**Quantum Confinement in High Electron Mobility Transistors**

Shovon Pal, Sascha R. Valentin, Arne Ludwig and Andreas D. Wieck

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68374

#### Abstract

[39] Kiehl RSollner T. High Speed Heterostructure Devices. 1st ed. Boston: Academic Press;

[40] Chu BH, Kang BS, Wang HT, Chang CY, Tseng Y, Goh A, Sciullo A, Wu WS, Lin JN, Gila BP, Pearton SJ. AlGaN/GaN HEMT and ZnO nanorod‐based sensors for chemical and bio‐applications. In: SPIE OPTO: Integrated Optoelectronic Devices 2009 Feb 12 (pp. 72162A–72162A). San Jose, CA, USA. International Society for Optics and Photonics.

[41] Kang BS. Fabrication and Characterization of Compound Semiconductor Sensors for Pressure, Gas, Chemical, And Biomaterial Sensing (Doctoral dissertation, University of

1994.

64 Different Types of Field-Effect Transistors - Theory and Applications

Florida).

Modulation-doped semiconductor nanostructures exhibit extraordinary electrical and optical properties that are quantum mechanical in nature. The heart of such structures lies in the heterojunction of two epitaxially grown semiconductors with different band gaps. Quantum confinement in this heterojunction is a phenomenon that leads to the quantization of the conduction and the valence band into discrete subbands. The spacing between these quantized bands is a very important parameter that has been perfected over the years into device applications. Most of these devices form lowdimensional charge carriers that potentially allow optical transitions between the subbands in such nanostructures. The transition energy differences between the quantized bands/levels typically lie in the infrared or the terahertz region of the electromagnetic spectrum and can be designed according to the application in demand. Thus, a proper understanding and a suitable external control of such intersubband transitions (ISTs) are not only important aspects of fundamental research but also a necessity for optoelectronic device applications specifically towards closing the terahertz gap.

Keywords: heterojunction, HEMT, terahertz, infrared, intersubband transition

#### 1. Introduction

Low-dimensional semiconductor heterostructures, otherwise known as semiconductor nanostructures, have tremendously revolutionized both the technical and the fundamental aspects of semiconductor industry in terms of device applications. With the ability to grow clean and high-quality samples, device implementations have become a huge success [1–3]. When the dimensions of a region with free carriers (electrons) are reduced as compared to the bulk and approach the deBroglie wavelength, the electronic motion is quantized, thus resulting in carrier confinement that is quantum mechanical in origin. The phenomenon has

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been widely used for carrier confinement in one, two and three dimensions that consequently gives rise to nanostructures such as quantum wells, quantum wires and quantum dots, respectively. Due to the quantum confinement, the energy bands (i.e. the conduction and valence bands) are quantized into discrete energy levels/bands and are no longer continuous as in the bulk systems. These quantized energy states are known as subbands for 2D or 1D systems and sublevels for 0D systems. The energetic spacings between these quantized subbands and the sublevels are very important parameters that define the device applications both from an optical and from an electrical point of view.

The intersubband spacings in GaAs-based 2D systems are typically in the order of 10–30 meV [4, 5], as seen in the case of two-dimensional electron gas (2DEGs) with a triangular confinement potential formed across a GaAs/AlxGa1<sup>x</sup>As heterojunction (x being typically 0.3) of a high electron mobility transistor (HEMT) structure. The intersubband transitions (ISTs) typically cover the terahertz (THz) or far-infrared region of the electromagnetic spectrum. However, in the case of a square potential well or in a different material system such as GaN/AlGaN heterojunction, these spacings can be designed to be even in the mid-infrared or near-infrared region. Stacking of quantum wells can further enhance the response of intersubband resonance (ISR), and such designs are the key for various applications like photodetectors or intersubband lasers [6]. One of the very common and sophisticated examples in this regard is the quantum cascade laser [7–9], which is based on the cascade phenomena and intersubband transitions across many layers of quantum wells. Such compact and powerful lasers are used for practical applications in THz spectroscopy [10–13], sensing technology [14, 15], biomedical applications [16, 17] and also in security applications [11, 18]. Structures based on quantum wells have also made significant advancement in the detector technology, for example, quantum well infrared photodetectors [19, 20]. In this chapter, we present a broad overview of the ISTs in a 2DEG formed at the GaAs-AlxGa1<sup>x</sup>As interface of a HEMT structure. We also discuss possible methods to probe the spacing between the subbands and also to tune them significantly by applying an external bias across the sample. Furthermore, we present a fundamental study on the coupling of the ISRs with the 2DEG cyclotron resonance in the presence of tilted magnetic fields. The knowledge of ISTs and the ability of wide electrical tuning of these resonances are then exploited to study the light-matter interaction at THz frequencies in these HEMT structures. The integrated device with 2DEG in a HEMT structure and metamaterials (frequency-selective artificially designed structures) is electrically driven from an uncoupled to a coupled regime of light-matter interaction and then again back to the uncoupled regime. A strong coupling is thus observed when the frequencies of both systems are brought in resonance with each other, manifested as an avoided crossing at that point.

#### 2. High electron mobility transistor design

The low-dimensional charge carriers, trapped in the heterojunction of the HEMT design, form the core of such field-effect transistors. This transistor design also goes by the name of modulation-doped field-effect transistors (MODFET). These designs are used in various high-power [21] and high-speed [22] electronics, high-resolution imaging [23] and various gas, chemical and biomedical applications [24]. We begin with the design concept of this semiconductor heterostructure along with an overview of its band structure (see Figure 1(a)) that is obtained by solving the Schrödinger-Poisson's equations self-consistently [25, 26] and adding the band discontinuity at the heterojunctions. A schematic of the layer sequence of the transistor structure is shown in Figure 1(b). On a semi-insulating GaAs substrate/wafer, we start the molecular beam epitaxy (MBE) growth by typically a 50-nm-thin GaAs layer. Then, approximately 10 periods of a GaAs/AlAs short period superlattice (SPS) are grown (not shown in the band diagram). The SPS layers help to smoothen the surface of the bare substrate for the later epitaxial growth and trap eventually surface-segregating unintentional impurities, which have always a tendency to stick at the stoichiometric interfaces of GaAs/AlAs. Moreover, this SPS keeps unwanted charge carriers away, forbidding them to tunnel into the 2DEG layer grown on top. Since the substrate is typically undoped (or semi-insulating), the conduction (or valence) band has no curvature at this point corresponding with Poisson's equation, which states that the charge density is proportional to the second derivative of the potential with respect to the space coordinate. After the growth of the SPS layer, the first charged layer is the 2DEG that is formed at the heterojunction of the

been widely used for carrier confinement in one, two and three dimensions that consequently gives rise to nanostructures such as quantum wells, quantum wires and quantum dots, respectively. Due to the quantum confinement, the energy bands (i.e. the conduction and valence bands) are quantized into discrete energy levels/bands and are no longer continuous as in the bulk systems. These quantized energy states are known as subbands for 2D or 1D systems and sublevels for 0D systems. The energetic spacings between these quantized subbands and the sublevels are very important parameters that define the device applications both from an

The intersubband spacings in GaAs-based 2D systems are typically in the order of 10–30 meV [4, 5], as seen in the case of two-dimensional electron gas (2DEGs) with a triangular confinement potential formed across a GaAs/AlxGa1<sup>x</sup>As heterojunction (x being typically 0.3) of a high electron mobility transistor (HEMT) structure. The intersubband transitions (ISTs) typically cover the terahertz (THz) or far-infrared region of the electromagnetic spectrum. However, in the case of a square potential well or in a different material system such as GaN/AlGaN heterojunction, these spacings can be designed to be even in the mid-infrared or near-infrared region. Stacking of quantum wells can further enhance the response of intersubband resonance (ISR), and such designs are the key for various applications like photodetectors or intersubband lasers [6]. One of the very common and sophisticated examples in this regard is the quantum cascade laser [7–9], which is based on the cascade phenomena and intersubband transitions across many layers of quantum wells. Such compact and powerful lasers are used for practical applications in THz spectroscopy [10–13], sensing technology [14, 15], biomedical applications [16, 17] and also in security applications [11, 18]. Structures based on quantum wells have also made significant advancement in the detector technology, for example, quantum well infrared photodetectors [19, 20]. In this chapter, we present a broad overview of the ISTs in a 2DEG formed at the GaAs-AlxGa1<sup>x</sup>As interface of a HEMT structure. We also discuss possible methods to probe the spacing between the subbands and also to tune them significantly by applying an external bias across the sample. Furthermore, we present a fundamental study on the coupling of the ISRs with the 2DEG cyclotron resonance in the presence of tilted magnetic fields. The knowledge of ISTs and the ability of wide electrical tuning of these resonances are then exploited to study the light-matter interaction at THz frequencies in these HEMT structures. The integrated device with 2DEG in a HEMT structure and metamaterials (frequency-selective artificially designed structures) is electrically driven from an uncoupled to a coupled regime of light-matter interaction and then again back to the uncoupled regime. A strong coupling is thus observed when the frequencies of both systems are brought in resonance with each other, manifested as an avoided crossing at

The low-dimensional charge carriers, trapped in the heterojunction of the HEMT design, form the core of such field-effect transistors. This transistor design also goes by the name of modulation-doped field-effect transistors (MODFET). These designs are used in various high-power [21]

optical and from an electrical point of view.

66 Different Types of Field-Effect Transistors - Theory and Applications

that point.

2. High electron mobility transistor design

Figure 1. (a) The conduction band diagram of a HEMT structure along the growth direction z. The growth starts from the substrate, that is from right to left in the above figure, after the growth of a 50-nm GaAs layer. μ<sup>m</sup> and μ<sup>s</sup> are the quasi-Fermi levels in the metal and semiconductor, respectively ðμ<sup>s</sup> � μ<sup>m</sup> ¼ eVgÞ. Vb is the built-in voltage. The Fang-Howard wavefunction of the ground state is also plotted across the heterojunction (which is assumed to be zero in the growth axis). (b) A schematic of the layer sequence.

undoped GaAs and an undoped Al0.33Ga0.67As spacer layer. Since the 2DEG is essentially electrons and negatively charged, the conduction band curves downwards and reaches the maximum slope at the heterojunction between the GaAs and the Al0.33Ga0.67As layer, at which point the conduction band (Ec(z)) jumps by ΔEc due to the band discontinuity. This is followed by the Al0.33Ga0.67As spacer layer where charge carriers are absent and the slope of the conduction band almost remains constant. In the doped Al0.33Ga0.67As layer, the positive charges of the donor ions cause the band to bend upwards, thus reversing the slope. Further moving to the GaAs layer, Ec(z) jumps downwards due to the band discontinuity and continues with a constant slope. On top of the GaAs layer, AlAs/GaAs SPS (also known as blocking barrier) is grown to prevent leakage of charge carriers in and out of the 2DEG channel and also to prevent leakage of surface charges into the channel. Finally, the band hits the gate grown on top of the sample with a barrier height equivalent to the Schottky barrier height. Ideally, metals (e.g. Cr or Au) are evaporated on the sample to serve as gates after the completion of the growth. The samples are typically grown by MBE. While a lot of work has been done previously using metallic Schottky gates, nonetheless, these gates suffer from huge drawbacks. These gates limit the forward bias voltage to the turn-on voltage of the Schottky diode. Furthermore, they fail to grow lattice matched on the semiconductor, are poly-crystalline and thus induce potentially a lot of strain on the semiconductor layer below. Moreover, they oxidize over time and thus may become highly ohmic. Due to high reflectivity and certain Drude absorption of their free charge carriers, such gates are also opaque to the incident light, thus limiting their application in optoelectronic devices. Recently, we have introduced epitaxial, complementary-doped, electrostatic and transparent gates that are grown on top of the sample [27–29]. These gates are grown within the UHV conditions of the MBE and thus incorporate a minimum of the unwanted impurities, leading to unpreceded gate perfection, reliability and reproducibility.

These gates circumvent all the abovementioned disadvantages of Schottky gates and are typically composed of a 25-nm-thick bulk carbon-doped GaAs layer (with an acceptor density of <sup>N</sup><sup>A</sup> <sup>¼</sup> <sup>3</sup> � 1018 cm�<sup>3</sup> ) followed by approximately 40 periods of carbon-delta-doped and 0.5 nm carbon-doped GaAs layers with an average acceptor density <sup>N</sup><sup>A</sup> <sup>¼</sup> <sup>1</sup> � 1019 cm�<sup>3</sup> . In order to solve Poisson's equation for the evaluation of the band structure, the knowledge of the charge density is necessary. However, it is not possible to calculate the density of charge carriers until the energy bands are known, thus requiring a self-consistent mechanism that is otherwise adopted in the 1D Poisson solver [26].
