Influence of the Bias Voltage on Effective Electron Velocity in AlGaN/GaN High Electron Mobility Transistors

Abstract

The small-signal S parameters of the fabricated double-finger gate AlGaN/GaN high electron mobility transistors (HEMTs) were measured at various direct current quiescent operating points (DCQOPs). Under active bias conditions, small-signal equivalent circuit (SSEC) parameters such as R_s and R_d, and intrinsic parameters were extracted. Utilizing f_T and the SSEC parameters, the effective electron velocity (${\nu }_{e-eff}$) and intrinsic electron velocity (${\nu }_{e-\mathrm{int}}$) corresponding to each gate bias (V_GS) were obtained. Under active bias conditions, the influence mechanism of V_GS on ${\nu }_{e-eff}$ was systematically studied, and an expression was established that correlates ${\nu }_{e-eff}$, ${\nu }_{e-\mathrm{int}}$, and bias-dependent parasitic resistances. Through the analysis of the main scattering mechanisms in AlGaN/GaN HEMTs, it has been discovered that the impact of V_GS on ${\nu }_{e-eff}$ should be comprehensively analyzed from the aspects of ${\nu }_{e-\mathrm{int}}$ and parasitic resistances. On the one hand, changes in V_GS influence the intensity of polar optical phonon (POP) scattering and polarization Coulomb field (PCF) scattering, which lead to changes in ${\nu }_{e-\mathrm{int}}$ dependent on V_GS. The trend of ${\nu }_{e-\mathrm{int}}$ with changes in V_GS plays a dominant role in determining the trend of ${\nu }_{e-eff}$ with changes in V_GS. On the other hand, both POP scattering and PCF scattering affect ${\nu }_{e-eff}$ through their impact on parasitic resistance. Since there is a difference in the additional scattering potential corresponding to the additional polarization charges (APC) between the gate-source/drain regions and the region under the gate, the mutual effects of PCF scattering on the under-gate electron system and the gate-source/drain electron system should be considered when adjusting the PCF scattering intensity through device structure optimization to improve linearity. This study contributes to a new understanding of the electron transport mechanisms in AlGaN/GaN HEMTs and provides a novel theoretical basis for improving device performance.

1. Introduction

Gallium nitride (GaN) materials are typical wide-bandgap semiconductor materials [1]. AlGaN/GaN HEMTs based on GaN materials are outstanding representatives of the new generation of semiconductor devices [2,3,4]. Owing to their superior performance, such as high electron velocity and high critical breakdown electric field, they hold broad market application prospects in high-frequency and high-power fields, including aerospace and mobile communication, among others [5,6,7]. Despite a series of scientific and technological breakthroughs in the study of AlGaN/GaN HEMTs, their power output and linearity have not yet fully reached the expected values due to non-ideal factors [8,9,10]. This has become an important factor restricting the large-scale commercial application of AlGaN/GaN HEMTs.

The channel electron velocity has a significant impact on device performance [11]. The electron velocity and maximum current-gain cutoff frequency (f_T) of AlGaN/GaN HEMTs remain a controversial issue [9]; the rapid decrease in g_m and f_T with increasing gate bias is believed to be related to effective electron velocity (${\nu }_{e-eff}$) [11,12]. However, much of the current research mainly focuses on the peak of electron velocity [9,13], which cannot fully reflect the operating mechanism of the device. There is relatively little research on the bias dependence of electron velocity. In the limited number of studies currently available on the bias dependence of electron velocity, the extraction of bias-related electron velocities is based on small-signal model parameters obtained through the COLD-FET method, without considering the bias dependence of parasitic resistances [14]. Due to the influence of bias voltage on the two-dimensional electron gas (2DEG) of the access area, the parasitic source and drain resistances (R_s and R_d) of AlGaN/GaN HEMTs have bias dependence [15,16,17]. R_s and R_d are important reasons for the inconsistency between the external effective parameters and intrinsic parameters of the device. Therefore, when studying the effect of bias voltage on ${\nu }_{e-eff}$, it is necessary to consider the bias dependence of R_s and R_d. Polar optical phonon (POP) scattering and polarization Coulomb field (PCF) scattering are the most important scattering mechanisms for AlGaN/GaN HEMTs, and their intensity is affected by bias voltage [18,19,20]. Therefore, when studying the effect of bias voltage on ${\nu }_{e-eff}$ in AlGaN/GaN HEMTs, it is necessary to systematically analyze the relationship between gate bias, parasitic resistance, scattering mechanism, and ${\nu }_{e-eff}$.

In this study, double-finger gate AlGaN/GaN HEMTs suitable for high-frequency applications were fabricated, and the broadband S parameters were measured under different gate bias conditions. Small-signal equivalent circuit (SSEC) parameters such as R_s and R_d, and intrinsic parameters were extracted under active bias conditions. The intrinsic electron velocity (${\nu }_{e-\mathrm{int}}$) dependent on gate bias is calculated using these SSEC parameters. Moreover, the ${\nu }_{e-eff}$ corresponding to each gate bias voltage is obtained through the f_T. We analyzed the mechanism by which bias voltage affects ${\nu }_{e-eff}$ and established a correlation expression between ${\nu }_{e-eff}$ and ${\nu }_{e-\mathrm{int}}$. This study is beneficial for understanding the electron transport mechanism of AlGaN/GaN HEMTs from a new perspective and provides a new theoretical basis for improving device performance, such as linearity.

2. Experiments

AlGaN/GaN heterostructure wafers were grown on 4H-SiC substrates via MOCVD. Above the substrate are a 1000 nm GaN buffer layer, 400 nm undoped GaN, 0.8 nm AlN, 21 nm Al_0.26Ga_0.74N, and 3 nm GaN. The electron mobility and 2DEG density of the wafer, obtained by Hall measurement, are 2073 [cm²/(V·s)] and 1.09 × 10¹³ cm⁻².

The structure of the AlGaN/GaN HEMTs used in this study is shown in Figure 1. The source and drain of the device are Ohmic contacts, which are formed by stacking Ti/Al/Ni/Au on AlGaN/GaN heterostructure wafers and then rapidly annealing in an N₂ environment. The gate is a Schottky contact, manufactured by depositing Ni/Au after electron beam lithography. The device is a central gate; the gate length (L_G) is 300 nm, and a gate width (W_G) is 40 × 2 μm. The device with 1 μm gate-source spacing (L_GS) is named as Sample 1, and the device with 2 μm L_GS is named as Sample 2. The I-V characteristics and S parameters were measured using the Keysight B1500A Semiconductor Device Parameter Analyzer(Keysight Technologies Inc., Santa Rosa, CA, USA) and the Keysight PNA-X Vector Network Analyzer.(Keysight Technologies Inc., Santa Rosa, CA, USA).

Figure 1. Schematic diagram of the AlGaN/GaN HEMTs used in this study.

3. Results and Discussion

The I-V characteristics of Sample 1 and Sample 2 are shown in Figure 2. The points with V_DS = 12 V and V_GS = 0 to −3.5 V (step: −0.5 V) were chosen as the direct current quiescent operating points (DCQOPs) to measure the small-signal S parameters corresponding to each gate bias condition. The frequency range for small-signal S parameter measurement is 0.5 to 40 GHz. The small-signal S parameter is converted to the H-parameter, and the current-gain modulus H₂₁ (dB) is obtained. Therefore, as shown in Figure 3 and Figure 4a, the f_T can be obtained by extrapolating H₂₁ (dB) [21,22,23,24]. For AlGaN/GaN HEMTs, the external effective electron velocity (experimental value) can be expressed as follows [25]:

$${\nu }_{e-\exp }=2·\pi ·f_T·L_G$$

(1)

Figure 2. The measured I-V characteristics of (a) Sample 1 and (b) Sample 2.

Figure 3. Method for obtaining f_T of AlGaN/GaN HEMTs through H₂₁ (taking the f_T of Sample 1 at DCQOPs of V_DS = 12 V, V_GS = −3 V as an example; f_T = 48.6 GHz).

Figure 4. (a) The f_T corresponding to each gate bias and (b) the ${\nu }_{e-\exp }$ corresponding to each gate bias for Sample 1 and Sample 2.

So, as shown in Figure 4b, the ${\nu }_{e-\exp }$ corresponding to each gate bias for the two samples can be obtained. From Figure 4b, it can be seen that ${\nu }_{e-\exp }$ reaches its peak at a V_GS of −3 V, and gradually decreases as V_GS increases from −3 V to 0 V. The phenomenon of ${\nu }_{e-\exp }$ decreasing with increasing V_GS will seriously affect the linearity of the device.

The phenomenon of effective electron velocity decreasing with increasing V_GS is related to the intrinsic electron velocity (${\nu }_{e-\mathrm{int}}$) and R_s and R_d, which are related to V_GS. The ${\nu }_{e-\mathrm{int}}$ of AlGaN/GaN HEMTs can be expressed as follows [26]:

$${\nu }_{e-\mathrm{int}}={\displaystyle \frac{g_{m-\mathrm{int}}}{C_{gs}+C_{gd}}}·L_G$$

(2)

Among them, $g_{m-\mathrm{int}}$ is the intrinsic transconductance, and $C_{gs}$ and $C_{gd}$ are intrinsic gate-source and gate-drain capacitors, which are directly extracted under active bias conditions based on the SSEC shown in Figure 5 [27,28,29,30,31]. Figure 6 shows the calculated ${\nu }_{e-\mathrm{int}}$ corresponding to each gate bias of Sample 1 and Sample 2.

Figure 5. Topology diagram of SSEC for AlGaN/GaN HEMTs (parasitic parameters unrelated to bias are not depicted in this figure).

Figure 6. The ${\nu }_{e-\mathrm{int}}$ corresponding to each gate bias for Sample 1 and Sample 2.

From Figure 6, it can be seen that ${\nu }_{e-\mathrm{int}}$ reaches its peak at a V_GS of −3 V and then decreases significantly as V_GS increases from −3 V to 0 V. The magnitude of $v_{e-\mathrm{int}}$ is determined by the x-direction electric field under the gate (E_x) and the scattering mechanisms. Existing research has shown that the change in the intensity of E_x is very slight when the gate bias is altered [32]. Therefore, the variation in $v_{e-\mathrm{int}}$ with V_GS is primarily determined by the scattering mechanisms. POP scattering and PCF scattering are the predominant scattering mechanisms in AlGaN/GaN HEMTs. As V_GS increases, both the temperature of polar optical phonons (T_POP) and the density of the two-dimensional electron gas (n_2DEG) increase, leading to enhanced POP scattering [33,34,35]. The enhancement of POP scattering intensity causes $v_{e-\mathrm{int}}$ to decrease with V_GS. When V_GS < −3 V, both T_POP and n_2DEG are lower, resulting in weaker POP scattering, making PCF scattering the dominant mechanism. During the process of increasing V_GS from −3.5 V to −3 V, the inverse piezoelectric effect (IPE) weakens, leading to a reduction in the additional polarization charge (APC) and a decrease in PCF scattering, which results in an increase in ${\nu }_{e-\mathrm{int}}$. The variation in ${\nu }_{e-\mathrm{int}}$ with V_GS is an important factor influencing the variation in effective electron velocity with V_GS. The above analysis indicates that the effects of POP scattering and PCF scattering on the variation trend of ${\nu }_{e-\mathrm{int}}$ with V_GS are opposite. Therefore, enhancing the PCF scattering strength corresponding to the electron system under the gate can reduce the magnitude of ${\nu }_{e-\mathrm{int}}$ at lower V_GS voltage ranges and compensate for the device linearity loss caused by the reduction in ${\nu }_{e-\mathrm{int}}$ due to the increased POP scattering caused by a higher V_GS. This results in a more gradual change in ${\nu }_{e-\mathrm{int}}$ with V_GS and thereby improves the device’s linearity across the entire operating voltage range. Sample 2, with its larger L_GS and L_GD values, corresponds to a stronger additional scattering potential, which leads to more intense PCF scattering in the under-gate electron system. As a result, the variation in ${\nu }_{e-\mathrm{int}}$ with V_GS is more gradual, as illustrated in Figure 6.

Figure 7 shows the R_s and R_d corresponding to each gate bias for Sample 1 and Sample 2. These values are directly extracted under active bias conditions based on the SSEC shown in Figure 5 [27,28,29,30,31]. Due to the modulation of R_s and R_d on the gate-source voltage and drain-source voltage [26,36], ${\nu }_{e-eff}$, the externally measured effective electron velocity, is less than ${\nu }_{e-\mathrm{int}}$. Considering these modulation effects, the relationship between ${\nu }_{e-eff}$, ${\nu }_{e-\mathrm{int}}$, and parasitic resistance can be expressed as follows:

$${\nu }_{e-eff}={\displaystyle \frac{{\nu }_{e-\mathrm{int}}}{[1+(\frac{{\epsilon }_0{\epsilon }_{AlGaN}W}{d})·R_s·{\nu }_{e-\mathrm{int}}]}}-(R_s+R_d)·g_{ds}·{\nu }_{e-\mathrm{int}}$$

(3)

where ${\epsilon }_0$ is the dielectric constant of a vacuum, ${\epsilon }_{A\mathrm{l}G\mathrm{aN}}$ is the dielectric constant of AlGaN, W is the gate width, d is the barrier layer thickness, and g_ds is the drain conductance. Figure 8 displays the ${\nu }_{e-eff}$ calculated using Formula (3) and the effective electron velocity obtained experimentally (denoted as ${\nu }_{e-\exp }$), illustrating that the two values are consistent.

Figure 7. The R_s and R_d corresponding to each gate bias for (a) Sample 1 and (b) Sample 2.

Figure 8. Comparison of ${\nu }_{e-eff}$ obtained through Formula (3) with ${\nu }_{e-\exp }$ from experiments and comparison of effective electron velocity with ${\nu }_{e-\mathrm{int}}$ for (a) Sample 1 and (b) Sample 2.

Analysis of the relationship between the ${\nu }_{e-eff}$, parasitic resistances and ${\nu }_{e-\mathrm{int}}$ has revealed that both POP and PCF scattering can influence ${\nu }_{e-eff}$ by altering ${\nu }_{e-\mathrm{int}}$ and parasitic resistances. When the V_GS changes, the mechanisms by which POP and PCF scattering impact the ${\nu }_{e-\mathrm{int}}$ are similar to their effects on parasitic resistances [17,18]. As V_GS increases, the intensities of PCF and POP scattering exhibit opposite trends. Consequently, their counteracting effects can be utilized to moderate the changes in ${\nu }_{e-\mathrm{int}}$ and parasitic resistances induced by V_GS, thus enhancing linearity during the entire operating voltage range. However, in the PCF scattering model, the drain-source channel is divided into two systems: the under-gate electron system and the gate-source/drain electron system [37]. As shown in Figure 9a, the impact of PCF scattering on ${\nu }_{e-\mathrm{int}}$ is realized by the scattering action of the APC present in the gate-source/drain regions on the electrons located in the area under the gate. The additional scattering potential generated by the APC present in the gate-source/drain regions can be expressed as follows [37]:

$$\begin{array}{l}{V}_{APC-present in GS/GD}\left(x,y,z\right)=-{\displaystyle \frac{e}{4\pi {\epsilon }_s{\epsilon }_0}}{\displaystyle {\int }_{-L_{\mathrm{GS}}-\frac{L_{\mathrm{G}}}{2}}^{-\frac{L_{\mathrm{G}}}{2}}d{x}^{\prime }}{\displaystyle {\int }_0^{W_{\mathrm{G}}}\frac{\Delta {\rho }_{APC-GS}}{\sqrt{{\left(x-x^{\prime }\right)}^2+{\left(y-y^{\prime }\right)}^2+z^2}}d{y}^{\prime }}\\ -{\displaystyle \frac{e}{4\pi {\epsilon }_s{\epsilon }_0}}{\displaystyle {\int }_{\frac{L_{\mathrm{G}}}{2}}^{L_{\mathrm{GD}}+\frac{L_{\mathrm{G}}}{2}}d{x}^{\prime }}{\displaystyle {\int }_0^{W_{\mathrm{G}}}\frac{\Delta {\rho }_{APC-GD}}{\sqrt{{\left(x-x^{\prime }\right)}^2+{\left(y-y^{\prime }\right)}^2+z^2}}d{y}^{\prime }}\end{array}$$

(4)

where $\Delta {\rho }_{APC-GS}$ and $\Delta {\rho }_{APC-GD}$ are the amounts of APC present in the gate-source/drain regions. The $V_{APC-present in GS/GD}$ scatters the electrons located in the area under the gate, thereby affecting ${\nu }_{e-\mathrm{int}}$. Conversely, as shown in Figure 9b, the impact of PCF scattering on R_s and R_d is achieved through the scattering action of the APC present in the region under the gate on the electrons located in the gate-source/drain regions. The additional scattering potential generated by the APC present in the region under the gate can be expressed as follows [37]:

$$V_{APC-present in G}\left(x,y,z\right)=-{\displaystyle \frac{e}{4\pi {\epsilon }_s{\epsilon }_0}}{\displaystyle {\int }_{-\frac{L_{\mathrm{G}}}{2}}^{\frac{L_{\mathrm{G}}}{2}}d{x}^{\prime }}{\displaystyle {\int }_0^{W_{\mathrm{G}}}\frac{\Delta {\rho }_{APC-G}}{\sqrt{{\left(x-x^{\prime }\right)}^2+{\left(y-y^{\prime }\right)}^2+z^2}}d{y}^{\prime }}$$

(5)

where $\Delta {\rho }_{APC-G}$ is the amount of APC present in the region under the gate. The $V_{APC-present in G}$ scatters the electrons located in the gate-source/drain regions, thereby affecting R_s and R_d. When the under-gate electron system experiences strong PCF scattering, the PCF scattering in the gate-source/drain electron system might be weak. Therefore, when adjusting the intensity of PCF scattering to influence the device linearity by optimizing the device structure, the mutual effects of PCF scattering on the under-gate electron system and the gate-source/drain electron system should be considered. For the two samples in this study, since L_GS is greater than L_G, the under-gate electron system experiences stronger PCF scattering. Consequently, the impact of PCF scattering on ${\nu }_{e-\mathrm{int}}$ is greater than its impact on R_s and R_d.

Figure 9. Schematic of the influence of the APC on the (a) under-gate electron system and (b) gate-source/drain electron system in the PCF scattering model.

4. Conclusions

In summary, based on the measured wideband small-signal S parameters of AlGaN/GaN HEMTs, the ${\nu }_{e-eff}$ is calculated using the f_T obtained. SSEC parameters such as R_s and R_d and intrinsic parameters were extracted under active bias conditions. And the ${\nu }_{e-\mathrm{int}}$ corresponding to each V_GS was also calculated. We analyzed the mechanism by which V_GS affects ${\nu }_{e-eff}$ and established an expression for the relationship between ${\nu }_{e-eff}$, ${\nu }_{e-\mathrm{int}}$, and parasitic resistances. By analyzing the main scattering mechanisms in AlGaN/GaN HEMTs, it was found that the impact mechanism of V_GS on ${\nu }_{e-eff}$ needs to be comprehensively analyzed from two aspects: ${\nu }_{e-\mathrm{int}}$ and parasitic resistances. On the one hand, the change in V_GS will affect the intensity of POP scattering and PCF scattering, leading to a change in ${\nu }_{e-\mathrm{int}}$. The trend of ${\nu }_{e-\mathrm{int}}$ changing with V_GS has a direct impact on ${\nu }_{e-eff}$ and plays a dominant role in the trend of ${\nu }_{e-eff}$ changing with V_GS. On the other hand, due to the presence of parasitic resistance, ${\nu }_{e-eff}$ is smaller than ${\nu }_{e-\mathrm{int}}$. Due to the differences in APC between the gate-source/drain regions and the under-gate region, when optimizing the device structure to adjust the intensity of PCF scattering to influence device linearity, the mutual effects of PCF scattering on the under-gate electron system and the gate-source/drain electron system must be considered. This study comprehensively elucidates the impact mechanism of gate bias on ${\nu }_{e-eff}$ from both intrinsic and parasitic aspects, which is beneficial for understanding the electron transfer mechanism of AlGaN/GaN HEMTs from a new perspective and provides a new theoretical basis for improving the linear performance of the devices.