional Approach (High injection) Region x i (um)x i+1 (um)Qm EB (fC)Qm BE (fC) BE %Q n 50%(Q p -Q pC ) 50%Q n Q pC 50%(Q p -Q pC ) Qm BE Qm EB EB EB

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn BC Space-Charge-Region analysis : From quasi-static analysis [ dV C = -1 ] Limits defined at 50 % of the transferred uncompensated charge Regional Approach (High injection) Region x i (um)x i+1 (um)Qm BC (fC) BC > : Injection layer BC BC Qm BC

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Regional Approach (High injection) C = dQ C / dV BE  = dQ / gm F 5.Computations : Region x i (um) x i+1 (um)  Q m (fC)  Q C (fC) E B C Region x i (um)x i+1 (um)Qm EB (fC)Qm BE (fC) BE Region x i (um)x i+1 (um)Qm BC (fC) BC Region x i (um)x i+1 (um)  Q m (fC)  Q C (fC)  ps  E BE B BC C+WI Total W E (um)W BE (um)W B (um)W I (um)W BC (um)W C (um) Transit times Widths C BE = 7.49 fF /um 2

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

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

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn um0.28 um0.43 um W BC vs. I V BC = -2 V Plot of W BC vs. I C for N EPI = { , , , } 0.54 um 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. W BC appears to be very close to the width of the BC SCR defined by the electric field. The maximum value of W BC is 0.55 mm, close from the theory (W BC ≈ W EPI ) Note that when the doping concentration of the epitaxy layer is very low, W BC 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 W BC vs. I V BC = -0.5 V Plot of W BC vs. I C for N EPI = { , , , } BC At V BC = -0.5 V, W BC 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 W BC vs. I V BC = 0.4 V Plot of W BC vs. I C for N EPI = { , , , } BC BC At V BC = 0.4 V, the BC SCR must vanish as the transfer current increases (quasi-saturation region). As expected, W BC decreases with I C, 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 W BC (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 W I vs. I C Plot of W I vs. I C for N EPI = (left) & (right) and V BC = {-2V, -1V, -0.5V, 0V, 0.2V, 0.4V, 0.6V} The injection width W I behaves as expected: W I = 0 before the high-injection regime starts and then increases sharply up to a maximum value close to W EPI. When the doping of the epitaxy is high (right figure), the curves at V BC <0 are affected by the avalanche current. The shape of the W I 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 C bc vs. I C Plot of C BC vs. I C for N EPI = (left) & (right) and V BC = {-2V, -1V, -0.5V, 0V, 0.2V, 0.4V, 0.6V} The BC capacitance is strongly current dependant in the high injection region with a different behavior whether quasi-saturation or high injection occurs. In all cases, C BC goes up again at very high I C. This behavior should be compared with AC simulations for validation.

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn C BC Plot of C BC vs. I C & C BC vs. V BC for N EPI = { , , } C BC is then compared to its equivalent plate capacitance of width W BC. Discrepancies occur but the capacitance behavior is fairly well matched. Despite the offset issue at high current, the slope is identical. On the right : The C BC vs. V BC is plotted for various values of N EPI, As expected by the theory, C BC is roughly proportional to the square root of N EPI.

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Transit times Transit times vs. I V BC = -0.5 V (Left) & V BC = 0.4 V (Right) The transit-time components are plotted vs. I C for two different values of V BC and N EPI = cm -3. In both cases, T BC is the major contribution to T F at low injection due to the very wide BC SCR. T BE is entirely responsible of the increase in T F at very low injection but decreases sharply with I C. However, it remains greater than T E in the high injection region leading to a possible overestimation of W BE. As expected T B and T C become predominant at very high injection.

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Transit times Transit times vs. N VBC = -0.5 V (Left) & VBC = 0.4 V (Right) The transit-time components are plotted vs. N EPI for the same two values of V BC as in the previous peak f T (N EPI = ). T BC is indeed the dominant term and the only component affected by N EPI

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

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn Conclusion 1.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 2.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 3.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 I C 4.Perspectives Extraction of a first order set of HICUM parameters 2D extension, S node