^{1,a)}

### Abstract

Wide-band-gap GaN and Ga-rich InGaN alloys, with energy gaps covering the blue and near-ultraviolet parts of the electromagnetic spectrum, are one group of the dominant materials for solid state lighting and lasing technologies and consequently, have been studied very well. Much less effort has been devoted to InN and In-rich InGaN alloys. A major breakthrough in 2002, stemming from much improved quality of InN films grown using molecular beam epitaxy, resulted in the bandgap of InN being revised from 1.9 eV to a much narrower value of 0.64 eV. This finding triggered a worldwide research thrust into the area of narrow-band-gap group-III nitrides. The low value of the InN bandgap provides a basis for a consistent description of the electronic structure of InGaN and InAlN alloys with all compositions. It extends the fundamental bandgap of the group III-nitride alloy system over a wider spectral region, ranging from the near infrared at (0.64 eV for InN) to the ultraviolet at (3.4 eV for GaN) or (6.2 eV for AlN). The continuous range of bandgap energies now spans the near infrared, raising the possibility of new applications for group-III nitrides. In this article we present a detailed review of the physical properties of InN and related group III-nitride semiconductors. The electronic structure, carrier dynamics, optical transitions, defect physics, doping disparity, surface effects, and phonon structure will be discussed in the context of the InN bandgap re-evaluation. We will then describe the progress, perspectives, and challenges in the developments of new electronic and optoelectronic devices based on InGaN alloys. Advances in characterization and understanding of InN and InGaN nanostructures will also be reviewed in comparison to their thin film counterparts.

This review would not have been written without the invitation of Professor J. M. Poate and Professor E. E. Haller. I am grateful to have the opportunity to present recent developments in the research field of InN and In-rich group-III nitrides. I wish to acknowledge collaborations and discussions with Dr. W. Walukiewicz, Dr. H. Lu, Dr. W. J. Schaff, Professor E. E. Haller, Professor Y. Nanishi, Dr. K. M. Yu, Dr. J. W. Ager III, and Dr. S. X. Li. This work was supported, in part, by the National Science Foundation under Grant No. EEC-0425914, and in part by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under the Department of Energy Contract No. DE-AC02-05CH11231.

I. INTRODUCTION

II. NARROW BANDGAP OF InN

A. Optical properties

B. Band structure

1. calculations of conduction band

2. First-principle calculations

C. Carrier recombination dynamics

III. InGaN AND InAlN ALLOYS

A. Bandgap and band alignment

1. Bowing of bandgap and critical point energies

2. Band alignment and offset

B. Electronic properties

1. Native defects and -type doping

2. -type doping

3. Surface properties

4. Radiation resistance

5. Transport properties

C. Pressure behavior and lattice properties

1. Hydrostatic pressure coefficient and deformation potentials

2. Piezoelectric properties

3. Phonon structures and dynamics

IV. NEW APPLICATIONS

A. Photovoltaics

B. Solid state lighting and and terahertz emission

C. Chemical sensors and field-effect transistors

V. GROUP III-NITRIDE NANOSTRUCTURES

A. InN nanostructures: Optical properties

B. InN nanostructures: Electronic properties

C. In-rich InGaN nanowires

VI. CONCLUSIONS AND OUTLOOKS

### Key Topics

- III-V semiconductors
- 144.0
- Band gap
- 102.0
- Doping
- 49.0
- Phonons
- 37.0
- Photonic bandgap materials
- 37.0

## Figures

(a) The CIE chromaticity diagram, where the wavelength is given in nm and main LED materials are shown. (b) The external quantum efficiency of commercial and LEDs (points) shown together with the luminous human eye response (curve). Reference 3.

(a) The CIE chromaticity diagram, where the wavelength is given in nm and main LED materials are shown. (b) The external quantum efficiency of commercial and LEDs (points) shown together with the luminous human eye response (curve). Reference 3.

Absorption and photoluminescence of a high-quality, intrinsic InN film measured at 12 K. The solid line through the absorption data points is a sigmoidal fit. Reference 21.

Absorption and photoluminescence of a high-quality, intrinsic InN film measured at 12 K. The solid line through the absorption data points is a sigmoidal fit. Reference 21.

Absorption (a) and PL (b, log scale) spectra of InN measured at a wide range of temperatures. Panel (c) shows the temperature dependence of the PL peak and the bandgap determined from the absorption curves. The solid curve shows a fit to the bandgap with the standard Varshni’s equation. Reference 21.

Absorption (a) and PL (b, log scale) spectra of InN measured at a wide range of temperatures. Panel (c) shows the temperature dependence of the PL peak and the bandgap determined from the absorption curves. The solid curve shows a fit to the bandgap with the standard Varshni’s equation. Reference 21.

Integrated PL intensity as a function of excitation intensity for a -plane InN film. The solid lines are power law fits. The inset shows the power law index being a constant independent of free electron concentration. Reference 49.

Integrated PL intensity as a function of excitation intensity for a -plane InN film. The solid lines are power law fits. The inset shows the power law index being a constant independent of free electron concentration. Reference 49.

(a) PL spectra of an -plane InN film with and polarization, respectively. (b) Measured absorption coefficient squared of the -plane film as a function of photon energy for the two polarizations. The inset shows the full transmission spectra. Reference 50.

(a) PL spectra of an -plane InN film with and polarization, respectively. (b) Measured absorption coefficient squared of the -plane film as a function of photon energy for the two polarizations. The inset shows the full transmission spectra. Reference 50.

Calculated conduction and valence band dispersion of InN using the model. The Fermi level for is shown. Reference 20.

Calculated conduction and valence band dispersion of InN using the model. The Fermi level for is shown. Reference 20.

Absorption edge (optical bandgap) plotted as a function of electron concentration. The calculated results are also shown. Reference 65.

Absorption edge (optical bandgap) plotted as a function of electron concentration. The calculated results are also shown. Reference 65.

Effective electron mass as a function of electron concentration. The curves are calculated dependences based on the nonparabolic dispersion using different values. References a 20, b 38, 68, and 69, c 7, d 39, e 56, and f 70.

Effective electron mass as a function of electron concentration. The curves are calculated dependences based on the nonparabolic dispersion using different values. References a 20, b 38, 68, and 69, c 7, d 39, e 56, and f 70.

Effective electron mass at the conduction band minimum at the point as a function of the -point direct bandgap in various semiconductors. The solid line is a fit to Eq. (6) which leads to a universal . Refs: a 20, b 56, c 7.

Effective electron mass at the conduction band minimum at the point as a function of the -point direct bandgap in various semiconductors. The solid line is a fit to Eq. (6) which leads to a universal . Refs: a 20, b 56, c 7.

(a) The breakdown of the common-cation rule in Zn-VI, Cd-VI, and In-V semiconductors. (b) Trend of direct bandgaps in group III-V semiconductors.

(a) The breakdown of the common-cation rule in Zn-VI, Cd-VI, and In-V semiconductors. (b) Trend of direct bandgaps in group III-V semiconductors.

(a) Atomic orbital energies of group III and V elements. (b) conduction and valence band edges of related group III-V semiconductors with respect to (see Sec. III B). Reference 73.

(a) Atomic orbital energies of group III and V elements. (b) conduction and valence band edges of related group III-V semiconductors with respect to (see Sec. III B). Reference 73.

First-principle calculation of the conduction and valence bands of wurtzite InN near the point. Analytical dispersions using parameters listed in Table II agree well with these curves. Reference 55.

First-principle calculation of the conduction and valence bands of wurtzite InN near the point. Analytical dispersions using parameters listed in Table II agree well with these curves. Reference 55.

First-principle calculation of the band structure of wurtzite InN in the entire Brillouin zone. The Fermi stabilization level is also shown (see Sec. III B). Reference 85.

First-principle calculation of the band structure of wurtzite InN in the entire Brillouin zone. The Fermi stabilization level is also shown (see Sec. III B). Reference 85.

Experimentally measured real (dashed line) and imaginary (full line) part of the ordinary dielectric function of wurtzite InN as determined from -plane (a) and -plane (b) films. Critical points are marked by arrows. Reference 44.

Experimentally measured real (dashed line) and imaginary (full line) part of the ordinary dielectric function of wurtzite InN as determined from -plane (a) and -plane (b) films. Critical points are marked by arrows. Reference 44.

(a) Differential transmission of three InN samples with different electron concentrations under a pump fluence of . Electron concentration: sample A: , sample B: , and sample C: . Reference 90. (b) Recombination lifetime vs carrier concentration. The samples with high electron concentrations were Si-doped, while the rest were not intentionally doped. References a 90 and b 91.

(a) Differential transmission of three InN samples with different electron concentrations under a pump fluence of . Electron concentration: sample A: , sample B: , and sample C: . Reference 90. (b) Recombination lifetime vs carrier concentration. The samples with high electron concentrations were Si-doped, while the rest were not intentionally doped. References a 90 and b 91.

Radiative lifetime of carriers in InN as a function of temperature. The solid line indicates a power law fit to sample A. The two red dots show the measured total lifetime in sample A. Reference 90.

Radiative lifetime of carriers in InN as a function of temperature. The solid line indicates a power law fit to sample A. The two red dots show the measured total lifetime in sample A. Reference 90.

(a) Differential transmission spectrum at different time delays after the pump pulse is turned off. (b) Carrier temperature recorded at 300 K as a function of time delay calculated from (a). The solid curve is the expected behavior calculated using a LO phonon scattering model. Reference 93.

(a) Differential transmission spectrum at different time delays after the pump pulse is turned off. (b) Carrier temperature recorded at 300 K as a function of time delay calculated from (a). The solid curve is the expected behavior calculated using a LO phonon scattering model. Reference 93.

(a) Room-temperature PL spectrum (dashed) and absorption squared (solid) of InN and with different compositions. Ref. 92. (b) Room-temperature absorption curves of alloys with different compositions, from which the bandgap is determined as a function of . Reference 94.

(a) Room-temperature PL spectrum (dashed) and absorption squared (solid) of InN and with different compositions. Ref. 92. (b) Room-temperature absorption curves of alloys with different compositions, from which the bandgap is determined as a function of . Reference 94.

(a) Bandgap of InGaN and InAlN as a function of Ga or Al molar fraction. The solid and dashed lines are bowing curves [Eq. (13)] with best-fit bowing parameters. (b) The bandgap of InGaN, InAlN, and AlGaN plotted as a function of in-plane lattice constant . The solid lines show the bowing dependence using the best-fit bowing parameters determined from (a). References 92, 94, and 95.

(a) Bandgap of InGaN and InAlN as a function of Ga or Al molar fraction. The solid and dashed lines are bowing curves [Eq. (13)] with best-fit bowing parameters. (b) The bandgap of InGaN, InAlN, and AlGaN plotted as a function of in-plane lattice constant . The solid lines show the bowing dependence using the best-fit bowing parameters determined from (a). References 92, 94, and 95.

Bandgap and critical point energies of (a) InGaN (Ref. 45) and (b) InAlN (Ref. 43) as a function of the indium molar fraction. The solid lines represent the best fits using a bowing equation for determining the bowing parameters.

Bandgap and critical point energies of (a) InGaN (Ref. 45) and (b) InAlN (Ref. 43) as a function of the indium molar fraction. The solid lines represent the best fits using a bowing equation for determining the bowing parameters.

in InGaN alloys with respect to the natural conduction and valence band edges assuming no strain and polarization effects. The band edges of several other semiconductors are also shown. The energy is referenced to the vacuum level. Reference 67.

in InGaN alloys with respect to the natural conduction and valence band edges assuming no strain and polarization effects. The band edges of several other semiconductors are also shown. The energy is referenced to the vacuum level. Reference 67.

Band bending (a and b) and charge distribution (c and d) near the surface of a -type (a and c) and -type (b and d) InN film. The bulk doping level in each case is labeled by and , respectively. Reference 139.

Band bending (a and b) and charge distribution (c and d) near the surface of a -type (a and c) and -type (b and d) InN film. The bulk doping level in each case is labeled by and , respectively. Reference 139.

(a) Angle-resolved photoemission spectroscopy photocurrent intensity map of a -type InN showing the quantized energy levels in the surface layer. Calculated subband dispersion shows clearly the band nonparabolicity (solid curves). (b) band diagram and energy levels. Refs. 157 and 159

(a) Angle-resolved photoemission spectroscopy photocurrent intensity map of a -type InN showing the quantized energy levels in the surface layer. Calculated subband dispersion shows clearly the band nonparabolicity (solid curves). (b) band diagram and energy levels. Refs. 157 and 159

as a function of bias voltage determined by ECV measurements for unintentionally doped and Mg-doped InN along with two calculated curves for and . The inset shows the band bending configuration calculated for the unintentionally doped (a) and Mg-doped (b) films at their respective peak in the main plot. Ref. 139

as a function of bias voltage determined by ECV measurements for unintentionally doped and Mg-doped InN along with two calculated curves for and . The inset shows the band bending configuration calculated for the unintentionally doped (a) and Mg-doped (b) films at their respective peak in the main plot. Ref. 139

InN and InGaN alloys behave very differently from GaAs and GaN when irradiated with high-energy particles. Here the electron concentration is shown as a function of displacement damage dose. References 67 and 166

InN and InGaN alloys behave very differently from GaAs and GaN when irradiated with high-energy particles. Here the electron concentration is shown as a function of displacement damage dose. References 67 and 166

(a) As-grown InN electron density and mobility as a function of film thickness. Closed symbols are grown on a GaN buffer, open are on AlN buffer, and dotted symbols are grown directly on sapphire. Reference 145. (b) Electron mobility as a function of free electron concentration in as-grown InN films and films irradiated with 2 MeV or ions. References 176 and 177

(a) As-grown InN electron density and mobility as a function of film thickness. Closed symbols are grown on a GaN buffer, open are on AlN buffer, and dotted symbols are grown directly on sapphire. Reference 145. (b) Electron mobility as a function of free electron concentration in as-grown InN films and films irradiated with 2 MeV or ions. References 176 and 177

Calculated electron mobility as a function of alloy composition in (a) InGaN and (b) InAlN. Main scattering mechanisms limiting the mobility are shown. References 178.

Calculated electron mobility as a function of alloy composition in (a) InGaN and (b) InAlN. Main scattering mechanisms limiting the mobility are shown. References 178.

Hydrostatic pressure coefficients of the bandgaps of InN, GaN, AlN, and their alloys. Refs: a 59, b 183, c 58, d 63, e 180, f 60, g 62, h 61.

Hydrostatic pressure coefficients of the bandgaps of InN, GaN, AlN, and their alloys. Refs: a 59, b 183, c 58, d 63, e 180, f 60, g 62, h 61.

(a) Calculated phonon dispersion and density of states in wurtzite InN. Ref. 48 (b) Composition dependence of the and modes in alloys. References 196 and 197.

(a) Calculated phonon dispersion and density of states in wurtzite InN. Ref. 48 (b) Composition dependence of the and modes in alloys. References 196 and 197.

The bandgap of the group III-nitride alloys as a function of the -axis lattice constant, compared to the visible colors, solar spectrum, and wavelength.

The bandgap of the group III-nitride alloys as a function of the -axis lattice constant, compared to the visible colors, solar spectrum, and wavelength.

(a) Calculated efficiency of high-quality InGaN/Si two junction solar cells as a function of InGaN bandgap. The physical thickness of the Si junction is labeled for each curve. (b) Isoefficiency plot of an triple-junction solar cell as a function of the bandgaps of the two InGaN junctions. Reference 211.

(a) Calculated efficiency of high-quality InGaN/Si two junction solar cells as a function of InGaN bandgap. The physical thickness of the Si junction is labeled for each curve. (b) Isoefficiency plot of an triple-junction solar cell as a function of the bandgaps of the two InGaN junctions. Reference 211.

characteristic of an solar cell under dark and UV-enhanced illuminated conditions. The device structure is schematically shown on the top. Reference 229.

characteristic of an solar cell under dark and UV-enhanced illuminated conditions. The device structure is schematically shown on the top. Reference 229.

(a) Photoluminescence peak energy of films with composition covering the entire range . Refs. 61 and 95. (b) Electroluminescence spectra of MQW LEDs. The In fraction is 0.18, 0.41, and 0.46 for the blue, green and red emitting devices, respectively. Reference 234. (c) MQWs with different InN well widths emitting near . Calculated dependence assuming different internal electric field is also shown. Reference 235.

(a) Photoluminescence peak energy of films with composition covering the entire range . Refs. 61 and 95. (b) Electroluminescence spectra of MQW LEDs. The In fraction is 0.18, 0.41, and 0.46 for the blue, green and red emitting devices, respectively. Reference 234. (c) MQWs with different InN well widths emitting near . Calculated dependence assuming different internal electric field is also shown. Reference 235.

(a) InN nanowire arrays grown on Si substrate by MBE. (b) The epitaxial interface between the InN nanowire and Si where an AlN buffer layer was used. Reference 260.

(a) InN nanowire arrays grown on Si substrate by MBE. (b) The epitaxial interface between the InN nanowire and Si where an AlN buffer layer was used. Reference 260.

(a) Correlation of electron concentration with the PL integral intensity and bandgap in InN NWs. Reference 266. (b) A schematic band diagram illustrating the electron-hole recombination between the conduction band (CB) and valence band (VB) of an InN NW, where an electron accumulation layer exists on the surface due to surface Fermi level pinning. (c) PL spectra measured at 17 K for InN bulk and InN quantum dots with different heights. The insert shows the peak energy as a function of dot height. The solid line (dotted line) is calculated by effective mass approximation using as the electron effective mass. Reference 277. (d) Lasing of InN nanobelts at high photoexcitation intensities. The inset shows the emission intensity as a function of excitation intensity. Reference 276.

(a) Correlation of electron concentration with the PL integral intensity and bandgap in InN NWs. Reference 266. (b) A schematic band diagram illustrating the electron-hole recombination between the conduction band (CB) and valence band (VB) of an InN NW, where an electron accumulation layer exists on the surface due to surface Fermi level pinning. (c) PL spectra measured at 17 K for InN bulk and InN quantum dots with different heights. The insert shows the peak energy as a function of dot height. The solid line (dotted line) is calculated by effective mass approximation using as the electron effective mass. Reference 277. (d) Lasing of InN nanobelts at high photoexcitation intensities. The inset shows the emission intensity as a function of excitation intensity. Reference 276.

(a) PL emission of NWs . (b) PL peak intensities as a function of peak wavelength for different compositions. (c) Optical absorption spectra . (d) Bandgap plotted as a function of In fraction for PL, absorption and EELS, and a bowing equation fit to absorption data. Reference 295.

(a) PL emission of NWs . (b) PL peak intensities as a function of peak wavelength for different compositions. (c) Optical absorption spectra . (d) Bandgap plotted as a function of In fraction for PL, absorption and EELS, and a bowing equation fit to absorption data. Reference 295.

## Tables

Recommended values of basic physical parameters of wurtzite InN, AlN, and GaN. Values not referenced were calculated from commonly accepted parameters.

Recommended values of basic physical parameters of wurtzite InN, AlN, and GaN. Values not referenced were calculated from commonly accepted parameters.

Physical parameters of wurtzite InN, AlN, and GaN. Values are theoretical except those in parenthesis which are experimental values.

Physical parameters of wurtzite InN, AlN, and GaN. Values are theoretical except those in parenthesis which are experimental values.

Recommended values of basic physical parameters of zincblende InN, AlN, and GaN.

Recommended values of basic physical parameters of zincblende InN, AlN, and GaN.

Recommended values of basic physical parameters of interfaces and alloys between wurtzite InN, AlN and GaN.

Recommended values of basic physical parameters of interfaces and alloys between wurtzite InN, AlN and GaN.

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