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ScienceDirect Procedia Computer Science 85 (2016) 581 – 587

International Conference on Computational Modeling and Security (CMS 2016)

Comparative Simulation of GaAs and GaN based Double Barriers-Resonant tunneling Diode Man Mohan Singha,*, M.J. Siddiquib, Anupriya Saxenac a

Research Scholar, Aligarh Muslim Universirt, Aligarh, UP-202002, India b Professor, Aligarh Muslim Universirt, Aligarh, UP-202002, India c Assistant Professor, PIET-Sitapura, Jaipur, Rajasthan-303905, India

Abstract

In this work, we propose GaN based Double Barrier-Resonant Tunneling Diode (DBRTD) model and it is compare with GaAs based Quantum DBRTDs at room temperature. This comparison can be utilized to improve the performance of the RTD at higher frequencies. This paper also demonstrates the potential impact of doping concentration on current density of the device. Quantum tunneling mechanism results, based on non-equilibrium Green’s function formalization within ballistic limits, shows high peak current with GaN RTD and achieves high peak to valley ratio as compared to GaAs RTD. Furthermore, comparison helps in analyzing the better device between both models. Simulation of the device has been performed with the use of Atlas Silvaco and Nextnano3 tool which confirms the various results presented in this research. 2015The TheAuthors. Authors.Published Published Elsevier B.V. © 2016 byby Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of the 2016 International Conference on Computational Modeling and Peer-review under responsibility of the Organizing Committee of CMS 2016 Security (CMS 2016).

Keywords: Quantum tunneling; RTD, Double Barriers; III-V group semiconductors; GaN based Quantum Structures.

*

Corresponding Author: Email addresses: [email protected] (Man Mohan Singh)

1877-0509 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of CMS 2016 doi:10.1016/j.procs.2016.05.224

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1. Introduction Resonant tunneling devices are the key factor to enhance the performance of any circuit which requires high switching speed along with negative differential resistance. Currently, GaN based resonant tunneling diodes give bistable and enhanced characteristics for ultrafast nonvolatile memories [1]. Investigation of Resonant tunneling effect for designing of ultramodern electronic devices is significant for application in nanotechnology [2]. DBRTs have the vibrant feature to propose novel circuits that utilize its properties of bistability, multi-valued logic with positive feedback, such as compact modeling of oscillators [3-4]. Among all the features related to resonant tunneling, Negative differential resistance (NDR), nonlinearity and device operation at Terahertz frequencies are more important, includes peak or steps in the current-voltage (I-V) curves [5]. The simplest RTD can be modeled with quantum well (GaAs or GaN) sandwiched in between two undoped tunnel barriers (AlGaAs or AlGaN) [6-7]. But fabrication of this device is quite complex, we have to use different approaches to fabricate the DBRTs. In late 1960’s, Molecular beam epitaxial technique has invented to realize these nanostructures along with large mean free path. But, in today’s era, the semiconductor industries grow a lot and fabricate these devices with Silicon on insulator (SOI), Metal –Insulator-Metal (MIM) nanostructures [8]. In recent years, RTDs have widely deliberate because they can achieve ultra-high speed operation and high functionality with reduced circuit complexity and low power consumption owing to their negative differential resistance (NDR) features [9-10]. Fermi Energy with band gap is an important factor of a material used to simulate these nano-dimension heterostructure. Here, we simulate the GaAs/AlGaAs and GaN/AlGaN heterostructure under the consideration of NEGF boundary conditions. Also compare these two structures in context with their Band gap edges, doping concentration and Current density- voltage (J-V) characteristics. These devices are used in many Terahertz applications and provide more accurate results in optical devices due to fewer losses [11]. Moreover, Film-Diode Technology which is extremely compact with low cost use these RTDs for the fabrication of both integrated circuits and discrete diodes for millimeter wave applications [12]. Some Biomedical applications also use these terahertz devices for imaging systems and radiations [13]. This paper compared two proposed models of RTDs and concludes drawn characteristics by varying device parameter. Remainder of this paper is organized as follows. The next section includes the basic concepts or theories of proposed model. In section 3, we discuss the device structure along with layer dimensions. Simulation results are discussed in section 4. Finally, concludes the paper in last section. 2. Theoretical Model and Basics As we know, Quantum devices like RTDs work on the Quantum resonant tunneling concept within ballistic limits. When the size of the conductor becomes lesser to their mean free path, conductor approaches to its limiting values. When these limits reach beyond phase relaxation length, then quantum comes into play an important role in the heterostructure [14]. Schrodinger wave equation plays an important role in resonant tunneling; the probability of tunneling of an electron through quantum well has been calculated through the Green Function and Schrodinger wave equation.

2.1. Double Barrier Quantum Structure The basic quantum structure of the device is shown in the Fig. 1, which includes the quantum well sandwiched between two barriers. Double barrier means number of undoped barrier are two, which are grown on undoped quantum well along with two heavily doped contact and for providing metal contact we use the gold (Au). Some offsets are required for proper working of the device so we give 0.2 eV offset in case of GaAs based RTD. As electron transport is required for carry the functionality of electron tunneling under the bias voltage. Because the electron wavelength are comparable with characteristic dimensions of the DBQW structure, the wave nature of electrons leads to quantum phenomena such as tunneling, interference, energy quantization, etc. As a result, resonant tunneling phenomena occur in DBQW structures and form the basis for RTD operation [15].

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2.2. Resonant Tunneling Discrete energy levels are present in the quantum structure to provide the energy to the electrons for tunneling are called resonant states. When some voltage is applied to the device then electron get excited and their energy reaches to the energy equals to one of the resonant state. By this electron can easily tunnel through the barriers. As we know many resonant states are present in the quantum structure, which helps in gives many peaks in the device characteristics and get many NDR regions. From the above Fig. 1, we easily analyze the resonant levels.

Fig.1. Energy of Resonant levels and width of the quantum well with double barriers

As shown in figure-1, width of well in this device be represented as W. And E1, E2 and E3 are the resonant energy levels with the energy be given by୬ ൌ େ୵ ൌ

୦మ ୬మ ଼୫‫ כ‬୛మ

ሺͳሻ

Here, n is the number of resonant levels and w is the width of well,୬ is the energy of the resonant level, h is Planck’s constant and m is the effective mass of the electrons. Above figure and the energy of resonant level are taken in account for the calculation of tunneling probability. Non-equilibrium Green function (NEGF) normalization is used for tunneling of electrons in the quantum structure with ballistic limits. So tunneling current is given by ൌ

୯ ଶ஠԰

‫ ׬‬୉ ሺሻሺሻ†ሺʹሻ

Here, ԰ ൌ ŠȀʹɎǡ and h is Planck’s constant. ܶሺ‫ܧ‬ሻ is the probability of electron emit from the emitter, q is the charge and the ୉ is given by୉ ൌ

୩୘Ǥ୫‫כ‬ ஠԰మ

Ž ቂͳ ൅ ‡š’ ቀ

୉ూ ି୉ ୩୘

ቁቃሺ͵ሻ

 ‡”‡ǡ୊ ‹•–Š‡ ‡”‹Ž‡˜‡Ž‘ˆ‡‹––‡”ǡ‹•ƒ„•‘Ž—–‡–‡’‡”ƒ–—”‡‹‡Ž˜‹ƒ†‹•‘Ž–œƒ…‘•–ƒ–Ǥ 2.3. Ballistics Quantum Transport When the dimensions of a conductor go below the certain characteristic lengths such as phase relaxation length and mean free path of electron and shows the non-ohmic behaviour [16]. As we decrease the dimensions of a conductor below its mean free path then conductor reaches its limiting values. But for proper working of quantum mechanics this limit is not considerable alone. As the dimensions of conductor are smaller than Phase-relaxation length, quantum mechanics applies and interference-related effects come into play. For higher mobility, we use the material like GaAs or GaN with modulated doped heterostructure or quantum wells, phase-relaxation length goes down up to few micrometers at low temperature. Thus For mesoscopic transport simulation, ballistic quantum transport plays an important role. The mesoscopic transport has been described by Landauer [17] for multi-terminal

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devices. And it is equivalent to Non-equilibrium Green’s function (NEGF) formalization for ballistic quantum tunneling. According to this phenomenon, the Fermi Dirac function inside contact λ is given byͳ ሺͶሻ ‫ܨ‬ሺ‫ܧ‬ǡ ߤఒ ሻ ൌ  ͳ ൅ ‡š’ሾሺ‫ ܧ‬െ ߤఒ ሻȀ݇ܶሿ Here, λ is the contact and ߤఒ is the chemical potential in the contact, E is the energy and k is the Boltzmann’s constant. 3. Proposed Device Structures This section includes the proposed models of GaN/AlGaN and GaAs/AlGaAs material hetrostructure used in simulation. The 2D structure of ƒ•/Ž଴Ǥଷ ƒ଴Ǥ଻ • and ƒ/Ž଴Ǥଷ ƒ଴Ǥ଻  is shown in Fig. 2. This structure has been grown with molecular beam epitaxial (MBE) structure in controlled environment of layer thickness and doping concentration [18]. Attaining such nanoscale geometries was impossible until the recent development of thin-film semiconductor crystal-growth techniques such as molecular beam epitaxial growth of wafers [19].

Fig.2. Moderately doped proposed DBRTD 2D structure full view

Table-1. Layers of proposed DBRTD Simulation Material

Thickness, Distance (nm)

Thickness, Distance (nm)

Layers

ƒ•/Ž଴Ǥଷ ƒ଴Ǥ଻ •

ƒ/Ž଴Ǥଷ ƒ଴Ǥ଻ 

Metal, top contact(Au)

Gold (Au) = 0.5 nm

Gold (Au) = 0.5 nm

Doping (ͳǤʹ ‫Ͳͳ כ‬ଵ଼ Ȁ…ଷ)

Doped GaAs = 12nm

Doped GaN = 12nm

Spacer layer

Undoped GaAs = 3nm

Undoped GaN = 3nm

Barrier

Ž୶ ƒଵି୶ •ሺx=0.3) = 3nm

Ž୶ ƒଵି୶ ሺx=0.3) = 3nm

Undoped Well

GaAs = 4nm

GaN = 4nm

Barrier

Ž୶ ƒଵି୶ •ሺx=0.3) = 3nm

Ž୶ ƒଵି୶ ሺx=0.3) = 3nm

Spacer layer

Undoped GaAs = 3nm

Undoped GaN = 3nm

Doping (ͳǤʹ ‫ Ͳͳ כ‬Ȁ… )

Doped GaAs = 12nm

Doped GaN = 12nm

Metal, bottom contact(Au)

Gold (Au) = 0.5 nm

Gold (Au) = 0.5 nm

ଵ଼

ଷ

Man Mohan Singh et al. / Procedia Computer Science 85 (2016) 581 – 587

The above-proposed device has two barriers, well, spacer and contact layers within quantum heterostructure shown in Table.1. Table gives the details of layers used in designing of both the DBRTDs along with doping concentration value and material used. The cross-section of the device is 10nm long and 41nm thick (10nm x 41nm). And the model used for electron tunneling is NEGF with contact block reduction technique within ballistic limits. The structure of this device is shown in the Fig.2, which gives the idea that, how the device looks alike. Doping concentration of the device is moderate in nature to make this device compatible with other circuits and systems made by this device. 4. Simulation Results The above devices are simulated with Atlas Silvaco and Nextnano3 tool and then calculate the Fermi energy band gap and electrical characteristics of both the devices. Firstly, we simulate both the devices and plot the characteristics of Energy band gap, Fermi levels at zero bias also calculate the J-V characteristics of both the devices. Finally, compare both the devices and analyze which is more suitable for the higher frequency applications. 4.1. Simulated Band Gap Energies Band gap energies are the key point for any electron to tunnel from emitter to collector in quantum devices. Here, both the material either GaAs or GaN is direct band gap which is useful for fast tunneling from valance band to conduction band. Although, GaN is wurtzite crystal structure and has hexagonal crystal system, but it has very high band gap which is useful in multiple resonant peaks. Instead of this GaAs is zinc blende crystal structure which is non-magnetic in nature. Fig. 3(a-b) gives the band gap energies along with valance and conduction band energies.

Fig.3. Simulated conduction, valance band & Energy band gap at No bias Voltage- (a) GaAs/AlGaAs RTD, (b) GaN/AlGaN RTD

According to Vigard's Law, the relation between band gap and its composition (x) can be calculated as-

‫ܧ‬௚ǡ஺௟ீ௔஺௦ ൌ ‫ܧݔ‬௚ǡ஺௟஺௦ ൅ ሺͳ െ ‫ݔ‬ሻ‫ܧ‬௚ǡீ௔஺௦ ሺͷሻ ‫ܧ‬௚ǡ஺௟ீ௔ே ൌ ‫ܧݔ‬௚ǡ஺௟ே ൅ ሺͳ െ ‫ݔ‬ሻ‫ܧ‬௚ǡீ௔ே ሺ͸ሻ Calculated band gap energies lie between AlAs (E g=2.16 eV) and GaAs (Eg=1.42 eV) and exact values we get from the simulation for GaAs based RTD (E g=1.83 eV). Similarly, in the case of AlGaN we get the E g = 4.1 eV. So it validates that further simulation will be correct as we proceed this structure for further simulation. From the Fig. 3,

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it is clear that, conduction band tilted without applying any voltage such that some electron tunnel through the device. 4.2. Current-Voltage Characterization on varying doping concentration A current-voltage characteristic of any device gives behaviour to perform on applying voltage to it. Current density (J)-voltage characteristics of double barrier resonant tunneling diode for different materials i.e. GaAs, GaN are shown in Fig. 4(a-b) at two doping concentration. Here we are using ballistic quantum transport and compare the current densities of both the models.

Fig. 4. J-V characteristics of GaAs RTD and GaN RTD at given doping conc.-(a) Doping = 1.2*1018/cm3, (b) Doping = 4.0*1018/cm3

In the above figure, it is clear that GaN based resonant tunneling diode have multiple peaks but at higher voltage. Initially, very small current has been drawn through GaN RTD due to larger band gap in the material. On the other hand, GaAs based RTD gives current at very low voltage i.e. 0.3 volts for peak value. But for achieving very high peak current, we have to use GaN/AlGaN RTD with multiple peaks. 5. Conclusion Electrical characteristics have been improved by using Gallium Nitride heterostructure. Some parameters are compared to analyze the performance of proposed GaN/AlGaN over GaAs/AlGaAs RTD. Energies of the valance and conduction band has been calculated and simulated. Peak value of 14.26*105 A/cm3 has been calculated in GaN RTD at 1.2*1018 /cm3 doping concentration which is quit high as compared to GaAs RTD. Conduction Band has been tilted at zero bias in the case of GaN RTD which shows higher mobility of electron in the device. Multiple peaks are obtained in GaN RTD which confirms the resonant levels with higher energy exist in the device as compared to the Gallium Arsenide RTD. Acknowledgements Authors are grateful to ‘‘Council of Scientific & Industrial Research (CSIR)’’ under Junior Research Fellowship (JRF) scheme supported by the MHRD, Government of India, New-Delhi. Authors are also thankful to Chairman of Department of Electronics Engineering, AMU Aligarh for providing necessary research facilities. References 1. Nagase, Masanori, and Takashi Tokizaki. "Bistability Characteristics of GaN/AlN Resonant Tunneling Diodes Caused by Intersubband Transition and Electron Accumulation in Quantum Well." Electron Devices, IEEE Transactions on 61, no. 5 (2014): 1321-1326.

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