Intrinsic Small-Signal Equivalent Circuit of GaAs MESFET s

Transcription

1 Intrinsic Small-Signal Equivalent Circuit o GaAs MESFET s M KAMECHE *, M FEHAM M MELIANI, N BENAHMED, S DALI * National Centre o Space Techniques, Algeria Telecom Laboratory, University o Tlemcen, Algeria Université de Tlemcen, BP 30,Chetouane, Tlemcen Tel : , Fax : mo_kameche@yahoor Abstract : Finite Element Time Domain Method is used to determine the intrinsic elements o a broadband small-signal equivalent circuit (SSEC) o FET s The values o the dierents elements are calculated rom the Y parameters o the intrinsic MESFET, which are obtained rom the Fourier analysis o the device transient reponse to voltage-step perturbations at the drain and gate electrodes The success o this analysis depends crucially on the accuracy o the values calculated or the instantaneous currents at the electrodes during the transient As application we have determined the SSEC or the case o a vertical drain and source contacts GaAs MESFET s I INTRODUCTION Usually, the SSEC o a FET s is designed by choosing a topology, so that each element provides a lumped approximation to some physical aspect o the device A SSEC which is commonly accepted is ormed o iteen dierent requency-independent elements: eight o them corresponding to the external parasitic eects and normally considered independent o the bias point, and the other seven describing the intrinsic behavior o the FET and dependent on the biasing conditions In this paper we describe a theoretical procedure to calculate the intrinsic elements o the FET SSEC starting rom the Y parameters obtained by using o a Finite Element Method (FEM) simulation The FEM includes all the mechanisms relevant to the transport in small semiconductor devices (nonstationary eects, velocity overshoot, etc) For a given operating point, the Y parameters are obtained rom the Fourier analysis o the device transient response to voltage-step perturbations at the drain and gate electrodes The validity o the intrinsic SSEC proposed can be veriied by checking the requency dependence o the calculated elements operating point we apply a voltage-step perturbation o amplitude 'V j at electrode j, and that I i (t) is the current response at electrode i the complex Yij parameter will be given by the relation between the Fourier components o both signals, and can be shown to be[1]: Re > Im I i I 0 j i > I t sint dt ³ i i j 0 > > I t cos t dt ³ i i j 0 (1) () where I i (0) and I i () are the stationary currents at electrode i beore and ater the voltage perturbation respectively Figure 1 shows the small-signal equivalent circuit o the intrinsic FET, where Cds, and correspond to the drain-source, gate-source and gate-drain capacitances respectively Ri is the resistance o the ohmic channel between the source and the gate 0 represents the steady-state transconductance, and W the delay time o the transistor gds is the drain conductance For a given bias point, the elements o this intrinsic equivalent circuit can be obtained rom the complex Y parameter corresponding to that point 1 0 exp - jw II THEORETICAL ANALYSIS In this technique, we employ the Fourier decomposition o the FET response to transient excitations Let us suppose that over the stationary Figure 1 :Small-signal equivalent circuit o the intrinsic FET

2 The Yij parameter will be given by a simple circuit analysis [], [3]: In the ollowing, i=1 will stand or the gate and i= or the drain Y Ri j D D ¹ j (3) Y (4) 1 j Y exp 0 W 1 j 1 j Ri gds j( ) Y Cds with (5) (6) D 1 Ri From these expressions, and separating the Y parameters into their real and imaginary parts, the equivalent circuit elements can be ound analytically: Im Y 1 (7) Im> ReY 1 (8) ImY ¹ Ri Re> Y@ Im> R e > (9) The program used in simulation contains the implementation o Poisson s equation and the current continuity equation in discrete orm by the use o the inite element method [4] A sel consistent solution to the two equations is ound by using a Scharetter- Gummel approach [5], where Poisson s equation and current continuity equation are solved ater each time step until the solution has converged The classical semiconductor equations assume that the carrier velocities are an instantaneous unction o the local electric ield and that the mobility and diusion coeicients are unctions o electric ield alone (some models take into account urther temperature dependence) The choice o a suitable diusivity model poses some undamental problems As is well know, or ields below the threshold ield, the diusivity can be deined through a generalized Einstein relationship: D E ) µ ( E ) K bt q n ( (14) where K b is the Boltzmann coeicient and T n is the electron temperature assumed isotropic This relationship becomes invalid or E>E C In this case, the diusivity may be modeled as an Einstein relation in lattice temperature T with one additional Gaussian term, to give [6]: K ª º b T E 4000 D( E) µ ( E) 800exp (15) q «1650 ¹» ¼ The diusivity dependence on the electric ield has been computed according to the relations (14) and (15) Figure 3 represents a comparison between these results and those obtained rom Monte Carlo simulations o Pozela and Reklaitis [7] ReY Im> 1 Ri 0 1 (10) W Cds > Ri Re> 1 Im 1 1 arcsin ¹ () > Im (1) gds Re> (13) Figure : Several models o the diusivity-electric ield relation at room temperature

3 III RESULTS AND DISCUSSION The simulated results (MEF) o the current versus gate-voltage curves o the device (igure 3) compared with the meaured reults MEAS) [8] are shown in igure 4 A variable mesh spacing is used to optimize speed and accuracy o the solution (Figure 4) The mesh spacing criteria was based on the potential dierence between the mesh nodes The space steps are restrained to a maximum o a Debye length in the active channel and or numerical stability it has been ound that an average step width o around 0,03 µm in the active channel is necessary or a doping level o cm -3 In order to achieve a physically meaningul solution, the time step 't is limited to less than the dielectric relaxation time and to avoid degrading the accuracy o the numerical solution, 't is usually selected to lie in the range (10 to 5) s Figure 3: Two-dimensional cross section o a 05µm MESFET geometry Transient data The device was also analyzed with regard to their transient behaviors In order to determine the our Y parameters, two excitations are needed: one in the gate voltage and the other in the drain voltage It must be stressed that the voltage-step amplitude must be suiciently small, so as to avoid harmonic excitation in the device response, and large enough to get signiicant variations in the currents that dominate over numerical and physical noise We have applied 'V 1 =015V or the case o the gate and 'V =05V or the case o the drain Figure 5 illustrates the transient response o the gate and the drain currents at the bias point V GS =-10V, V DS =0V A signiicant source current was ound only during the irst 1ps ater the step was applied This spike is proportional to the time derivative o the applied voltage perturbation and is pure displacement current The correct evaluation o these current spikes is essential [1] In our case this is assured by the value adopted or the time step (10s) in the simulation, which is small enough to this purpose The duration o the transient changes depending on the operating point The intrinsic Y parameters were obtained rom the transients o igure 8 by means o (1) and () The inal step in this procedure is to apply (7)-(13) to the previous Y parameters in order to determine the values o the SSEC elements The dependence on requency o the intrinsic elements obtained in this way is shown in igure 6 Beore averaging the parameters over requency, we plot versus requency the relative parameter, deined as an oset plus the parameter at requency point divided by the average With the exception o the transconductance which varies slightly according to the requency and the channel resistance which starts to decrease rom 3 GHz It can be observed that all o them are requency constant at least-up to 55 GHz This means that the proposed SSEC describes correctly the AC behavior o the MESFET or this bias point, where the drain current is not very high and the accumulation o carriers between the gate and the drain is not important The value o cut-o requency T can be calculated by dividing by (+) We get T =15 GHz Figure 4 :Comparison o the simulated characteristics I-V with Finite Element Method and measured [8]

4 CONCLUSION A inite element method or the calculation o the FET SSEC has been described and applied to MESFET s The method consists in the excitation o the dierent elements rom the requency dependent Y parameters o the intrinsic FET, obtained rom the Fourier analysis o the device transient reponse to voltage perturbations at the terminals inally, the inite element method, which uses a correcting actor to model the ield-dependent diusivity-to-mobility ratio, has been a powerul tool to check the validity o small-signal models Figure 6 : Elements o the intrinsic small-signal equivalent circuit at the working point in saturation corresponding to V GS =-1V, V DS =V (a) capacitances, (b) conductances, (c) intrinsic resistance and delay time Figure 5 : Transient reponse in the gate and drain currents o MESFET to a voltage step o amplitude and applied at t=0 over the stationary point corresponding to V GS =-1V, V DS =15V (a) 'V GS =015V, (b) 'V DS =05V

5 REFERENCES [1] TOMAS GONALE and DANIEL PARDO «Monte Carlo Determination o The Intrinsic Small-Signal Equivalent Circuit o MESFET s»ieee TRANSACTIONS ON ELECTRON DEVICES, VOLED-4, No4,APRIL 1995 [] DAMBRINE G, CAPPY A HELIODORE F and PLAYE E «A New Method For Determining The FET Small-Signal Equivalent Circuit» IEEE TRANSACTIONS ON Microwave Theory and Techniques, VOLMTT-36, pp51-59, JULY 1988 [3] MKAMECHE and M FEHAM Finite Element Determination o the Intrinsic Small- Signal Equivalent Circuit o MESFET s microwave Journal, Vol 44, No 8, pp 84-9, August 001 [4] M KAMECHE «Analysis and Modeling o the Microwave MESFET by Finite Element Method», Thesis o Master, University o Tlemcen, Algeria, (000) [5] L SCHARFETTER and H K GUMMEL «Large-Signal Modeling o GaAs MESFET Operation» IEEE TRANSACTIONS ON ELECTRON DEVICES, VOLED-30, pp , 1983 [6] RODERICK W McCOLL, RONALD L CARTER, JOHN MOWENS and TSAY-JIU SHIEH «GaAs MESFET Simulation Using PISCES With Field Dependent Mobility- Diusivity Relation» IEEE TRANSACTIONS ON ELECTRON DEVICES, VOLED-34, NO10, OCTOBER 1987 [7] POELA J and REKLAITIS A «Electron Transport Properties in GaAs at High Electron Field» Solid State Electronics VOL3, pp97-933, 1980 [8] P R Riemenschneider and K L Wang A Finite-Element Program or Modeling Transient Phenomena in GaAs MESFET s,, IEEE TRANSACTIONS ON ELECTRON DEVICES, VOLED-30, NO9, SEPTEMBER 1983