HICUM/Level0 - a simplified compact bipolar transistor model

IEEE BCTM 6.2

-

HICUM/LeveIO A simplified compact bipolar transistor model All. Schroter', S. Lehmann', H. Jiang2,S. Komarow'

' Chair for Electron Devices and Integrated Circuits, Dresden Universityof Technology, 01062 Dresden, Germany JazzSemiconductor,431 1 Jamboree Rd., Newport Beach, CA 92661, USA Abstract A simple compact bipolar transistor model is presented, combining the simplicity of the SPICE Gummel-Poon model (SGPM) with major features of HICUM. Experimental results are shown for a 150 GHz SiGe BiCMOS process.

1 Introduction Advanced compact models such as HICUM [l] and MEXTRAM [2] eliminate many of the deficiencies of the SGPM that have started to seriously limit RF circuit design in SiiSiGe bipolar and BiCMOS technologies. However, these advanced models are also more complicated than the SGPM with respect to equivalent circuit (EC), model equations, parameter extraction and computational effort. Thus, the availability of a less complicated model can have certain advantages such as: During the conceptual circuit design phase, it is often advantageous to start with a simple transistor model that is easily understandable for designers, but contains the essential transistor features. This facilitates a quick evaluation of the basic circuit functionality, before spending time on longer optimization cycles, using a more accurate model. Also, being able to start with a simple-model and then gradually move to a sophisticated model provides a better feeling for the impact of certain effects on circuit characteristics. In larger circuits often only few (very) critical transistors need to be represented by a very accurate model that takes into account all relevant physical effects; the other transistors can be represented by simple models. While integrated circuit design and optimization generally requires geometry scalable models, sometimes discrete devices have to be dealt with. Model parameter determination from such a "single geometry transistor" naturally is thus quite difficult for sophisticated models, unless they are simplified with respect to, e.g., geometry effects. Another example are variable capacitors (varactors) that are often realized as transistors, but can be described by simple transistor models. To address above issues, a simplified compact bipolar transistor model, called HICUM/LevelO or just HICUM/LO in this paper, has been developed on the basis of the full version, called HICUM/L2, that is described in [l]. HICUM/LO combines the simplicity of the SGPM in terms of equivalent circuit and some of its model equations with several important features of HICUM. As a result, HICUMILO is a more physics-based and accurate model than the SGPM, but also reduces parameter extraction efforts, especially for single transistor sizes, compared to HICUM/L2 and the SGPM. This paper presents the fundamental equations of the 0-7803-7561-0/02/$17.00 02002 IEEE

new model, alternatives for parameter extraction and first experimental results.

2 Equivalent circuit Fig. 1 shows the large-signal equivalent circuit of the simplified model. Compared to HlCUWL2, the following simplifications have been made in the EC topology: The perimeter base node (B') has been eliminated by properly merging the respective internal and external counterparts of the BE depletion capacitance C,E, the base resistance rB, the BC depletion capacitance Cic, and the base current components across the BE and BC junction. The BE tunnelling current, the substrate coupling network, the parasitic substrate transistor, and the capacitance for modeling AC emitter current crowding have been omitted. In advanced processes, the internal BC depletion capacitance Cici is not only usually physically different from the external BC depletion capacitance CicX but also very important for accurately modeling the Early effect, lowcurrent transit time and avalanche current; thus, the parameter sets for Cici and Cicx are kept separately. However, Csx can be distributed across rB using a partitioning parameter fBc (similar to XCJc in the SGPM). In the EC implementation, this leads to an enlarged effective internal BC capacitance CiCi that actually consists of two separately evaluated capacitances. Two parasitic capacitance elements, generally resulting from isolations and fringing fields are included as CBE,,~~ and CBCpar.

E Fip 1: Equivalent circuit for HICUWLevelO (for npn transistors).

The model is being programmed in Verilog/AMS, facilitating a quick evaluation across simulators and eliminating the significant burden of typical compact model implementation issues. After thorough testing has been completed, the VeriloglAMS code will be made publicly

112

IEEE BCTM 6.2 available and is intended to serve as reference for the implementation of compiled versions.

3 Model equations A main feature of HICUM/LO is the decoupling of DC and AC behavior which makes parameter extraction easier but results in a reduced validity range and physical basis of a bipolar transistor model. Below, the charge storage elements are discussed first, since they have been a major cause for the inadequacy of the SGPM and also of high importance for typical applications of bipolar transistors. A. Charge storage elements

All depletion charges and capacitances are described with the same equations as in HICUM/L2. Therefore, a smooth limitation at high forward bias as well as collector punch-through are included also in HICUM/LO. A main improvement over the SGPM is the formulation of the forward minority charge Qf which is based on HICUM's accurate description of the transit time q. As in HICUM/L2, the bias dependence of the latter is modeled as the sum 7, = Tfo(vB,c.) + ATf(iTf9 V ~ E , ) (11 with the low-current component zm, the high-current component AT^, and iTfas the forward transfer current. While zm is described the same way as in HICUM/L2 (e.g. [3][1]), the current dependence of A q is simplified by neglecting the bias dependent collector current spreading formulation (cf. [4]). However, the bias independent collector current spreading factor , f remains included in the critical current ICK[4][3], resulting in a more physical geometry dependence of the low-field internal (epi-)collettor resistance. Thus, the base and collector component of A q are merged in HICUM/LO and described by

where the last term represents a possible emitter contribution, and w is the normalized injection width in the collector [3]. The model parameters in the above , ahc,TfEo and gaE. The minority charge expression are,,q Qf is calculated analytically by integrating zf over ITf. The reverse minority charge is simply Q+,iT, with the reverse transit time zr as model parameter.

B. DC characteristics The derivation of a simplified transfer current equation starts with the original generalized Integral Charge-Control Relation (GICCR) [5] in HICUMR2, exp(vB,E#/vT)- exp(vB,c,/VT) . (3) IT= ' Qpo+ hjeiQiEi + hjciQjci+ QfT + QrT ' hjEi and hjci are weighting factors for HBTs that take into account bandgap variations; Q ~ and E ~ Qjci are the depletion ~ equal to charges of the infernal transistor; Qnand Q r are Of and Q, for BJTs, but can include weighted charge components for HBTs. At high current densities, (3) results

in a non-linear implicit equation for iT for any realistic current dependence of the charge components. As a first simplification step, the zero-bias hole charge QN is replaced by a different reference hole charge, (4) that is defined at some arbitrary forward bias point vBlP at which vwc=O and the minority charge is negligible. The main reason for this step is that in HICUM/LO (like in the SGPM, too) the infernal BE depletion charge is not available anymore, and using the total BE depletion charge would make (3) inaccurate. Normalizing the charge terms Q ~ o= Q ~ +o hjeiQjEi,op

I

Qio

and separatingthe term containingthe charge AQ~E~ to ( = Q j ~ i - Q j ~ gives i,~~)

Since hjeiAQjEfi