Enhancement-mode GaN-based high electron mobility transistors are essential for switching applications in power electronics. A heavily Mg-doped pGaN region is a critical feature of these devices. It pulls the Fermi energy level toward its valence band, depleting the two-dimensional electron gas region at the AlGaN/GaN interface at equilibrium. While a step profile of Mg doping in the pGaN region is desirable, it is difficult to achieve due to the out-diffusion of Mg-dopants, and the barrier AlGaN layer becomes unintentionally p-doped. This p-doping primarily leads to traps in the AlGaN barrier, leading to gate current through trap-assisted tunneling (TAT) and degradation of mobility due to the diffusion of the Mg-dopants to the channel region. The contribution of holes in the channel region and mobility degradation on the transistor characteristics are well understood. Here, we report the effect of TAT, which requires an improved understanding as it determines the key gate characteristics and transistor behavior. An increased TAT current increases the gate current and degrades the sub-threshold slope, which deteriorates transistor characteristics. However, TAT current makes the surface potential less sensitive to the change in gate voltage in the subthreshold regime, resulting in an increased transistor threshold voltage. Hence, an increase in the threshold voltage from the TAT current improves the fail-safe operation required for power-electronic applications. We show that the gate current and threshold voltage need to be tuned together for the desired performance of the enhancement-mode transistors.

Topics
Doping, Electronic band structure, Semiconductors, Electrical properties and parameters, Field effect transistors, Schottky diodes, Power electronics, Two-dimensional electron gas, Electrostatics, Multilayers

GaN-based high electron mobility transistors (HEMTs) have received significant attention for radio frequency (RF) and power-electronic applications.1–4 A default unintentionally doped depletion-mode (D-mode) transistor from AlGaN/GaN heterostructures and their variants are generally used for RF applications for high RF output power at high voltage operations.5–9 However, a significantly high threshold voltage enhancement-mode (E-mode) transistor is preferable for fail-safe operation in power-electronic applications, preventing untoward device turn-on.10,11 Several techniques have been demonstrated to make the threshold voltage large and positive, including recessed-barrier structures with an insulating layer preventing gate leakage, fluoride treatment of the barrier layer, a charge trapping insulating layer deposited on the barrier layer, p-type NiOX gate dielectric, and a heavily Mg-doped pGaN capped layer.12–17 Of all the proven techniques, the pGaN/AlGaN/GaN heterostructure has received immense attention due to the controllability and reproducibility of growth and the potential to get a significantly high threshold voltage of operation without any hysteresis despite Mg out-diffusion into the channel.18,19 Various characteristics of pGaN-gated HEMTs have been studied for mobility degradation, buffer leakage characteristics, the effect of carbon and iron doping of the buffer, dynamic linear resistance, trapping effects, and gate current characteristics and transport mechanisms.20–24 One of the central thrusts of the efforts is directed toward increasing the threshold voltage without changing the other characteristics. These efforts have investigated various effects, including pGaN doping density, gate metal work function variation, and barrier layer thickness.25–27 However, there is a lack of a unified analytical model that combines these effects in a common framework, including the effect of gate leakage current upon the threshold voltage. This work bridges this gap, and an analytical model is developed here, validated using experiments and technology computer-aided design (TCAD) simulation. It is demonstrated that a higher gate leakage current through trap-assisted tunneling tends to make the channel surface potential less sensitive to the gate voltage, making the threshold voltage more positive at the expense of poor subthreshold characteristics. The experimental transfer and output characteristics manifest the predicted devices' comportment. The analytical model allows us to predict the E-mode behavior of the transistor intuitively, delineating design rules for the heterostructure.

A schematic of the pGaN-gated device heterostructure is shown in the inset of Fig. 1. The un-doped GaN channel region is grown on a C-doped GaN, which is grown on a p-type silicon substrate with AlN/GaN super-lattice pairs as an inter-layer to reduce defect densities in the channel region. The heavily Mg-doped pGaN region unintentionally dopes the barrier layer (AlxGa1−xN). The process flow involves device isolation by inductively coupled-plasma reactive-ion etching, gate delineation by pGaN etching, ohmic contact formation by metal deposition and rapid thermal annealing, and gate metal deposition and annealing. The gate metal is assumed to cover the entire pGaN region without any underlap for modeling. If the gate metal is not aligned to pGaN, the small underlap region's impact on the device is small due to the high doping of the pGaN region. The energy band diagram of the device at zero bias is shown in Fig. 1, as obtained from the self-consistent simulation of the Schrodinger and Poisson equation. Because the Mg doping is graded due to the process of doping and diffusion, we have implemented a uniform doping concentration of N A G ∼ 4 × 10 19 c m − 3 for the pGaN-gate and a decreased N A ∼ 5 × 10 18 c m − 3 doping for the AlGaN barrier layer, approximating the Mg secondary-ion mass spectroscopy (SIMS) profile (not shown). The hole concentration in the pGaN is ∼5 × 1017 cm−3, obtained by assuming 0.15 eV as the Mg activation energy in GaN.28 The metal–pGaN junction forms a Schottky contact with a 1.8 eV barrier for the holes.29 The pGaN region creates a parabolic barrier for holes at the metal/pGaN region, followed by a quasi-neutral region owing to the heavy p-doping. The pGaN/AlGaN interface carries a two-dimensional hole gas (2DHG) due to polarization, band offset, and p-doping. The AlGaN barrier band edges are quadratically bent due to the ionization of Mg acceptors. The equilibrium Fermi-level is pulled away from the GaN-channel conduction band edge, making the transistor enhancement mode.

FIG. 1.
The energy band diagram of the pGaN-gated HEMT at zero bias. The pGaN gate turns the transistor into E-mode. The inset shows a schematic of the device structure used in this work.
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The energy band diagram of the pGaN-gated HEMT at zero bias. The pGaN gate turns the transistor into E-mode. The inset shows a schematic of the device structure used in this work.

FIG. 1.
The energy band diagram of the pGaN-gated HEMT at zero bias. The pGaN gate turns the transistor into E-mode. The inset shows a schematic of the device structure used in this work.
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The energy band diagram of the pGaN-gated HEMT at zero bias. The pGaN gate turns the transistor into E-mode. The inset shows a schematic of the device structure used in this work.

Close modal

The measured drain-to-source current ( I D S ) vs gate-to-source ( V G S ) of the device as a function of various drain-to-source voltages ( V D S ) is shown in Fig. 2(a). The devices show the same threshold voltage ( V T = ∼ 2.5 V ) for all V D S⁠, which is reasonable given the long gate length for these devices. The V T is extracted by extrapolating the linear part of the transfer characteristics and identifying the voltage axis intercept. The same characteristics in the semi-logarithmic axes are shown in the inset. The devices show an ON/OFF current ratio of >108 with a sub-threshold swing that lasts over seven decades of current. The typical output characteristics of the transistor (⁠ I D S vs V D S⁠) for various V G S are shown in Fig. 2(b). The gate current characteristics are shown in the inset of Fig. 2(a). The gate current increases with increasing gate bias; however, it remains significantly low at a ratio of <10−4 with respect to I D S at the highest V G S measured here.

FIG. 2.
Experimental and theoretical (a) transfer and (b) output characteristics family are shown. The gate current is shown in the inset of (a).
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Experimental and theoretical (a) transfer and (b) output characteristics family are shown. The gate current is shown in the inset of (a).

FIG. 2.
Experimental and theoretical (a) transfer and (b) output characteristics family are shown. The gate current is shown in the inset of (a).
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Experimental and theoretical (a) transfer and (b) output characteristics family are shown. The gate current is shown in the inset of (a).

Close modal

The pGaN region of the heterostructure pulls the Fermi energy level down toward the valence band, depleting the equilibrium two-dimensional electron gas (2-DEG) at the AlGaN/GaN heterostructure and making the transistor enhancement mode. The pGaN region Mg doping concentration is large at >1019 cm−3. The gate stack is similar to a metal/pGaN Schottky diode and p–i–n diode (pGaN-Gate/i-AlGaN-Barrier/n-GaN-channel) in series. As a positive gate voltage is applied, the p–i–n diode is forward-biased, and the electron and hole quasi-Fermi levels split up. The electron quasi-Fermi level is pulled toward the conduction band edge of the GaN channel, and 2DEG appears. The hole quasi-Fermi level is pulled down, and a 2DHG is formed in the pGaN. The i-AlGaN barrier separates the 2DEG and 2DHG. However, Mg out-diffuses into the AlGaN region, making it p-type and creating traps. This effect leads to trap-assisted tunneling (TAT) current, primarily determining the gate current and surface potential. Hence, the electrostatic control of the channel region by the gate voltage requires a deeper understanding, including an analytical model capturing the operation of the device, enabling an understanding of how TAT plays a significant role. Here, we develop this model, which explains the experimentally observed characteristics. The approximation of the analytical model is validated by matching it with a detailed numerical simulation using Synopsys TCAD, which includes incomplete ionization (Mg activation energy in AlGaN 0.2 eV), ideal piezo-electric polarization charges, traps in AlGaN (mentioned later), and tunneling at interfaces above/below the pGaN and channel (electron effective mass 0.27m0). Similar models and parameters are included in our analytical model.

The energy band diagram of the device under a gate voltage of VGS/VT = 0.6 is shown in Fig. 3(a). As V G S is increased from zero, the electron quasi-Fermi level Efn is raised toward the conduction band edge Ec, forming a 2DEG channel at the AlGaN/GaN interface. The density in 2DHG increases as holes are pushed toward the pGaN/AlGaN interface, and 2DEG tends to appear at the AlGaN/GaN interface. The gate stack behaves as two diodes connected back to back: metal/pGaN Schottky diode and pGaN/depleted-AlGaN/GaN-channel p–i–n diode, which is schematically shown in Fig. 3(a). The V G S can be expressed as
(1)
where V r is the reverse bias voltage at the Schottky diode and V p i n is the voltage across the p–i–n diode. The voltage drop in the quasi-neutral p-region is neglected in Eq. (1) due to its heavy doping and nearly flat band edge profile. The high doping and a negligible voltage drop over the quasi-neutral p-region sustains the required current. The V p i n is related to the barrier height ( φ b n )⁠, built-in potential ( V b i )⁠, the surface potential at the pGaN/AlGaN interface ( ψ 1 )⁠, the voltage drop across the barrier ( V b )⁠, and the potential at the AlGaN/GaN interface ( ψ 2 ) as
(2)
FIG. 3.
(a) Simulated band diagram at VG/VT = 1.5 V, (b) electric field profile, and (c) trap concentration profile in AlGaN are shown. The trap-assisted tunneling current is schematically shown in the inset of (b).
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(a) Simulated band diagram at VG/VT = 1.5 V, (b) electric field profile, and (c) trap concentration profile in AlGaN are shown. The trap-assisted tunneling current is schematically shown in the inset of (b).

FIG. 3.
(a) Simulated band diagram at VG/VT = 1.5 V, (b) electric field profile, and (c) trap concentration profile in AlGaN are shown. The trap-assisted tunneling current is schematically shown in the inset of (b).
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(a) Simulated band diagram at VG/VT = 1.5 V, (b) electric field profile, and (c) trap concentration profile in AlGaN are shown. The trap-assisted tunneling current is schematically shown in the inset of (b).

Close modal
The change in ψ 1 in Eq. (2) is very small since the interface is in accumulation and considered a constant equal to the activation energy of Mg in GaN. The electrons in the channel form a sheet charge of 2DEG. The following equation relates the potential at the AlGaN/GaN interface with electron density:26 
(3)
where k is the Boltzmann constant, T is the temperature, n s is the electron density at the AlGaN/GaN interface, and D is the 2D density of states. γ 0 in Eq. (3) is an experimentally determined constant.
The V b is determined as a function of position from the consideration that the net charge is zero as
(4)
where σ h 1 is the hole density in the pGaN at the pGaN/AlGaN interface, σ h 2 is the accumulated spillover hole density in the AlGaN (Region-I, thickness t 1⁠) having a space charge density of σ b 1⁠, σ b 2 is the space charge density in the rest of AlGaN (Region-II, thickness t 2⁠), σ T 1 is the trapped charge in Region-I, σ T 2 is the trapped charge in Region-II, and σ c is the net space charge density due to C-doped GaN. The various charges of Eq. (4) are shown in Fig. 1. The two different AlGaN regions are illustrated in Fig. 3(b). Applying the Gauss law at the AlGaN/GaN-channel yields
(5)
where ε AlGaN ( ε GaN ) is the dielectric constant of AlGaN (GaN), ξ 2 is the electric field in AlGaN at the AlGaN/GaN-channel interface, ξ c h is the electric field in channel at the AlGaN/GaN-channel interface, and σ p is the polarization at the same interface. Applying the Gauss law at the GaN-channel/C-doped GaN buffer interface leads to
(6)
where ξ c - GaN is the electric field in the C-doped GaN. It is assumed that the electric field is constant over the thickness of the channel due to lower doping from Mg-out diffusion and ξ c - GaN is negligible. Combining Eqs. (5) and (6), we get
(7)
The electric field in the depletion Region-II of AlGaN is linearly dependent on position. The hole spillover compensates Mg acceptors in Region I, verified later by matching the electric field profiles in analytical and TCAD simulations, leading to σ h 2 = σ b 1⁠. So, the electric field in Region-I ( ξ 1 ) at x = − t 2 can be expressed as
(8)

It is assumed that space charge density in Region-II is due to uncompensated Mg acceptors ( σ b 2 = q N A t 2 )⁠.

The electric field in the AlGaN near the pGaN/AlGaN interface ( ξ 0 ) can be expressed as
(9)
Hence, V b can be finally determined by integrating the electric field in Eqs. (7)–(9) as
(10)
The total AlGaN thickness from Eq. (10) is given by t AlGaN = t 1 + t 2⁠. The electric field profile within the AlGaN region is shown in Fig. 3(b). As V p i n increases, the spilling over of the holes increases, and t 2 decreases. The crossing over from Region-I to Region-II is gradual, and we have considered a hole density of p = 1016 cm−3 at the cross-over region and treated it as a fitting parameter. The hole density is given by
(11)
where N V is the room temperature effective density of states and E V and E F p are valence band edge and hole quasi-Fermi level, respectively. E V is given by
(12)
where E g is the GaN bandgap and Δ E V is valence-band offset at the AlGaN/GaN interface. The origin of position ( x = 0 ) is defined at the AlGaN/GaN interface. Using Eqs. (11) and (12), we get
(13)
Equation (13) determines the thickness of Region-II. The trapped charges are calculated by integrating the product of trap concentration profile and trap occupation. It may be noted that the effects of σ T 1 and σ T 2 are negligible and not considered further for simplicity. The effect of σ T 1 and σ T 2 are described in the supplementary material document. The unintentional doping of the AlGaN barrier leads to acceptor-type traps,30 which are considered to have an exponential profile with respect to the energy below midgap, as shown in Fig. 3(c). It is likely that trap density is position dependent in the AlGaN barrier. We have considered a constant doping and trap density in the AlGaN as an equivalent description, which is valid considering the AlGaN barrier is very thin. Assuming any other profile will lead to adding an integral term related to the trap profile to the equations for trapped charges without additional insight. The traps are most likely associated with the out-diffusion of Mg as these traps are absent for depletion-mode HEMTs where the pGaN layer is not used. The TAT current through the p–i–n diode is schematically shown in the inset and computed using the model considered in Ref. 31. The electron current injection from the channel to the traps in AlGaN is given by
(14)
where c L is the capture rate, f T is the occupational probability of traps at an energy level E T and position x, and N T is the trap concentration in AlGaN. c L for Eq. (13) is determined from
(15)
where σ n is the capture cross section and D L ( k , x ) is the tunneling probability through the partial AlGaN barrier from 0 to x where the trap is located, which is computed using WKB approximation.
The electron emission current from traps in AlGaN to pGaN is given by
(16)
where e R is the emission rate, which is determined from
(17)
The trap occupation probability f T is given by
(18)
where E F T is the Fermi level for traps. The value of E F T is chosen such that J c L and J e R are equal.
Combining Eqs. (14)–(18), the total trap-assisted tunneling current is computed as
(19)
The tunneling current through the metal/pGaN Schottky diode is modeled as Fowler–Nordheim tunneling, and it is given by Ref. 32,
(20)
where ξ is the electric field at the metal/pGaN interface and is given by ξ = q N A G W d ε GaN⁠, where W d = 2 ϵ G a N ( V b i + V r ) q N A G is the depletion region width, in which V r is obtained by equating the tunneling current of the metal/pGaN Schottky diode [Eq. (20)] with the TAT current of the p–i–n diode [Eq. (19)] as J G = J s c h o t t k y = J T A T⁠.
The drain current is given by Ref. 33,
(21)
where W is the width of the transistor, μ is the mobility of electrons in the channel, L is the gate length, and n s is obtained from Eq. (3). The drain current in Eq. (21) is limited by the access region resistance at the high gate bias. Hence, the drain and gate voltages are modified to include the effect of series resistance.

The drain current in Eq. (21), derived using the electrostatics and gate current continuity, is used for matching between the family of experimental data, and analytical modeling of the transfer, output, and gate characteristics of the device are shown in Figs. 2(a) and 2(b). They match for all bias conditions, including both sub-threshold and above-threshold characteristics. The corresponding matching for the gate current is shown in the inset of Fig. 2(a). As a further confirmation of the analytical model, we have validated the intermediate potential V r and V p i n in the gate stack and the voltage across the AlGaN barrier layer V b and surface potential ψ 2 [Figs. 4(a) and 4(b)] with that of the calibrated TCAD model. The TCAD model is matched to the same output, transfer, and gate characteristics as the analytical model, with identical device and physics-based model parameters. The good matching of the intermediate potentials between analytical and TCAD models validates the assumptions and the analytical model. Figure 4(c) shows the 2DEG density as a function of V p i n⁠. It is interesting to note the effect of dividing AlGaN thickness over t 1 and t 2⁠. The partial depletion of AlGaN produces an accurate matching for 2DEG. The traditional assumption of the complete depletion of AlGaN underestimates 2DEG density. Figure 4(d) shows the effect of the voltage drop across the reverse bias gate Schottky diode when TAT carries the current through the AlGaN barrier. It increases the threshold voltage of the transistor by dropping a fraction of the input gate voltage and reducing the gate current. It may be noted that the threshold voltage does not change without TAT in the AlGaN barrier.

FIG. 4.
Validation of model with TCAD. The matching of the (a) intermediate potentials V r and V p i n with gate voltage and (b) ψ 2 and V b between TCAD simulation and analytical modeling are shown. The inset in (b) shows a typical band diagram identifying the intermediate potentials. (c) The electron density in the channel is computed using the model with partial and complete depletion of the AlGaN barrier layer. An accurate description with partial depletion reproduces the observed characteristics. (d) The comparison of transfer characteristics with and without Schottky contact is shown.
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Validation of model with TCAD. The matching of the (a) intermediate potentials V r and V p i n with gate voltage and (b) ψ 2 and V b between TCAD simulation and analytical modeling are shown. The inset in (b) shows a typical band diagram identifying the intermediate potentials. (c) The electron density in the channel is computed using the model with partial and complete depletion of the AlGaN barrier layer. An accurate description with partial depletion reproduces the observed characteristics. (d) The comparison of transfer characteristics with and without Schottky contact is shown.

FIG. 4.
Validation of model with TCAD. The matching of the (a) intermediate potentials V r and V p i n with gate voltage and (b) ψ 2 and V b between TCAD simulation and analytical modeling are shown. The inset in (b) shows a typical band diagram identifying the intermediate potentials. (c) The electron density in the channel is computed using the model with partial and complete depletion of the AlGaN barrier layer. An accurate description with partial depletion reproduces the observed characteristics. (d) The comparison of transfer characteristics with and without Schottky contact is shown.
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Validation of model with TCAD. The matching of the (a) intermediate potentials V r and V p i n with gate voltage and (b) ψ 2 and V b between TCAD simulation and analytical modeling are shown. The inset in (b) shows a typical band diagram identifying the intermediate potentials. (c) The electron density in the channel is computed using the model with partial and complete depletion of the AlGaN barrier layer. An accurate description with partial depletion reproduces the observed characteristics. (d) The comparison of transfer characteristics with and without Schottky contact is shown.

Close modal

The critical dependence of the threshold voltage on TAT is a manifestation of the dependence of ψ 2 on V G S⁠. For a given change V G S⁠, a larger TAT current requires a smaller change in ψ 2 to sustain the increased gate current. Hence, ψ 2 is relatively insensitive to V G S⁠, and a large V G S is required to invert the channel, increasing the threshold voltage of the transistor. We have plotted the threshold voltage as a function of increasing capture section (equivalently increases TAT current) to show the effect of TAT on the threshold voltage in Fig. 5(a). An enhanced TAT current increases the threshold voltage of the transistor. A similar exercise is done for the current through the reverse bias metal/pGaN Schottky diode, which is also shown in Fig. 5(b). A higher leakage current through the Schottky gate increases the voltage drop across the p–i–n diode and decreases the threshold voltage. As a further validation of the model, the change in threshold voltage is plotted for change in AlGaN thickness, Al composition, and pGaN Mg doping concentration for both simulations and experiments, as shown in Fig. 5(c). The good matching further corroborates the validity and robustness of the analytical model across all the device parameters.

FIG. 5.
The modeled changes in the threshold voltage for varying (a) TAT and (b) Schottky gate currents are shown. The gate current at the respective threshold voltages is plotted on the Y2 axis. A higher TAT and lower Schottky currents increase the threshold voltage. However, the gate current increases for both the cases. (c) Change in threshold voltage is plotted with varying AlGaN thickness, Al composition, and pGaN Mg doping concentration for both simulations and experiment. They closely match for all the cases, confirming the validity and robustness of the model.
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The modeled changes in the threshold voltage for varying (a) TAT and (b) Schottky gate currents are shown. The gate current at the respective threshold voltages is plotted on the Y2 axis. A higher TAT and lower Schottky currents increase the threshold voltage. However, the gate current increases for both the cases. (c) Change in threshold voltage is plotted with varying AlGaN thickness, Al composition, and pGaN Mg doping concentration for both simulations and experiment. They closely match for all the cases, confirming the validity and robustness of the model.

FIG. 5.
The modeled changes in the threshold voltage for varying (a) TAT and (b) Schottky gate currents are shown. The gate current at the respective threshold voltages is plotted on the Y2 axis. A higher TAT and lower Schottky currents increase the threshold voltage. However, the gate current increases for both the cases. (c) Change in threshold voltage is plotted with varying AlGaN thickness, Al composition, and pGaN Mg doping concentration for both simulations and experiment. They closely match for all the cases, confirming the validity and robustness of the model.
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The modeled changes in the threshold voltage for varying (a) TAT and (b) Schottky gate currents are shown. The gate current at the respective threshold voltages is plotted on the Y2 axis. A higher TAT and lower Schottky currents increase the threshold voltage. However, the gate current increases for both the cases. (c) Change in threshold voltage is plotted with varying AlGaN thickness, Al composition, and pGaN Mg doping concentration for both simulations and experiment. They closely match for all the cases, confirming the validity and robustness of the model.

Close modal

In summary, we have shown the importance of the gate current and trap-assisted tunneling through the AlGaN barrier in determining the threshold voltage and transistor characteristics. We have developed an analytical model that relates the trap-assisted tunneling current to the threshold voltage, highlighting its importance and trade-off with gate leakage characteristics. The analytical model explains the experimental characteristics of a pGaN-gated transistor. The assumptions in the analytical model are validated by matching the characteristics with a TCAD model. The model includes various parameters, including AlGaN thickness, AlGaN composition, and doping concentrations. The effect of the changes in these parameters is presented. A family of curves can be generated along with the sensitivity of critical device parameters on device structures, which can be used as a guideline to design structures meeting specific requirements.

See the supplementary material for effect of trapped charges in the AlGaN barrier layer.

The authors have no conflicts to disclose.

Ranie S. Jeyakumar: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). J. J. James: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal). Swaroop Ganguly: Funding acquisition (equal); Investigation (equal); Methodology (equal). Dipankar Saha: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal).

The data that support the findings of this study are available within the article.

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