A New Study on the Temperature and Bias Dependence of the Kink Effects in S₂₂ and h₂₁ for the GaN HEMT Technology

Abstract

The aim of this feature article is to provide a deep insight into the origin of the kink effects affecting the output reflection coefficient (S₂₂) and the short-circuit current-gain (h₂₁) of solid-state electronic devices. To gain a clear and comprehensive understanding of how these anomalous phenomena impact device performance, the kink effects in S₂₂ and h₂₁ are thoroughly analyzed over a broad range of bias and temperature conditions. The analysis is accomplished using high-frequency scattering (S-) parameters measured on a gallium-nitride (GaN) high electron-mobility transistor (HEMT). The experiments show that the kink effects might become more or less severe depending on the bias and temperature conditions. By using a GaN HEMT equivalent-circuit model, the experimental results are analyzed and interpreted in terms of the circuit elements to investigate the origin of the kink effects and their dependence on the operating condition. This empirical analysis provides valuable information, simply achievable by conventional instrumentation, that can be used not only by GaN foundries to optimize the technology processes and, as a consequence, device performance, but also by designers that need to face out with the pronounced kink effects of this amazing technology.

1. Introduction

With the aim of enabling microwave engineers to exploit advanced transistor technologies at their best, increasing attention is being given to the investigation of the kink effects in the output reflection coefficient (S₂₂) and the short-circuit current-gain (h₂₁) of solid-state electronic devices made with different semiconductor materials, like silicon (Si), gallium arsenide (GaAs), and gallium nitride (GaN) [1,2,3,4,5,6,7,8,9,10,11,12,13]. The kink in S₂₂ consists in the change of the concavity of the function Im(S₂₂) versus Re(S₂₂) (i.e., from convex to concave and vice versa), while the kinks in h₂₁ consist of peaks that are detectable by plotting the magnitude of h₂₁ in dB versus the frequency on a log scale. As the kink effects can be interpreted in terms of the transistor equivalent-circuit elements, many studies have been developed to identify those ones playing a dominant role, depending on the specific case study. The origin of the kink effect in S₂₂ has been mostly ascribed to high values of the transconductance (g_m) [1,4,5,6], whereas h₂₁ can be affected by a first kink, originating from the resonance between the extrinsic inductances and the intrinsic capacitances [7,8,9,12,13], and a second kink, arising from the resonance of the extrinsic reactive elements [12,13]. It is worth underlining that an accurate study of the kink effects in S₂₂ and h₂₁ parameters of microwave transistors represents a powerful tool for microwave engineers for fabrication, modeling and design purposes. Device technologists might enhance or alleviate the kinks in S₂₂ and h₂₁, depending on the application constraints, simply through optimization of the device layout and structure. Device modelers can exploit the kinks in S₂₂ and h₂₁ for extracting equivalent circuit parameters (e.g., the resonance frequency associated with the first kink in h₂₁ has been used to accomplish the challenging task of determining the intrinsic output capacitance [7,8]). Circuit designers should properly take into account the kink effect in S₂₂, especially for the design of broadband output matching networks [14,15]. In addition, circuit designers can benefit from the kinks in h₂₁ as they enable achieving an increase in the current gain at the resonant frequencies. However, so far, the interest in obtaining active transistor operation at frequencies beyond the cut-off frequency (f_T) has been focused on bipolar transistors (e.g., by proper design of the so-called resonance phase transistor [16,17,18,19,20,21]), recent studies have shown that the achievement of a current gain even at frequencies higher than f_T is achievable also in FET transistors, owing to the kinks in h₂₁ [12,13].

This feature article is focused on investigating the kinks in S₂₂ and h₂₁ for the gallium-nitride (GaN) high electron-mobility transistor (HEMT) technology, which is receiving increasing attention for high-temperature and high-power applications at high frequencies [22,23,24,25,26,27,28,29]. In particular, the kinks are studied at different ambient (i.e., case) temperatures (T_a) and bias voltages (V_GS and V_DS). The study consists of a comprehensive examination of the experimental results based on scattering (S-) parameter measurements and an exhaustive interpretation of the achieved findings using the transistor equivalent-circuit model. Although GaN HEMT is used as a case study, the reported study is technology-independent as it is based on a standard equivalent circuit topology for FETs, thus making the achieved finding representative and generalizable for any FET. This is confirmed by previous studies which have already demonstrated that the appearance or absence of the kinks in S₂₂ and h₂₁ is simply rooted in the values of the equivalent circuit elements of the tested FET, besides the analyzed frequency range [1,6,9,12,13].

The remainder of this article is organized as follows. Section 2 is devoted to the analysis of the kink effect in S₂₂; Section 3 is focused on the investigation of the kink effects in h₂₁; and Section 4 summaries the main conclusions.

2. Kink Effect in S₂₂

The studied solid-state electronic device is a GaN HEMT with a gate length of 0.25 μm and a gate width of 1.5 mm (i.e., 10 × 150 μm) (see Figure 1a). It was manufactured in the GH25-10 technology by United Monolithic Semiconductors (UMS) [30,31,32], using an AlGaN/GaN heterostructure grown on silicon carbide (SiC) substrate with a field plate for power applications. This foundry process, entitling a power density of 4.5 W/mm with typical f_T of 25 GHz, is optimized for X-band (i.e., 8–12 GHz) high-power applications. The S-parameters were measured from 0.2 to 65 GHz under different bias conditions and at four ambient temperatures: 35 °C, 90 °C, 145 °C, and 200 °C. Subsequently, the h₂₁ parameter was straightforwardly calculated from the measured S-parameters by using conventional transformation formulas [33]. Figure 1b shows the small-signal equivalent circuit used for modelling the tested transistor. Firstly, the extrinsic elements were determined from S-parameters at “cold” pinch-off condition (i.e., V_DS = 0 V and V_GS = −4 V) and, subsequently, the intrinsic elements were calculated from the intrinsic admittance (Y-) parameters at each bias point [12].

Figure 2 and Figure 3 show the S-parameters measured at the four investigated ambient temperatures with V_DS = 30 V and for two values of V_GS: −3.5 V and −3.1 V, respectively. It can be observed that S₂₂ of the tested device is affected by the kink effect under both bias conditions. As illustrated in Figure 2f and Figure 3f, the kink effect can be detected also as a dip in the magnitude of S₂₂, due to two zeros occurring between two poles. This is in line with findings from previous studies showing that the kink effect in S₂₂ can be analyzed also in terms of poles and zeros [2,3,4,6]. The shape of the kink effect strongly depends on the combined effects of equivalent circuit elements whose values might remarkably vary with the operating conditions. By heating the device, the kink effect gets less pronounced and this can be attributed to the reduction of g_m which is associated to a decrease of the average velocity of the electrons drifting in the 2-D electron gas (2DEG) channel. As a matter of fact, g_m plays a dominant role in determining the appearance and the shape of the kink effect in S₂₂. A higher temperature leads also to a decrease in the drain-source resistance (R_ds), moving the starting point of S₂₂ closer to the short-circuit condition. By increasing T_a from 35 °C to 200 °C when V_GS is −3.5 V, g_m and R_ds decrease from 225.7 to 186.8 mS and from 189.7 to 146.7 Ω, respectively. Given the same increase in T_a but with V_GS = −3.1 V, g_m and R_ds decrease from 347.9 to 215.4 mS and from 138.9 to 135.2 Ω, respectively.

The reduction of g_m and R_ds at higher temperatures can be, respectively, noticed from the decrease in the low-frequency magnitudes of the forward transmission (S₂₁) and reflection coefficient S₂₂ (see Figure 2e,f and Figure 3e,f), since at relatively low frequencies S₂₁ and S₂₂ can be linked to g_m and R_ds as follows [34]:

$$S_{21}=-2g_{mExtr}\left(R_0//R_{dsExtr}\right)$$

(1)

$$S_{22}=\frac{R_{dsExtr}-R_0}{R_{dsExtr}+R_0}$$

(2)

$$g_{mExtr}=\frac{g_m}{1+g_m{R}_s+R_{ds}^{-1}\left(R_s+R_d\right)}$$

(3)

$$R_{dsExtr}^{-1}=\frac{R_{ds}^{-1}}{1+g_m{R}_s+R_{ds}^{-1}\left(R_s+R_d\right)}$$

(4)

where R₀ is the characteristic resistance (i.e., 50 Ω), while g_mExtr and R_dsExtr represent the extrinsic transconductance and drain-source resistance.

To focus attention on the V_GS dependence, Figure 4 illustrates the S-parameters measured at T_a = 35 °C, V_DS = 30 V and with V_GS equal to −3.5 V and −3.1 V. By varying V_GS from −3.5 to −3.1 V, the improvement of g_m leads to an increase of the low-frequency magnitude of S₂₁ and to an enhancement of the kink effect in S₂₂, whereas the decrease of R_ds leads to a shift of the starting point of S₂₂ towards the short-circuit condition.

As can be observed in Figure 5, the kink effect in S₂₂ vanishes when V_DS reaches 0 V and, in line with this finding, the dip in the magnitude of S₂₂ disappears. This is because, by reducing V_DS, g_m decreases and, in addition, its role is further diminished by the decrease of R_ds. As a matter of fact, R_ds is connected in parallel with the voltage-controlled current source (i.e., g_me^−jωπmV) and thus its reduction tends to short circuit the contribution of g_m, thereby contributing to the suppression of the kink effect in S₂₂ and to the decrease in the low-frequency magnitude of S₂₁ (see Equation (1)). The reduction of g_m and R_ds at lower V_DS can be, respectively, noticed from the decrease in the low-frequency magnitude of S₂₁ (see Figure 5e) and the shift of the starting point of S₂₂ closer to the short-circuit condition (see Figure 5d).

Figure 6a reports the comparison between measured and simulated S₂₂ at T_a = 35 °C, V_DS = 30 V, and V_GS = −3.1 V. Although the extraction of a model that can faithfully reproduce the behavior of a device with a large gate periphery over a broad frequency range reaching very high frequencies is quite a challenging task, the standard equivalent-circuit model is able to mimic the general trend of the measurements and, in particular, to predict the kink in S₂₂ and the dip in its magnitude too (see Figure 6b). Furthermore, as will be seen in the next section, the extracted model also allows the prediction of the two kinks in h₂₁. It is worth noticing that, in accordance with what is stated above, the kink effect in the simulated S₂₂ can be suppressed by reducing g_m and/or R_ds (see Figure 6c–f). This is because S₂₂ becomes kink-free by nullifying the value of g_m and/or its contribution. On the other hand, by increasing R_ds at a very high value, the shape of S₂₂ is modified somewhat and the starting point of S₂₂ shifts towards the open-circuit condition but with the kink effect still affecting S₂₂ (see Figure 6g,h). It is worth noticing that although changing only one element of the model might be not physically representative of a real device, repeating this type of analysis enables understanding of how each element impacts on the appearance and shape of the kinks and the physical soundness of the achieved outcomes is guaranteed by the fact that the equivalent-circuit model is a physically meaningful representation of the FET behavior. As an example, this type of powerful analysis has been conducted in a pioneering study to explore the origin of the kink effect in S₂₂ by varying the intrinsic element values, showing that g_m plays a dominant role [1].

As is well known, the most popular technique for determining the extrinsic circuit elements for FETs is based on using S-parameters measured under “cold” conditions (V_DS = 0 V, i.e., passive device) [35,36,37,38,39]. As there are no electrons drifting from source to drain when V_DS = 0 V, g_m is equal to zero, thus implying that S₂₁ becomes equal to S₁₂ and S₂₂ turns out to be kink-free. This is illustrated in Figure 7, showing S-parameters measured at two typical bias points used for modeling purpose: “cold” unbiased (i.e., V_GS = 0 V) and pinched-off (i.e., V_GS = −4 V) conditions. By moving from an open-channel to pinch-off condition, the starting point of S₂₂ shifts from the short-circuit to the open-circuit condition (see Figure 7d), owing to the increase of R_ds, but without the occurrence of the kink effect as g_m is kept at zero by biasing the device under “cold” condition.

3. Kink Effects in h₂₁

Figure 8 and Figure 9 report the measured h₂₁ at the four investigated ambient temperatures with V_DS = 30 V and for two values of V_GS: −3.5 V and −3.1 V, respectively. It is found that two peaks appear in h₂₁ at each bias condition. It has already been demonstrated in previous works that the first peak is due to the resonance between the extrinsic inductances and the intrinsic capacitances [7,8,9,12,13], whereas the second peak is due to the resonance of the extrinsic inductive and capacitive contributions [12,13]. The experiments show that the second peak is substantially insensitive to T_a, as expected considering that the extrinsic reactive elements are mostly temperature-independent, and the first peak is roughly independent of T_a, consistently with the slight temperature dependence of the intrinsic capacitances.

To focus attention on the V_GS dependence, Figure 10 illustrates h₂₁ measured at T_a = 35 °C, V_DS = 30 V and with V_GS equal to −3.5 V and −3.1 V. By varying V_GS from −3.5 to −3.1 V, the improvement of g_m leads to an increase of the low-frequency magnitude of h₂₁ but the two peaks are mostly insensitive to this variation of V_GS.

As can be observed in Figure 11, the first peak disappears at zero V_DS, owing to the reduction of R_ds that tends to short circuit the intrinsic capacitive contributions [7,9,12]. On the other hand, the second peak is mostly insensitive to V_DS, owing to the bias independence of the extrinsic reactive elements [12].

Figure 12a reports the comparison between measured and simulated h₂₁ at T_a = 35 °C, V_DS = 30 V, and V_GS = −3.1 V. As can be observed, the standard equivalent-circuit model is able to predict the two peaks in h₂₁. Figure 12b illustrates that a reduction of g_m results in a dramatic degradation of the low-frequency magnitude of h₂₁ but with the two peaks still affecting h₂₁. It is worth noticing that the first kink effect in the simulated h₂₁ vanishes by reducing R_ds to zero (see Figure 12c), whereas h₂₁ is substantially insensitive to an increase of R_ds (see Figure 12d).

4. Conclusions

We have reported a thorough and critical investigation of the kinks in S₂₂ and h₂₁ parameters for solid-state electronic devices. To gain a comprehensive and in-depth understanding of their origin, we have developed a measurement-based analysis focusing on a GaN HEMT as a case study. However, the achieved outcomes can be straightforwardly generalized to other FET types, since a standard topology of FET equivalent circuit has been successfully used for analyzing and comprehending the experiments. We have shown that the kink in S₂₂ depends on both temperature and bias conditions, the first peak in h₂₁ depends slightly on temperature and strongly on bias conditions, and the second peak in h₂₁ is substantially bias- and temperature-insensitive. We have reported an exhaustive interpretation of the experimental findings by using a standard transistor equivalent-circuit model as it allows capturing all the three observed kinks. The origin of the kink effect in S₂₂ is mostly due to a high value of g_m, the first peak in h₂₁ originates from the resonance between the extrinsic inductances and the intrinsic capacitances, and the second kink in h₂₁ originates from the resonance of the extrinsic inductive and capacitive contributions. A reduction of g_m allows only suppression of the kink effect in S₂₂, while a reduction of R_ds leads to the suppression of the kink effect in S₂₂ and the first peak in h₂₁ by short circuiting the contributions of g_m and intrinsic capacitances. On the other hand, it has been shown that the second peak in h₂₁ still occurs, independently of the reduction of g_m and R_ds.