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 Day 3A, May 29, 2008, Pisa

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

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

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

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 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

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 Collector current: boundary conditions Collector current: boundary conditions

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

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

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

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

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

21 Recall g 12 =dI b /dV ce next

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

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

24 y Base-spreading resistance

25 Capacitance Capacitance V Generally: Specifically: 1 2

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

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

34 How does Si get-in on the act?

35 Developing an expression for f max Assumption and conditions:

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

37 HF MOS What is this?