1. Introduction

The GaN/AlGaN HEMTs devices still suffer from gate leakage and reliability problems. Many groups have been investigating the gate leakage^{[1, 2]} and reliability issues^{[3, 4]}, however, the physical basis of the gate leakage and the reliability problem has not been fully understood. The means of the electrical parameters characterize the gate leakage reliability, which has limited sensitivity. Low frequency noise (LFN) measurements are helpful for getting deeper information about the nature of the defects and their evolution before and after application of the stress^{[5, 6]}. Although as early as 2001, Kotchetkov et al. proposed a gate voltage low frequency noise model based on mobility fluctuation^[7]. Meanwhile, Han et al. reported a gate current low frequency noise model based on carrier number fluctuation, which includes thermal activation, tunneling, random walk of electrons^[8]. Later, Katz et al. believed that the surface potential fluctuation is responsible to gate current low frequency noise^[9]. Rao et al. found that the gate current noise spectra show up as random telegraph signal noise, and it has a weak correlation with the drain current noise^{[10, 11]}. Marko et al. thought that gate current RTS is due to modulation of the gate current in the percolation path of the action of single defects^[12]. Karboyan et al. found that a higher leakage current can generate numerous traps, leading to a change of the number of carriers^[13]. Rendek and Šatka et al. studied gate current noise during the illumination and its slow relaxation to the initial value after the illumination^{[14, 15]}. Kumar et al. studied different types of noise and their possible reasons^[16]. Tartarin et al. researched gate defects in AlGaN/GaN HEMTs by low frequency noise measurements^[17]. Xu et al. considered space charge limited gate current noise in AlGaN/GaN HEMTs^[18]. Most research about the gate current noise is only related to the phenomenon described; a small model was established, and the existing models cannot explain the newly discovered phenomenon, such as space charge limited gate current noise. In this paper, the mechanism of the gate current 1/$f$ noise is introduced, a gate current 1/$f$ noise model containing trap-assisted tunneling current and space charge limited current is built, and the gate current noise model is successfully employed to explain the simulated and the measured results.

2. Model

The gate current noise model will be divided into two parts, at low gate voltage, there is the trap-assisted tunneling current noise, while at high gate voltage, due to the interaction between the thermal active defect and the carriers induced by piezoelectric relaxation, resulting in a space charge limited current noise^[19]. As is shown in Fig. 1, the possible leakage current paths come from the gate electrode.

Studies suggest that there are two gate leakage paths^[20]: (1) the electrons which come from the gate electrode may pass through the AlGaN layer to the two-dimensional electron gas (2DEG) conducting channel, it becomes the trap assisted tunneling current. (2) The electrons which come from the gate electrode may be accumulated on the side of the semiconductor surface, or it becomes a hot carrier injection to the drain by being thermally activated, generating a gate-to-drain leakage current, which is a space charge limited current. Meanwhile, it will generate RTS noise from the trap-to-trap mechanism or the conductive transition, where the space charge limited current threshold gate voltage ($V_{x} =qn_0 L^2/\varepsilon )$ is defined as the voltage when the charge transfer time $t_{\rm tr} =L/V_{\rm d} =L^2/\mu V$ is equal to the medium relaxation time $t_{\rm relax} =\rho \varepsilon =\varepsilon qn_{_0 } \mu$ ^[19]. If $V_{\rm g}$ $<$ $V_{x}$, gate leakage is the corresponding path (1). If $V_{\rm g}$ $>$ $V_{x}$, gate leakage is the corresponding path (2).

Next, we discuss the gate current noise model. Each trap causes an RTS in the gate current with amplitude $\Delta I=aJ_{\rm G}$, average time in the low state (filled trap) $\tau _{\rm off}$ and average time in the high state (empty trap) $\tau _{\rm on}$. Thus the power spectral density (PSD) is given by^[21],

$\begin{equation} \label{eq1} S_{\rm RTS} =\frac{4(aJ_{\rm G})^2f_{\rm T} (1-f_{\rm T} )\tau _{\rm C} }{1+(\omega \tau _{\rm C})^2}, \end{equation}$

(1)

$\begin{equation} \label{eq2} (\tau _{\rm C})^{-1}=(\tau _{\rm off} )^{-1}+(\tau _{\rm on} )^{-1}. \end{equation}$

(2)

The trap occupation probability

$\begin{equation} \label{eq3} f_{\rm T} =\tau _{\rm off} /(\tau _{\rm off} +\tau _{\rm on} ). \end{equation}$

(3)

The RTS time constants are

$\begin{equation} \label{eq4} \frac{1}{\tau _{\rm on} }=\frac{1}{\tau _0 }T(E_x )f_{\rm T}, \end{equation}$

(4)

$\begin{equation} \label{eq5} \frac{1}{\tau _{\rm off} }=\frac{1}{\tau _0 }T(E_x )(1-f_{\rm T} ), \end{equation}$

(5)

where $\tau _0$ is a characteristic time constant and $T(E_x)$ is the transmission coefficient for electron tunneling between the AlGaN interface and the considered trap position at the considered trap energy.

If $V_{\rm g}$ $<$ $V_{x}$, the gate current is based on the TSB model^[22]. The current through the Schottky barrier with an arbitrary potential profile through

$\begin{equation} \label{eq6} \begin{split} J_{\rm G} = {}& \frac{4\pi qm^\ast }{h^3}\int_0^\infty T (E_x )\;\times \\[2mm]& \int_0^\infty {\left[f_{\rm s} (E_{\rm p} +E_x )-f_{\rm m} (E_{\rm p} +E_x )\right]} {\rm d}E_{\rm p} {\rm d}E_x, \\ \end{split} \end{equation}$

(6)

where $T(E_{x})$ is the tunneling probability for $E_x =\frac{h^2}{2m^\ast }k_x^2$, i.e., the energy component normal to the Schottky interface, $f_{\rm s}$ and $f_{\rm m}$ are Fermi-Dirac distribution functions in the semiconductor and in the metal, respectively, and $E_{\rm p} =\frac{h^2}{2m^\ast }(k_y ^2+k_z ^2)$ i.e., the energy component parallel to the interface. $T(E_x)$ was calculated under the Wentzel-Kramers-Brillouin (WKB) approximation as follows.

$\begin{equation} \label{eq7} T(E_x )=\exp \left[-2\frac{\sqrt {2m^\ast } }{\hbar }\int_{x_1 }^{x_2 } {\sqrt {\phi (x)-E_x} {\rm d}x} \right]. \end{equation}$

(7)

The defect has the following exponentially decaying distribution into the depth, $x$, from the surface:

$\begin{equation} \label{eq8} N_{\rm T} (x)=N_{\rm T0} \exp (-x/\lambda ). \end{equation}$

(8)

The PSD, given by all the traps, and assumed uncorrelated, can be obtained by the superimposition,

${S_{{\rm{ig}}}} = A\int_0^{{x_{{\rm{max}}}}} {\int_0^{{\phi _{\rm{B}}}} {{S_{{\rm{RTS}}}}} } (x,E){N_{\rm{T}}}({E_x}){\rm{d}}E{\rm{d}}x,$

(9)

where $A$ is the device area and $E=$ 0 corresponds to the bottom of the conduction band $E_{\rm C}$ at the substrate interface.

$\begin{equation} \begin{split} \label{eq10} S_{\rm ig} ={}& \frac{4a^2I_{\rm G}^2}{A}\int_0^{x_{\rm max } } {\int_0^{\phi _{\rm B} } {\frac{f_{\rm T} (E)[1-f_{\rm T} (E)]\tau _{\rm C} (E_x )}{1+\left[{\omega \tau _{\rm C} (E_x )} \right]^2}} } \\[3mm]& \times N_{\rm T} (E_x ){\rm d}E{\rm d}x. \end{split} \end{equation}$

(10)

Since the function $f_{\rm T} (E)[1-f_{\rm T} (E)]\approx kT\delta (E-E_{\rm F})$, it follows that

$\begin{equation} \label{eq11} S_{\rm ig} =\frac{4a^2I_{\rm G} ^2kTN_{\rm T} (E_x )}{A}\int_0^{x_{\rm max } } {\frac{\tau _{\rm C} (E_x )}{1+[\omega \tau _{\rm C} (E_x )]^2}} {\rm d}x. \end{equation}$

(11)

If $V_{\rm g}$ $>$ $V_{x}$, the electrons that tunnel from the gate can be localized in the surface defects (most likely nitrogen vacancies) and/or dangling bonds, not only the trap assisted tunneling current, but also the space charge limited current. It can travel over multiple barriers with spacing and barrier height $E_{\rm a}$, as shown in Fig. 1. of gate current path (2). Space charge limited current noise is superimposed by RTS noise. The time constant of the charge fluctuation can be calculated based on a hot carrier induced trap model^[23], $(\tau _{\rm i})^{-1}=(\tau _{\rm c})^{-1}+(\tau _{\rm e})^{-1}$.

The ratio $\tau _{\rm c}/\tau _{\rm e}$ is related to the trap energy relative to the Fermi energy level, $E_{\rm T} -E_{\rm F}$, and degeneracy factor $g$,

$\begin{equation} \label{eq12} \frac{\tau _{\rm c} }{\tau _{\rm e} }=\frac{\left\langle {\tau _{\rm H} } \right\rangle }{\left\langle {\tau _{\rm L} } \right\rangle }=g{\rm e}^{-(E_{\rm c} \;-\;E_{\rm T}\; -\;\Phi _{\rm AlGaN} \;+\; qV_{\rm g} )\; /\; kT}, \end{equation}$

(12)

where $E_{\rm c}$ is the conduction band energy of GaN, $\mathit{\Phi} _{\rm AlGaN}$ is the height of AlGaN barriers, and $V_{\rm g}$ is the gate voltage.

$\begin{equation} \label{eq13} \tau _{\rm c} =1/\sigma n\bar {v}=\tau _{\rm c0} \exp (E_{\rm a}/KT), \end{equation}$

(13)

where $\sigma$ is the capture section of carriers, $\bar {v}$ is the carriers average speed of thermal motion, $n$ is the 2DEG concentration, $\tau _{\rm c0}$ is the inverse phonon frequency, and $E_{\rm a}$ is the activation energy associated with the surface trap-to-trap current conduction.

Then, the total expression for the gate current noise is

$\begin{equation} \begin{split} \label{eq14} S_{\rm ig} ={}& \frac{4a^2I_{\rm G} ^2kTN_{\rm T} (E_x )}{A}\int_0^{x_{\rm max } }\left[{\frac{\tau _{\rm C} (E_x )}{1+[\omega \tau _{\rm C} (E_x )]^2}} \right. \\[3mm]&{} \left. +\frac{\tau _{\rm C0} \exp (E_{\rm a} /kT)}{1+[\omega /\sigma n\bar {v}]^2}\right]{\rm d}x. \end{split} \end{equation}$

(14)

3. Experiment and analysis

In order to validate the proposed model, we measured the gate-drain current and gate current noise in AlGaN/GaN HEMTs by using a purposely designed measurement setup.

3.1 The device under test

It consisted of a 200 nm GaN buffer layer and a 20 nm Al$_{0.3}$Ga$_{0.7}$N layer is grown on a high resistivity SiC substrate by metal organic chemical vapor deposition (MOCVD). A Schottky gate contact of Ni/Au (20 nm/20 nm) is formed by electron beam evaporation. Ohmic contacts of the Ti/Al/Ni/Au (20 nm/120 nm/55/45 nm) are created for the drain and source regions by electron beam evaporation. The transistor has a gate width of 100 $\mu$m, and a gate length of 0.6 $\mu$m. The device structure is shown in Fig. 2.

3.2 Experiment

The difference of our experiment with Xu^[19] is that they are measuring $I_{\rm gs}$-$V_{\rm gs}$, however, the authors believe that the gate leakage current due to space limitations is mainly produced in the drain terminal, and $I_{\rm gd}$ is more sensitive to its changes; therefore, we use the semiconductor parameter analyzer HP4156B to measure the electronic parameters $I_{\rm gd}$-$V_{\rm gs}$ of the device under different bases ($V_{\rm gs}$ $<$ $V_{x}$ and $V_{\rm gs}$ $>$ $V_{x})$.

Gate current 1/$f$ noise of all devices is measured by a noise testing and analyzing system of an electronic device based on a virtual instrument, which is developed in our lab. It includes four parts, bias circuits, low-noise preamplifier, data acquisition card and microcomputer. The source and drain of the device are grounded, it is the means $V_{\rm s} =V_{\rm b} =$ 0 V. All tests are carried out in a shield room at room temperature. The device operates in the linear region in the noise measurement.

3.3 Results analysis of electrical parameter analysis

Measured $I_{\rm gd}$-$V_{\rm gs}$ curves of the end test device show predominantly a power law rather than exponential current voltage dependences, as illustrated in Fig. 3. For $V_{\rm gs}$ $<$ 0.6 V, the $I_{\rm gd}$-$V_{\rm gs}$ slope is 1, which indicates an ohmic relationship. At the same time, the gate stack works as a capacitor to accumulate carriers inside the leakage path. This indicates that the increase in gate current is caused by merely an expansion of the leakage path due to the stress applied. The newly created conductive paths have similar trap-related transport characteristics to those which originally existed in the unstressed device. When the traps are being filled up with increasing gate voltage, a sudden increase in current is expected. When the gate bias increases until injected carriers exceed the number of electrons originally located in the conductive path, the $I_{\rm gd}$-$V_{\rm gs}$ slope increases to a value of 2 indicative of an SCLC flow. This result has the same trend as Wei's^[19].

3.4 1/$\boldsymbol{f}$ noise tests and simulation results

The gate current 1/$f$ noise of an AlGaN/GaN HEMT device under different biases is shown in Fig. 4. There are two groups of curves corresponding to the two cases. In case 1, $V_{\rm g}$ $=$ 0.6 V, $V_{x}$ $=$ 1.0 V, where $V_{\rm g}$ $<$ $V_{x}$, the gate current 1/$f$ noise complies with Eq. (11). It is superimposed by the RTS noise and background 1/$f$ noise, where the RTS noise is induced by the trap assisted tunneling processes of deep traps (as is shown in Fig. 1, gate current path (1)). The simulation results and experimental data are shown in Fig. 4 curve 1, the gray line shows the measured data, and the black line represents the simulation result. Most of these two curves coincide. In case 2, $V_{\rm g}$ $=$ 1.1 V, $V_{x}$ $=$ 1.0 V, where $V_{\rm g}$ $>$ $V_{x}$, gate current 1/$f$ noise complies with Eq. (14), where it is superimposed by RTS noise and space charge limited current noise. The former is induced by the trap assisted tunneling processes of deep traps (as is shown in Fig. 1, gate current path (1)), while the latter is induced by being piezoelectric induced surface carrier thermally activated (as is shown in Fig. 1, gate current path (2)). The simulation results and experimental data are shown in Fig. 4 curve 2, the gray line shows the measured data, and the black line represents the simulation result. Most of these two curves coincide. All these results are consistent with the result of Xu^[18].

The simulation using MATLAB software, based on the multi-parameter 1/$f$ noise model. Simulation parameters are used as follows: trap density $N_{\rm T}$ $=$ 1 $\times$ 10$^{18}$ cm$^{-3}$, $N_{\rm T0}$ $=$ 1.5 $\times$ 10$^{17}$ cm$^{-3}$, the height of the AlGaN barrier $\mathit{\Phi} _{\rm b}$ $=$ 1.62 eV, capture section of carriers $\sigma$ $=$ 1.2 $\times$ 10$^{-16}$ cm$^2$, activation energy $E_{\rm a}$ $=$ 0.201 eV, channel mobility $\mu$ $=$ 1420 cm$^2$/(V$\cdot$s), GaN permittivity $\varepsilon$ $=$ 10.1, conduction band discontinuity $\Delta \Phi _{\rm C}$ $=$ 0.37 V, and channel carrier concentration $n$ $=$ 1 $\times$ 10$^{13}$ cm$^{-3}$.

4. Conclusion

Gate current 1/$f$ noise in AlGaN/GaN HEMTs is studied theoretically and experimentally. A gate current 1/$f$ noise model containing trap-assisted tunneling current and space charge limited current is built, which is based on the fluctuations of the number of carriers in the two-dimensional electron gas (2DEG) channel of AlGaN/GaN HEMTs. Experiments show that, if $V_{\rm g}$ $<$ $V_{x}$ (critical gate voltage of dielectric relaxation), the $I_{\rm g}$-$V_{\rm g}$ slope is 1, meanwhile, gate current 1/$f$ noise comes from the superimposition of trap-assisted tunneling RTS (random telegraph noise). While, $V_{\rm g}$ $<$ $V$, the $I_{\rm g}$-$V_{\rm g}$ slope is suddenly increasing from 1 to 2, gate current 1/$f$ noise comes from not only the trap-assisted tunneling RTS, but also the space charge limited current RTS. This indicates that gate current 1/$f$ noise of the GaN-based HEMTs device is sensitive to the interaction of defects and the piezoelectric relaxation. The simulation results are in good agreement with the experimental results. It provides a useful characterization tool for deeper information about the defects and their evolution in AlGaN/GaN HEMTs.