1. 1 Heterojunction Bipolar Transistors Heterojunction Bipolar Transistorsfor High-Frequency Operation D.L. Pulfrey Department of Electrical and Computer Engineering University of British Columbia Vancouver, B.C. V6T1Z4, Canada pulfrey@ece.ubc.ca http://nano.ece.ubc.ca Day 3A, May 29, 2008, Pisa

2. 2Outline What are the important features of HBTs? What are the useful attributes of HBTs? What are the determining factors for I C and I B ? Why are HBTs suited to high-frequency operation? How are the capacitances reduced?

3. 3 Schematic of InGaP/GaAs HBT Epitaxial structure Dissimilar emitter and base materials Highly doped base Dual B and C contacts Identify W B and R B

4. 4 HETEROJUNCTION BIPOLAR TRANSISTORS The major development in bipolar transistors (since 1990) HBTs break the link between N B and  Do this by making different barrier heights for electrons and holes N B can reach 1E20cm -3 e-e- h+h+ Key feature is the wide-bandgap emitter - this improves f T and f max - this allows reduction of both W B and R B SHBT An example of Bandgap Engineering

5. 5 Selecting an emitter for a GaAs base AlGaAs / GaAs InGaP / GaAs

6. 6 InGaP/GaAs and AlGaAs/GaAs Draw band diagrams for different  emitter

7. 7 Preparing to compute I C Preparing to compute I C Why do we show asymmetrical hemi-Maxwellians?

8. 8 Current in a hemi-Maxwellian Full Maxwellian distribution Counter-propagating hemi-M's for n 0 =1E19/cm 3 / 1E20 What is the current?

9. 9 Density of states Recall: In 1-D, a state occupies how much k-space? What is the volume in 3-D? If k x and k y (and k z in 3-D) are large enough, k-space is approximately spherical Divide by V (volume) to get states/m 3 Use parabolic E-k (involves m*) to get dE/dk Divide by dE to get states/m 3 /eV

10. 10Velocities Turn n(E) from previous slide into n(v) dv using  v R = 1E7 cm/s for GaAs Currents associated with hemi-M's and M's = 1E7 A/cm 2 for n 0 =6E18 /cm 3 * What is J e,total ?

11. 11 Collector current: boundary conditions Collector current: boundary conditions

12. 12 Reduce our equation-set for the electron current in the base What about the recombination term?

13. 13 Diffusion and Recombination in the base Diffusion and Recombination in the base In modern HBTs W B /L e << 1  and is constant Here, we need:

14. 14 Collector current: controlling velocities Collector current: controlling velocities Diffusion (and no recombination) in the base: Note: - the reciprocal velocities - inclusion of v R necessary in modern HBTs * * Gives limit to validity of SLJ

15. 15 Comparing results Comparing results What are the reasons for the difference?

16. 16 Base current: components Base current: components Which I B components do we need to consider? (iv)

17. 17 Base current components and Gummel plot Base current components and Gummel plot What is the DC gain? I C (A/cm 2 ) V BE (V) I B (injection) I B (recombination) ICIC

18. 18 Preparing for the high-frequency analysis Make all these functions of time and solve! Or, use the quasi-static approximation

19. 19 The Quasi-Static Approximation q(x, y, z, t' ) = f( V Terminals, t') q(x, y, z, t' )  f( V Terminals, t < t')

20. 20 Small-signal circuit components g m = transconductance g o = output conductance g  = input conductance g 12 = reverse feedback conductance

21. 21 Recall g 12 =dI b /dV ce next

22. 22 Small-signal hybrid-  equivalent circuit What are the parasitics?

23. 23 HBT Parasitics HBT Parasitics C EB and R B2 need explanation

24. 24 y Base-spreading resistance

25. 25 Capacitance Capacitance V + + - - Generally: Specifically: 1 2

26. 26 E BC QNE QNC QNB  V BE +  Q E,j is the change in charge entering the device through the emitter and creating the new width of the depletion layer (narrowing it in this example), in response to a change in V BE (with E & C at AC ground). It can be regarded as a parallel-plate cap. W B2 W B1 What is the voltage dependence of this cap? Emitter-base junction-storage capacitance Emitter-base junction-storage capacitance

27. 27 E BC QNE QNC QNB  V BE +  Q E,b is the change in charge entering the device through the emitter and resting in the base (the black electrons), in response to a change in V BE (with E & C at AC ground). It’s not a parallel-plate cap, and we only count one carrier. Emitter-base base-storage capacitance: concept Emitter-base base-storage capacitance: concept

28. 28 B QNB n(x) x n(W B ) WBWB For the case of no recombination in the base: What is the voltage dependence of C EB,b ? Emitter-base base-storage capacitance: evaluation Emitter-base base-storage capacitance: evaluation

29. 29 Base-emitter transit capacitance: evaluation Base-emitter transit capacitance: evaluation Q = 3q q e = -2q What are q 0 and q d ? Where do they come from ?

30. 30 f T from hybrid-pi equivalent circuit g 0 and g  set to 0 f T is measured under AC short-circuit conditions. We seek a solution for |ic/ib| 2 that has a single-pole roll-off with frequency. Why? Because we wish to extrapolate at -20 dB/decade to unity gain.

31. 31 Extrapolated f T Extrapolated f T Assumption: Conditions: Current gain: Extrapolated f T :

32. 32 Improving f T Improving f T III-V for high g m Implant isolation to reduce C  Highly doped sub-collector and supra-emitter to reduce R ec Dual contacts to reduce R c Lateral shrinking to reduce C's

33. 33 Designing for high f T values Why do collector delays dominate ?

34. 34 How does Si get-in on the act?

35. 35 Developing an expression for f max Assumption and conditions:

36. 36 Improving f max Pay even more attention to R b and C  Final HF question: How far behind are Si MOSFETs?

37. 37 HF MOS What is this?