advantages device simulator combining electron transport...

VLSI DESIGN1998, Vol. 8, Nos. (1-4), pp. 495-500Reprints available directly from the publisherPhotocopying permitted by license only

(C) 1998 OPA (Overseas Publishers Association) N.V.Published by license under

the Gordon and Breach Science

Publishers imprint.Printed in India.

Advantages of Semiconductor Device SimulatorCombining Electromagnetic and Electron

Transport Models*

S. M. SOHEL IMTIAZ, SAMIR M. EL-GHAZALY and ROBERT O. GRONDIN

Department of Electrical Engineering, Telecommunications Research Center, Arizona State University,Tempe, AZ 85287-7206

(Received 18 May 1997; In finalform 10 July 1997)

Physical simulation of semiconductor devices at high frequencies involves not onlysemiconductor transport issues but also electromagnetic wave propagation issues. Inorder to obtain the nonlinear and the large-signal characteristics of the semiconductordevices, an electromagnetic model should replace the traditional quasi-static model inthe device simulator. In this paper, the advantages of a semiconductor device simulatorcombining an electromagnetic and an electron transport models are presented. Thisstudy is based on a semiconductor device simulator that couples a semiconductor modelto the 3D time-domain solution of Maxwell’s equations. The electromagnetic wavepropagation effects on the millimeter-wave FETs are thoroughly analyzed. The use ofthe electromagnetic model over the conventional quasi-static model provides the actualdevice response at high frequencies. It also shows the nonlinear energy build-up alongthe device width whereas the quasi-static model provides a linear increase of energy. Thecombined model is capable of predicting the device nonlinearity and harmonicdistortion of amplifier circuits at large signal.

Keywords." Device simulation, hydrodynamic models, FDTD, full-wave simulators

1. INTRODUCTION

With the advancement of semiconductor technol-ogy, the techniques required to analyze, design,and optimize the semiconductor devices are be-coming increasingly sophisticated. The computersimulation programs are now essential tools for

device engineers. These numerical simulationsbased on physical modeling can be used to predictand provide better understanding of the devicebehavior. However, the down-sizing of the activedevice dimensions has presented new challenges tothe device and circuit designer. In submicronsemiconductor devices, several new transport

* This work is supported by the Army Research Office under contract # DAAH04-95-1-0252.tCorresponding author. Phone: 602-965-5322, Fax: 602-965-8325, Email: [email protected].

495

496 S.M.S. IMTIAZ et al.

phenomena develop and, consequently, have to beconsidered in device modeling. The electrons donot reach equilibrium transport conditions whiletraveling along the conducting channel. To in-corporate the effects of nonstationary dynamics insemiconductor devices, the hydrodynamic modelbased on moments of Boltzmann’s transportequation is used [1- 3]. The transport parametersare taken as functions of average electron energyrather than the local electric field.The device modeling at high frequencies requires

special attention. At high frequencies, the couplingbetween the electrons and the propagating electro-magnetic waves can not be neglected in submicrondevices. The short period of the propagating EMwave approaches the electron relaxation time andas the electrons need a finite time to adjust theirvelocities to the changes in field, electron transportis directly affected by the propagating wave. Insuch cases, the quasi-static semiconductor devicemodels fail to represent accurately the exact deviceresponse. In addition, the electrodes extendingalong the device width behave like transmissionlines with nonlinear characteristics. These facts callfor the necessity of incorporating wave effects ina three-dimensional model. This goal can beachieved by taking full account of the varyingfields inside the device. The acceptable method forrepresenting these various forces is to combine an

electromagnetic model with a semiconductor de-vice model which leads to the Combined Electro-magnetic and Solid-State (CESS) simulator [4].On the other hand, the increasing demand of

processing and transmitting more informations at afaster rate, drives the analog and digital electronicsystems to operate at higher clock speeds. At thesame time, to curtail the production cost, themanufacturers are more inclined towards heavilydensed integrated circuits. In these high densityintegrated circuits, there are many closely spacedactive and passive devices. As a result, there aresome detrimental effects on the circuit performanceat high frequencies due to crosstalk caused bycoupling, surface waves and radiation effects. Insuch cases, the circuit modeling issue becomes more

intensive. The circuit design should be based on

advanced global model which takes the electro-magnetic wave effects into consideration.The issues like device-wave interaction, electro-

magnetic coupling, discontinuity problem, linearand nonlinear behavior of passive and activedevices, and EM radiation effects are addressedin the global modeling. The computer memoryrequirement as well as the simulation time isreduced by using a hybridization approach inglobal modeling. The amplifier is divided intothree regions, preserving the physical character-istics of the amplifier circuit by taking thereflections at the breaking points into considera-tion. The full-wave analysis of each region isperformed individually and coupled to the nextstage properly with all the required informationsfrom the preceding stage. This technique enablesone to use large space step, and hence, large timestep in matching networks.

2. NUMERICAL MODEL

The CESS simulator is a physically based modelwhich takes care of nonisothermal transport andnonstationary electron dynamics as well as elec-tromagnetic wave propagation effects. This modelcouples the hydrodynamic model to a 3D time-domain solution of Maxwell’s equations. Thehydrodynamic model is based on the moments ofthe Boltzmann’s transport equation obtained byintegration over the momentum space. The elec-tromagnetic wave propagation effects can becompletely characterized by solving Maxwell’sequations. These equations are first-order linearlycoupled differential equations relating the fieldvectors, current densities and charge densities at

any point in space at any time. The couplingbetween the two models is established by using thefields obtained from the solution of Maxwell’sequation in the semiconductor model to calculatethe current densities inside the device. Thesecurrent densities are used to update the electricand the magnetic fields using Maxwell’s equations

ADVANTAGES OF COMBINED SIMULATORS 497

with an applied high frequency sinusoidal excita-tion. The initialization is provided by solving thehydrodynamic model for the dc charges andcurrents in response to a specified dc operatingpoint. In this manner, the coupling between thetwo models results in the overall high frequencycharacteristics of the semiconductor devices. Thedetails of the mathematical representation and thecoupling procedure can be found in [4]. The finite-difference time-domain scheme is used in semi-conductor device discretization.

3. RESULTS AND DISCUSSION

The MESFET (Fig. 1) used in this work have thefollowing parameters. Gate-source spacing0.41am, gate-drain spacing=0.561am, gatelength=0.24gm, undoped GaAs thickness0.31am, active layer thickness=0.1 gm, gatewidth= 250 gm. In order to validate the CESSsimulator, a MODFET structure similar to Shawkiet al. [5] is simulated to compare the performances.The transconductances are compared with/withouttaking the traps into account. They exhibit reason-able agreement with each other in Figure 2.To demonstrate the electromagnetic-wave pro-

pagation effects for MESFET, a sinusoidal excita-tion of peak 0.1 V and frequency 80 GHz is appliedbetween the gate and the source electrodes. Theexcitation is applied as a plane source at z-0, asshown in Figure 1. The CESS model is then solvedfor a few rf cycles to avoid the effects of the

Outputr. Voltage

YVgs Source Gate Drain

(0,0,0),

EM WavePropagation

FIGURE The simulated MESFET structure.

800

600

This Work ."’"’-

ith Traps Lg=0.15 umVdd=2.6V

"l I"’-0.6 -0.4 -0.2 0,0 0.2 0,4

Gate Bias (V)

FIGURE 2 Comparison of transconductance of MODFETwith Ref. [5] with or without including the traps.

transients on the ac solution. The output isobtained across the drain and the source at severalpoints along the device width in the z-direction.The output voltage wave, as shown in Figure 3,first decreases and then increases along the devicewidth. Early in the simulation, the electronic effectis not present and the wave amplitude decreasesalong the device width. Later, as more and more

electromagnetic energy is propagated along thedevice width, the wave energy builds up, and thewave amplitude increases. This figure clearly

0.6

0.2

z=31 umz=94 um .....

z=156 um _,,;""z=219 um ,’7_

-,, ’,, .......; ,.. :., f.:..::

"’"" ’. ll.

",.’1.*...:

-0.6 ..0 10 20 30

Time (ps)

FIGURE 3 The electromagnetic wave propagation effects onoutput voltages of MESFET for different device widths.


demonstrates the direct relationship between thedevice gain characteristics and the electromagneticwave propagations.The advantage of using the electromagnetic

model in device simulation is demonstrated inFigure 4. MESFET is simulated using the quasi-static model as well as the CESS simulator. Inquasi-static model, Poisson’s equation is solved toget the electric fields. In electromagnetic model,Maxwell’s equations are solved to obtain theelectric and the magnetic fields. In Figure 4, theoutput voltage wave monotonously increasesalong the device width in quasi-static model. Onthe other hand, in electromagnetic model, theoutput voltage wave nonlinearly increases with thedevice width. This phenomenon is expected due tothe device-EM wave interaction. The exchange ofenergy between the electrons and the electromag-netic wave takes place along the device width. Thisbehavior is absent when the output is obtainedfrom the quasi-static analysis. This figure stronglysupports the use of the electromagnetic model fordevice simulation at high frequencies.To demonstrate the large signal potential of the

CESS simulator, the gain of a 0.5 lam 1000 lmMESFET is calculated for a small signal of 0.1 V

0.4

0.3

0.2

0.1

0.00 50 100 150 200 250

Gate Width (urn)

FIGURE 4 The comparison of output voltage variations withdevice-width obtained from the electromagnetic model and thequasi-static model for MESFET.

and a large signal of 0.3 V. As shown in Figure 5,the gain becomes lower as the amplitude increases,which is expected. The strength of this approach isnot in simply confirming that larger amplitudesreduce the gain, but in estimating the reductiondirectly, using the physical model.The potential of the CESS model is further

investigated by simulating an amplifier circuit withinput and output matching networks as shown inFigure 6. The physical simulation of the entireamplifier is performed using a global modelingtechnique [6]. The optimized transistor parameters(in terms of maximum gain) used in the amplifier

12

Small Signal (0.1V)Largo Signal (0.3V)

0 2 4 6 8 10 12

Frequency (GHz)

FIGURE 5 The comparison of gain characteristics ofMESFET at small and large signal operations.

(Source) Input Matchlntwork

FIGURE 6 GaAs transistor amplifier with input and outputmatching networks.

ADVANTAGES OF COMBINED SIMULATORS 499

are: gate length=0.221am, aspect ratio=2.5 andthe active layer doping=2.2xl017/cm3. The am-

plifier is designed for 40 GHz frequency. Theentire amplifier is simulated by applying a smallsignal of amplitude 0.1 V and large signal ofamplitudes 0.3 and 1.0 V at different frequencies.In Figure 7, $21 is presented for small and largesignals at different frequencies. At the designfrequency of 40 GHz, the gain is 7.38 dB for smallsignal and 6.44 and 5.15 dB for.large signals of 0.3and 1.0 V, respectively. Thus it is observed that forthe same design the gain drops at large signals. Insmall signal, the gain drops slightly as thefrequency is shifted away from the 40 GHz point.On the other hand, in large signal, the gainreduction at frequencies other than design fre-quency is higher. Nonlinearity in the devicebehavior is evident from this figure.Once the large signal response of the amplifier is

obtained, it is interesting to study its frequencycontent and to identify the harmonics. The outputwave contains a significant amount of third andfifth harmonic components as shown in Figure 8.For the large signal input of 0.3 V, the outputpower contains 4.8%, 11.6% and 13% of the

o20

o,....,.o..,0’l"$21 Input=0.IV

,t.-. $21 Input=0.3V$21 Input=1.0V

|"

30 40 50 60

Frequency (GHz)

FIGURE 7 The dependence of scattering parameter S21 onfrequency at small and large signals for the amplifier with theoptimized transistor.

0

-5.

-10.

-15,

-20

-25

-3025

Third Harmonict Fifth Harmonic

30 35 40 45 50 55

Input Signal Frequency (GHz)

FIGURE 8 The intermodulation distortion at the third andthe fifth harmonic components for the large signal of amplitude0.3 at 30, 40 and 50 GHz.

fundamental at 30, 40 and 50 GHz, respectively, atthe third harmonic. The fifth harmonic contains6%, 0.7% and 0.3% of the fundamental at 30, 40and 50 GHz, respectively. This shows that aconsiderable amount of power is transferred atthe harmonic components. Thus the global modelis able to predict the nonlinearity of the devicebehavior and show the different harmonic compo-nents generated at the amplifier output due tononlinearity.

4. CONCLUSIONS

Advantages of semiconductor device and circuitsimulator combining an electromagnetic and anelectron transport models are presented. Thesimulation confirms that a significant device-waveinteraction takes place in semiconductor devices athigh frequencies. The use of the electromagneticmodel over the conventional quasi-static modelprovides the actual device response at highfrequencies. It also shows the nonlinear energybuild-up along the device width whereas the quasi-static model provides a linear increase of energy.An approach towards global modeling of milli-


meter-wave circuits is also presented in this paper.The global model is able to characterize theelectromagnetic coupling, device-EM wave inter-action and the EM radiation effects of the veryclosely spaced integrated circuit amplifier. Theglobal modeling technique is capable of represent-ing the nonlinearity and the harmonic distortion ofthe amplifier circuit. More effects will be added inthe future including thermal and packaging effects.By incorporating all these effects in the circuitsimulation, a milestone will be reached towards thecomprehensive global modeling.

References

[1] Carnez, B., Cappy, A., Kaszynski, A., Constant, E. andSalmer, G., "Modeling of a sub-micrometer gate Field-effect transistors including effects of nonstationary elec-tron dynamics", J. Appl. Phys., 51(1), 784-790, Jan. 1980.

[2] Snowden, C. M. and Loret, D., "Two-.dimensional hot-electron models for short-gate-length GaAs MESFET’s",IEEE Trans. Electron Devices, ED-34(2), 212-223, Feb.1987.

[3] E1-Ghazaly, S. M. and Itoh, T., "Two-dimensionalnumerical simulation ofshort-gate-length GaAs MESFETsand application to the traveling Gunn domain phenomen-on", Int. J. Numerical Modeling, 1, 19-30, Jan. 1988.

[4] Alsunaidi, M. A., Sohel Imtiaz, S. M. and E1-Ghazaly,S. M. "Electromagnetic wave effects on microwavetransistors using a full-wave time domain model", IEEETrans. Microwave Theory Tech., 44, 799-808, June 1996.

[5] Shawki, T., Salmer, G. and E1-Sayed, O., "MODFET 2-Dhydrodynamic energy modeling: optimization of subquar-ter-micron gate structure", IEEE Trans. Electron Devices,37, 21-30, Jan. 1990.

[6] Sohel Imtiaz, S. M., "Physical simulation of highfrequency semiconductor devices and amplifier circuits",Ph.D. Dissertation, May 1997.

Authors’ Biographies

S. M. Sohel Imtiaz was born in Dhaka, Bangla-desh, in 1966. He received the B.S. and the M.S.

degree in electrical engineering in 1988 and 1990,respectively, from Bangladesh University of En-gineering and Technology (BUET), Dhaka. Hereceived his Ph.D. degree in electrical engineeringfrom Arizona State University in 1997. Dr. Imtiazworked as a Lecturer in the department ofelectrical engineering in BUET from 1989 to1991. His research interests include modeling,simulation and characterization of microwavesemiconductor devices and circuits, device-waveinteractions, numerical techniques, and the simu-lation of microwave amplifiers. He joined MicroLinear Corporation. as a Sr. Device Engineer inJune 1997.

Samir M. EI-Ghazaly received the Ph.D. degree,in Electrical Engineering, from the University ofTexas at Austin, Texas, in 1988. He joined ArizonaState University as Assistant Professor in August1988, and became Associate Professor in 1993. Dr.E1-Ghazaly is a senior member of IEEE, an electedmember of Commissions A and D of URSI, amember of Tau Beta Pi, Sigma Xi and Eta KappaNu. He is the secretary of US National Committeeof URSI, Commission A. He is also the Chairmanof the Chapter Activities Committee of the IEEEMicrowave Theory and Techniques Society.Robert Grondin was born and raised in

Michigan. He attended the University of Michi-gan obtaining the BS, MS and Ph.D. degrees.From 1981 to 1983 he was a post-doctoralresearch associate at Colorado State university.In 1983 he joined the faculty of the Departmentof Electrical Engineering at Arizona State Uni-versity where he is presently an associate profeg-sor. He is a senior member of the IEEE and amember of the AAAS.

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