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

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

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.

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

InP DHBT Frequency Performance Geometrical parameters: Frequency characteristic: Device Lein [um] Ae [um2] Ac [um2] T5B3H7 5.0 2.7 8.6 T7B3H7 7.0 3.9 10.9 T10B3H7 10.0 5.7 14.3 An InP DHBT large-signal model must predict the frequency characteristic dependence on bias and on geometry

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

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!

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

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)

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

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

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 AC model of bipolar transistor: Total emitter-collector delay: Diffusion charge partitionen with Fex

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

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

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).

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

Small-signal modeling

Resistance Extraction: Standard method Open-Collector Method: HBT base current flow: 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

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

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!

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

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.

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

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

Base-collector capacitance extraction Base-collector capacitance modelling: Model parameters: Base-collector capacitance extraction

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.

Direct parameter extraction verification Small-signal equivalent circuit S-Parameters Model Parameter Value Rbx [] 8.0 Cbcx [fF] 10.1 Rbi [] 11.1 Cbci [fF] 3.0 Rcx [] 2.6 Rbci [k] 56.0 Re [] 2.7 gmo [mS] 773 Cbe [fF] 340.8 d [pS] ≈0 Rbe [] 34.6 Cceo [fF] 6.8

Scalable UCSD HBT model verification

Scalable Agilent HBT model verification

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

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!

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!

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