In polycrystalline semiconductors the trapping of charge at the grain boundaries has a decisive influence on the electrical transport properties through the formation of electrostatic potential barriers. By proper materials processing many interesting device applications can be realised, which exploit the electrical activity of these interfaces. In this review, the authors describe both the origin and the consequences of the charge capturing at grain boundaries. Special emphasis is given to polycrystalline compound semiconductors, where they summarise the present knowledge on the interface microstructure and its electrical properties. The model of a double Schottky barrier is shown to provide a quantitative basis for understanding the wide range of electrical phenomena in this class of materials. The steady-state current-voltage characteristic becomes highly non-linear through the interplay between the applied bias and the occupation of the defect states at the interface and in the depletion regions. For large potential barriers, high doping levels and elevated bias, large electric fields build up in the depletion regions. This triggers minority carrier generation through impact ionisation by hot majority carriers and strongly enhances the non-linearities in the charge transport. The dynamic electrical properties are probed by AC admittance or pulse measurements and can be traced back to the finite relaxation times of the trapped electron and hole charges. Comparing the experimental results with the theoretical predictions allows one to obtain valuable information on the electronic grain boundary parameters. The relationship between the observed electrical properties and the electronic structure of the junctions is discussed in detail, with ZnO varistors providing the majority of the experimental data. First indications for a general picture of the grain boundary electronic structure appropriate for all compound semiconductors are presented.

https://iopscience.iop.org/article/10.1088/0268-1242/5/2/001/pdf

Electrical properties of grain boundaries in polycrystalline compound semiconductors

This review presents the available experimental and theoretical understanding on the structure and electronic properties of grain boundaries in semiconducting materials. High-resolution electron microscope images of interfaces are interpreted within the framework of the structural unit model of grain boundaries, and the electronic properties of the grain boundaries discussed with relation to the popular symmetric Schottky barrier model for charge trapping and potential barrier formation. It is shown that these models give some limited understanding of the physical processes that occur at grain boundaries in elemental semiconductors, but that in compound semiconducting materials the effects of non-stoichiometry at the boundary regions must also be considered. Segregation of impurity and dopant species to the boundaries can have significant influence on their electrical properties, and the question of what structural or chemical features are responsible for the observed properties is posed. Diffusion at semiconductor grain boundaries is also discussed, and finally the electrical properties of zinc oxide varistor material are presented in the light of the models of carrier interactions with grain boundaries.

http://iopscience.iop.org/article/10.1088/0022-3719/18/21/008/pdf

Grain boundaries in semiconductors

Transport properties of Bi-rich Bi-Sb alloys

The authors reported on the experimental investigation of the high-temperature electrical resistance of graphene. The test structures were fabricated by using the focused ion beam from the single and bilayer graphene produced by mechanical exfoliation. It was found that as temperature increases from 300to500K, the resistance of the single, and bilayer graphene interconnects drops down by 30% and 70%, respectively. The quenching and temperature dependence of the resistance were explained by the thermal generation of the electron-hole pairs and carrier scattering by acoustic phonons. The obtained results are important for the proposed graphene interconnect applications in integrated circuits.

High-temperature quenching of electrical resistance in graphene interconnects

A review of the electronic properties of pure bismuth is given. Theoretical ideas on the band structure of bismuth and the dispersion relation for electrons near the bottom of the conduction band are briefly outlined. The experiments considered are those which give the most precise information on the Fermi surface (quantum effects in conductivity, cyclotron resonance, size effects, magnetoplasma waves, etc.) and on the electron energy spectrum near the bottom of the conduction band (studies in the quantum limit, infra-red magneto-reflection). The validity of the Cohen model as a first approximation to the electron spectrum in bismuth is established, and deviations from this model are described. Experiments are proposed which may give additional information on electrons in bismuth.

Electrons in bismuth

Measurements are presented of cyclotron resonance on n-type semiconducting Bi1-xSbx alloys within the wavelength range of 4 mm and a temperature of 4.2 K. The anisotropy of cyclotron masses can be explained by means of an ellipsoid as a model of the iso-energy surface. This model resembles that of electrons in pure Bi except of the stretching of the ellipsoids. It is found that the mass values strongly depend on the antimony concentration.



Es wurden Messungen der Zyklotronresonanz an n-halbleitenden Bi1-xSbx-Legierungen im Wellenlangenbereich von 4 mm bei 4,2 K durchgefuhrt. Die Anisotropie der Zyklotronmasse last sich mit einem Ellipsoid als Modell der Isoenergieflache erklaren. Dieses Modell ahnelt dem der Elektronen in reinem Bi bis auf die Streckung der Ellipsoide. Es wird gefunden, das die Massenwerte stark von der Antimonkonzentration abhangen.

Cyclotron Resonance of n-Type Semiconducting Bi1-XSbx Alloys

The galvanomagnetic properties of conduction electrons in n-type inversion layers adjacent to the grain boundary in p-type InSb bicrystals in magnetic fields up to 18 T and temperatures down to 2 K are investigated. The observed quantum oscillations of the magnetoresistivity result from a superposition of the Shubnikov-de Haas effect in two occupied subbands. The electron densities of subbands nsi (ns1 = 3.5 × 1011 cm−2; nso = 1.1 × 1012 cm−2) and the effective cyclotron mass of the subbands mci (mc1 = (0.016 ± 0.004) m0; mco = (0.026 ± 0.003) m0) are evaluated. Besides the Shubnikov-de Haas oscillations in high magnetic fields (B > 5 T) the Hall resistivity shows the characteristic features of the quantized Hall plateaus in finite regions of the magnetic field B. Simultaneously the diagonal resistivity ϱxx drops to a minimum. Other characteristic features of a two-dimensional electron gas confined in the symmetrical potential well of the grain boundary are obtained.



Es werden die Magnetotransporteigenschaften der Leitungselektronen in n-Inversionsschichten von Korngrenzen in p-Typ InSb-Bikristallen in Magnetfeldern bis 18 T und Temperaturen bis 2 K untersucht. Die beobachteten Quantenoszillationen des Magnetowiderstandes resultieren aus der Uberlagerung von SdH-Oszillationen in zwei besetzten Subbandern. Die Elektronenkonzentration in diesen Subbandern nsi (ns1 = 3,5 × 1011 cm−2; nso = 1,1 × 1012 cm−2) und die entsprechenden effektiven Zyklotronmassen mci (mc1 = (0,016 ± 0,004) m0; mco = (0,26 ± 0.003) m0) werden ermittelt. Neben den SdH-Oszillationen weist die Feldabhangigkeit des Hallwiderstandes in hohen Magnetfeldern (B > 5 T) eine fur den quantisierten Halleffekt charakteristische stufenformige Struktur auf. Bei Feldwerten, bei der der Hallwiderstand Plateaus aufweist, zeigt die Diagonalkomponente des elektrischen Widerstandes ϱxx scharfe Minima. Es werden weitere charakteristische Eigenschaften eines zweidimensionalen Elektronengases im symmetrischen Potentialtopf der Korngrenze gefunden.

Two-Dimensional Electron Gas in the n-Inversion Layer of p-Type InSb Bicrystals

In Bi1−xSb, alloys with x = 0.13 to 0.25 the electrical transport properties (electrical resistance, magnetoresistance, and Hall effect) in the temperature interval T = 1.8 to 77 K in weak magnetic fields ( μB ≪ 1) are investigated. In alloys with x = 0.19 and x = 0.23 the dependence of the galvanomagnetic properties on the hydrostatic pressure are also investigated. The rapid increase of the charge-carrier concentration in alloys with x > 0.22 and the qualitatively different pressure dependence of the gelvanomagnetic properties for this two alloys are explained by the overlapping of the conduction band at L with a valence band at an other point of the Brillouin zone, which begins at x ≈ 0.22. A semimetal-semiconductor transition is detected in Bi1−xSb, alloys with x > 0.22 under high hydrostatic pressure.



In Bi1−xSb,-Legierungen mit x = 0,13 bis 0,25 werden die elektrischen Transporteigenschaften (elektrischer Widerstand, Magnetowiderstand und Helleffekt) im Temperaturbereioh T = 1, s bis 77 K in schwachen Magnetfeldern ( μB ≪ 1) untersucht. In Legierungen mit x = 0,19 und x = 0,23 wird auserdem die Abhiingigkeit der galvanomagnetischen Eigenschaften vom hydrostatischen Druck untersucht. Der rasche Anstieg der Ladungstriigerkonzentration in Legierungen mit x > 0,22 und die qualitativ unterschiedlichen Druckabhiingigkeiten der galvanomagnetischen Eigenschaften dieser beiden Legierungen werden durch die bei x ≈ 0,22 beginnende uberlappung des Leitungsbandes in L mit einem Valenzband in einem anderen Punkt der Brillouinzone erkliirt. In Bi1−xSb,-Legierungen mit x > 0,22 kann unter Einwirkung von hydrostatischem Druck ein Halbmetall-Halbleiter-ubergang orzeugt werden.

The Semiconductor-Semimetal Transition in Bi1-xSbx Alloys withx ≧ 0.22

The magnetotransport properties of conduction electrons in n-type inversion layers adjacent to the grain boundary in p-type InSb bicrystals are investigated under high hydrostatic pressure (up to 103 MPa) in magnetic fields up to 15 T. A rapid decrease of the carrier concentration in the inversion layer is observed when hydrostatic pressure is applied. From the quantum oscillations of the magnetoresistivity the characteristic parameters of the electric subbands (subband population nsi, subband energies EF — EI, and the effective cyclotron masses m*i) and their pressure dependences are established. A simple theoretical model taking into account the pressure dependence of the energy band structure of pure InSb is proposed to describe the found experimental-data. Under high pressures and in high magnetic fields it is verified experimentally that the Hall resistivity gxy is quantized into integer multiples of h/e2.



Es werden die Magnetotransporteigenschaften der Leitungselektronen in einer n-leitenden Inver-sionsschicht von Korngrenzen in p-Typ InSb-Bikristallen unter hohem hydrostatischen Druck (bis 103 MPa) in Magnetfeldern bis 15 T untersucht. Mit wachsendem Druck wird eine schnelle Abnahme der Ladungstragerkonzentration in der Inversionsschicht beobachtet. Durch Auswer-tung der Quantenoszillationen des Magnetowiderstandes QXX konnen die charakteristischen Parameter der elektronischen Subbander (Subbandbesetzung nSi, Subbandenergien Ef — Ef und die effektiven Zyklotronmassen m*i) und deren Druckabhangigkeit bestimmt werden. Zur Erklarung der experimentellen Ergebnisse wird ein einfaches theoretisches Modell vorgeschlagen, das die Druckabhangigkeit der Bandstruktur von reinem InSb berucksichtigt. Unter hohem Druck und in hohen Magnetfeldern (B > 5 T) werden experimentelle Bedingungen realisiert, bei denen der Hall-Widerstand QXy in ganzzahligen Vielfachen von h/e2 quantisiert ist.

Quantum properties of the two-dimensional electron gas in the n-inversion layers of InSb grain boundaries under high hydrostatic pressure

Quantized Hall Effect in the n‐Inversion Layer in InSb Grain Boundaries

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