Scaling Rules for MultiFinger Structures of 0.1μ m Metamorphic HighElectronMobility Transistors
 Author: Ko PilSeok, Park HyungMoo
 Organization: Ko PilSeok; Park HyungMoo
 Publish: Journal of electromagnetic engineering and science Volume 13, Issue2, p127~133, 30 June 2013

ABSTRACT
We examined the scaling effects of a number of gate_fingers (
N ) and gate_widths (w ) on the highfrequency characteristics of 0.1μ m metamorphic highelectronmobility transistors. Functional relationships of the extracted smallsignal parameters with total gate widths (w_{t} ) of differentN were proposed. The cutoff frequency (f_{T} ) showed an almost independent relationship withw_{t} ; however, the maximum frequency of oscillation (f_{max} ) exhibited a strong functional relationship of gateresistance (R_{g} ) influenced by bothN andw_{t} . A greaterw_{t} produced a higherf_{max} ; but, to maximizef_{max} at a givenw_{t} , to increaseN was more efficient than to increase the single gate_width.

KEYWORD
Scaling Rule , HEMT , SmallSignal Parameters , Gate Width.

Ⅰ. Introduction
Highelectronmobility transistors (HEMTs) have been highlighted as essential highfrequency devices for various stateoftheart microwave or millimeterwave application systems, such as satellite communication, electronic warfare, radiometry, base stations, and smart weapons [13]. These systems require not only excellent radio frequency (RF) characteristics but also highpower performances for their specific applications [4]. The enhancement of power characteristics can be achieved by improving the current level or breakdown voltage of the HEMTs. A variety of methods have been used to increase the power performance of HEMTs these include the GaN/AlGaN material system [5,6], the gatefieldplate technique [7,8], and the adoption of composite channel systems [9,10]. Most of these methods have focused on the enhancement of transistor power by increasing the breakdown voltage. These technologies, however, have some drawbacks, such as high cost and difficulty in material growth of the composite channel HEMTs, poor RF characteristics of the GaN HEMTs, and low electron mobility and large increase in the parasitic capacitances of the gatefieldplated HEMTs. As a consequence, in many application achieving a large current level by simply increasing the transistor gate_width (
w ) has been one of the most economic and practical methods in terms of circuit design and device fabrication.A very long gate width or multifinger gates are effective, but an increase in w gives rise to a large gate resistance (
R_{g} ), thereby causing degradation of noise characteristics [11] and the maximum frequency of oscillation (f_{max} ) [12]. Therefore, it preferable to achieve a long effective gate width with no significant increase or even reduction inR_{g} . The use of a widehead Tgate was reported [11] as an exemplary method for suppressingR_{g} ; however, this technique has a limit in expanding the gate head because high sourcetodrain channel resistance is unavoidable under increased sourcedrain spacing for accommodating a wide gatehead dimension; consequently, the structural instability of the Tgate increases in this structure. Even though studies [1315] have documented the critical role ofR_{g} in the highfrequency characteristics of HEMTs based on a smallsignal equivalent circuit model, there has been minimal investigation in reducingR_{g} in HEMTs with long gate_ widths or multifinger gates. In this study, we investigated the multifinger structures of the HEMTs affectingR_{g} and highfrequency characteristics. BecauseR_{g} is strongly influenced by a number of gate_fingers (N ) and gate_widths (w ) of the device structure, we examined the effects of all these parameters onR_{g} and the device characteristics by using various combinations of structural parameters for the 0.1μ m depletionmode InGa As/InAlAs metamorphic HEMT (MHEMT). To investigate the effects ofN andw , 12 different gate peripheries were fabricated with various gate fingers (2, 4, and 6) and gate widths (25, 40, 50, and 70μ m). Except for the variations inN andw , we maintained the same epitaxial structure, gate length of 0.1μ m, and sourcedrain spacing of 2μ m for all fabricated devices, as described in the next section.The MHEMT micrograph of the HEMT with four fingers is shown in Fig. 1.
Ⅱ. Device Fabrication
As shown in Fig. 2, the MHEMT epitaxial structure was grown by molecular beam epitaxy on a semiinsulating GaAs substrate. The structures consisted of the following layers from the bottom: a 1000nm In_{x}Al_{1x}As linearly graded buffer layer with an indium mole fraction, x, linearly graded from 0 to 0.5; a 300nm undoped In_{0.52}Al_{0.48}As buffer layer; a silicon deltadoped plane (1.3×10^{12}/cm^{2}), a 4nm undoped In_{0.52}Al_{0.48}As spacer layer; a 23nm undoped In_{0.53}Ga_{0.47}As channel layer; a 3nm undoped In_{0.52}Al_{0.48}As spacer layer; a silicon delta doped plane (4.5×10^{12}/cm^{2}); a 15nm undoped In_{0.52} Al_{0.48}As Schottky barrier layer; and a 15nm ntype In_{0.53}Ga_{0.47}As cap layer (6×10^{18}/cm^{3}). The grown epitaxial layer showed a twodimensional electron carrier density (
n_{s} ) of about 3.5×10^{12}/cm^{2} and a Hall mobility of about 9,700 cm^{2}/Vsec at room temperature.To fabricate the MHEMTs, we first isolated active areas by using mesa etching with an etchant of phosphoric acid/H_{2}O_{2}/H_{2}O (1:1:60) to reduce the thickness to 200nm. AuGe/Ni/Au (140/30/160 nm) ohmic metallization showed a specific contact resistance of about 5×10^{―7} Ωcm^{2} after rapid thermal annealing at 320℃ for 60 seconds in a vacuum. An electron beam lithography system (EBPG4HR, Leica Microsystems Ltd., Buffalo Grove, IL, USA) was used to perform 0.1
μ m Tshaped gate patterning upon completion gate_recess, gate metallization was performed by evaporating Ti/Au (50/400 nm) followed by metal liftoff. The MHEMTs were passivated with the Si_{3}N_{4} films (80 nm). Finally, a Ti/Au (30/700 nm) airbridge interconnection was made to connect the source pad.Ⅲ. Analysis of Device Scaling
The DC characteristics of each MHEMT were measured in an HP 4156 DC parameter analyzer. Drain current (
I_{ds} ) versus gate voltage (V_{gs} ) and transfer characteristics of the MHEMTs (at a drain voltage [V_{ds} ] of 1.2 V) were measured at variousN andw values. With the total gate width (w_{t} ), the saturation drain current (I_{dss} ) and maximum transconductance (g_{m,max} ) were linearly increased at constant slopes of about 0.58 mA/μ m and 0.57 mS/μ m, respectively, as shown in Fig. 3. Thew_{t} is hereafter defined as “total gate width” and given by the product ofN andw . The scaling rules for these parameters are then simply expressed as:Highfrequency characteristics of the fabricated MHEMTs were measured in the frequency range of 0.5 to 50 GHz using an HP8510C network parameter analyzer (Agilent Technologies, Palo Alto, CA, USA). Cutoff frequency (
f_{T} ) andf_{max} were determined by extrapolating theh_{21} andU gain curves, respectively, at a slope of 6 dB/octave. The DC and RF data were measured from each gate type of the MHEMTs at six different dies a 2.5×2.5 cm^{2} specimen. The averagef_{T} andf_{max} from the MHEMTs with 12 different gate types measured from six different dies were plotted respectively in Fig. 4 with their standard deviations (1σ ). Thef_{T} increased slightly in a smallw_{t} region and was saturated to a frequency of about 100 GHz; on the other hand, thef_{max} decreased continuously with thew_{t} in our whole experimental range ofw_{t} , and the reduction ratio was a function ofN .[Fig. 3.] Idss and gm versus wt of the metamorphic highelectron mobility transistors at various N.
To examine the effects of
N andw_{t} on the smallsignal parameters directly affectingf_{T} andf_{max} , all the parameters shown in Eqs. (2) and (3) [16,17] were extracted from the fabricated MHEMTs by the Dambrine method [18] and curvefitted to simple functions ofw_{t} . As shown in Table 1, gatetosource capacitance (C_{gs} ), gatetodrain capacitance (C_{gd} ), drain conductance (G_{ds} ), and intrinsic transconductance (g_{m,int} ) were proportional tow_{t} .However, intrinsic resistance (
R_{i} ) and source resistance (R_{s} ) were inversely proportional tow_{t} . All these parameters were functions ofw_{t} . But were not functions ofN ; however, one exception wasR_{g} , which was a function of bothw_{t} andN .The relationships of the fitted parameters with
w_{t} can be explained as follows.C_{gs} is a function ofC_{gso} which is gatetosource capacitance per unit gate width, and therefore is expressed aswhere
C_{gso} is about 0.00089 pF/μ m in our case. In the case of theC_{gd} , yaxis intercepts should also be considered. A nonzeroC_{gd} at zerow_{t} can be formed between the gate bus line and drain pad and this parasitic capacitance, in fact, has been observed in earlier studies [13,19,20]. In our case, the yaxis intercept ofC_{gd} was about 0.0049 pF, and the proportionality constant was about 0.000087 pF/μ m. The linear relationship ofG_{ds} withw_{t} can be understood such that the total sourcedrain conductance is given by (dI_{ds} /dV_{ds} per unit gate width)×w_{t} , and the corresponding proportionality constant was about 0.0355 mS/μ m in our case.R_{s} andR_{i} were inversely proportional tow_{t} and curvefitted in the same way with the proportionality constants of about 190 and about 1,580 Ω？μ m, respectively. The linear increase ofg_{m,int} withw_{t} can be explained by the linear scaling rule ofg_{m,ext} withw_{t} , as shown in Eq. (1); the proportionality constant was about 0.614 mS/μ m.R_{g} is a function of bothN andw_{t} , as shown in Fig. 5, and can be expressed as Eq. (5) whereρ_{G} is the resistivity of the gate metal, andA is the crosssectional area of the gate.R_{o} is the yaxis intercept obtained by linear curve fitting. This relationship can be obtained by assuming the gradual (linear) reduction in gate current (I_{g} ) density as the open end is approached, as illustrated in Fig. 6, and an essentially uniform displacement current fed from the bottom of the gate to the channel region of the HEMTs [21]. In the openended gate structure shown in Fig. 6,I_{g} and the infinitesimal change ofV_{gs} (δV_{gs} ) overδx are given by Eqs. (6) and (7),where
L andh are gatelength and gateheight, respectively. The minus sign in Eq. (7) indicates that gate voltage decreases with increasingx . Atx =0,V_{gs} is equal toV_{gs0} , gate terminal voltage. Gate voltageV_{gs} (x ) is obtained by integrating Eq. (7) with the boundary condition atx =0.The average gate voltage is equal to the integral of
V_{gs} (x ) fromx =0 toW and then divided byW . After carrying out the definition, we find the average value to beThe average intrinsic gate resistance inside the gate electrode region from
x =0 tow is then given by:Investigations have focused on
R_{o} ,R_{g} whenw approaches zero [21,22]; however, the model forR_{o} , is still not fully understood. In our case, the yaxis intercepts of the MHEMTs (N =2, 4, and 6) range from about 0.6 to 0.9 Ω, with the corresponding proportionality constants of about 0.0123, 0.0021, and 0.000515 Ω/μ m, respectively, as shown in Fig. 4. Therefore, the scaling rules of the smallsignal parameters can be summarized as follows:f_{T} andf_{max} can be calculated by substituting each smallsignal parameter of Eqs. (2) and (3) with the curvefitting equations in Table 1. The calculated results are plotted in Fig. 4 with measurements at eachN andw_{t} . Good agreement was obtained from the calculatedf_{T} andf_{max} with the measured data over the entire range of measuredw_{t} . Some discrepancies between the measurements and the calculations are due to the errors associated with the device process in pattern lithography. Becauseg_{m} andC_{gs} are both proportional tow_{t} , as shown in Eq. (2),f_{T} is not a function ofw_{t} . From our calculations contained in Fig. 3,f_{T} showed an almost constant frequency of about 100 GHz above aw_{t} of about 100μ m. Below thisw_{t} f_{T} a slight increase withw_{t} owing to the yaxis intercept effect ofC_{gd} , as observed in many earlier studies [23,24]. Sincef_{max} is a strong function ofR_{g} as shown in Eq. (3), it is affected by bothN andw_{t} . If we assume thatG_{ds} is negligible (ideal case without channel length modulation), Eq. (3) is simply expressed as [25]:Because
f_{T} is almost constant, we therefore obtain:Eq. (15) shows that a careful combination of
N andw_{t} is required to achieve a maximumf_{max} in a given device technology. Obviously, a greaterw_{t} produces a higherf_{max} ; however, to increase the number of gatefingers by reducing the unit gate width is more efficient than to simply increase the singlegate_width in order to maximizef_{max} at a givenw_{t} .Ⅳ. Conclusion
We investigated the effects of
N andw on the RF characteristics of 0.1μ m depletionmode multifinger MHEMTs and their smallsignal parameters.C_{gs} ,C_{gd} ,G_{ds} , andg_{m,int} were all proportional tow_{t} ; however,R_{i} andR_{s} were inversely proportional tow_{t} .R_{g} was proportional to bothw_{t} and 1/N ^{2}.f_{T} andf_{max} were calculated by using the smallsignal models and curvefitting equations from each extracted smallsignal parameters. The calculations showed good agreements with the measurements, and the results demonstrated that a greaterw_{t} produces a higherf_{max} ; however, to maximizef_{max} at a givenw_{t} , increasing the number of gate_fingers is more efficient than increasing the singlegate width. On the other hand,f_{T} showed an almost independent relationship withw_{t} . To our knowledge, this is the first successful demonstration of multifinger gatewidth scaling effects (individual effect ofN andw_{t} ) on HEMT devices operating at millimeterwave frequencies.

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[Fig. 1.] Micrograph of the fabricated chip with the fourfinger metamorphic highelectronmobility transistors.

[Fig. 2.] Epitaxial structure of the metamorphic highelectron mobility transistor.

[Fig. 3.] Idss and gm versus wt of the metamorphic highelectron mobility transistors at various N.

[Fig. 4.] Average fT and fmax as functions of the wt measured from the metamorphic highelectronmobility transistors of twelve different gate types and six different dies (calculation, solid line; measurement, symbols).

[Table 1.] Fitting equations of the smallsignal parameters

[Fig. 5.] Extracted Rg as functions of wt (fitting, solid line; measurement, symbols).

[Fig. 6.] Distribution of gate current in the gatewidth direction.