Impact of Output Conductance on Current-Gain Cut-Off Frequency in In_xGa_1-xAs/In_0.52Al_0.48As Quantum-Well High-Electron-Mobility Transistors on InP Substrate

Abstract

In this study, we investigated the impact of intrinsic output conductance (g_oi) on the short-circuit current-gain cut-off frequency (f_T) in In_xGa_1-xAs/In_0.52Al_0.48As quantum-well (QW) high-electron-mobility transistors. At its core, we attempted to extract values of f_T using a simplified small-signal model (SSM) of the HEMTs and to derive an analytical formula for f_T in terms of extrinsic model parameters that are related with intrinsic model parameters of a general SSM. We projected how f_T was influenced by g_oi in HEMTs, emphasizing that the improvement in electrostatic integrity would also be of critical importance to fully benefit from scaling down L_g.

1. Introduction

The excellent carrier transport properties of In_xGa_1-xAs/In_0.52Al_0.48As material systems (x > 0.53) on an InP substrate, together with advances in material growth and device fabrication, have made In_xGa_1-xAs/In_0.52A_0.48As quantum-well (QW) HEMTs a strong candidate for high-frequency and terahertz (THz) system applications, as well as quantum computing applications [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Recent reports on the In_xGa_1-xAs/In_0.52A_0.48As QW HEMTs, with a f_T value in excess of 700 GHz [17,18] and noise temperature of 2 K at cryogenic operation [19], have been published.

Until now, paths to improve the f_T in HEMTs have involved reducing L_g down to below 30 nm, improving the mobility of two-dimensional electron gas (μ_n,2-DEG) in a QW channel, and minimizing all the parasitics such as series resistance and gate-fringing capacitance components [20,21,22,23,24,25,26,27,28,29,30,31].

In principle, the f_T of a HEMT in saturation is a figure of merit that is widely benchmarked to evaluate the suitability of HEMTs for high-frequency analog, mixed-signal, and logic applications. Moreover, the physical meaning of f_T is fundamentally indicative of electron transport through the intrinsic region of the QW channel. It is known that f_T increases with the decrease in L_g due to the reduction in the electron transit time under the gate, while parasitic components hinder f_T from linearly increasing with a reciprocal of L_g. Despite the fact that the impact of short-channel-effects (SCEs) on the logic characteristics of the HEMT has been extensively investigated [32,33], there have been few reports on how SCEs analytically affect the f_T of a HEMT as L_g scales down to below 100 nm.

In this study, we extracted and analyzed values of the f_T in In_0.8Ga_0.2As/In_0.52A_0.48As QW HEMTs on an InP substrate with L_g values ranging from 260 to 25 nm in three different manners: (i) a least-squares fit using experimental S-parameter data, (ii) a projection from both simplified and general small-signal models (SSMs), and (iii) a calculation from an analytical formula. These allowed us to systematically investigate how f_T was affected by g_oi as L_g aggressively scales down in these devices.

2. Fabrication Process

Figure 1 provides a description of the heterostructure used for device fabrication in this study. All the epitaxial layers were grown by metal–organic chemical vapor deposition (MOCVD) on a 3-inch semi-insulating InP substrate with a crystal orientation of (100). A strained 5 nm thick In_0.8Ga_0.2As subchannel layer was incorporated to enhance the carrier transport properties in the QW channel, together with a 3 nm thick undoped InP layer as a gate recess etch stopper. It also featured a multilayer cap design to enhance the tunneling efficiency between the heavily doped capping layer and the In_0.8Ga_0.2As composite QW channel layer through an In_0.52Al_0.48As barrier layer in the source and drain access regions. The capping layer design consisted, from top to bottom, of a 12 nm thick heavily doped In_0.53Ga_0.47As subcapping layer with a Si doping concentration of 2 × 10¹⁹ cm⁻³ to lower the actual metal–semiconductor contact resistivity (ρ_c), and a 15 nm thick heavily doped In_0.52Al_0.48As subcapping layer with a Si doping concentration of 5 × 10¹⁸ cm⁻³ to lower the overall potential barrier across the In_0.52Al_0.48As barrier in the source and drain access regions. In a Hall epi wafer without the multilayer capping design, the Hall mobility (μ_{n_hall}) and two-dimensional electron gas density (n_2-DEG) were measured to be around 13,500 cm²/V·s and 1.78 × 10¹² cm⁻² at room temperature, and 33,800 cm²/V·s and 1.74 × 10¹² cm⁻² at 77 K, respectively.

The device fabrication was comparable in detail to that we previously reported [34]. It involved a two-step recess process with a gate-to-channel distance (t_ins) of approximately 5 nm, as shown in Figure 2. The process began with device isolation by means of mesa etching using a dilute H₃PO₄-based wet-etching solution. Source-to-drain spacing (L_SD) was scaled down to 1 μm, and a nonalloyed metal stack of Ti/Mo/Ti/Pt/Au (5/10/10/10/25 nm) was used to form S/D ohmic contacts. Here, we intentionally thinned the S/D ohmic metals to 60 nm to obtain a uniform coating of the first ZEP e-beam resist in a trilayer e-beam resist scheme during T-gate e-beam lithography. From transmission-line method (TLM) analysis, an extremely low ohmic contact resistivity (ρ_c) of 9.4 × 10⁻⁸ Ω cm² and an excellent standard deviation (σ) of 9.9 × 10⁻⁹ Ω cm² across a 3 inch wafer were obtained. After contact pad formation of Ti/Au (20/500 nm), a 20 nm thick SiO₂ was created between the source and drain ohmic contacts by plasma-enhanced chemical vapor deposition (PECVD). After a gate recess process, a SiO₂-assisted T-gate with a metal stack of Pt/Ti/Pt/Au was created using a JBX-9300FS e-beam lithography machine operating at 100 kV, with the T gate placed in a tightly spaced source and a drain with less than 50 nm alignment accuracy. In this way, devices with three different L_g values of 260, 87, and 25 nm, were fabricated.

3. Theoretical Analysis of f_T

f_T in an HEMT is defined as a frequency such that its short-circuit current gain (h₂₁(f)) becomes a unity. This is mathematically given as

$$\left|h_{21}\left(f=f_T\right)\right|={\left|i_d/i_g\right|}_{v_{ds}=0}=1$$

(1)

Historically, f_T was extracted by using a least-squares fit of |h₂₁(f)|² with a slope of −20 dB/decade, which was transformed from the measured S-parameter data. In parallel, small-signal equivalent circuit models of HEMTs have been constructed to describe the high-frequency characteristics not only within but also beyond the measured frequency ranges. Figure 3a represents the most widely used general SSM of HEMTs. According to the previous report by Tasker and Hughes [35], a 1^st-order analytical formula for f_T was derived as

$$f_T=\frac{1}{2\pi }·\frac{g_{mi}}{\left[C_{gs}+C_{gd}\right]·\left[1+\left(R_s+R_d\right)g_{oi}\right]+C_{gd}{g}_{mi}\left(R_s+R_d\right)}$$

(2)

Using the equation above, many researchers have carried out delay time analysis [7,36,37,38,39,40], where the total delay (τ) of the HEMT consists of three terms: the intrinsic delay (τ_t), the delay through C_gd associated with the Miller effect (τ_ext), and the parasitic delay due to the series resistances of R_s and R_d (τ_par). Mathematically, the total delay and three delay terms are given as follows:

$$\tau ={\left(2\pi f_T\right)}^{-1}={\tau }_t+{\tau }_{ext}+{\tau }_{par}$$

(3)

$${\tau }_t=\frac{C_{gs\_i}+C_{gd\_i}}{g_{mi}}$$

(4)

$${\tau }_{ext}=\frac{C_{gs\_ext}+C_{gd\_ext}}{g_{mi}}$$

(5)

$${\tau }_{par}=\left(R_s+R_d\right)·\left\{C_{gd}+\left(C_{gs}+C_{gd}\right)·\left(g_{oi}/g_{mi}\right)\right\}$$

(6)

In most cases, the right-hand side (RHS) of Equation (6) is simplified as τ_par ~ C_gd (R_s + R_d), because the open-circuit voltage gain (g_mi/g_oi) was sufficiently large. As a result, this delay has been interpreted as the delay due to the parasitic series resistances of R_s and R_d. However, as L_g aggressively scales down, this is no longer true, and the impact of g_oi should be carefully considered. Moreover, it would be imperative to accurately extract the values of R_s and R_d; otherwise, this would affect not only other small-signal model parameters but also the delay terms even with the same f_T value.

Alternatively, a simplified SSM of the HEMT is shown in Figure 3b, where all the model parameters, such as g_{m_ext}, g_{o_ext}, C_{gs_ext}, C_{gd_ext}, and C_{ds_ext}, include the effects of the series resistance components (R_g, R_s, and R_d). As in [41,42], all the model parameters in Figure 3a,b could be extracted analytically from the measured S-parameter data.

Table 1. Modeled parameters of both general and simplified small-signal models (SSMs) for In_0.8Ga_0.2As/In_0.52Al_0.48As QW HEMTs with L_g = 260/87/25 nm, W_g = 2 $\times$ 20 μm, and R_s/R_d/R_g = 3.8/3.8/6 Ω.

	General SSM					Simplified SSM
Lg (nm)	gmi (mS/μm)	goi (mS/μm)	Cgs (fF/μm)	Cgd (fF/μm)	Cds (fF/μm)	gm_ext (mS/μm)	go_ext (mS/μm)	Cgs_ext (fF/μm)	Cgd_ext (fF/μm)	Cds_ext (fF/μm)
260	3.5	0.05	2.15	0.24	0.11	2.26	0.04	1.48	0.25	0.06
87	4.25	0.36	1.05	0.14	0.09	2.42	0.20	0.68	0.16	0.03
25	4.43	0.74	0.61	0.1	0.23	2.33	0.39	0.40	0.13	0.13

shows the modeled parameters of both general and simplified SSMs for In_0.8Ga_0.2As/In_0.52Al_0.48As QW HEMTs on InP substrate with L_g = 260, 87, and 25 nm [18]. Using the definition above, an analytical formula for the f_T of Figure 3b is expressed as

$$f_T=\frac{1}{2\pi }·\frac{g_{m\_ext}}{C_{gs\_ext}+C_{gd\_ext}}$$

(7)

Figure 4a plots three different types of short-circuit current gain against the measured frequency together with the least-squares fits with a slope of −20 dB/decade: (i) measured |h₂₁(f)|², (ii) simulated |h₂₁(f)|² from Figure 3a, and (iii) simulated |h₂₁(f)|² from Figure 3b. Figure 4b plots the locally extrapolated f_T at each frequency with a slope of −20 dB/decade. Note that both small-signal modeled current gains are in excellent agreement with the measured one, and their projected values of f_T are consistent with those from the analytical formula in Equation (7).

Table 2. Values of f_T extracted in different manners for the same family of In_0.8Ga_0.2As/In_0.52Al_0.48As QW HEMTs with L_g = 260/87/25 nm.

	Using a Least-Square Fit from 1 to 50 GHz			Using Analytical Equations (GHz)
Lg (nm)	From Measured S Parameters	From the General SSM	From the Simplified SSM	From Equation (7)
260	207	207	207	207
87	453	454	454	454
25	703	706	706	706

summarizes the f_T values using the different approaches explained above, indicating that the simplified SSM provides a fairly accurate value of f_T in a HEMT. In comparison with the approach using Equation (2), the approach proposed in this paper does not need to accurately extract values of R_s and R_d. Instead, the simplified SSM, which is from the extrinsic perspective of the equivalent circuit, can be robustly constructed directly from the measured small-signal S parameters of the device, where f_T can be analytically and uniquely given by Equation (7). To see how the intrinsic output conductance (g_oi) affects the f_T of short-L_g HEMTs, we derived analytical expressions for g_{m_ext}, C_{gs_ext}, and C_{gd_ext} in terms of the model parameters of the general SSM (Figure 3a). In the course of correlating admittance parameters between the general and simplified SSMs, Kirchhoff’s voltage and current laws, respectively, yield

$$g_{m\_ext}\approx \frac{g_{mi}}{1+g_{mi}{R}_s+g_{oi}\left(R_s+R_d\right)}$$

(8)

$$C_{gs\_ext}\approx \frac{C_{gs}\left[\left(1+g_{mi}{R}_d\frac{C_{gd}}{C_{gs}}\right)+\left(1+\frac{C_{gd}}{C_{gs}}\right)g_{oi}{R}_d\right]}{1+g_{mi}{R}_s+g_{oi}\left(R_s+R_d\right)}$$

(9)

$$C_{gd\_ext}\approx \frac{C_{gd}\left[\left(1+g_{mi}{R}_s\right)+\left(1+\frac{C_{gs}}{C_{gd}}\right)g_{oi}{R}_s\right]}{1+g_{mi}{R}_s+g_{oi}\left(R_s+R_d\right)}$$

(10)

Here, we made two approximations: (i) ignorance of the 2^nd-order of the frequency terms (ω²), and (ii) ignoring the effect of τ. This makes sense because the effects of both were negligible in the measured frequency ranges from 1 to 50 GHz. Interestingly, all the three equations contain the same form of the denominator, including the terms of g_mi × R_s and g_oi × (R_s + R_d). Both make the extrinsic model parameters apart from the intrinsic model parameters. Plugging the results obtained in Equations (8)–(10) to Equation (7), we can derive Equation (2) and obtain a complete picture how f_T evolves with g_oi in an HEMT.

4. Results and Discussion

We now look into the impact of short-channel effects (SCEs) on f_T. To do so, we arbitrarily varied values of the intrinsic output conductance in Figure 3a for the devices with three different values of L_g, reconstructed new sets of the general SSM for each intrinsic output conductance, and extracted values of g_{m_ext}, C_{gs_ext}, C_{gd_ext}, and f_T using the approaches explained in Equations (8)–(10). Figure 5a–c plot g_{m_ext}, C_{gs_ext}, and C_{gd_ext}, respectively, as a function of the intrinsic output conductance for the same family of devices. Symbols correspond to those from the small-signal modeling with the measured intrinsic output conductance for each device, whereas lines correspond to the projected ones that come from Equations (8)–(10) with different values of the intrinsic output conductance. First, C_{gs_ext} was nearly independent of g_oi. Because the ratio of C_gd/C_gs is typically much smaller than a unity, the second term in the square bracket of numerator of C_{gs_ext} is approximated to g_oi × R_d, and C_{gs_ext} is denominated by the first term of the numerator in square brackets. It makes C_{gs_ext} independent of g_oi. In the case of g_{m_ext}, the results in this study are broadly consistent with those from DC analysis [43]. g_{m_ext} is increasingly degraded by g_oi as L_g scales down aggressively. Figure 6 shows the two terms of C_{gd_ext} for each L_g device. Looking at the second term in the square brackets (solid lines in Figure 6), it is no longer negligible and actually comparable to C_gd × (1+g_mi R_s) at a g_oi of around 1 mS/μm. Overall, C_{gd_ext} increases with g_oi. It should be emphasized that the dependencies of g_{m_ext} and C_{gd_ext} on g_oi, especially in short-L_g devices, are exactly where f_T is deteriorated.

Next, we investigated how the degree of SCEs affects f_T in detail. Figure 7 plots the projected f_T for the devices with three different values of L_g, as a function of g_oi. Symbols correspond to the measured f_T for each L_g device. The worse the SCEs, the more seriously f_T degrades, which is the case for the device with L_g = 25 nm. For example, if improving a value of g_oi by a quarter for the device with L_g = 25 nm, it is projected that the f_T would considerably improve from 706 to 802 GHz. Strikingly, this improvement would be comparable to or even surpass the benefit from scaling down L_g. This reveals that it would be of equal importance to pay close attention to the SCEs to maximize the improvement in the f_T, in addition to the reduction in L_g and parasitic components, and the improvement in carrier transport properties in the In_xGa_1-xAs/In_0.52Al_0.48As QW channel layer. Unless g_oi is carefully engineered, indium-rich In_xGa_1-xAs/In_0.52Al_0.48As QW HEMTs with x > 0.53 and short L_g, which were originally incorporated to improve the high-frequency characteristics of the device, would be likely to deteriorate the electrostatic integrity of HEMTs and eventually be of no use in boosting f_T.

5. Conclusions

In summary, we investigated the impact of the electrostatic integrity of HEMTs on f_T from the perspective of the simplified small-signal equivalent circuit. We extracted values of all the extrinsic model parameters and f_T for In_0.8Ga_0.2As QW HEMTs with L_g = 260, 87, and 25 nm from the perspective of a simplified SSM, together with analytical expressions. In this way, we successfully explained the behavior of f_T in those devices with respect to electrostatic integrity. As L_g considerably scaled down, we found that the degradation of the f_T become more prominent. This is because the increase in the intrinsic output conductance caused the increase in the total extrinsic gate capacitance and the decrease in the extrinsic transconductance, leading to the degradation of f_T. The results of this study indicate that it will be of great importance to pay close attention to SCEs to obtain a maximum improvement in f_T in short L_g HEMTs.