## Influence of Nitrogen Doping on the Properties of GaAs Semiconductor using MAPS-Abinit Module

**Introduction**

GaAs is one of the most widely used semi-conductors in industries involved in many different type of applications such as integrated circuits, infrared light-emitting diode (LED), laser diode, solar cells, etc. Similarly, GaN semiconductors are gaining increasing importance due to their remarkable properties such as a large band gap and low dielectric constant. Such property makes them potential key materials for high-density data devices or for undersea optical communication systems.

The doping of GaAs semiconductors with Nitrogen atoms is then expected to allow triggering the appropriate properties of the semiconductors towards a specific application. The ternary GaAs_{x}N_{1-x} complexes have therefore been widely studied and appear as potentially interesting system for application in optical and electronics such as infrared diode laser, light detectors [1], solar cells [2] or optical fibers [3].

In this case study we used Abinit [4] module within MAPS Platform [5] to study the effect of an increasing amount of Nitrogen on the structural and optical properties of the GaAs_{x}N_{1-x} complex.

**Method**

GaAs zinc blend structure was build using MAPS crystal builder. The space groupe F-43m (space group number 216) and cell parameter a = 5.6535 Å were selected. The Gallium atoms were placed at the position (0.0 ; 0.0 ; 0.0) and the Arsenic atoms at the position (0.25 ; 0.25 ; 0.25). This conventional cell was then optimized.

The different ternary complexes (GaAs_{x}N_{1-x}, x = 0.25, 0.5, 0.75 or 1.0) were obtained by replacing 1, 2, 3 or all Ga atoms from the conventional cell structure (see Figure 1). The volume of the new systems was, optimized. The cell parameters and density were extracted from the optimized systems.

Finally, the band structure, density of state and optical susceptibility tensors of the different optimized systems were computed using Abinit. These data directly gave access to the band gap (E_{g}) of the different compounds. In addition, the complex dielectric function (ε(ω)), dielectric constant (ε_{0}), refractive index (n(ω)) and absorption coefficient (I(ω)) were computed using the following expression:

In the previous equations, the susceptibility tensor was approximated by a susceptibility function since the non-diagonal terms of the susceptibility tensor were negligible (ε_{xy} = ε_{yz} = ε_{xz} = 0) and all diagonal terms were equals (ε_{xx }= ε_{yy }= ε_{zz} = ε).

The different simulations were performed using PW92 [6] LDA functional and Fritz-Haber Institute norm conserving pseudopotentials. An energy cutoff of 600 eV was used together with a k-point grid of 6x6x6.

**Results**

**1.Structural Properties**

As shown in Figure 2, the cell parameter of the ternary complex decreases almost linearly from 5.53 Å for GaAs to 4.31 Å for GaN. These values are in good agreement with previous experimental and theoretical results [7-13].

This behavior respects the Vegard’s law that states that the cell parameter of an alloy can be expressed as a linear combination of the cell parameters of the different pure elements pondered by their concentration in the system.

**2. Band Structure and Band Gap**

The band structures of GaAs and GaN semiconductors (see Figure 3) show that the band gap of both alloys is direct and located at the gamma point. The computed band gap of GaAs and GaN alloys were in good agreement with previous theoretical results [7-12].

In most ternary alloys the Vegard’s law can also be extended to the band gaps. For GaAsN ternary complexes, experimental studies found a red shift of the adsorption and therefore a band gap diminution when doping GaAs semiconductors with a small amount of Nitrogen [14]. Such behavior was completely unexpected since the band gap of GaN has a significantly higher value than that of GaAs. Our calculations allowed to reproduce well the band gap diminution and the minimum band gap was found for x = 0.25.

**3. Optical properties**

The frequency dependent dielectric matrix was computed for each of the different alloys. The dielectric constant of each material was extracted from there and is reported in Figure 5. Once again, the computed dielectric constant of GaAs and GaN were validated against previous experimental and theoretical values [7-12].

Figure 5 shows that, interestingly, the dielectric constant goes through a maximum for x = 0.25 (value for which the band gap is minimum) before reducing linearly until x = 1 (GaN semi-conductor).

Other optical properties such as the frequency dependent absorption coefficient or refractive index were also computed for all the systems (see Figure 6). The maximum absorption coefficient is shifted toward higher photon energy values when the amount of Nitrogen in the system increase.

The refractive index at low frequency is decreasing when x increases from about 3.5 to 2.3. For very high frequency it converges toward 1.00 in all cases. It also reaches a maximum of decreasing intensity that appears at increasing frequency values when the Nitrogen concentration increases.

Nitrogen appears, therefore, as a very interesting doping agent for GaAs. Indeed, since some property evolve linearly upon Nitrogen doping and others do not, a wide number of possibility seems to exist for fine tuning of the properties of GaAs towards a desired set of values.

**Conclusion**

In this study we used MAPS Builder, Abinit module and MAPS Analysis tools to study the impact of Nitrogen doping on the structural and optical properties of GaAs semi-conductor. The cell parameters as well as the dielectric function, band gap, absorption coefficient and refractive index of the ternary GaAs_{x}N_{1-x} alloys were computed and analyzed within MAPS platform.

This study shows that Nitrogen doping induces a very unusual evolution of some parameters (band gap, dielectric constant) for low N concentration. Since GaAs is one of the most widely used semi-conductor, such ability could lead to important industrial applications.

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