ZHOU Weijian,CHENG Zhiqun,LIU Jun

(K ey Laboratory of RF Circuits and Sy stems,Ministry of Education,H angzhou D ianzi University,Hangzhou 310018,China)

As the variety of application and complexity of the integrated circuit increase, single transistor fitting due to exists some l im itations,such as:(1)relies on a“golden”wafer which is typically very difficult to obtain,or is s imply not available;(2)often results in unrealistic/nonphysical parameter values;(3)can only produce the s imple equivalent circuit due to lack of sufficient geometry related info rmation; (4)usually provides a library with a very l im ited number of transistors,unless t ime and resource are unl im ited.In order to overcome this deficiencies,physica-l based and predictive modeling strategy should be pursuited.Because a process-based scalable approach enables extraction of an accurate physics-based equivalent circuit with a realistic representation of parasitic components,maintains physical values of extracted parameters,and enables efficient model generation of transistors with different configurations.Thus, scalable device models are becom ing crucial for the circuit design.

In this paper, scalable HICUM model for high speed SiGeHBTs,based on device physics and general scaling rules isdevelopedwith the great a mount of flex-i bility and provides excellentmodel accuracy.It ishighly desirable. Implementation of the scalable HICUM model inADS andH spice s imulation sof tware and ver-i ficationwith measure ment data is also presented.

1 ScalableModel

In this section, the procedure of constructing a scalable modelw ill be introduced.HICUM is based on an extended and generalized Intergal Charge-Control Relation(GICCR)[1].The HICUM parameter extrac-tionmethodology for a single transistor geom etry is described in Re.f[2-7].It is also built as a turnkey solution in ICCAP[6].The biasing conditions ofm easurement setups and the parameter constrains are set to be the sa m e for each device.In thisway,theHICUM model parameters for devices with different sizes are extracted from the same conditions for geometry scaling parameters extraction.

HICUM is a physics-based compactmodel dedicated to vertical BJT s andHBTs.The large-signal equivalent circuit of themodel is given in Fig.1.It is composed of 5 internal nodes(B*,B',E',C',S')and 4 external nodes(B,E,C,S)to take into account the internal transistor,the em itter periphery and the extrinsic transistor regions.One additional node T j enablesmodeling of sel-f heating.

Fig.1 Large-signal HICUM equivalent circuit and the her mal network used for sel-f heating calculation

According to device physics,in HICUM the AC and DC characteristics are strongly coupled,e.g.,the current gain fal-l off at high current densities is determ ined by the diffusion charges computed from the transit t ime[1]. So the parameter extraction of HICUM needsmore effort and endurance.

After the para metersvalues ofHICUM model are extracted from a series of HBTs.So me curves are drawn with e m itter length(Le)asX-axis and parameters value as Y-axis,meant mi e,setting e m itterw idth(We)as a fix value.The various geo metries range from We=0.3 μm～0.9 μ m,Le=0.5 μm ～ 20.3 μ m according to em itter size.Including all physical effects, the HICUM model features about 100 para meters, the followings just list some main para meters,scalable equations,and graphs which are related to IV,CV,Ft and S para meters extraction.Table.1 shows the ports of theHICUM scalable equations of the para meters,c10a,c10b andmcfa etc.are the scalable para meters in the equations.

Table 1 Scalable equations

Fig.2 Co mparision ofmeasure ment and scalable equations

It is shown from Table.1 that the scaling equations of parameters are functions of em itter's w idth(We)and length(Le).By the random algorithm to fit the measured values of individual devices, scalable parameters can be evaluated in a straightforwardway.Fig.2 show s typical plots such asC10,MCF andQP0 etc.scalable parameters'fitting plots.Parts of plots are shown here due to the space l im itation of the paper.

From the graph,it is visual to check out whether some para meters are deviating from the physics-based rules.If so,the specific device should be chosen,and readjust the relevant parameter values,m aking all the parameters satisfy the physicalmechanisms.

2 Imple mentation and Verification of the ScalableModel

Whenwe verify the correctness of the scalablemode,l firstly,we can develop the scalable model into Veri-l og-A code fo rma,t and mi ple mented in ICCAP with hpeesofs mis mi ulator to verify.Secondly,the scalable model is verified in ICCAP,having a link toH spice.The scalablemodel is verified extensively with measured I V,CV,Ft and AC small signal setups from each individual device.S mi ulation results show quite good fit to measurement results.Some of the selected comparison plots are shown in Fig.3.(a)～(g).Fro m the plots,we can see the IV,CV,Ft and S parameters are fittingwel.l

Fig.3 The comparison between s imulation results and measure ments

3 Conclusion

In this paper,we have presented a procedure for extraction of scalable para meters of high speed S iGe HBTs.The scaling is mainly based on the em itter w idth and length.The scaling para meters in the scala-ble equations are extracted directly from the measurement data of various geom etries at fixed length or w idth.The scalablemodel s imulation results show good fit to I V,CV,parasitic resistances and S parameters up to 30 GHz.

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周伟坚(1984-),男,浙江湖州人,硕士研究生,主要研究方向为射频元器件的建模,jesse_1984@126.com;

程知群(1964-),男,安徽巢湖人,教授,主要研究方向为微波射频集成电路设计与系统集成,zhiqun@hdu.edu.cn。