Accurate numerical modelling the GaAs MESFET current-voltage characteristics

In this paper, we present a computing model of the current-voltage (I-V) characteristics of a gallium arsenide Schottky barrier field effect transistor called GaAs MESFET. This physical model is based on the two-dimensional analysis of the Poisson equation in the active region under the gate. In thi...

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Дата:	2004
Автори:	Merabtine, N., Khemissi, S., Zaabat, M., Belgat, M., Kenzai, C.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2004
Назва видання:	Semiconductor Physics Quantum Electronics & Optoelectronics
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/119205
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	Accurate numerical modelling the GaAs MESFET current-voltage characteristics / N. Merabtine, S. Khemissi, M. Zaabat, M. Belgat, C. Kenzai // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 4. — С. 389-394. — Бібліогр.: 10 назв. — англ.

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spelling	irk-123456789-1192052017-06-06T03:03:12Z Accurate numerical modelling the GaAs MESFET current-voltage characteristics Merabtine, N. Khemissi, S. Zaabat, M. Belgat, M. Kenzai, C. In this paper, we present a computing model of the current-voltage (I-V) characteristics of a gallium arsenide Schottky barrier field effect transistor called GaAs MESFET. This physical model is based on the two-dimensional analysis of the Poisson equation in the active region under the gate. In this frame, we elaborated a simulation software based on analysis of expressions that we have previously set up [1-3], the obtained theoretical results are discussed and compared to the experimental ones. 2004 Article Accurate numerical modelling the GaAs MESFET current-voltage characteristics / N. Merabtine, S. Khemissi, M. Zaabat, M. Belgat, C. Kenzai // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 4. — С. 389-394. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS: 85.30.Tv http://dspace.nbuv.gov.ua/handle/123456789/119205 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	In this paper, we present a computing model of the current-voltage (I-V) characteristics of a gallium arsenide Schottky barrier field effect transistor called GaAs MESFET. This physical model is based on the two-dimensional analysis of the Poisson equation in the active region under the gate. In this frame, we elaborated a simulation software based on analysis of expressions that we have previously set up [1-3], the obtained theoretical results are discussed and compared to the experimental ones.
format	Article
author	Merabtine, N. Khemissi, S. Zaabat, M. Belgat, M. Kenzai, C.
spellingShingle	Merabtine, N. Khemissi, S. Zaabat, M. Belgat, M. Kenzai, C. Accurate numerical modelling the GaAs MESFET current-voltage characteristics Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Merabtine, N. Khemissi, S. Zaabat, M. Belgat, M. Kenzai, C.
author_sort	Merabtine, N.
title	Accurate numerical modelling the GaAs MESFET current-voltage characteristics
title_short	Accurate numerical modelling the GaAs MESFET current-voltage characteristics
title_full	Accurate numerical modelling the GaAs MESFET current-voltage characteristics
title_fullStr	Accurate numerical modelling the GaAs MESFET current-voltage characteristics
title_full_unstemmed	Accurate numerical modelling the GaAs MESFET current-voltage characteristics
title_sort	accurate numerical modelling the gaas mesfet current-voltage characteristics
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	2004
url	http://dspace.nbuv.gov.ua/handle/123456789/119205
citation_txt	Accurate numerical modelling the GaAs MESFET current-voltage characteristics / N. Merabtine, S. Khemissi, M. Zaabat, M. Belgat, C. Kenzai // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 4. — С. 389-394. — Бібліогр.: 10 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv	AT merabtinen accuratenumericalmodellingthegaasmesfetcurrentvoltagecharacteristics AT khemissis accuratenumericalmodellingthegaasmesfetcurrentvoltagecharacteristics AT zaabatm accuratenumericalmodellingthegaasmesfetcurrentvoltagecharacteristics AT belgatm accuratenumericalmodellingthegaasmesfetcurrentvoltagecharacteristics AT kenzaic accuratenumericalmodellingthegaasmesfetcurrentvoltagecharacteristics
first_indexed	2025-07-08T15:25:21Z
last_indexed	2025-07-08T15:25:21Z
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fulltext	Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 389-394. © 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 389 PACS: 85.30.Tv Accurate numerical modelling the GaAs MESFET current-voltage characteristics N. Merabtine1, S. Khemissi2, M. Zaabat3, M. Belgat4, C. Kenzai4 1 Laboratoire Electromagnetisme et Telecommunication, Electronics Department, Faculty of Engineering, University, Mentouri, Constantine, Algeria E-mail: na_merabtine@hotmail.com 2 Departement de Seti, Faculté de technologie Université de khenchla, Algeria E-mail: saadekhemissi@yahoo.fr 3 Physics department, University of Oum-El-Bouaghi, Algeria E-mail: Zaabat@hotmail.com 4 Laboratoire des Couches Minces et Interfaces, Département de physique Faculté des Sciences, Université Mentouri de Constantine E-mail: musbelgat@yahoo.fr Abstract. In this paper, we present a computing model of the current-voltage (I-V) characteristics of a gallium arsenide Schottky barrier field effect transistor called GaAs MESFET. This physical model is based on the two-dimensional analysis of the Poisson equation in the active region under the gate. In this frame, we elaborated a simulation software based on analysis of expressions that we have previously set up [1-3], the obtained theoretical results are discussed and compared to the experimental ones. Keywords: gallium arsenide, field effect transistor, Poisson equation. Manuscript received 11.08.04; accepted for publication 16.12.04. 1. Introduction Essentially, the Gallium Arsenide Field Effect Transistors (GaAs FET) are high-speed and high- frequency devices. In this paper, we propose a simulation of the current-voltage (I-V) characteristics of a short-gate GaAs MESFETs. Computer-aided analysis is a useful technology for studying physical phenomena in semiconductors. Here, we presented two-dimensional simulation of GaAs MESFET considering the physical model. Two-dimensional solution of the Poisson equation has been obtained taking into account structure study results. 2. Physical model Fig. 1 shows a normal planar GaAs MESFET simulated in this paper. Two-dimensional physical model is used to solve the Poisson equation. This equation known in semiconductor physics is used in all the models to explain the different physical phenomena specific to the GaAs MESFET [4-6]. But the main problem for these models lies in the coupling of partial and nonlinear differential equations, which require to be simultaneously solved. The difficulty of putting down a valid hypothesis for the limit conditions at the free interface requires the resort to approximations the negligence of a certain number of terms that act negatively on the model exactness [4-6]. In this paper, we present an analytical model that combines the description of physical phenomena and simplicity of solving the respective mathematical equation. 3. Determination of the two-dimensional voltage in the active region The two-dimensional solution of differential equations using the Green method gives a distribution of the electric field under the region of the space charge area (SCA). The general Poisson equation is given by ε ρ− = ∂ ∂ + ∂ ∂ =Δ ),(),( 2 2 2 2 yx y V x VyxV cc c . (1) To calculate the voltage under the gate, the SCA is divided into two main regions shown in Fig. 1. • The region (1) is directly under the gate, it is considered as a region controlled by the gate. We use the uni-dimensional approximation to calculate the composant of the relation of the voltage Vq(x,y) specific to this region. • The region (2) outside the first region is considered as uncontrolled by the gate. The two-dimensional voltage of the channel under the gate is given as follows: Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 389-394. © 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 390 Fig. 1. Depletion regions controlled (1) and uncontrolled (2) by the gate. Fig. 2. Active area distribution according to the electric field variation. Fig. 3. Parasitic resistance of GaAs MESFET. ),(),(),( yxVyxVyxV lqc += , (2) where ,),(),(),( )( 0 gbi xh y d y d q VVdyyxeNyydyyxeNyxV ++ ε + ε = ∫∫ (3) and ( ) ( ) ( ) ( ) ( )yk Lk xkA Lk xLkAyxV ds l 1 1 1 1 1 1 1 sin sinh sinh sinh )(sinh),( ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − = (4) with [ ]∫ −= a qc s dyykyVyV a A 0 11 )sin(),0(),0(2 (5) and [ ]∫ −= a qc d dyykyLVyLV a A 0 11 )sin(),(),(2 . (6) dA1 and sA1 are the Fourier coefficients for the gate supplementary voltage for the drain and source sides, respectively [5], and a k 21 π = . If considering (3) and (4), the total voltage expression becomes ∫ +−+ ε = )( 0 ),(),(),( xh bigl d c VVyxVydyyxeNyxV . (7) 4. Current-voltage characteristics To calculate the drain current expression as a function of the drain voltage for different values of the gate voltage, we use the following hypothesis: • we neglect the current in the Y-axis, this approximation is valid for the short-gate components; • we suppose the electrons mobility constant; • we derived the channel in three regions according to the electric field value (Fig. 2) [6]. 5. Determination of the current general equation To calculate the drain current general equation, we used the uni-dimensional approximation to simplify the mathematical expressions. We also use the following expressions: dx dVNeµEyNeµJ dnxdnx −=−= )( r , (8) the drain current expression is given by ∫ ∫−=−= )( )(s a xh xxd dyJZdsJI , (9) using single integrals, the current expression is obtained by relation ( )⎥⎦ ⎤ ⎢⎣ ⎡ −−− ε = 3322 2 3 1)( 2 )( sdsd nd d hhhha L ZµeNI (10) where ( ) 2/1 2 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ε = gbi d s VV eN h , (11a) ( ) 2/1 2 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ −+ ε = gbid d d VVV eN h (11b) are the widths of the space charge area (SCA) respectively source side and drain side. Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 389-394. © 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 391 Fig. 4. Comparison of the I-V characteristics measured and calculated by the simulation for MESFETs 1 (a) and 2 (b). Fig. 5. Effect of the parasitic resistances on the I-V characteristics for MESFETs 1 (a) and 2 (b). Fig. 6. Effect of the side voltages Vls and Vld on the I-V characteristics for MESFETs 1 (a) and 2 (b). Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 389-394. © 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 392 Defining the pinch-off current Ip is given by L aZeNI d p ε μ = 2 )( 33 (12) and the pinch-off voltage Vp is given by 2 2 aeNV d p ε = . (13) The general equation expression IP in the channel becomes ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − +⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ −= 2/32/3 3 2 3 2 p gbi p gbid p d pd V VV V VVV V V II . (14) 6. Effect of the mobility law The hypothesis of the constant mobility and the independency of the electric field in the n-type GaAs can not convey the physical phenomena. The analytical expression of the mobility variations with the electric field used by us is a simplified relation [7, 8] given as follows: • for the weak electric field where E < E0 µ = µ0; (15a) • for the high electric field beyond E0 (E > E0) 2/12 0 0 1 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − + μ =μ sE EE . (15b) This mobility law allows to obtain the different expressions of the drain current in different operation regimes. Id (Vd,Vg) characteristics of the GaAs MESFET corresponding to different operation regimes obey the equations considered below. Table 1. Transistor L, μm A, μm Z, μm MESFET 1 1 0.153 300 MESFET 2 0.5 0.1435 300 Transistor μ0, m2/V⋅s Nd, 1023m–3 MESFET 1 0.4000 1.17 MESFET 2 0.4000 1.31 Transistor Vs, m/s Vbi,V Vp,V MESFET 1 3.6 ⋅103 0.85 1.93 MESFET 2 7.3 ⋅103 0.85 1.93 Table 2. Transistor a1 b1 c1 Vl /Vp MESFET 1 –0.10 0.10 0.05 0.01 MESFET 2 –0.14 0.10 0.04 0.01 6.1. Linear regime This regime exists as far as La occupies all the channel, it corresponds to the weak field area where the mobility is equal to µ0. The drain current expression in this regime is given as ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − +⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ −= 2/32/3 3 2 3 2 3 2 p gbi p gbid p d pld V VV V VVV V VII (16) where a d pl L aZµNeI ε = 2 3 0 22 . 6.2. Pinch-off regime As the drain voltage increases, the electric field in the channel increases beyond E0 .The channel under the gate can be then represented by two regions. One region of the length La in which the field is inferior to E0 and the electron mobility is constant and given by µ = µ0. Another region of the length Lb (L = La + Lb) in which the field is superior to the field E0 but inferior to the field Em, and the electron mobility is given by the expression (15b). First region: for E < E0 and 0 < x < La ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − −⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ −= 2/32/3 3 2 3 2 p gbi p gbida p da d pl a V VV V VVV V V I LI L . (17) Second region: for E0 < E < Em and La < x < L ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ +⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ − − = 2/32/3 3 2 p gbida p gbid p dad d ps b V VVV V VVV V VV I LI L (18) where 2/12 01 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − + = s p ps E EE I I . 6.3. Saturation regime In this case, the channel under the gate is divided into three regions La, Lb, and Lc where L = La + Lb + Lc. ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − −⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ −= 2/32/3 3 2 3 2 p gbi p gbida p da d pl a V VV V VVV V V I LI L , (19) Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 389-394. © 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 393 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ +⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ − − = 2/32/3 3 2 3 2 p gbida p gbidm p dadm d ps b V VVV V VVV V VV I LI L , (20) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ +⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ − − = 2/32/3 3 2 3 2 p gbidm p gbid p dmd d ps c V VVV V VVV V VV I LI L (21) where Vda and Vdm are successively maximum and pinch- off voltages for linear regimes. 7. Effect of the voltage Vl (x, y) The effect of the voltage Vl(x,y) is taken into consideration in the following expressions of the drain and gate voltages: Vd → Vd + Vld and Vg → Vg + Vls (22) where ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π == a hAhVV ss slls 2 sin),0( 1 , (23a) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π == a hAhLVV dd dlld 2 sin),( 1 . (23b) The coefficient expressions sA1 and dA1 are very complex [6], they are essentially related to the polarization voltages Vd and Vg and to the voltages Vbi and Vp: ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − −− += 2/1 1111 c V VVV baVA p lgbi p s , (24a) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − −−+ += 2/1 1111 c V VVVV baVA p lgbid p d . (24b) For uniform doping, the coefficients a1, b1, c1, and Vl are constants. 8. Effect of parasitic elements The characteristics that we have presented are those concerning internal or intrinsic dimensions (Id, Vd, Vg). To obtain the external or extrinsic characteristics (Ids, Vds, Vgs) of the component, we have to take into consideration the effect of the parasitic access source resistance Rs, the drain resistance Rd and also the effect of the resistance Rp parallel to the channel on the polarization voltages values (Fig. 3). To obtain the real expressions of the characteristics Ids(Vds, Vgs), we have to substitute the intrinsic terms by the extrinsic terms in all the previous relations. Therefore Vd = Vds + Vld – (Rs + Rd)Id, (25a) Vg = Vgs + Vls – RsId, (25b) Id = Ids – (Vd/Rp). (25c) 9. Results and discussion In order to validate the I-V characteristics of the GaAs MESFET set up in the previous work, a simulation software based on different formulas and equations is exposed, as well as the obtained results and their discussions. The numerical calculation of the drain current as a function of the polarization voltage calls the expressions (16) - (21) previously established. The study has been carried out on two MESFET 1 and MESFET 2 [6] parameters of which are summarized in the following Table 1. To calculate the voltages Vld and Vls (expressions (23a) and (23b)), the values of the used parameters a1, b1, c1, and Vl/Vp are tabulated in the Table 2. In order to check the validity of our model, we have compared the theoretical results with the experimental ones for the MESFET 1 and MESFET 2. In Figs 4a and b, we have respectively represented the comparison of the measured Ids(Vds,Vgs) characteristics and the calculated ones by the simulation for the MESFET 1 and MESFET 2. In the linear regime, i.e., at a weak drain voltage polarization, we notice a good agreement between the experimental values and the simulation ones for both transistors. When the drain voltage increases and becomes more important, we notice a certain difference between the experimental values and the results of the simulation. This difference progressively increases until the saturation. This difference is mainly caused by the approximations made in the mathematical model and the simulation software, it also stems from the geometric parameters effects and existence of parasitic quantum phenomenon, which we have not taken into consideration. In the saturation regime, when the drain voltage gets important, we notice that the theoretical results are in a good agreement with experimental ones. In conclusion, we also remark that the theoretical and the experimental results have the similar behavior towards the drain voltage and coincide well, notably at high values of the Vds voltage. This shows that the method is well founded. • Effect of source and drain parasitic resistances In order to put into evidence the effects of the source and drain parasitic resistances Rs and Rd on the I-V characteristics of the GaAs MESFET, in Figs 5a and b, in the case of the previous two transistors, we present the variations of the drain current as a function of the drain voltage with and without the parasitic resistance. • Effect of the voltage Vl (x, y) When solving the two-dimensional Poisson equation, it should be taken into consideration two voltages existing at the sides of the conducting channel: Vls source side and Vld drain side. Despite their very Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 389-394. © 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 394 weak values, these voltages influence the I-V static transistor characteristics. In Figs 6a and b, we present the effect of these side voltages for two studied structures. 10. Conclusion In this paper, we have proposed an analytical study of the I-V characteristics of the GaAs MESFET. The influence of parasitic elements and sides voltages Vls and Vld on the drain current Ids expression has been established, these latest voltages resulted from the two-dimensional analysis of the Poisson equation by the Green technique. This study allowed us to carry out a synthetic approach to this two-dimensional analysis to realize a valid exactness of the analytical model for static characteristics of the GaAs MESFET composant. References 1. S. Khemissi, Master thesis // Faculty of Sciences, Constantine University (2003). 2. N. Merabtine, Ph.D thesis // Faculty of Engineering, Constantine University (2003). 3. M. Zaabat. Ph.D thesis // Faculty of Technology, Oum El Bouaghi University (2004). 4. J. Haslett et al. // IEEE Trans. Electron. Devices 47 (5) (2000). 5. H. Tran et al. // Ibid. 39 (9) (1992). 6. B. Janiguez et al. // Ibid. 46 (8) (1999). 7. S.P. Chin, C.Y. We // Ibid. 40 (4) (1993). 8. K.M. Shin, D.P. Klamer, J.I. Lion // Solid State Electronics 35 (11) (1992). 9. C.S. Chang, D.Y. Day // IEEE Trans. Electron. Devices 36 (2) (1989). 10. S.P. Murray, K.P. Roenker // Solid State Electronics 46 (2002).

Accurate numerical modelling the GaAs MESFET current-voltage characteristics

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