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1. Introduction
Compound materials from group III-N achieved significant progress in optoelectronic devices for a broad range of applications [1-6]. The AlGaN/GaN HEMTs have been successfully used for high power, high speed and high temperature operations [7, 8], because its properties are consistent for high frequency and power that allow obtaining extremely high power densities in RF HEMT [9]. However, by switching the AlGaN barrier layer with InAlN, the device performance may still be improved [10].
Recently, it has been proven that InAlN transistors have good performance for applications in power device applications due to its strong piezoelectric effect at the interface [11]. Meanwhile, the sheet concentration in the channel of 1013 cm-2 by the difference in spontaneous polarization is larger than the other HEMTs devices based of III-V [12, 13].
The electron sheet density of 1.9 × 1013 cm-2 in the proposed device [14] with 30 nm T-shaped gate length has been obtained with SiC substrates, and a maximum oscillation frequency of 340 GHz. At Vgs = 1 V, the maximum drain saturation current density of 1.65 A/mm has been reported in 70 nm gate length In0.17Al0.83N/AlN/GaN HEMT with a 1 nm AlN spacer layer thickness [15], and the peak transconductance above of 380 mS/mm. The device [16] has a 13 nm thick AlInN barrier layer containing 81% Al. Hall- Effect measurements at 77 K give a sheet carrier density of 2.5 × 1013 cm-2.
The proposed model of In0.17Al0.83N/AlN/GaN heterostructures was improved. In this work we investigate the impact of spacer layer (AlN) thickness on the electronic properties and current-voltage characteristics using the nextnano simulator [17]. The analysis of the 2DEG interface charge density was accomplished by a self-consistent solution of Schrödinger and Poisson equations. The energy eigenvalues and eigenvectors are obtained by self-consistently solving these equations.
2. Self-consistently model for 2D-electron gas interface charge density
Table I illustrate the standard definitions of used symbols. By finite difference method (FDM) we solve the Schrödinger and Poisson equations self-consistently and derive the conduction band, and wave-function of 2DEG in the channel [18]. The Schrödinger equation is [19]:
Table I List of symbols.
| Symbol | Description |
|---|---|
| 𝜓 | Wave function |
| E | The energy |
| 𝜑 | The electrostatic potential |
| m * | The effective mass |
| ε s | The dielectric constant |
| ℏ | Planck’s constant divided by 2π |
| n(z) | The electron density distribution |
| 𝜎 | The sheet charge density at the interface |
| ΔE c | The conduction band discontinuity |
| E k | The Eigenenergy of the k-th state |
| N D (z) | The ionized donor concentration |
| n k | The electron occupation at k-th state |
| ε AlInN | The dielectric constants of AlInN barrier |
| ε GaN | The dielectric constants of GaN channel |
| P sp | The spontaneous polarization |
| e 31, e 33 | Piezoelectric constants |
| C 13, C 33 | Elastic constants |
| a(0), a(x) | The values of lattice constant |
| μ n | The drift mobility of electron |
| W | The width of channel layer |
| V th | The threshold voltage |
The Poisson’s equation in one dimension is [20]:
The potential energy expressed [21, 22]:
where 𝜓(z) and n(z) are related by [23]:
For each state, the electron density can be described by [24]:
Polarization sheet charge can be deduced at interface of InAlN/GaN by [21]:
and 𝜎 is given by the following relationship [21]:
It can be expressed spontaneous polarization by [25]:
The current drain-source is given by [26]:
As the current is constant in the channel, Eq. (9) can be integrated from drain-source [27]:
where V
DS
is much lower than
The current of drain -source saturation is given by [27]:
As we know that these equations are difficult to solve analytically, we used the nextnano device simulation software [16].
3. Device structure
The cross sectional view of In0.17Al0.83N/GaN device is depicted in Fig. 1, our device is grown on an insulating Silicon carbide substrate (SiC), a 2 μm undoped GaN semi-insulating layer, and an AlN spacer layer with various thickness (d), and basically composed of an 8 nm undoped InAlN barrier layer, the device structures are T-shaped passivated with SiN recessed gate length of 70 nm.
Finally, the source-drain spacing is 2 μm. In our calculations, the AlN thickness is used as a parameter. The 2-DEG is formed at the heterointerface of In0.17Al0.83N/GaN as shown in Fig. 1.
4. Results and discussions
Figure 2 displays the calculated band diagram, and wave-function of 2DEG in the channel of In0.17Al0.83N/GaN HEMT structures without and with a 1 nm AlN spacer, under zero applied voltage.
Figure 2 Electron density (ns) and gamma conduction band energy (E c ) of In0.17Al0.83N/GaN HEMTs with and without an AlN spacer layer.
We found that the sheet carrier density in the 2-D electron gas is in the order of 1019 cm-3. It was observed enhanced electron confinement with AlN spacer layer. The height of a potential barrier affects how the wave function penetrates the barrier layer. The AlN spacer significantly increases the barrier height and therefore suppresses this effect, due to the fact that AlGaN is a ternary material.
4.1. Sheet carrier concentration (n s )
The variation of the 2D-electron gas density for different AlN spacer layer thicknesses is shown in Fig. 3. The higher the spacer layer thickness the better the sheet charge density (ns), with an almost linear dependence on the AlN spacer layer thickness range between 0.5 nm and 2 nm. The increase in electron density is due to the effect of piezoelectric and spontaneous polarization.
Figure 3 Mobility and sheet carrier concentration (ns) of 2D -electron gas (2DEG)Vs AlN spacer layer thickness.
Due to the significant polarization effect, the AlN spacer may cause an increase in dipole scattering and, as a result, the 2-D electron gas mobility will decline. Spacer enhances conduction band shift below this critical thickness, which effectively reduces the penetration of the wave function into the AlN barrier and thus reduces the effect of alloy disorder diffusion. The electron sheet density of 1.81 × 1013 cm-2 is roughly similar to that calculated in [15] for 1 nm AlN layer.
Also in Fig. 3, we found that the electron mobility increases while increase the AlN interlayer thickness.
For 1.5 nm AlN, we observe the highest mobility (1380 cm2/V.s) for this structure, the sheet carrier concentration reached 2.5 × 1013 cm-2. Also, we see the electron mobility of 1253 cm-2/V.s, which is very similar to those obtained by Tingting et al. [15].
4.2. Transfer characteristics
Figure 4 a) illustrates the transfer characteristics of In0.17Al0.83N/GaN HEMT for
Figure 4 Transfer characteristics of In0.17Al0.83N/AlN/GaN HEMTs for different AlN spacer layer thickness values. a)I DS as a function of V GS , b) g m as a function of V GS .
The thickness of the AlN spacer layer increased from 0.5 nm to 2 nm. It is reported here that the drain current increases by increasing the AlN thickness. The maximum drain-source current for 1.5 nm AlN is 1.81 A/mm due to the increase of the mobility with spacer layer and 2D-electron gas density, while it decreases to 0.82 A/mm for d = 2 nm due to the mobility degradation.
We have determined the transconductance at each bias (V GS ) as in the relationship below:
The transconductance’s bias dependent on
All the device’s maximums of transconductance (
The simulated transfer characteristics (Fig. 5) with a 1 nm AlN interlayer show good agreement with the previously reported experimental results [15].
Figure 5 Comparison between the results of simulations and experimental [15] transfer characteristics of In0.17Al0.83N/AlN/GaN HEMTs at V DS = 7 V.
4.3. Output characteristics
Figure 6 illustrates the simulated drain current (
Figure 6 Drain characteristics of In0.17Al0.83N/GaN HEMTs without an AlN spacer layer. The gate-source voltage is stepped in +1 V steps from -3 V to 1 V.
When the gate-to-source voltage changed from -3 V to 1 V, with the gate biased equal to 1 V , the maximum drain saturation current density was found to be 0.96 A/mm, this significant drain current is due to effects of the strong polarization in In0.17Al0.83N/GaN barrier layer, and the InAlN/GaN interface reached with (2DEG) sheet carrier density. Also, the short distance of drain-source plays an essential role because it reduces the parasitic resistance.
The characteristics with a 0.5 nm AlN spacer layer are illustrated in Fig. 7. The highest value of drain current density was 1.48 A/mm (at V GS = +1 V).
Figure 7 Drain characteristics of In0.17Al0.83N/GaN HEMTs with 0.5 nm spacer layer. The gate-source voltage is stepped in +1 V steps from -3 V to 1 V.
As seen from Fig. 8, for 1.5 nm AlN, we find that saturated drain current density was 1.81 A/mm, which reflects the high electron density in this newly proposed structure owed to AlN material that holds the highest spontaneous polarization among all III-N.
Figure 8 Drain characteristics of In0.17Al0.83N/GaN HEMTs with 1.5 nm spacer layer. The gate-source voltage is stepped in +1 V steps from -3 V to 1 V.
With a 1 nm AlN spacer layer, we also report an excellent agreement between experimental data [15] and simulation results (see Fig. 9).
Figure 9 Comparison of experimental (symbols) [15] with simulated data of output characteristics of In0.17Al0.83N/GaN HEMTs.
5. Conclusion
In summary, we have studied the electronic and electric properties of InAlN/GaN HEMT. We find that a very high electron charge density can be produced due to the strong piezoelectric effect at the interface. The electron density increases with the increase of the AlN thickness.
The increase in electron density is mainly due to the higher piezoelectric charge. Furthermore, we observed that with the optimum thickness (1.5 nm) of the AlN spacer for the In0.17Al0.83N/GaN device, the electron density extremely raises close to 2.5 × 1013 cm-2, allowing an electron mobility considerably over of 1350 cm2/V.s.
The simulations results find an excellent agreement with the experimental data.
