High-electron-mobility transistors (HEMTs) have been highlighted as essential high-frequency devices for various state-of-the-art microwave or millimeter-wave application systems, such as satellite communication, electronic warfare, radiometry, base stations, and smart weapons [1-3]. These systems require not only excellent radio frequency (RF) characteristics but also high-power 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 gate-fieldplate 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 gate-field-plated 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 multi-finger 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 in R_{g}. The use of a wide-head T-gate was reported [11] as an exemplary method for suppressing R_{g}; however, this technique has a limit in expanding the gate head because high source-to-drain channel resistance is unavoidable under increased source-drain spacing for accommodating a wide gate-head dimension; consequently, the structural instability of the T-gate increases in this structure. Even though studies [13-15] have documented the critical role of R_{g} in the high-frequency characteristics of HEMTs based on a small-signal- equivalent circuit model, there has been minimal investigation in reducing R_{g} in HEMTs with long gate_ widths or multi-finger gates. In this study, we investigated the multi-finger structures of the HEMTs affecting R_{g} and high-frequency characteristics. Because R_{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 on R_{g} and the device characteristics by using various combinations of structural parameters for the 0.1-μm depletion-mode InGa- As/InAlAs metamorphic HEMT (MHEMT). To investigate the effects of N and w, 12 different gate peripheries were fabricated with various gate fingers (2, 4, and 6) and gate widths (25, 40, 50, and 70 μm). Except for the variations in N and w, we maintained the same epitaxial structure, gate length of 0.1-μm, and source-drain spacing of 2-μm for all fabricated devices, as described in the next section.
The MHEMT micrograph of the HEMT with four fingers is shown in Fig. 1.
As shown in Fig. 2, the MHEMT epitaxial structure was grown by molecular beam epitaxy on a semi-insulating GaAs substrate. The structures consisted of the following layers from the bottom: a 1000-nm In_{x}Al_{1-x}As linearly graded buffer layer with an indium mole fraction, x, linearly graded from 0 to 0.5; a 300-nm undoped In_{0.52}Al_{0.48}As buffer layer; a silicon delta-doped plane (1.3×10^{12}/cm^{2}), a 4-nm undoped In_{0.52}Al_{0.48}As spacer layer; a 23-nm undoped In_{0.53}Ga_{0.47}As channel layer; a 3-nm undoped In_{0.52}Al_{0.48}As spacer layer; a silicon delta- doped plane (4.5×10^{12}/cm^{2}); a 15-nm undoped In_{0.52} Al_{0.48}As Schottky barrier layer; and a 15-nm n-type In_{0.53}Ga_{0.47}As cap layer (6×10^{18}/cm^{3}). The grown epitaxial layer showed a two-dimensional 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 200-nm. AuGe/Ni/Au (140/30/160 nm) ohmic metallization showed a specific contact resistance of about 5×10^{―7} Ω-cm^{2} after rapid thermal annealing at 320℃ for 60 seconds in a vacuum. An electron beam lithography system (EBPG-4HR, Leica Microsystems Ltd., Buffalo Grove, IL, USA) was used to perform 0.1-μm T-shaped gate patterning upon completion gate_recess, gate metallization was performed by evaporating Ti/Au (50/400 nm) followed by metal lift-off. The MHEMTs were passivated with the Si_{3}N_{4} films (80 nm). Finally, a Ti/Au (30/700 nm) air-bridge interconnection was made to connect the source pad.
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 various N and w 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/μm and 0.57 mS/μm, respectively, as shown in Fig. 3. The w_{t} is hereafter defined as “total gate width” and given by the product of N and w. The scaling rules for these parameters are then simply expressed as:
High-frequency 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). Cut-off frequency (f_{T} ) and f_{max} were determined by extrapolating the h_{21} and U 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 average f_{T} and f_{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). The f_{T} increased slightly in a small w_{t} region and was saturated to a frequency of about 100 GHz; on the other hand, the f_{max} decreased continuously with the w_{t} in our whole experimental range of w_{t}, and the reduction ratio was a function of N.
To examine the effects of N and w_{t} on the small-signal parameters directly affecting f_{T} and f_{max}, all the parameters shown in Eqs. (2) and (3) [16,17] were extracted from the fabricated MHEMTs by the Dambrine method [18] and curve-fitted to simple functions of w_{t}. As shown in Table 1, gate-to-source capacitance (C_{gs}), gate-to-drain capacitance (C_{gd}), drain conductance (G_{ds}), and intrinsic transconductance (g_{m,int}) were proportional to w_{t}.
However, intrinsic resistance (R_{i}) and source resistance (R_{s}) were inversely proportional to w_{t}. All these parameters were functions of w_{t}. But were not functions of N; however, one exception was R_{g}, which was a function of both w_{t} and N.
The relationships of the fitted parameters with w_{t} can be explained as follows. C_{gs} is a function of C_{gso} which is gate-to-source capacitance per unit gate width, and therefore is expressed as
where C_{gso} is about 0.00089 pF/μm in our case. In the case of the C_{gd}, y-axis intercepts should also be considered. A non-zero C_{gd} at zero w_{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 y-axis intercept of C_{gd} was about 0.0049 pF, and the proportionality constant was about 0.000087 pF/μm. The linear relationship of G_{ds} with w_{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/μm in our case. R_{s} and R_{i} were inversely proportional to w_{t} and curve-fitted in the same way with the proportionality constants of about 190 and about 1,580 Ω？μm, respectively. The linear increase of g_{m,int} with w_{t} can be explained by the linear scaling rule of g_{m,ext} with w_{t}, as shown in Eq. (1); the proportionality constant was about 0.614 mS/μm.
R_{g} is a function of both N and w_{t}, as shown in Fig. 5, and can be expressed as Eq. (5) where ρ_{G} is the resistivity of the gate metal, and A is the cross-sectional area of the gate. R_{o} is the y-axis 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 open-ended gate structure shown in Fig. 6, I_{g} and the infinitesimal change of V_{gs} (δV_{gs}) over δx are given by Eqs. (6) and (7),
where L and h are gate-length and gate-height, respectively. The minus sign in Eq. (7) indicates that gate voltage decreases with increasing x. At x=0, V_{gs} is equal to V_{gs0}, gate terminal voltage. Gate voltage V_{gs} (x) is obtained by integrating Eq. (7) with the boundary condition at x=0.
The average gate voltage is equal to the integral of V_{gs} (x) from x=0 to W and then divided by W. After carrying out the definition, we find the average value to be
The average intrinsic gate resistance inside the gate electrode region from x=0 to w is then given by:
Investigations have focused on R_{o}, R_{g} when w approaches zero [21,22]; however, the model for R_{o}, is still not fully understood. In our case, the y-axis 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/μm, respectively, as shown in Fig. 4. Therefore, the scaling rules of the small-signal parameters can be summarized as follows:
f_{T} and f_{max} can be calculated by substituting each small-signal parameter of Eqs. (2) and (3) with the curve-fitting equations in Table 1. The calculated results are plotted in Fig. 4 with measurements at each N and w_{t}. Good agreement was obtained from the calculated f_{T} and f_{max} with the measured data over the entire range of measured w_{t}. Some discrepancies between the measurements and the calculations are due to the errors associated with the device process in pattern lithography. Because g_{m} and C_{gs} are both proportional to w_{t}, as shown in Eq. (2), f_{T} is not a function of w_{t}. From our calculations contained in Fig. 3, f_{T} showed an almost constant frequency of about 100 GHz above a w_{t} of about 100-μm. Below this w_{t} f_{T} a slight increase with w_{t} owing to the y-axis intercept effect of C_{gd}, as observed in many earlier studies [23,24]. Since f_{max} is a strong function of R_{g} as shown in Eq. (3), it is affected by both N and w_{t}. If we assume that G_{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 and w_{t} is required to achieve a maximum f_{max} in a given device technology. Obviously, a greater w_{t} produces a higher f_{max}; however, to increase the number of gate-fingers by reducing the unit gate width is more efficient than to simply increase the single-gate_width in order to maximize f_{max} at a given w_{t}.
We investigated the effects of N and w on the RF characteristics of 0.1-μm depletion-mode multi-finger MHEMTs and their small-signal parameters. C_{gs}, C_{gd}, G_{ds}, and g_{m,int} were all proportional to w_{t}; however, R_{i} and R_{s} were inversely proportional to w_{t}. R_{g} was proportional to both w_{t} and 1/N^{2}. f_{T} and f_{max} were calculated by using the small-signal models and curve-fitting equations from each extracted small-signal parameters. The calculations showed good agreements with the measurements, and the results demonstrated that a greater w_{t} produces a higher f_{max}; however, to maximize f_{max} at a given w_{t}, increasing the number of gate_fingers is more efficient than increasing the single-gate width. On the other hand, f_{T} showed an almost independent relationship with w_{t}. To our knowledge, this is the first successful demonstration of multi-finger gate-width scaling effects (individual effect of N and w_{t}) on HEMT devices operating at millimeter-wave frequencies.