# Anomalous capacitance-voltage profiles in quantum wells explained by a quantum mechanical model

15 Feb 1997-Journal of Applied Physics (American Institute of Physics)-Vol. 81, Iss: 4, pp 2030-2032

TL;DR: In this article, the authors developed a quantum mechanical model for understanding and explaining the capacitance-voltage (C-V) carrier profiles observed in quantum wells (QW), which considers the effects of field and quantum confinement of the carriers in the well.

Abstract: We have developed a quantum mechanical model for understanding and explaining the capacitance–voltage (C–V) carrier profiles observed in quantum wells (QW). The external field imposed on the QW during C–V profiling changes the carrier distribution of the system. This model considers the effects of field and quantum confinement of the carriers in the well. The results obtained by iterative solutions of Schrodinger’s and Poisson’s equations give a better understanding of the experiments than the previous models where quantum confinement is ignored.

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TL;DR: In this paper, the authors consider semiconductor devices that are composed of two parts: a small quantum structure constituting the active region, and a classical environment with larger typical length scales.

Abstract: We consider semiconductor devices that are composed of two parts: first, a small quantum structure constituting the active region, and second, a classical environment with larger typical length scales. While in general the classical environment should be represented by a drift–diffusion model, we consider here only simple contacts which we take as ideal metals with infinite conductivity. The transport through the quantum structure is described as in the Landauer–Buttiker formalism through electronic scattering wave functions which define the electron density in the quantum system. Further sources of the self-consistent Coulomb field are layers of classical charges in the contacts at each of the interfaces to the quantum system. We present further a capacitance model that takes into account the openness of the quantum structure and the existence of finite contacts embedding the system. As particular quantum structures we study simple tunneling barriers.

9 citations

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TL;DR: In this paper, the photoluminescence (PL) emissions from In x Ga 1−− x N/GaN QW structures have been reported, where, for successive annealing operations, the PL peak suffers a primary red shift, followed by a blue shift.

Abstract: In x Ga 1 − x N/GaN heterostructures and quantum wells (QWs) are particularly important in the application of III–V nitride materials for light emitting diodes and laser diodes. The photoluminescence (PL) emissions from In x Ga 1 − x N/GaN QW structures have been reported, where, for successive annealing operations, the PL peak suffers a primary red shift, followed by a blue shift. The observed phenomenon remains unexplained because of its complexity. This paper is intended towards a proper explanation of the observed experimental results through suitable quantum mechanical models and computations, whether the band gap of InN is 1.95 eV or 0.7 eV.

8 citations

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TL;DR: An alternative method for band offset measurement in quantum wells has been outlined in this article, where the band offset is determined from a comparison of experimental results and theoretical computations of the temperature dependent total charge content of a quantum well.

Abstract: Band discontinuity is an important parameter for the design of heterojunction based electronic and opto electronic devices. An alternative method for band offset measurement in quantum wells has been outlined in this paper. The band offset is determined from a comparison of experimental results and theoretical computations of the temperature dependent total charge content of a quantum well. In spite of the simplicity of the measurement procedures the result at its best has an error around ±2%.

4 citations

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TL;DR: In this article, a non sheet-like distribution function for quasi-two-dimensional carriers is proposed that incorporates the effect of the polarization field in wide band-gap group-III nitrides.

Abstract: Wide band-gap group-III nitrides are important for the design of optical devices in the blue and blue–green region. Owing to their wurtzite structure, these materials have a strong inherent polarization field that affects carrier distribution, exciton stability and hence influences the optical properties of the devices. So far, carriers have been assumed to have a sheet-like character. In this paper a non sheet-like distribution function for these quasi two-dimensional carriers is proposed that incorporates the effect of the polarization field. Here GaN/InGaN/GaN and AlGaN/GaN/AlGaN quantum wells have been studied. The polarization field causes the electron and hole wave functions to separate out, thus causing decrease of emission strength and strong reduction of exciton binding energy. This treatment explains well the qualitative nature of carrier distribution in the well. The polarization field changes with GaN mole fraction present in the tertiary nitride layer. The effect of mole fraction on carrier distribution has also been studied. It is found that, inside the well, the hole distribution changes a little more with change in mole fraction than the electron distribution, but for all practical purposes the net change in the distribution pattern is negligible.

3 citations

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TL;DR: In this article, different base layer designs for npn GaN-based heterojunction bipolar transistors (HBTs) were simulated using a drift-diffusion transport model, and the effects of both emitter and collector doping on the dc performance of the HBTs were also investigated.

Abstract: Different base layer designs for npn GaN-based heterojunction bipolar transistors (HBTs) were simulated using a drift–diffusion transport model. The use of AlGaN/GaN superlattice bases did not produce working devices for any of the conditions investigated. InGaN/GaN base layers did produce acceptable dc current gains by enhancing electron transport. Grading of the InGaN layer composition produced the highest gains. The effects of both emitter and collector doping on the dc performance of the HBTs was also investigated.

2 citations

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IBM

^{1}TL;DR: In this paper, the eigenstate of an isolated quantum well subject to an external electric field was analyzed and a quadratic Stark shift was found whose magnitude depended strongly on the finite well depth.

Abstract: We present variational calculations of the eigenstates in an isolated-quantum-well structure subjected to an external electric field. At weak fields a quadratic Stark shift is found whose magnitude depends strongly on the finite well depth. In addition, the electric field induces a spatial shift of the particle wave function along or opposite to the field direction, depending on the sign of the particle mass. This field-induced spatial separation of conduction and valence electrons in GaAs quantum wells decreases the overlap between their associated wave functions, leading to a reduction of interband recombination.

644 citations

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TL;DR: In this article, the conduction band discontinuity ΔEc was found to be 0.248 eV, corresponding to about to 0.66 ΔEg rather than Dingle's commonly accepted value 0.85 Δ Eg, attributed to compositional grading during LPE growth.

Abstract: The Debye length smearing that occurs in C‐V profiling has precluded the use of C‐V profiling from an adjacent Schottky barrier to measure the magnitude of energy band discontinuities at barriers in isotype heterojunctions. It is observed, however, that in such a process both the number of the charge carriers and the moment of their distribution are conserved. This information permits the extraction of values for both the conduction band discontinuity ΔEc and any interface charge density. This technique and experimental results for an LPE‐grown n‐N GaAs‐Al0.3Ga0.7As heterojunction are described. We find ΔEc =0.248 eV, corresponding to about to 0.66ΔEg rather than Dingle’s commonly accepted value 0.85ΔEg . The difference is attributed to compositional grading during LPE growth.

355 citations

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TL;DR: The results support recent theoretical calculations from which a monotonic increase in \ensuremath{\Delta}${E}_{c}$ with strain in this heterostructure system is predicted.

Abstract: The variation of the potential of a quantum well is similar to that of a deep trap. In that respect a quantum well can capture and emit carriers in much the same way as a trap. The thermal emission energy from a quantum well is closely related to the appropriate band offset. With that in mind, we have carried out deep-level transient spectroscopy measurements on Schottky-barrier diodes containing one or more pseudomorphic ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{Al}}_{0.2}$${\mathrm{Ga}}_{0.8}$As (0lx\ensuremath{\le}0.18) quantum wells. The objective was to estimate the conduction-band offset, \ensuremath{\Delta}${E}_{c}$, as a function of x and the resulting strain. From detailed balance between emission and capture, an Arrhenius-type expression was derived to analyze the transient emission data. It is seen that the percentage band offset \ensuremath{\Delta}${E}_{c}$/\ensuremath{\Delta}${E}_{g}$ varies from 62% for x=0.07 to 70% at x=0.18. Furthermore, a linear interpolation of the data leads to \ensuremath{\Delta}${E}_{c}$/\ensuremath{\Delta}${E}_{g}$=58% at x=0, which is close to the widely accepted value. Our results support recent theoretical calculations from which a monotonic increase in \ensuremath{\Delta}${E}_{c}$ with strain in this heterostructure system is predicted.

79 citations

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TL;DR: In this article, the authors presented variational calculations of subband eigenstates in an infinite quantum well with an applied electric field using Gram-Schmidt orthogonalized trial wave functions.

Abstract: We present variational calculations of subband eigenstates in an infinite quantum well with an applied electric field using Gram–Schmidt orthogonalized trial wave functions. The results agree very well with the exact numerical solutions even up to 1200 kV/cm. We also show that for increasing electric fields the energy of the ground state decreases, while that of higher subband states increases slightly up to 1000 kV/cm and then decreases for a well size of 100 A.

36 citations

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TL;DR: In this article, the interface region generated by molecular beam epitaxial regrowth has been studied in detail, and the measured concentration of the interface states are in the range 1.2 × 1010 to 7.05 × 1011 cm−2.

Abstract: The interface region generated by molecular beam epitaxial regrowth has been studied in detail. Regrowth was carried out on epitaxial GaAs after a variety of realistic device processing steps. Combinations of wet chemical etching and ion milling with and without annealing were used with the objective of establishing the best procedure for integrated technologies during regrowth. Capacitance voltage measurements showed perturbations in the carrier profile corresponding to depletion and accumulation regions at the interface which are directly related to interface states at and around the regrowth interface. The measured concentration of the interface states are in the range 1.2 × 1010 to 7.05 × 1011 cm−2. The former is one of the lowest reported till date. The concentration of deep traps in the regrown layer and interface, observed by deep level transient spectroscopy, is much lower than the interface state density. Their contribution to carrier perturbation is insignificant, except in one case where an electron trap has a rather high concentration. Results of secondary ion mass spectroscopy indicate that the presence of carbon at the regrown interface is not principally responsible for creating the high resistivity interface region. Our data favor the concept of a disordered region created at the interface during regrowth. Interface state density and trap densities are much larger in the wet chemically etched samples, which is further supported by the results of temporal photoresponse measurements on junction photodiodes. The overall characteristics of the dry etched regrowth interfaces seem to be much more promising than the wet chemical etched ones.

26 citations