Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s

1. Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska** *DTU Electrical Engineering, Electromagnetic Systems Group, Technical University of Denmark DK-2800 Kgs. Lyngby Denmark **III-V Lab, F-91461 Marcoussis France

2. Outline • The ”InP/InGaAs DHBT” device • Specific modeling issues for III-V HBT devices: -The integral charge control relation (ICCR) for HBT modelling -Charge and transit-time modelling in III-V HBT devices -Temperature effects and self-heating • Small-signal modellng: Direct parameter extraction • Scalable large-signal model verification • Summary 2

3. The ”InP/InGaAs DHBT” Device • The introduction of an wide-gap emitter and collector to form a Double Heterojunction Bipolar Transistor (DHBT) offers several advantages over Homojunction Bipolar Transistors: - Higher fT and fmax characteristic - increased breakdown voltage - better performance under saturation operation Indicated in red are the 1.5µm and 0.7µm InP/InGaAs DHBT technologies developed at the III-V Lab.

4. The ”InP/InGaAs DHBT” Device • InP/InGaAs DHBT allows simultaneously high output power and high frequency: - mm-Wave power amplifiers - VCOs for PLLs - Electronic laser drivers and transimpedance amplifiers for ultra-high bit rate optoelectronics (>100Gbit/s operation) III-V Lab’s 0.7µm InP/InGaAs DHBT: Emitter Base plug Collector

5. InP DHBT Frequency Performance Geometrical parameters: Frequency characteristic: • An InP DHBT large-signal model must predict the frequency characteristic dependence on bias and on geometry

6. HBT large-signal model topology Agilent ADS SDD implementation: Circuit diagram of HBT model: • The large-signal topology is nearly identical for the various HBT models (UCSD HBT model, Agilent HBT model, FBH HBT model)

7. The integral charge control relation DC model of bipolar transistor: 1D BJT cross-section: Base Current Reverse Operation Base Current Forward Operation Net Transport Current Hole concentraction The transport current in a npn transistor depends directly on the hole charge!

8. The Gummel-Poon model for BJTs Gummel-Poon model formulation: Normalized base charge:

9. Extended GP model for HBTs Energy band diagram for abrupt DHBT: HBT modeling approach: ≈1 in HBTs • In an abrupt DHBT additional transport mechanisms such as thermionic emission over the barrier and tunneling through it tend to drag the ideality factor away from unity (NF>1). • The collector blocking leads to earlier saturation at high collector voltages (the so-called ”soft knee” effect)

10. Forward Gummel-plot for InP DHBT device Nf=1.14 • Base current in UCSD HBT model:

11. Forward Gummel-plot for InP DHBT device • Nf=1.14 • Base current in Agilent HBT model:

12. Charge modeling in III-V HBT • In any transistor a change in bias requires charge movement which takes time: - built up depletion layers in the device - redistribution of minority carriers Total emitter-collector delay: AC model of bipolar transistor: • Diffusion charge partitionen with Fex

13. Transit time formulation Analytical transit-times: Velocity-field diagram for InP: Base thickness (assumed constant) (varies with bias) Collector thickness Velocity modulation effects in collector: • Collector transit-time c increase with electrical field • Collector transit-time c decrease with current due to modulation of the electrical field with the electron charge (velocity profile modulation) • Intrinsic base-collector capacitance Cbci decrease with current

14. Transit time formulation: Full depletion Slowness of electrons in InP: Collector transit-time model: Base-collector capacitance model: • Formulation used in UCSD HBT model

15. Inclusion of self-heating Self-Heating formulation: Thermal network • The thermal network provides an 1.order estimate of the temperture rise (delT) in the device with dissipated power (Ith).

16. InP HBT self-heating characteristic • Self-heating in HBT devices manifests itself with the downward sloping Ic-Vce characteristic for fixed Ib levels.

17. Small-signal modeling

18. Resistance Extraction: Standard method HBT base current flow: Open-Collector Method: • Rbx underestimated due to shunting effect from forward biased external base-collector diode! Saturated HBT device: • Re overestimated due to the intrinsic collector resistance! Standard method only good for Rcx extraction

19. Emitter resistance extraction Forward biased HBT device: Notice: Rbi extracted assuming uncorrected Re value. Re can be accurately determined if correction is employed

20. Extrinsic base resistance extraction (I) Circuit diagram of HBT model: • Distributed base lumped into a few elements • The bias dependent intrinsic base resistance Rbi describes the active region under the emitter • The extrinsic base resistance Rbx describes the accumulative resistance going from the base contact to the active region • Correct extraction of the extrinsic base resistance is important as it influence the distribution of the base-collector capacitance fmax modeling!

21. Extrinsic base resistance extraction (II) Linearization of capacitance: Base-collector capacitance model: K1=0.35ps/V Ae=4.7m2 Wc=0.13m Physical model Low current linear approximation: Characteristic current Linear approx. • Linear approximation only valid at very low collector currents.

22. Extrinsic base resistance extraction (III) Base-collector splitting factor: Linearization of splitting factor: K1=0.35ps/V Ae=4.7m2 Wc=0.13m X0=0.41 Physical model Zero-bias splitting factor: Linear approx. • Base collector splitting factor follows linear trend to higher currents.

23. Extrinsic base resistance extraction (IV) Improved extraction method: Effective base resistance model: Rbx extraction method: • Extrinsic base resistance estimated from extrapolation in full depletion.

24. Intrinsic base resistance extraction Improved Semi-impedance circle method: (Rbx, Re, Rcx de-embedded) Rbi in InP DHBT devices is fairly constant versus base current

25. Base-collector capacitance extraction Base-collector capacitance modelling: • Model parameters: • Base-collector capacitance extraction

26. Intrinsic element extraction Intrinsic hybrid-pi equivalent circuit • The influence from the elements Rbx, Rbi, Re, Rcx, Cbcx, and Cceo are removed from the device data by de-embedding to get to the intrinsic data.

27. Direct parameter extraction verification Small-signal equivalent circuit S-Parameters

28. Scalable UCSD HBT model verification

29. Scalable Agilent HBT model verification

30. Large-signal characterization setup Single-finger device • Load pull measurements not possible. Load and source fixed at 50Ω. • Lowest measurement loss at 74.4GHz

31. Large-signal single-tone verification Measurements versus UCSD HBT model: • The large-signal performance at 74.4GHz of the individual single-finger devices is well predicted with the developed UCSD HBT model except for low collector bias voltage (Vce=1.2V). mm-wave verification!

32. Large-signal single-tone verification Measurements versus Agilent HBT model: • The large-signal performance at 74.4GHz of the individual single-finger devices is well predicted with the developed Agilent HBT model. The agreement at lower collector bias voltage is better. mm-wave verification!

33. Summary • The InP/InGaAs DHBT can be modeled accurately by an extended Gummel-Poon formulation - thermionic emission and tunneling - collector blocking effect - collector transit-time physical modeling • Small-signal InP/InGaAs HBT modeling -unique direct parameter extraction approach • Scalable large-signal HBT model verfication -RF figure-of-merits and DC characteristics -mm-wave large-signal verification