Intersubband transitions in GaN-based heterostructures

Intersubband transitions in GaN-based heterostructures

Intersubband transitions in GaN-based heterostructures 13 A. Ajay, E. Monroy University Grenoble-Alpes, CEA, IRIG-PHELIQS, Grenoble, France 13.1 I...

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Intersubband transitions in GaN-based heterostructures

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A. Ajay, E. Monroy University Grenoble-Alpes, CEA, IRIG-PHELIQS, Grenoble, France

13.1 Introduction III-nitride semiconductors (GaN, AlN, InN, and their alloys) have made the implementation of full-color optoelectronics possible due to their large direct bandgap energy and doping capabilities. Heterostructures of these materials are found in the marketplace for a variety of applications, such as blue laser diodes or light-emitting diodes for household lighting. These materials are also currently used in high-power electronics because of their mechanical/thermal robustness, high electrical breakdown fields, and high electron mobility. Furthermore, III-nitrides are currently the most promising solid-state alternative to mercury lamps as ultraviolet emitters. In the last decade, III-nitrides have also attracted attention for the fabrication of intersubband (ISB) devices operating in the infrared domain. The interest of these materials stems first from their large conduction band offset (≈1.8 eV for GaN/AlN [1–3]), which makes it possible to fabricate devices in the 1.3–1.55 μm wavelength window used for fiber optic communications [4–6]. But GaN is transparent in a large spectral region, notably for wavelengths longer than 360 nm (bandgap), except for the reststrahlen band (from 9.6 to 19 μm). Absorption in the range of 7.3–9 μm is observed in bulk GaN substrates [7–9], and it is attributed to the second harmonic of the reststrahlen band. Although this second band might hinder the fabrication of wave-guided devices in this spectral region, its effect in planar devices with micrometer-sized active regions is negligible [10, 11], since the absorption coefficient related to two-phonon processes is much smaller than the one associated with ISB transitions. There is also an interest to push the III-nitride ISB technology toward the terahertz frequency range, wavelengths >20 μm, where GaN-based devices have the potential to operate at room temperature due to the large longitudinal optical (LO) phonon energy of GaN (92 meV, about three times that of GaAs). In addition to the extended wavelength accessibility, the strength of the Fröhlich interaction in these polar materials results in sub-picosecond ISB relaxation times, in the 100–400 fs range for transitions in the near- and mid-IR spectral regions [12–16]. This feature is interesting for the fabrication of ultrafast photodetectors and modulators. On the contrary, III-nitrides do not present problems of intervalley scattering, since the L and X points are much higher in energy (>2 eV) than the Γ point. Another potential advantage is the fact that GaN can be grown on large Si(111) wafers with a reasonable crystalline quality [17], which opens perspectives of integration with the mature silicon technology. Mid-infrared Optoelectronics. https://doi.org/10.1016/B978-0-08-102709-7.00013-9 © 2020 Elsevier Ltd. All rights reserved.

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13.2 Properties of III-nitride semiconductors The most stable crystallographic arrangement of III-nitride semiconductors is the hexagonal (α) wurtzite phase. The wurtzite structure, represented in Fig.  13.1A, is described through the use of four Miller-Bravais indices (hkil), where h, k, and i=−(h+k) are associated to vectors separated by 120 degree that sit perpendicular to the c-axis. The c-(0001), m-(10–10), a-(11–20), and (11–22) planes are indicated in Fig. 13.1A. The [0001] axis is considered positive when the <0001> vector along the bond between a metal and a nitrogen atom points from metal to nitrogen. Conventionally, (0001) crystals are called metal-polar and are typically preferred over (000-1) N-polar as they are more chemically stable and their surface morphology can be more easily controlled during the growth. The difference in electronegativity between N and metal atoms displaces the bond electrons toward the N atom, so that each atomic bond is an electrical dipole. In turn, the low symmetry of the crystal does not allow a mutual annulation of the electric dipoles associated to the bonds, resulting in a macroscopic spontaneous polarization field along the <0001> axis. The magnitude of polarization has a dependency on the ideality of the crystal, the cation-nitrogen bond length, and the chemical properties of the cation; hence, there is a difference in the magnitude of polarization for the various binary compounds (see Table 13.1 [18, 19, 26]). Piezoelectric polarization can also present in III-nitride heterostructures, due to the significant lattice mismatch between binary compounds (see Fig. 13.1B). Stress leads to deformations in the lattice according to Hooke’s law:

σ ij = ∑ cijkl ε kl (13.1) kl

Fig. 13.1  (A) Schematic description of the wurtzite crystalline structure with the c and a lattice constants. Various crystallographic planes are presented. (B) Variation of the bandgap energy at low temperature with the in-plane lattice constant a in III-nitride ternary alloys (AlGaN, InGaN, and AlInN). Inset: Bandgap energies and conduction band offsets between binary compounds at low temperature.

Intersubband transitions in GaN-based heterostructures 541

Table 13.1  Material parameters of III-nitrides Parameters (units)

Symbol

GaN

InN

AlN

Ref.

Lattice constants (nm)

a c PSP

0.3189 0.5185 −0.034

0.3545 0.5703 −0.042

0.3112 0.4980 −0.090

[18]

e31 e33 c11 c12 c13 c33 EG ΔECB

−0.49 0.73 390 145 106 398 3.51 0

−0.57 0.97 223 115 92 224 0.69 2.22

−0.60 1.46 396 137 108 373 6.2 1.8

[20]

me∗ aa (a-axis) ac (c-axis) D1 D2 D3 D4 D5 D6

0.2 −4.9 −11.3 −3.7 4.5 8.2 −4.1 −4.0 −5.5

0.07 −3.5 −3.5 −17.1 7.9 8.8 −3.9 −3.4 −3.4

0.3 −3.4 −11.8 −3.7 4.5 8.2 −4.1 −4.0 −5.5

[18, 25] [18]

Spontaneous polarization (Cm−2) Piezoelectric constants (Cm−2) Elastic constants (GPa)

Bandgap (eV) Conduction band offset with GaN (eV) Electron effective mass Deformation potentials (eV) a=hydrostatic deformation potential Di=valence band uniaxial deformation potential

[19]

[21, 22]

[18, 23] [3, 24]

where cijkl is the elastic tensor, and σij and εkl represent the stress and strain, respectively. In turn, the lattice deformation produces a polarization vector, whose components are calculated as Pj = ∑e jkl ε kl

(13.2)

kl

The expressions cijkl and ejkl are transformed to cmn, ejm by replacing m,n = {xx, yy, zz, yz, zx, xy} with m,n = {1, 2, 3, 4, 5, 6}. Due to the crystallographic symmetry, the only nonzero elastic constants are c11=c22, c12=c21, c13=c31=c23=c32, c33, c44=c55, c66=(c11 −c21)/2, and the nonzero piezoelectric constants are e31=e32, e33, and e15=e24. The values of elastic and piezoelectric constants (e31 and e33) for binary compounds are listed in Table 13.1 [20–22]. For a discussion on the value of e15, see Ref. [27]. In the case of biaxial stress of a material grown along the <0001> direction (σxx=σyy and σzz=0), piezoelectric polarization can be expressed as  c  Pzz = 2  e31 − e33 13  ε xx (13.3) c33   All III-N materials present direct bandgap, varying from 0.69 eV for InN to 3.51 eV for GaN and 6.2 eV for AlN (values at low temperature). The energy bandgap and the Varshni parameters that describe their evolution with temperature are summarized in

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Table  13.1. The bandgap of the ternary alloys is obtained by a quadratic interpolation of the energy of the corresponding binary compounds, using bowing parameters, namely b=0.68 eV for AlGaN, b=2.1 eV for InGaN, and b=4.4 eV for AlInN [23]. The conduction band offsets between binary compounds are represented in the inset of Fig. 13.1B (≈1.8 eV for AlN/GaN [3] and ≈2.2 eV for GaN/InN [24]). The bottom of the conduction band in GaN is well approximated by a parabolic ∗ ∗ dispersion relation with effective mass mGaN  = 0.2 for GaN, mInN  = 0.12 for InN, and ∗ mAlN = 0.3 for AlN [25, 26]. Regarding the hole effective mass, there is a large dispersion of data in the literature (mh∗ = 0.3–2.2 for GaN), partially due to the strong nonparabolicity of the valence band and to the proximity of the heavy hole, light hole, and spin-orbit subbands. However, as III-nitride ISB devices are unipolar with transitions taking place between confined levels in the conduction band, the uncertainty in the value of mh∗ does not have any effect on the device design.

13.3 Intersubband absorption in polar GaN/AlGaN quantum wells The profile of {0001}-oriented GaN/AlGaN QWs is strongly affected by the presence of spontaneous and piezoelectric polarization [20]. Fig. 13.2A presents the band diagram of 2.1-nm-thick GaN QWs in a GaN/AlN multiquantum well (MQW) structure with

Fig. 13.2  (A) Band diagram of a (0001)-oriented GaN/AlN QW in an infinite superlattice with 3-nm-thick AlN barriers and 2.1-nm-thick GaN QWs. The structure is considered strained on an AlN substrate. The squared electron wave functions of the ground hole state, h1, and the ground and excited electron states, e1 and e2, are presented. (B) Variation of e2−e1 as a function of the QW thickness in GaN/AlN MQW structures with 3-nm-thick barriers. Lines represent theoretical calculations for wells grown on the (0001), (11–22), and (1–100) planes. Squares are experimental data from Refs. [28, 29].

Intersubband transitions in GaN-based heterostructures 543

3-nm-thick AlN barriers, with the squared wavefunctions of the first and second electron confined levels e1 and e2 and the first hole confined level h1. Fig. 13.2B illustrates the variation of e2 − e1 as a function of QW width, comparing different crystallographic orientations. In (0001)-oriented polar QWs the ISB energy is strongly influenced by the internal electric field, which blueshifts the transition and reduces the oscillator strength. The infrared absorption of AlN/GaN MQWs has been extensively studied. Fig.  13.3 shows the ISB absorption of AlN/GaN structures with 3-nm-thick AlN Wavelength (µm) 2.4 2.2

2

1.6

1.8

Wavelength (µm) 2

1.4

1.8

1.6

1.4

1.2

6 ML 5 ML 1.3 nm

1.5 nm

1.8 nm

4 ML

Absorbance (arb. units)

Absorbance (arb. units)

9 ML 8 ML 7 ML 6 ML 5 ML

1.0 nm 1.3 nm

1.45 nm 1.3 nm 1.5 nm

2.5 nm

0.5

0.6

(A)

0.7 0.8 Energy (eV)

1.0

0.9

0.6

0.7

(B)

Wavelength (µm) 1.8 1.7 1.6

1.5

1.4

0.8 0.9 Energy (eV) Wavelength (µm)

1.3

1.2

1.8 1.7 1.6

1.5

1.4

0.8

0.9

Energy (eV)

1.2

1.5 nm

67 meV

0.7

1.3

Absorbance (arb. units)

Absorbance (arb. units)

1.3 nm

(C)

1.1

1.0

1

(D)

0.7

0.8

0.9

1

Energy (eV)

Fig. 13.3  (A, B) Absorbance spectra of samples consisting of 20 periods of (0001)-oriented GaN/AlN QWs with 3-nm-thick AlN barriers and various QW thicknesses (indicated in the figure). Vertical lines mark the mean energies of structures with a QW thickness equal to an integer number of monolayers (ML). The curves are vertically shifted for clarity. (C) Absorbance of a sample with a 1.3-nm QW (full line) and the corresponding Lorentzian fit (dashed line). (D) Absorbance of a sample with 1.5-nm-thick QWs (solid line), with Lorentzian fitting curves (dotted lines) and sum of Lorentzian fits (dashed line). Reprinted, with permission, from M. Tchernycheva, L. Nevou, L. Doyennette, F. Julien, E. Warde, F. Guillot, E. Monroy, E. Bellet-Amalric, T. Remmele, M. Albrecht. Systematic experimental and theoretical investigation of intersubband absorption in GaN∕AlN quantum wells Phys. Rev. B 73 (2006) 125347. © 2006 The American Physical Society.

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b­ arriers and various GaN well thicknesses (note that one GaN monolayer is approximately 0.25 nm). The samples show a pronounced absorption, attributed to the e1→e2 transition. The full width at half maximum (FWHM) of the absorption line is in the range of 70–100 meV for QWs doped at 5×1019 cm−3, with a record small linewidth of ≈ 40 meV observed in nonintentionally doped structures [30]. In general, the spectral profile presents Lorentzian shape, but it can also consist of two or three well-defined Lorentzian peaks, as illustrated in Fig. 13.3C and D. These peaks are associated to inplane fluctuations of the QW thickness, and they fit well the expected values of e1→e2 in wells with a thickness equal to an integer number of GaN monolayers. Using binary compounds (GaN/AlN) the e2−e1 transition energy can be tuned in the 1.0–3.5 μm spectral range by increasing the QW thickness from 1 to 7 nm, keeping the AlN barrier thickness in the 1.5–5.1 nm range [3, 28, 31–38]. For QWs larger than ≈ 5 nm, the first two confined electron levels are located within the triangular section of the QW. Therefore, their distance in energy no longer depends on the well thickness. Instead, to shift the ISB absorption toward longer wavelengths, it is necessary to attenuate the electric field in the well, which can be achieved by incorporating Ga in the barriers. Thus, by changing the well thickness and AlGaN composition in the barriers, the ISB absorption can be tuned to reach mid-IR region up to 10 μm [10, 39–50], as illustrated in Fig. 13.4. A further redshift of the ISB absorption, to attain wavelengths longer than above 20 μm, requires band engineering to compensate the internal electric field in the QWs. A first proposed architecture consisted of a three-layer well (step-QW), as described in

Fig. 13.4  Room-temperature TM-polarized IR photo-induced absorption spectra measured in GaN/AlGaN superlattices with different barrier Al contents and QW width, grown either on sapphire or on Si(111) templates. Reprinted, with permission, P.K. Kandaswamy, H. Machhadani, C. Bougerol, S. Sakr, M. Tchernycheva, F.H. Julien, E. Monroy. Midinfrared intersubband absorption in GaN/ AlGaN superlattices on Si(111) templates Appl. Phys. Lett. 95 (2009) 141911. © 2009 American Institute of Physics.

Intersubband transitions in GaN-based heterostructures 545

Fig. 13.5 [51–54]. Fig. 13.5C shows the conduction band diagram of a step-QW consisting of Al0.1Ga0.9N/GaN/Al0.05Ga0.95N (3/3/10 nm). In this structure, the “barrier” comprises the high-Al-content AlxGa1−xN layer and the GaN layer, and the “well” is the low-Al-content AlxGa1−xN layer. The design creates a flat band in the “well” by having the “barrier” balanced at the same average Al content. ISB absorption in the 22–70 μm range has been reported using the step-QW design [52, 53]. Alternative designs based on four layers [51, 55], which can represent improvements in terms of robustness and linewidth [51], or enhancement of the tunneling transport [55]. Doping is an important issue in structures for ISB optoelectronics. The presence of electrons in the QWs is required to observe ISB absorption, which can be achieved by doping with silicon or germanium [56–58]. But high doping levels lead to a significant blueshift of the absorption due to many-body effects [11, 33, 59]. Ge-doped structures systematically show reduced ISB line broadening compared to Si-doped QWs [58],

Fig. 13.5  (A) Schematic description of an Al0.05Ga0.95N/Al0.1Ga0.9N/GaN (10/3/3 nm) step-QW structure. (B) High-angle annular dark-field scanning transmission electron microscopy image of the active region in (A). (C) Conduction band profile of a single period of the structure, including the squared wavefunctions of levels e1 and e2. (D) Transmission spectra for transverse magnetic (TM, square) and transverse electric (TE, circle) polarized light at T=4.7 K. Reprinted, with permission, from H. Machhadani, Y. Kotsar, S. Sakr, M. Tchernycheva, R. Colombelli, J. Mangeney, E. Bellet-Amalric, E. Sarigiannidou, E. Monroy, F.H. Julien. Terahertz intersubband absorption in GaN/AlGaN step quantum wells Appl. Phys. Lett. 97 (2010) 191101. © 2010 American Institute of Physics.

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which points to an increase in interface roughness in the case of doping with silicon. Studies of the effect of the dopant location have shown a significant reduction of the ISB absorption linewidth using δ-doping with silicon donors placed at the end of the QW (topmost area when growing along [0001]) [60]. This is attributed to reduced interface roughness. It was also theorized that doping the QWs should lead to redshifted [61] and stronger [62] ISB absorption in comparison to doping the barriers, although experimental results were not conclusive. In polar III-nitride QWs, the magnitude of the carrier distribution depends not only on the density of n-type dopants but also on the presence of nonintentional dopants, and on the carrier redistribution due to the internal electric field. The large polarization discontinuities in the III-N material system can result in accumulation or depletion of charges in the wells, to the point of having a dominant contribution to the infrared absorption [28].

13.4 Quantum wells in alternative crystallographic orientations The internal electric field characteristic of III-nitride heterostructures complicates the design of ISB devices. Furthermore, the electric field is highly sensitive to strain, and binary III-nitride compounds present significant lattice mismatch. A simple alternative to eliminate the internal electric field is the growth on nonpolar crystallographic planes, like m-{1–100} or a-{11–20} planes [63]. However, the lattice mismatch is larger along the c-axis (contained in these planes) than along the a-axis, which results in a high density of crystalline defects. Furthermore, the strong surface anisotropy makes it difficult to obtain atomically flat layers. A comparative study of a- versus m-oriented GaN/AlN MQWs grown on free-standing GaN substrates by plasma-assisted molecular beam epitaxy shown that m-plane structures present better structural and optical properties than their a-plane counterparts [64, 65]. Room-temperature ISB absorption in the 1.5–2.9 μm range was observed in m-plane GaN/AlN MQWs with different well widths. However, the ISB absorption band presents a Gaussian spectral profile with a FWHM comparable or larger than that measured in polar MQWs. This points to inhomogeneous broadening due to structural inhomogeneities, probably related to the stacking faults and dislocations observed in these strongly mismatched structures. On the other hand, the transition energy in nonpolar wells is redshifted in comparison to polar wells with the same dimensions, which is explained by the absence of internal electric field. By incorporating Ga in the MQWs barriers, the ISB absorption can be redshifted to the 4.0 to 5.8 μm range (310–214 meV) [64, 66–68], as illustrated in Fig. 13.6 for AlGaN/GaN MQWs deposited on bulk m-plane GaN. Here, the long wavelength limit is set by the absorption associated with the second order of the reststrahlen band in the GaN substrates. Similar to the c-plane, the ISB absorption is highly stable with temperature (see Fig. 13.6A). Mid-IR absorption shifts only 1.6–2.6 meV from 10 to 300 K [68], to be compared to 3.5–5.2 meV in the case of AlGaAs/GaAs and 6.2–12 meV [69–71] in the case of AlSb/InAs [72]. This is explained by the heavy effective mass of the electron in GaN and the relatively low nonparabolicity of the conduction band.

Intersubband transitions in GaN-based heterostructures 547

Fig. 13.6  (A) Temperature dependence of the ISB absorption [extracted from TM-polarized transmission (Tp)/TE-polarized transmission (Ts)] spectrum of m-plane GaN/Al0.485Ga0.515N (2.85/3.20 nm) QWs doped with silicon at 7.0×1018 cm−3. The spectra are vertically shifted for clarity. (B) Measured (solid lines) and calculated (dashed lines) intersubband absorption from m-plane GaN/Al0.485Ga0.515N (2.85/3.20 nm) QWs with various doping levels. The spectra are normalized to their maximum, and vertically shifted for clarity. Panel (A) reprinted, with permission, from T. Kotani, M. Arita, K. Hoshino, Y. Arakawa. Temperature dependence of mid-infrared intersubband absorption in AlGaN/GaN multiple quantum wells Appl. Phys. Lett. 108 (2016) 052102 and (B) from T. Kotani, M. Arita, Y. Arakawa. Doping dependent blue shift and linewidth broadening of intersubband absorption in non-polar m-plane AlGaN/GaN multiple quantum wells Appl. Phys. Lett. 107 (2015) 112107. © 2015 American Institute of Physics.

Unfortunately, m-plane GaN/AlGaN QWs absorbing in the mid-IR require high Al contents in the AlGaN barriers (>25%), which results in stacking faults and strong alloy inhomogeneities [73–75]. It is necessary to reduce the Al mole fraction of the QW barriers below 10% to enable growth without epitaxy-induced defects (see Fig.  13.7A). The ISB energy in such structures is much smaller, though. They display low-temperature (T=5–10 K) ISB absorption in the 1.5–9 THz range [76, 77], as shown in Fig. 13.7B. The effect of the doping density on the ISB behavior was studied on m-plane GaN/AlGaN structures absorbing in the mid- and far-IR, as illustrated in Figs. 13.6B and 13.7B. Increasing the silicon or germanium concentration in the QWs leads to a blueshift of the ISB absorption due to the exchange interaction and depolarization shift, and to broadening due to scattering by ionized impurities [58, 66, 76, 78].

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Fig. 13.7  Cross-section high-angle annular dark-field scanning transmission electron microscopy image of an m-GaN/Al0.075Ga0.925N (10/18.5 nm) MQW viewed along (A) the <0001> zone axis and (B) the <11–20> zone axis. (C) Normalized TM-polarized ISB absorption of GaN/Al0.075Ga0.925N (10/18.5 nm) MQWs with different doping levels (indicated in the figure). Samples were doped with Si (right) or with Ge (left). Panels (A and B) reprinted, with permission, from C.B. Lim, A. Ajay, C. Bougerol, B. Haas, J. Schörmann, M. Beeler, J. Lähnemann, M. Eickhoff, E. Monroy. Nonpolar m-plane GaN/ AlGaN heterostructures with intersubband transitions in the 5–10 THz band. Nanotechnology 26 (2015) 435201. © 2016 IOP Publishing Ltd. All rights reserved and (C) from C.B. Lim, A. Ajay, C. Bougerol, J. Lähnemann, F. Donatini, J. Schörmann, E. Bellet-Amalric, D.A. Browne, M. Jiménez-Rodríguez, E. Monroy. Effect of doping on the far-infrared intersubband transitions in nonpolar m-plane GaN/AlGaN heterostructures. Nanotechnology 27 (2016) 145201. © 2016 IOP Publishing, Ltd. and from C.B. Lim, A. Ajay, J. Lähnemann, C. Bougerol, E. Monroy. Effect of Ge-doping on the short-wave, mid- and far-infrared intersubband transitions in GaN/AlGaN heterostructures. Semicond. Sci. Technol. 32 (2017) 125002. © 2017 IOP Publishing, Ltd. All rights reserved.

From the viewpoint of electron transport, the observation of negative differential resistance in m-plane GaN/AlGaN double-barrier heterostructures confirms the ­feasibility of resonant tunneling in this crystallographic orientation, and paves the way to nonpolar ISB devices for THz applications [79].

13.5 Nanowire heterostructures The nanowire geometry is an interesting alternative for devices requiring low defect density in the active region and the combination of materials with large lattice mismatch. For instance, it could facilitate the integration of binary GaN and AlN compounds for near- and mid-IR applications. It is important to note that the reduction of the amount of absorbing matter in a nanowire ensemble in comparison with a

Intersubband transitions in GaN-based heterostructures 549

planar layer (often called “filling factor”) can come without degradation of the total absorption, since standing nanowires behave like a light concentrator [80, 81]. A requirement for the fabrication of certain types of electrically driven ISB devices is the implementation of quantum barriers that electrons can traverse via resonant tunneling transport. For III-nitride nanowires, resonant tunneling has been demonstrated in the case of an axial double barrier [82], axial multiple barriers [83], and core-shell double barriers [84]. The observation of ISB transitions in GaN/AlN nanodisks on GaN nanowires was first reported in a GaN/AlN MQW structure in a nanowire with Si-doped barriers [85], but the first systematic study in GaN/AlN heterostructures varying well size and doing level made use of germanium as n-type dopant in the GaN quantum wells [86]. The well sizes were varied in the 2–8 nm range. However, the intraband absorption was strongly blueshifted due to many-body effects [86] so that the longer peak absorption wavelength was only 1.95 μm, and the linewidth was in the order of 400 meV. This was understood to be arising from nonuniform diameter distribution along the length of the nanowires. Recently, GaN/AlN (2/3 nm) wells in a nanowire with more uniform diameter distributions were developed (see scanning transmission electron microscopy images in Fig.  13.8A and B), and they resulted in improved ISB absorption linewidths in the order of 200 meV at 1.55 μm [56, 57], as shown in Fig. 13.9 (samples NS1 and NS2). In this case, the ISB absorption could be observed using both germanium and silicon as n-type dopant in the wells. The improved homogeneity made it possible to observe absorption for lower doping levels than in Ref. [86], thereby reducing the blueshift due to many-body effects. However, the linewidths were still broad compared to GaN/AlN quantum wells. This was ascribed to the geometrical dispersion in nanowire dimensions along the entire nanowire ensemble. Using larger GaN/AlN wells (4/3 nm, 5.7/3 nm) on GaN nanowires, the ISB absorption can be extended to longer wavelengths, effectively covering the 1.4–3.4 μm spectral range (samples A1, A2, A3 and B1 in Fig. 13.9). However, in the largest wells in this series (5.7 nm), it was observed that the interface of AlN when grown on GaN was sharp, whereas the interface of GaN grown on AlN extended by around 1.5–2 nm (see Fig.  13.8G and H), which was attributed to the instability of the GaN on AlN interface under stress [87, 88]. Such an asymmetry influences the confinement of carriers in these structures, and contributed to the redshift of the ISB transition. An alternative approach to shift the absorption toward mid-IR wavelengths consists in the introduction of the ternary alloy AlGaN in the barriers instead of AlN, since this results in the reduction of the axial internal electric field. Fig.  13.8C–E shows GaN/Al0.4Ga0.6N (4/3 nm) wells grown on GaN nanowires, with homogenous size distribution along the length of the nanowire [89]. Structurally the ternary compound represents a reduction of misfit in comparison to AlN barriers. Certain compositional inhomogeneities were observed in these samples, as shown in Fig. 13.8F. In spite of that, ISB absorption was observed in the range of 4.5–6.4 μm, as depicted in Fig. 13.9 (sample C3). Another approach to the fabrication of nanowire heterostructures consists of etching down an originally planar structure [81, 90, 91]. This procedure is generally referred

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Fig. 13.8  High-angle annular dark-field scanning transmission electron microscopy images and corresponding intensity profiles of the active region of a nanowire from samples containing (A, B) GaN/AlN (2/3 nm), (C–F) GaN/Al0.4Ga0.6N (4/3 nm), and (G, H) GaN/AlN (5.3/3 nm) MQWs. Dark/bright contrast corresponds to Al/Ga-rich areas. The * symbol in (F) indicates a region of higher intensity corresponding to increased Ga content in the AlGaN barrier. Reprinted, with permission, from A. Ajay, R. Blasco, J. Polaczynski, M. Spies, M. den Hertog, E. Monroy. Intersubband absorption in GaN nanowire heterostructures at mid-infrared wavelengths. Nanotechnology 29 (2018) 385201. © 2018 IOP Publishing, Ltd. All rights reserved.

to as top-down method. The etching pattern can be defined using electron lithography, nanoimprint or colloidal masking, for instance. Top-down nanowires present well-controlled doping profile and heterostructure dimensions, and better wire-to-wire homogeneity, which facilitates their integration into large-scale devices. However, in this process the critical thicknesses are determined by the two-dimensional growth, and the dislocations generated in the two-dimensional epitaxial growth remain in the

Intersubband transitions in GaN-based heterostructures 551

Fig. 13.9  Normalized infrared absorption for TM-polarized light measured at grazing incidence (≈10 degree) from GaN nanowire samples containing (NS1, NS2) GaN/AlN (1.75/2.70 nm), (A1, A2, A3) GaN/AlN (4/3 nm), (B1) GaN/AlN (5.3/3 nm), and (C3) GaN/ Al0.4Ga0.6N (4/3 nm) MQWs. Spectra from samples with different doping levels in the GaN wells are vertically shifted for clarity. Reprinted, with permission, from A. Ajay, R. Blasco, J. Polaczynski, M. Spies, M. den Hertog, E. Monroy. Intersubband absorption in GaN nanowire heterostructures at mid-infrared wavelengths. Nanotechnology 29 (2018) 385201. © 2018 IOP Publishing, Ltd.

patterned nanowire array. There is also a risk of structural damage during the plasma etching process, which might lead to a degradation of the optical properties. Lähnemann et al. assessed the feasibility of the top-down method to fabricate GaN/ AlN nanopillars for ISB optoelectronic applications [81]. With this purpose, samples containing MQWs that displayed either near- or mid-IR ISB absorption (peak absorption at 1.5 and 4.4 μm, respectively) were etched into nano- and micropillar arrays in an inductively coupled plasma, and the effect of this process on the ISB absorption was analyzed. When the spacing of the pillar array is comparable to the wavelength of the investigated spectral region, the IR transmittance spectra are dominated by refraction effects, as well as photonic crystal modes, and the ISB absorption is masked by these features. However, electrodynamics simulations indicate that the ISB absorption is still present. For pillar spacings significantly smaller (≤1/3) than the intersubband wavelength, the ISB absorption is clearly observed. The magnitude and linewidth of the ISB absorption is preserved in spite of the low filling factor even when 80% or 90% of the material is etched away.

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13.6 Intersubband devices based on III-nitrides 13.6.1 Infrared photodetectors Near-IR photoconductive quantum well IR photodetectors (QWIPs) based on Sidoped GaN/AlN MQWs and operating around 1.5 μm [92, 93] have been reported. However, photoconductive devices display a low yield and high dark current, due to the high density of structural defects originated by the lattice mismatch between GaN and AlN. An alternative to circumvent the leakage problem consists in operating the device in the photovoltaic mode (i.e., at zero bias) [94–98], which is possible thanks to the intrinsic asymmetry of the potential profile in polar GaN/AlN MQWs [96, 99]. Advanced photovoltaic devices such as quantum cascade detectors (QCDs) operating at 1.55 μm have also been demonstrated using the GaN/AlGaN material system [100, 101]. They consist of several periods of an active QW coupled to a short-period superlattice, which serves as extractor [102, 103]. An example of a QCD design is depicted in Fig. 13.10A, including the general scheme of the structure, a view of a period of the active region by transmission electron microscopy and the band diagram of a period of the active region. Under illumination, electrons from the ground state of the active QW, e1, are excited to the upper state, e2, and then transferred to the extractor region (arrow in the figure) where they experience multiple relaxations toward the next active QW. Taking advantage of the polarization-induced internal electric, it becomes easy to design an efficient AlGaN/AlN (or GaN/AlGaN) electron extractor where the energy levels are separated by approximately the LO-phonon energy (≈90 meV). The peak responsivity of these GaN/AlGaN QCDs at room temperature was ≈10 mA/W [100, 104], and devices with a mesa size of 10×10 μm2 exhibited a −3 dB cutoff frequency at ≈40 GHz [104]. Pump and probe measurements of these devices pointed out an ISB scattering time in the active QW of 0.1 ps and a transit time through the extractor of 1 ps [105]. Following the observation of ISB transitions in GaN/AlN MQWs on GaN nanowires, the feasibility of ISB photodetection around 1.55 μm in single-nanowire QWIPs was demonstrated [106] (see Fig. 13.11). The single nanowires were electrically contacted on Si3N4 membranes, which facilitated structural evaluation of the same nanowire using scanning transmission electron microscopy and theoretical calculations to support the measurements. The ISB photocurrent was shown to vary linearly with the incident IR laser illumination (1.55 μm), as described in Fig.  13.11C, whereas the interband photocurrent exhibited a sublinear behavior when illuminating with an ultraviolet laser (325 nm). This was explained by the fact that the ISB processes are decoupled from surfaces states, unlike band-to-band transitions that are strongly sensitive to the Fermi level at the sidewall surfaces. Photoconductive QWIPs in the mid- and far-IR spectral regions benefit from a reduction of the lattice mismatch, which aids in their fabrication. Thus, photoconductive AlGaN/GaN devices operating in the 3–5 μm atmospheric window [107] and in the THz domain [108] have been demonstrated at low temperature (5 and up to 50 K, respectively). The active region of such detectors utilize a bound- to quasi-bound configuration following the step-QW design. On the other hand, Pesach et al. have

AIN Sapphire

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Fig. 13.10  (A) QCD design for operation at 1.5 μm. The active region contains 40 periods of a GaN absorbing QW and an AlN/AlGaN extractor. In the middle, transmission electron microscopy image of a period of the active region. On the right side, conduction band diagram. (B) QCD for operation in the mid-IR. In this case, a period of the active region consists of a GaN absorbing well and an AlGaN/GaN extractor. (C) Photovoltaic (zero bias) spectral response of GaN-based QCDs. All the devices contain 40 periods in the active region and were grown on AlN-on-sapphire templates by PAMBE. The devices responding in the near-IR were measured at room temperature, whereas those with peak response in the mid-IR were measured at 80 K.

Intersubband transitions in GaN-based heterostructures 553

AlGaN:Si

Active QW: 6 ML GaN Injector: 6 ML AIN / 4 ML AI0.3Ga0.7N

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Fig. 13.11  (A) Sketch of a single-nanowire QWIP, depicting also the contact scheme for photocurrent measurements. (B) Normalized near-IR spectral photocurrent response for two nanowires (NW 1 and NW 2) measured at 1 V bias. The response was averaged over several different illumination powers. The inset shows the spectral response of NW 1 at different illumination levels on a semilogarithmic scale. The diameter of the laser spot was always 2 mm. The error bars account for the uncertainty in the calculation of the impinging irradiance due to the error in estimation of the spot size for different laser diodes. (C) Linearity of the intersubband photocurrent for four different nanowires (NWs 1−4) measured in vacuum at an illumination wavelength of 1.55 μm (laser spot diameter=2 mm, laser chopped at 647 Hz). Reprinted, with permission, from J. Lähnemann, A. Ajay, M.I. Den Hertog, E. Monroy. Near-Infrared Intersubband Photodetection in GaN/AlN Nanowires. Nano Lett. 17 (2017) 6954–60. © 2017 American Chemical Society.

Intersubband transitions in GaN-based heterostructures 555

demonstrated mid-IR QWIPs fabricated on m-plane GaN substrates [109]. Such devices consisted of In0.095Ga0.905N/Al0.07Ga0.93N (2.5/56.2 nm) and In0.1Ga0.9N/GaN (3/50 nm) MQWs, and displayed photocurrent peaks at 7.5 and 9.3 μm, respectively, when measured at 14 K. For the design of QCDs operating in the mid-IR, the near-IR design has to be modify by enlarging the GaN absorbing well and replacing the AlN/AlGaN extractor by an AlGaN/GaN structure. An example of such a design is presented in Fig. 13.10B, together with the low-temperature (80 K) spectral response of fabricated devices in Fig. 13.10C. The group of Prof. Gmachl has presented a detailed analysis of a GaN/ Al0.5Ga0.5N device fabricated by MOVPE, showing a peak responsivity of 100 μA/W at 4 μm and a detectivity of up to 108 Jones at the background limited IR performance temperature around 140 K [110]. The spectral response of such a device at low temperature (80 K) and room temperature is shown in Fig. 13.12.

13.6.2 Infrared emitters First reports of room-temperature ISB luminescence in the III-nitride material system were by optical pumping of GaN/AlN MQWs [111–113]. These structures utilized a three level system where the emission was associated to an e3−e2 ISB transition at 2–2.3 μm. The emission was only observed for transverse magnetic (TM) polarized excitation at wavelengths corresponding to the e1−e3 ISB transition. However, due

Fig. 13.12  Normalized photocurrent spectra of a QCD design with GaN/Al0.5Ga0.5N QWs with a nominal intersubband optical transition at 3.6 μm. Inset: Schematic of the fabricated device. Light is incident at the Brewster’s angle of 66 degree. OS and RS refer to the original structure and the reversed structure (reversing the growth sequence of the layers of the original design), respectively. A transverse magnetic (TM) over transverse electric (TE) selection ratio >20:1 is observed o, the OS configuration at 80 K. Reprinted, with permission, from Y. Song, R. Bhat, T.-Y. Huang, P. Badami, C.-E. Zah, C. Gmachl. III-nitride quantum cascade detector grown by metal organic chemical vapor deposition. Appl. Phys. Lett. 105 (2014) 182104. © 2014 American Institute of Physics.

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to the large lattice mismatch of the GaN/AlN system, the fabrication of GaN-based quantum cascade lasers operating in the near-IR does not appear feasible, despite several theoretical proposals [4, 114, 115]. Further research also provided mid-IR ISB electroluminescence measurements on chirped AlGaN/GaN MQW structures [116]. These structures demonstrated a large blueshift of the emission, from 10 to 6.9 μm, when increasing the bias voltage from 7 to 14 V. On the other hand, Prof. Gmachl et al. have reported ISB (fully TM-polarized) light emission in the mid-IR region from a GaN/Al0.65Ga0.45N quantum cascade structure grown by MOVPE [117]. For the device design, they demonstrated that introducing graded interfaces in the calculations had strong influence on the energy spectrum and the calculated transition levels [118]. It is hence important to take this factor into consideration to model devices fabricated by MOVPE, where the high growth temperature result interfaces that extend along several atomic layers. Taking this issue into consideration, Song et al. designed and demonstrated mid-IR emission at λ=4.9 μm (FWHM=110 meV) under pulsed operation at 80 K [117]. Finally, there is an increasing interest and research effort for the fabrication of GaN quantum cascade lasers in the far-IR, where it would be possible to exploit the large LO-phonon energy of III-nitrides (92 meV in the case of GaN) to realize devices operating at room temperature, and emitting in the 5–10 THz range, corresponding the reststrahlen band of GaAs. Various designs for a GaN-based THz quantum cascade laser have been proposed [119–133], all focusing on a resonant-phonon architecture. Although these publications propose solutions toward managing the optical/electronic design, the lattice mismatch and fabrication methodology, but the fabrication of a high-efficiency laser device still remains a challenge.

13.7 Conclusions This chapter reviews recent research on III-nitride ISB optoelectronics, paying particular attention to developments to cover the mid-IR spectral region. The large conduction band offset of the GaN/AlGaN system, and its sub-picosecond ISB scattering rate, makes them very promising materials for high-speed devices operating at the 1.3 and 1.55 μm telecommunication wavelengths and in the 3–5 μm atmospheric widow. The 8–12 μm atmospheric window is not accessible for these materials due to reststrahlen absorption. There is also an interest to fabricate GaN-based devices in the THz spectral region, motivated by the high LO-phonon energy in III-nitrides, which should allow the fabrication of devices in the whole 1–10 THz range, and operating at higher temperature than GaAs due to the reduced probability of thermally excited phonon emission. ISB transitions in polar GaN/AlGaN planar QWs and wells-in-a-nanowire can be tuned along the near- and mid-IR. Shifting the absorption toward longer wavelengths (>20 μm) can be achieved either by using nonpolar crystallographic orientations, or by band engineering to locally reduce the polarization-related internal electric field. Various prototypes of GaN-based QWIPs and QCDs with peak response in the nearand mid-IR, as well as in the THz domain, have been demonstrated. Regarding IR

Intersubband transitions in GaN-based heterostructures 557

emission, near-IR luminescence was observed in optically pumped GaN/AlN QWs, and mid-IR electroluminescence was measured on chirped AlGaN/GaN MQWs, and in quantum cascade GaN/AlGaN structures. Intense research efforts are now oriented toward the fabrication of a GaN-based quantum cascade laser, which could potentially operate at higher temperatures than GaAs-based devices thanks to the high energy of the LO-phonon in III-nitride semiconductors.

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