International Journal of Engineering Technology, Management and Applied Sciences. June 2015, Volume 3, Issue 6, ISSN

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1 Current Voltage and Transconductance 2-D Model for Dual Material Gate Al m Ga 1-m N/GaN Modulation Doped Field Effect Transistor for High Frequency Microwave Circuit Applications Rahis Kumar Yadav 1 Department of Electronics and Communication Engineering, SET, Sharda University Plot No , Knowledge Park III, Greater Noida, Uttar Pradesh, , India Pankaj Pathak 2 Department of Electronics and Communication Engineering, SET, Sharda University Plot No , Knowledge Park III, Greater Noida, Uttar Pradesh, , India R M Mehra 3 Department of Electronics and Communication Engineering, SET, Sharda University Plot No , Knowledge Park III, Greater Noida, Uttar Pradesh, , India ABSTRACT In this paper we present current voltage and trans-conductance model for Dual Material Gate AlGaN/GaN HEMT. Our proposed model demonstrates complete charge control in 2DEG based channel of the device in order to investigate the current-voltage as well as transfer characteristics of the device under various gate and drain biases. The proposed device structure uses GaN material capable to withstand higher breakdown voltage with polarization induced charge carrier density to achieve higher channel current density at higher operating voltages [24]. Our model and TCAD simulation results reveal that DMG AlGaN/GaN HEMT structure is capable of minimizing short-channel effects (SCEs) in a better way as compared to the available conventional devices due to the presence of the step in the channel potential distribution which is capable to screen the drain potential variation in the device operation. Our model accurately derives the currents by using accurate device threshold model based on analysis of two dimensional electron gas in the channel. It is found that work function difference of dual metal engineered gate design is reason behind the screening effect of the drain potential variation near the drain region resulting in suppressed drain induced barrier lowering (DIBL). The model effectively analyses current density in the device channels which is based on spontaneous and piezoelectric polarization induced 2-DEG density. High trans-conductance 162 ms/mm of our device model is attributed to improved charge control by dual material engineered gate structure design which further result in better electron transport properties in device channel. A good agreement between the results obtained from the model, ATLAS device simulator and published experimental data provides the validity and correctness of the proposed model. Keywords: HEMT-High electron mobility transistor, 2DEG-two dimensional electron gas, SCE- short channel effect, DMG-Dual Material Gate, DIBL-drain induced barrier lowering. 1. INTRODUCTION The high electron mobility transistor (HEMT) is also called heterostructure field-effect transistor (HFET), or modulation doped field-effect transistor (MODFET). Development of HEMTs started in 1980 [22], immediately after the successful experiments on modulation doped AlGaAs/GaAs heterostructures [23], which revealed the formation of a twodimensional electron gas (2DEG) with enhanced electron mobility. Compound semiconductor based hetrostructure devices based on AlGaAs/GaAs material system superseded MESFETS in terms of device switchnig speed. Presently device scientist shifted their focus on devices particularly fabricated using AlGaN/GaN as compound semiconductor material system. These GaN based devices are emerging as a better option for utilization in ultra high speed digital systems working and high power high frequency microwave applications. These are also suitable for advanced electronic system like radars and satelites operating at higher voltages and power. Device scintists. already already carried out lot of research work on AlGaAs/GaAs devices for optimization and performace enhancement The AlGaN/GaN High Electron Mobility Transistor (HEMT) or modulation doped field effect transistor (MODFET) are cutting edge technologies and need considerable attention of device engineers world wide for further innovation and performance optimization. AlGaN/GaN material system based hetrostructures devices are capable of providing high carrier saturation velocity, higher thermal stability while working at considerably higher breakdown voltages. The most important and rather 141

2 unique property of GaN based devices is pizoelectric and spontaneous polarization induced higher sheet charge density of 2-DEG at hetrointerface [1]. The gate engineered dual material gate AlGaN/GaN hetrostructure can meet the challenges of higher switching with higher output power density and operating voltages when compared with conventional AlGaAs/GaAs-HEMT [2],[3]. W. Long et al [4],[5] has fabricated a MODFET structure, the dual material gate DMGHFET, in which two different metals of different workfunction were used for making dual material gate by making them contact laterally. GaN material devices has problem of current collapse due to trapping/ detarpping states in deep forbidden gaps responsible for device performance degradation. A multi-layer structure of AlGaN/GaN double channel High Electron GaAsMobility Transistor (DC-HEMT) was presented with detailed design, fabrication and characterisation by Chu et. al.[6] having high current gain and minimized current collapse. An analytical model of potential and electric field distribution has been developed and reported for dual channel dual material gate DCDMG- AlGaN/GaN High Electron Mobility Transistor for introduction of step functions in each channel potential profile that provides screening effects in small channel devices finally suppressing short channel effects (SCE) and minmizing current collapse [19]. In this paper, we report a large signal and trans-conductance model depicting current voltage and transfer characteristics of DMG AlGaN/GaN HEMTs. Rongming Chu et al [6] have fabricated an efficient design of double channel structures also. Our proposed DMG AlGaN/GaN HEMT model incorporates dual material engineered gate approach in order to control electron transport effectively in the channel of HEMT device. However, so for no analytical large signal model is developed for DMG AlGaN/GaN HEMT which incorporates benefit of dual material gate in the single channel device structure. 2. MODEL DERIVATION The schematic view of the structure of double channel Al 0.3 Ga 0.7 N/ GaN HEMT, where L=1 µm is length of the gate metal as shown in Fig.1. The gate electrode is schottky barries placed on AlGaN cap layer of 3nm thickness.cap layer is further placed over Si doped barrier layer of 18 nm thickness. A spacer layer of 3 nm thickness is used between top barrier layer and 14nm thick GaN channel layer in order to reduce impurity scattering. Gate is made of Ni-Au forming Schottky junction with semiconductor. This metal gate modulate the charge in the two conducting channels (top channel and bottom channel) formed at hetrointerface of Al 0.3 Ga 0.7 N / GaN / Al m Ga 1-m N / GaN epi-layers in the device. Undoped AlGaN spacer layer is introduced to reduce ionized scattering in the device. In the device structure the source and drain + contact regions are uniformally doped as N d =10 26 m -3 to make ohmic contacts. It is assumed that Si doped Al 0.3 Ga 0.7 N barrier layer is fully depleted under normal operating conditions and electons are confined in both the channels to the GaN side hetrointerface forming 2-DEG for each channel. SOURCE GATE L 1 L 2 M 1 M 2 DRAIN Cap layer thickness (d c ) = 3 nm (intrinsic Al 0.3Ga 0.7N) N d + Barrier layer thickness (d b ) = 30 nm (Si-doped Al 0.3Ga 0.7N) N d Spacer layer thickness (d s ) = 3 nm (intrinsic Al 0.3Ga 0.7N) N d + 2-DEG Channel Channel layer thickness (d ch) = 2.5µm SAPPHIRE SUBSTRATE 142 Fig.1. Cross sectional schematic of DMG AlGaN/GaN HEMT grown on sapphire substrate based on [26], DMG gate length is L=L 1 +L 2 =1µm, L 1 =L 2 =0.5 µm, work function of gate metal M 1 =5.3V and M 2 =4.1V, Gate width (Z) =2x50μm, N d =2x10 24 m -3, N d + =1x10 26 m -3, 2DEG depth in intrinsic GaN layer is Δd. d=d c +d b +d s +Δd is distance of channel from dual material gate surface, Al mole fraction

3 For normally on device the Si-doped barrier layer is fully depleted without any gate bias and 2 DEG channel is available for current conduction. When an external bias is applied the n-al m Ga 1-m N barrier layer with Al mole fraction m=0.3 is depleted partially at the hetrointerface by the electron diffusion into the channel and partially at the gate surface due to Schottky barrier [7-9]. For complete charge control by the gate the channel region must completely overlap to deplete the n-algan layers so that only 2-DEG high mobility charge carriers take part in current conduction process in channel with out any parasitic conduction path. Considering spontaneous and pizoelectric polarization at the hetrointerface the sheet carrier concentration of 2-DEG in channel under M 1 is obtained [15] as (1) With as Al m Ga 1-m N dielectric constant, and m=0.3 is Al mole fraction in it, and are potentials under gate regions M 1 and M 2 respectively at any point x along the regions, as gate to source bias, as separation between gate and channel. The device threshold voltages is the gate to source voltage at which or becomes equal to double of flatband voltage and occurs under metal gate regions M 1 and M 2 for the channel and obtained [10] as where and is are the Schottky barrier height with gate regions M 1 and M 2 rsepectively, as the conduction band discontinuity at the Al m Ga 1-m N/GaN hetrointerface. N d is Si doping concentration of n-algan layer, net polarization induced sheet carrier density at the hetrointerfaces and obtained as ] (5) is higher than for Schottky junctions as M 1 has higher work function than that of M 2 thus will be effective threshold voltage overall 2DEG channel current control. Where and are spontaneous polarization of Al m Ga 1-m N and GaN compound semiconductor material respectively [1][11][12]. In our model piezoelectric polarization depends on the amount of strain developed at AlGaN/Gan hetrointerface in order to accommodate the difference in lattice constants of AlGaN and GaN materials. For fully satrained device piezoelectric polarization dependent charge density is obtained as for 0 m 1 (2) (3) (4) for 1 (6) Whre is lattice constant and are piezoelecric constants and and are elastic constants for hetrointerface12][13]. Increasing Al mole fraction in barrier layer increases lattice mismatch that further results in stain relaxation. For partially relaxed device with Al m Ga 1-m N layer thickness in the range of 18nm to 40 nm piezoelectric polarization induced charge density depends on the Al mole fraction as [14] (7) In above equation (7) device remains completely strained for Al molefraction up to 38% and partially relaxed for m from 38% to 67%. Device is fully relaxed for m greater than 67%. 143

4 Table 1. List of material parameters of Al m Ga 1-m N/GaN for m=0.30 lattice constant Ȧ lattice constant Ȧ piezoelectric constant (x,y) C/m 2 piezoelectric constant (z) C/m 2 elastic constant (x,y) G Pa elastic constant (z) G Pa spontaneous polarization GaN C/m 2 spontaneous polarization Al m Ga 1-m N C/m 2 [A] Current voltage characteristics model: Linear region model: Double channel device current can be obtained using current density equation for upper and lower channel as where Z is gate width, and are channel potential in upper channel along x axis respectively under M 1 and M 2 respectively, and are channel potential in lower channel along x axis respectively under M 1 and M 2 regions, q is electron charge, k is Boltzmann constant, T is ambient temperature. The field dependent electron mobility in each channel is obtained [16][17] as Where, µ 0 is low field mobility, is critical electric fields for the channel, and is saturation drift velocities of the electrons in channel. Using (1) and (16) in (12) we obtain (8) (9) (10) (11) (12) where (13) (14) Among the above listed series currents sources, and are more effective due to higher Schottky barrier height under gate region M 1, therefore, integrating (11) and (12) with boundary conditions at (15) By integrating (19) and (21) with boundary conditions at, the drain side for the channel ) (16) Where,, is total gate length, is applied drain bias, and are parasitic source and drain resistances respectively. The linear current equation for the device is obtained as (17) Where, (18) 144

5 Saturation region model: In saturation region, at onset of saturation the potential in the channels attains drain saturation voltage, and respectively under gate regions M 1 and M 2. Similarly, electric field attains critical value.we obtain two series currents in saturation region as and in the channel, where being more effective under M 1 region due to its higher work function, can be obtained from equation (17) by substituting by as where (19) (20) (21) (22) (23) (24) Where, (25) [B]Transfer characteristics model Modeling of trans-conductance parameter is important for prediction of microwave performances of DMG Al m Ga 1-m N/ GaN HEMT. Derivation of device trans-conductance: This parameter is important for optimization of DMG AlGaN/GaN HEMT high frequency behavior. This parameter is evaluated for the device as Using expression of in (26) we obtain channel trans-conductance in as (26) (27) 3. RESULTS AND DISCUSSIONS In order to verify the our proposed DMG AlGaN/GaN HEMT current voltage characteristics and transconductance model, the numerical model results obtained have been compared with simulated and experimental results [26]. Fig. 2 shows the device drain current in the channels as extracted from the proposed model, ATLAS device simulation [21] and experimental data. In this figure, the dash lines represent the model results while the solid lines display experimental data and triangular markers show simulated data for various gate to source bias. This figure clearly shows output characteristics of device in linear and saturation regions at gate to source voltages steps from -1.5, 0V and 2.0 V. The drain current of the device is increasing from approximately350 ma/mm to 750 ma/mm with increasing gate to source bias. These results are in close agreement wih reported experimental data. Fig.3 shows the input current voltage / transfer characteristics of dual material gate AlGaN/GaN HEMT depicting variation of drain current wih gate to source voltage at V ds = 10 V with gate width 2x 50 µm channel length of 1µm device. The DMG AlGaN/GaN HEMT shows high current density with respect to conventional single channel AlGaAs/GaAs HEMT and also have good control of gate voltage on device drain current[18][27]. The derived model results fit simulation and experimental data [26] reasonably well with a marginal discrepency at higher gate biases. This may be attributed to minor gate and substrate leakage current that become more dominent, at higher drain voltage, therefore, causing large electric fields at the drain end of the gate. Also, under the low gate biases the drain current of our 145

6 model is little higher than the experimental data, which might be attributed to the error of the calculated threshold voltages. The reason can be that the approximation of the full depletion is introduced to obtain the threshold voltage, which assumes that there is no free charge in the spacer layer and that the doners in the n-algan layer have been totally ionized. Thus we may interprete that there is no parasitric conduction path in Si doped n-algan barrier layer due to thin width and Schottky and hetrojunction depletion regions are overlapping each other. 146

7 4. CONCLUSIONS The current voltage characteristics and transconductance parameters of dual material gate DMG Al m Ga 1-m N/GaN MODFET has been first time examined by developing 2-D model for the device. The charge control expressions for device channel current and transconductance, have been derived based on compound semiconductor device physiscs. The model clearly proves the superiority of dual material gate Al m Ga 1-m N/GaN HEMT over conventional single material gate AlGaN/GaN HEMTs in terms of comparable current drive capability with minimization of short channel effects. This is possible due to better charge transport efficiency of device. The results obtained from our numerical model agree well with the simulated and experimental results within the reasonable range of ± 5%. It is evident from the results that DMG Al m Ga 1-m N/GaN HEMT introduces step functions in each channel potential profile due work functiomn differences in gate engineered dual material structure, thus providing screening effects in small channel devices and suppressing short channel effects (SCE). The enhanced channel potential near source further results into more uniform average drift velocity of electrons in both the channels. This further leads to improve carrier transport efficiency in our proposed device structure. Due to compratively higher break down electric field capability of GaN material, this MODFET is suitable for high power, high voltage and high speed microwave circuit applications. REFERENCES [1] O. Ambacher, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M.Murphy, W. J. Schaff, L. F. Eastman, R. Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck, Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures, J. Appl. Phys, vol. 85, no. 6, pp ,Mar [2] U. K. Mishra, P. Parikh, and Y. F. Wu, AlGaN/GaN HEMTs An Overview of Device Operation and Applications, Proc. IEEE, vol. 90, no.6, pp , Jun [3] K.Kasahara, N. Miyamoto, Y. Ando, Y. Okamoto, T. Nakayama, and M.Kuzuhara, Ka-band 2.3 W power AlGaN/GaN hetrojunction FET, in IEDM Tech. Dig., pp , Dec [4] W. Long, H. Ou, J. M. Kuo and K.K Chin., "Dual-Material G a t e (DMG) Field Effect Transistor, IEEE Trans. Electron Devices, vol. 46, pp , May [5] W. Long et.al. Methods for fabricating a dual material gate of a short channel field effect transistor, US Patent, US , Nov [6] ] Roanming Chu,Yugang Zhou, Zie Liu, Deliang Wang, Kevin J. Chen, AlGaN/GaN Double Channel HEMT, IEEE Transaction on Electron Devices, vol.52, no.4, Apr [7] P.M. Soloman and H Morkov modulation doped GaAs/AlGa As hetrojunction field effect transistor (MODFETs), ultrahighspeed device for supercomputers, IEEE Trans Electron Devices ED-31 (1984), [8] H. Morkov, H. Unlu and G.Ji, Principle of technology of MODFETs. Wiley, New York, 1991 [9] D. Delagebeaudeuf, NuyenT.Linh, Metal-(n)AlGaAs/ GaAs Two Dimensional Electron Gas FET, IEEE Trans Electron Devices, vol.ed-29, no.6, pp , Jun [10] S.M. Zee,Physics of semiconductor devices, Wiley New York, 2 nd Ed, [11] E.S. Hellman, The polarity of GaN: A critical review, MRS Internet J. Nitride Semiconduct. Res. 3, vol. 11, pp. 1-11, [12] Y.Zhang,I.P.Smorchkova, C.R.Elsass, S.Kellar, J.P.EIbbetson, S.Denbaars, U.K.Mishra ans J.Singh Charge control and mobility in AlGaN/ GaN Transistor:Experimental and theoretical studies J.Appl, vol.87, no11, pp , [13] T.Li,R.P.Joshi and C.Fazi Montecarlo evaluation of degeneracy and interface roughness effects on electron transport in AlGaN/ GaN hetrostructures J.Appl,Phys vol.88, no.2, pp ,2000. [14] O. Ambacher, B.Foutz J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M.Murphy, A.J. Sierakowski, W. J. Schaff, L. F. Eastman, R. Dimitrov, M. Stutzmann and A Mitchell Two-dimensional electron gases induced by spontaneous and piezoelectric polarization in undoped and doped AlGaN/GaN heterostructures, J. Appl. Phys, vol. 87, no. 1, pp , [15] Rashmi, A.Agrawal, S.Sen, S.Halder, R.S.Gupta, Analytical model for DC characteristics and small signal parameters of AlGaN/GaN Modulation Doped Field Effect Transistor for microwave applications, Microwave and Optical Technology Lett, vol.27, pp ,

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