Internal Piezoelectric Field Research Articles

Time Evolution of the Screening of Piezoelectric Fields in InGaN Quantum Wells

We have measured the time response of the emission spectra of In <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.07</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.93</sub> N quantum wells with widths of 2, 3, and 4nm in GaN following pulsed optical excitation. We observe a blue shift of the emission peak during the excitation and a subsequent red shift as the carriers recombine in the 3- and 4-nm wells, and a negligible shift for the 2-nm well. Using a comprehensive theory we are able to fit both the time evolution of the peak emission energy and the integrated emission intensity. The shift of the emission peak (by about 17 meV) arises from the balancing of the change in screening of the internal piezoelectric field as the carrier density changes and bandgap renormalization. We have projected the calculations to quantify the degree of screening at typical threshold carrier densities. At transparency we estimate carrier densities of 4.3times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">16</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> and 4.8times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">16</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for the 4- and 3-nm wells, respectively, which reduce the internal piezoelectric field in the well to 0.97times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> (4 nm) and 1.03times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> (3 nm) Vmiddotm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> compared with the unscreened value of about 1.23times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> Vmiddotm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . Thus, a substantial field remains in these wells under laser conditions. We find that this partially screened field is beneficial in reducing the threshold current compared with that of a square well for modal gains up to about 150 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> 1

In As ∕ In Ga As P sidewall quantum dots on shallow-patterned InP (311)A

Highly strained InAs quantum dots (QDs) embedded in InGaAsP are formed at the fast-growing [01−1] mesa sidewall on shallow-patterned InP (311)A substrates by chemical beam epitaxy. Temperature dependent photoluminescence (PL) reveals efficient carrier transfer from the adjacent dashlike QDs in the planar areas to the larger sidewall QDs resulting in well-distinguishable emission around 80K. The large high-energy shift of the PL from the sidewall QDs as a function of excitation power density is ascribed to the screening of the internal piezoelectric field. The linear polarization of the PL from the sidewall QDs is reversed compared to that of the quantum dashes in the planar areas due to the more symmetric shape and possible nonuniform strain in the sidewall QDs.

Impact of forward bias on electroluminescence efficiency in blue and green InGaN quantum well diodes: A comparative study

Electroluminescence (EL) spectral intensity in the high-brightness blue and green InGaN single-quantum-well (SQW) diodes has been comparatively studied over a wide temperature range and as a function of injection current. When the necessary forward bias conditions to get a certain current level are different, it is found that the anomalous EL quenching previously observed below 100 K for the SQW diodes strongly changes and shows a striking difference between the blue and green SQW diodes. This unusual EL evolution pattern is attributed to both internal and external fields, suggesting the importance of the internal piezoelectric field effects on the efficient carrier capture processes by localized tail states within the SQW under the presence of high-density misfit dislocations.

Strong optical nonlinearity in strain-induced laterally ordered In0.4Ga0.6As quantum wires on GaAs (311)A substrate

Strain-induced laterally ordered In0.4Ga0.6As on (311)A GaAs template quantum wires have been fabricated and identified with cross-section transmission electron microscopy technique to be of average length ∼1μm, and on average width and height of 23 and 2nm, respectively, under InGaAs coverage of six monolayers. The photoluminescence spectrum of a sample demonstrates unusually strong optical nonlinearity even at moderate excitation densities. The excitonic peak energy blueshifts by ∼25meV without essential contribution of the quantum wire excited states at elevating excitation density. Strong decrease of the polarization anisotropy and increase of the energy of excitonic photoluminescence are attributed to a combined action of the phase-space filling effects and the screening of the internal piezoelectric field by free carriers.

Determination of the piezoelectric field in InGaN quantum wells

In many studies, the value of the experimentally determined internal piezoelectric field has been reported to be significantly smaller than theoretical values. We believe this is due to an inappropriate approximation for the electric field within the depletion region, which is used in the analysis of experimental data, and we propose an alternative method. Using this alternative, we have measured the strength of the internal field of InGaN p-i-n structures, using reverse bias photocurrent absorption spectroscopy and by fitting the bias dependent peak energy using microscopic theory based on the screened Hartree-Fock approximation. The results agree with those using material constants interpolated from binary values.

Carrier dynamics and recombination in GaN quantum discs embedded in AlGaN nanocolumns

We report on the study of carrier dynamics and recombination by time resolved PL in GaN quantum discs embedded in Al0.16Ga0.84N nanocolumns, grown by MBE on AlN buffered Si (111) substrates. The emission band of GaN quantum discs and the Al0.16Ga0.84N nanocolumns are strongly overlapped and the standard analysis of PL decays is not useful to fully characterize the recombination kinetics. We make use of time resolved spectroscopy to clearly distinguish the different contributions to the PL spectra and therefore to obtain the intrinsic carrier time evolution in the quantum discs. We observe a dynamical red shift of the PL band together with a non exponential decay, very likely due to screening of the internal piezoelectric field provided by the photoinjected carriers. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Anisotropy of the electron energy levels in In xGa 1−xAs/GaAs quantum dots with non uniform composition

Atomistic simulations that use the Tersoff empirical potential accurately reproduce the effects of the presence of compositional disorder in strained semiconductor alloys. This method is applied to InGaAs quantum dot islands, for which gradients in the In composition distribution have been observed and accurately measured, and we demonstrate that the internal piezoelectric fields contribute strongly to the nature of the electron wavefunctions. The theoretical predictions are supported by experimental evidence: intersubband absorption measurements confirm that the p-states degeneracy for the electron first excited state is lifted and a minimum splitting of at least 5 meV is to be generally expected.

Influence of composition on the piezoelectric effect and on the conduction band energy levels of InxGa1−xAs∕GaAs quantum dots

We address fundamental issues relating to the symmetry of the shape and the nonuniform composition of InGaAs quantum dot islands. Using atomistic simulations in the framework of the Tersoff empirical potential, we study the effect of compositional gradients in the In distribution on the piezoelectric effect in quantum dots. We demonstrate that the internal piezoelectric fields contribute strongly to the experimentally observed optical anisotropies. This is confirmed by accurate high-resolution transmission electron microscopy analysis over hundreds of islands grown in different conditions that reveals the absence of structural anisotropy under our growth conditions.

Dynamical nonlinearity in strained InGaAs (311)A sidewall quantum wires

Significant optical nonlinearity has been found in InGaAs (311)A sidewall quantum wires by means of time resolved photoluminescence measurements. A strong reverse quantum confined Stark effect has been observed and attributed to the dynamical screening of both the internal piezoelectric field and the Coulomb interaction between carriers. The time evolution of the quantum wire emission has been reproduced by means of self-consistent calculations that take into account excitonic effects, strain, and induced piezoelectric charges.

Influence of Internal Electric Field on the Recombination Dynamics of Localized Excitons in an InGaN Double-Quantum-Well Laser Diode Wafer Operated at 450 nm

Optical and structural properties of an InGaN double-quantum-well (DQW) laser diode (LD) wafer that lased at 450 nm were investigated to discuss an enormous impact of a polarization-induced electric field on the recombination dynamics in InGaN quantum structures. The quantum-well (QW) structure was shown to have the well thickness as thin as approximately 1 nm and InN molar fraction x of approximately 14%. The gross effective electric field in the QW (FQW) was estimated to be 490 kV/cm from the Franz–Keldysh oscillation (FKO) period in the electroreflectance (ER) spectrum, implying that an internal piezoelectric field (Fpiz) of approximately 1.4 MV/cm was cancelled by the pn junction built-in field (Fbi) and Coulomb screening due to carriers in the DQW. The magnitude of FQW can be further weakened by applying reverse bias (VR) on the junction; the decrease in the photoluminescence (PL) lifetime at low temperature measured under VR was explained to be due to a recovery of electron-hole wavefunction overlap for small VR (|VR|<4 V), and due mainly to the tunneling escape of carriers through the barriers for larger VR. By applying an appropriate VR smaller than 4 V, electron-hole wavefunction overlap, which had been separated vertically along the c-axis due to quantum-confined Stark effect, could be partially recovered, and then the time-resolved PL signals exhibited a less-pronounced stretched exponential decay, giving a scaling parameter (β) of 0.85 and effective in-plane localization depth (E0) of 40–50 meV for the spontaneous emission. These values were closer to those of much homogeneous QWs compared to those reported previously for InGaN QWs having similar InN molar fractions. The use of very thin QWs is considered to bring easier Coulomb screening of FQW and population inversion under high excitation conditions.

Thickness dependence of transient absorption spectrum for InGaN thin films

Nondegenerate femtosecond pump and probe spectroscopy was performed in In0.10Ga0.90N/In0.03Ga0.97N multiple quantum wells and epilayers at room temperature. The structural dependence of the photoinduced differential absorption (Δα) spectrum was studied on four In0.10Ga0.90N layers of different thickness (5.5, 17, 34, and 66 nm). A single bulge was clearly observed in Δα spectra except for the 5.5 nm thick sample. The bulges are sharper in thicker In0.10Ga0.90N layer samples. These spectrum changes are caused by excitonic absorption quenching and screening of internal piezoelectric fields by photoinduced carriers. Both rapid and slow temporal behaviors were observed in transient absorption spectra. The results of time-resolved photoluminescence measurements and existence of saturation pump fluences indicate that trapped carriers in potential minima originate from In-rich regions and/or midgap carrier traps are responsible for the observed lasting screening of the internal electric field.

Nondegenerate pump and probe spectroscopy in InGaN thin films

Carrier dynamics in In0.10Ga0.90N/In0.03Ga0.97N multiple quantum wells and epilayers were studied by nondegenerate femtosecond pump and probe spectroscopy and by using monochromatic continuous wave light at room temperature. Structurally dependent transient absorption spectra were observed after pump pulse excitation. These spectral changes are caused by excitonic absorption quenching and screening of internal piezoelectric fields by photoinduced carriers. Both rapid (∼400 ps) and slow (∼90 μs) temporal behavior was observed in the transient absorption spectra. The results of time-resolved photoluminescence measurements and the existence of saturation pump fluences indicate that trapped carriers in potential minima originating from In-rich regions and/or midgap carrier traps are responsible for the lasting screening of the internal electric field.

Large excitation‐power dependence of pressure coefficients of InxGa1–xN/InyGa1–yN quantum wells

AbstractExcitation‐power dependence of hydrostatic pressure coefficients (dE/dP) of InxGa1–xN/InyGa1–yN multiple quantum wells is reported. When the excitation power increases from 1.0 to 33 mW, dE/dP increases from 26.9 to 33.8 meV/GPa, which is an increase by 25%. A saturation behavior of dE/dP with the excitation power is observed. The increment of dE/dP with increasing carrier density is explained by an reduction of the internal piezoelectric field due to an efficient screening effect of the free carriers on the field.

Study of light emission from GaN/AlGaN quantum wells under power-dependent excitation

We have performed a study of excitation power-dependent spectra of GaN/AlGaN single quantum wells (QWs). First, the experimental “blueshift” of the emission energy, due to screening of internal piezoelectric fields, was compared with the model calculations based on self-consistent solution of Schroedinger and Poisson equations. We found that, even for the highest applied levels of excitation power (2.5 MW/cm2), only 0.5×1012 cm−2 carriers were present in the QW layers. Second, we analyzed the evolution of power-dependent spectra of two single QW having different widths. For the thinner QW (2.1 nm), the peak corresponding to a QW photoluminescence (PL) emission dominates the entire spectrum in the whole range of the used excitation power. In the case of the wider QW (4.4 nm), for sufficiently high excitation power, we observe the effect of PL quenching. Using the rate equation model we show that the observed effect of the PL quenching can be associated with the reduction of exciton binding energy due to the many body interactions in the QW.

Midinfrared intersubband absorption on AlGaN/GaN-based high-electron-mobility transistors

Intersubband absorption measurements on two nominally undoped AlGaN/GaN-based high-electron-mobility transistors with different Al compositions in the barrier layer are presented. The first transistor with a barrier consisting of Al0.6Ga0.4N showed an absorption peak at 247 meV (1973 cm−1) with a full width at half maximum (FWHM) of 126 meV, while the second device utilizing an Al0.8Ga0.2N barrier had its peak at 306 meV (2447 cm−1) with a FWHM of 86 meV. Self-consistently computed potentials and intersubband transition energies showed good agreement with the experimental findings, and therefore confirmed previously published values for the internal piezoelectric field in such structures.

Structural and optical characterization of thick InGaN layers and InGaN/GaN MQW grown by molecular beam epitaxy

Thick In x Ga 1− x N (0.20< x<0.27) layers and InGaN/GaN multiple quantum wells (MQWs) are grown by plasma-assisted molecular beam epitaxy on GaN/Al 2O 3 templates. The strain and In-content is estimated from high-resolution X-ray diffraction, showing that the bulk samples are not fully relaxed. A bowing parameter of 3.6 eV is obtained from absorption measurements of In x Ga 1− x N layers. Strong In-dependent excitonic localization is observed in these bulk layers, leading to an increase in the absorption band edge with the In content. Regarding the MQWs structures, high-resolution transmission electron microscopy reveals an increase in the interface roughness for high In content. The dominant PL emission of the MQWs shows a red-shift when increasing the well thickness for a given In-content, due to internal piezoelectric field. The excitonic localization is studied and compared between thick layers and MQWs structures.

Effects of internal piezoelectric field on electronic states of InGaN quantum dots grown on GaN

We have calculated the electronic structure of an In 0.2Ga 0.8N pyramidal quantum dot (QD) in a GaN barrier layer using a polarization-potential-dependent sp 3 tight-binding method. A valence-force-field method was used for the strain calculation. For the QD with a bottom diameter of 86.4 Å, height of 20.8 Å, and facet inclination angle ( φ) of 30°, the maximum piezoelectric field is 1.64 MV/cm. The energy gap shows a red shift of 0.10 eV due to the quantum-confined Stark effect. The field causes a spatial separation of the electron and hole wave functions in the QD. The results are compared with those for the prismatic QD ( φ=90°).

Electrical Transport Properties in (111) Growth-Axis GaAlAs/GaInAs Heterostructures

The effect of an internal piezoelectric field on electrical transport phenomena has been studied in GaAlAs/GaInAs heterostructures grown on (001) and (111)B GaAs substrates. The two-dimensional electron gas (2DEG) in the structure was obtained by conventional modulation δ-doping in the barrier layer. The conductivity and Hall effect were studied at room temperature as a function of hydrostatic pressures up lo 1000 MPa. The observed pressure changes of the 2DEG concentration have been compared with theoretical predictions, taking into account the strain-induced electric fields in the harrier layer. The piezoresistive behaviour under uniaxial stress has also been determined. It was found that piezo-effects are more pronounced in the case of the material with the built-in piezoelectric field.

Impact of Internal Electric Field and Localization Effect on Quantum Well Excitons in AlGaN/GaN/InGaN Light Emitting Diodes

Strained InxGa1—xN quantum wells (QWs) on thick GaN base layers were investigated to verify the importance of localized QW excitons in their spontaneous emission mechanisms. A strength of the internal piezoelectric field (FPZ) across the QW increases with increasing x up to 1.4 MV/cm for x = 0.25, since the in-plain strain increases. For the QWs with the well thickness L greater than 3 nm, FPZ dominates the emission peak energy due to the quantum-confined Stark effect. Absorption spectra of both hexagonal and cubic InGaN QWs exhibited a broad band-tail regardless of the presence of FPZ normal to the QW plane. The luminescence peak energy of the 3 nm thick QWs was higher than the bandgap energy of the unstrained bulk crystal for x < 0.15, showing that doping of Si in barriers or injection of carriers effectively screens the field. The emission lifetime increased with increasing monitoring wavelength. Also, a temperature-induced change in the luminescence peak energy decreased with increasing x. The real-space variation of the luminescence peak energy was confirmed by the spatially-resolved monochromatic cathodoluminescence mapping method. The localization depth increases with increasing x. The carrier localization is confirmed to originate from the effective bandgap inhomogeneity due to a fluctuation of the local InN mole fraction, which is enhanced by the large and composition-dependent bowing parameter of InGaN material.

Localized quantum well excitons in InGaN single-quantum-well amber light-emitting diodes

Optical properties of the InGaN single-quantum-well amber light-emitting-diodes were investigated to verify the importance of localized quantum well (QW) excitons in their spontaneous emission mechanisms. The internal piezoelectric field (FPZ) across the QW of the order of 1.4 MV/cm was confirmed to point from the surface to the substrate. Transmittance and photovoltaic spectra exhibited a broad band tail state, and the emission lifetime increased with decreasing detection photon energy. The electroluminescence spectra did not show remarkable energy shift between 10 and 300 K. The spectra exhibited an exponential tail and the higher energy portion increased more rapidly than that of the lower energy one, reflecting a thermal distribution of the localized carriers within the tail states. Since the well thickness is only 2.5 nm and is atomically flat, the device is considered to exhibit reasonably efficient emission with the external quantum efficiency of 5% at 20 mA in spite of the presence of FPZ and large number of threading dislocations due to radiative decay of the localized QW excitons.