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Study of charge density at InxGa1-xN/GaN heterostructure interface Tasbirun Nahian Upal, Md. Ahsan Uddin, Mainul Hossain*, Faisal Jahan and Zahid Hasan Mahmood

Department of Applied Physics, Electronics and Communication Engineering, University of Dhaka, Dhaka-1000, Bangladesh

*email: mhnafeez@yahoo.com Abstract — Energy-bands in undoped InxGa1-xN/GaN

heterostructures have been simulated using 1D Poisson/Schrödinger solver: A Band Diagram Calculator, by self-consistent solution of Schrödinger and Poisson equations. The formation of two-dimensional electron gas (2DEG) and two-dimensional hole gas (2DHG) were observed at the interface of undoped InxGa1-xN/GaN based heterostructures. Charge concentrations throughout the structures were analyzed which show the confinement of charge in a quantum well at the heterointerface. Charge density as a function of depth from surface to substrate has also been presented in this paper. The formation of 2DEG and 2DHG and the dependence of their densities on layer thickness, alloy composition and temperature have been investigated.

Index Terms — Charge confinement, quantum well, heterostructure, 2DEG, 2DHG, InGaN, GaN

I. INTRODUCTION

III-Nitride wide band gap semiconductor materials have attracted considerable interest in recent years to emit light in ultra-violet/blue wavelength region as well as to provide high power and high frequency applications in devices like high electron mobility transistors (HEMTs). Such devices are mainly based on III-Nitride heterostructures. In III-Nitride heterostructures, the difference in the spontaneous and piezoelectric polarization between two different layers would result in a fixed sheet of polarization charge at the interface. This charge tends to attract high concentration of electrons or holes depending on the net polarization at the interface. The quantum well at the heterointerface confines electrons or holes in a direction perpendicular to the interface. For a net positive polarization at the interface this confinement results in 2DEG and for a net negative polarization this results in 2DHG.

Among the III-Nitrides, InN and its alloys are expected to be a highly promising material for the fabrication of high performance HEMTs. InN as a HEMT channel requires a larger band gap barrier to induce and confine electrons. The probable choices of barriers are GaN or AlN or their alloys with InN, InGaN or InAlN. The significant lattice mismatch between InN and GaN or AlN can result in a large piezoelectric charge, which is very advantageous for HEMT applications. In order to design and fabricate the InN-based HEMTs detailed understanding and proper inclusion of the effects of 2DEG and 2DHG are very much essential [1, 2].

In this study, the formation of 2DEG and 2DHG at interfaces of undoped InxGa1-xN/GaN heterostructures has been investigated numerically with 1D Poisson/Schrödinger

solver: A Band Diagram Calculator [3]. The Fermi level is taken as the reference energy level having 0.0eV energy. The variation of 2DHG density with layer thickness, alloy composition and temperature has also been simulated.

II. SIMULATION AND RESULT

In the present study, two types of heterostructures have been considered. The two layer structure as shown in Fig. 1a. consists of an InxGa1-xN layer, with x = 0.3, over a 50nm GaN buffer layer. The three layer structure as shown in Fig. 1b. consists of a cap layer of GaN on top of the InxGa1-xN layer.

Fig. 1a. InxGa1-xN/GaN two layered heterostructure Fig. 1b. GaN/InxGa1-xN/GaN three layered heterostructure

InxGa1-xN x=0.30

GaN Buffer Layer

50nm

GaN Cap layer

InxGa1-xN x=0.3 t=20nm >TC=2.25nm

GaN Buffer Layer

50nm

2009 2nd International Workshop on Electron Devices and Semiconductor Technology

978-1-4244-3832-7/09/$25.00 ©2009 IEEE

IEEE Catalog Number: CFP0926CISBN: 978-1-4244-3832-7

Library of Congress: 2009900354

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A. InxGa1-xN/ GaN Heterostructure

The value of x is taken to be 0.3. The thickness of GaN buffer layer is fixed at 50.0nm and the thickness of InxGa1-xN layer is increased starting from a small value of 2.0nm. Initially, there is no charge accumulation at the heterostructure interface. As the InxGa1-xN layer thickness is gradually increased, charge accumulation starts at the interface of the two layers. For a layer thickness of 4.0nm, the simulated band diagram is shown in Fig. 2.

Fig. 2. Band-diagram showing 2DHG formation

The valance band Ev has penetrated the Fermi level at the heterostructure interface. As it is evident that all the energy states below the Fermi level are occupied with electrons at room temperature, therefore, the penetration of the valence band into the Fermi level confirms the accumulation of holes in the quantum well at the interface of the InxGa1-xN/GaN heterostructure. The holes are confined in a direction perpendicular to the interface and are free to move in the other two dimensions. The thickness at which valence band just penetrates the Fermi Level to form 2DHG, is called the

Fig. 3. Determination of Critical Thickness for InxGa1-x N/GaN heterostructure

critical thickness, Tc. For this structure of InxGa1-xN/GaN with x = 0.3, Tc is found to be 2.25nm. With further increase in InxGa1-xN layer thickness, 2DHG density increases linearly as shown in Fig. 3.

When the InxGa1-xN layer thickness is increased further above 50nm, the 2DHG density reaches saturation, shown in Fig. 4. The saturated 2DHG density is found to be 2.28x1013cm-2.

Fig. 4. 2DHG reaches saturation for InxGa1-xN/GaN heterointerface

The charge concentration versus distance profile from surface to substrate is shown in Fig. 5. It shows a peak value at the interface which supports the fact that holes pile up at the heterointerface. For 10.0nm thick InxGa1-xN layer the hole density at interface is 5.7206x1020 cm-3.

Fig. 5. Charge Concentration versus Distance Profile

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For the InxGa1-xN/GaN heterostructure, the mole fraction x is varied for a fixed InxGa1-xN layer thickness. The InxGa1-xN layer thickness is taken to be 10nm which is greater than the critical thickness of 2.25nm for 2DHG formation.

It is observed that the 2DHG sheet density at the interface increases almost linearly with the increase in alloy composition for x•0.1

Fig. 6. Dependence of 2DHG density on Alloy composition

The density of 2DHG at the interface depends both on the InxGa1-xN thickness and alloy composition. Fig. 7. shows the change of 2DHG density with the layer thickness for different alloy compositions.

Fig. 7. Dependence of 2DHG density on Alloy composition and InxGa1-xN layer thickness

B. GaN/ InxGa1-xN/ GaN Heterostructure

The three layered heterostructure shown in Fig. 1b. is now considered. For thinner cap layer there is no charge accumulation at the interface between GaN cap layer and InxGa1-xN layer. If we increase the cap layer thickness, confinement of electrons at the interface between GaN cap layer and InxGa1-xN layer starts. Fig. 8. below shows the formation of 2DEG at the interface between GaN cap layer and InxGa1-xN layer and 2DHG at the interface between InxGa1-

xN layer and GaN buffer layer.

Fig. 8. Formation of 2DEG & 2DHG

Charge concentration as a function of depth from surface to substrate for the three layer structure is plotted in Fig. 9.

Fig. 9. Peaks formed due to electron and hole accumulation

The peaks confirm the accumulation of both electrons and holes at the two interfaces between InxGa1-xN layer and GaN cap layer and between InxGa1-xN layer and GaN buffer layer respectively.

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For the three layer structure the effect of the change in GaN cap layer thickness on the 2DHG and 2DEG density is shown in Fig. 10.

With the increase in GaN cap layer thickness, 2DHG density decreases and 2DEG density increases. Both 2DHG and 2DEG reaches saturation at about 3nm and 20nm GaN cap layer respectively.

Fig. 10. Variation of charge densities with the increase of GaN cap layer thickness

C. Effect of change in temperature on 2DHG density

For a two layered structure of InxGa1-xN/GaN, as shown in Fig. 1a, the dependence of 2DHG density at the heterointerface on temperature was studied. The result is shown in Fig. 11. The temperature range was taken from 173K (-1000C) to 373K (1000C). 2DHG density is found to decrease linearly with increase in temperature within the specified range.

Fig. 11. Change of 2DHG density with the increase in temperature

III. CONCLUSION

Charge densities in InxGa1-xN/GaN and GaN/InxGa1-xN/GaN heterostructures were studied. The variation of 2DHG and 2DEG densities on layer thickness, alloy composition and temperature were simulated. It has been successfully demonstrated that the 2DHG density at the interface of InxGa1-

xN/GaN heterostructure decreases linearly with increase in temperature. Thus, variation of temperature can affect the performance of devices based on of InxGa1-xN/GaN heterostructures.

ACKNOWLEDGEMENT

The authors wish to acknowledge the assistance and support of Professor Dr. Gregory L. Snider of the University of Notre Dame, USA and Dr. Arnab Bhattacharya, department of Condensed Matter Physics and Material Sciences, Tata Institute of Fundamental Research (TIFR), India.

REFERENCES

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[2] M. T. Hasan, A. G. Bhuiyan and A. Yamamoto, “Two dimensional electron gas in InN-based heterostructures:

Effects of spontaneous and piezoelectric polarization”, Solid-State Electronics, vol. 52, pp. 134–139, 2008.

[3] I.H. Tan, G. L. Snider, L. D. Chang, and E. L. Hu, “A self-consistent solution of Schrodinger-Poisson equation using a nonuniform mesh ”, J. Appl. Phys., vol. 68, no.8, pp. 4071-4076, October 1990.