Space‐charge‐limited currents: Refinements in analysis and applications to a‐Si1−xGex: H alloys

TL;DR: In this article, a new algorithm is described for deriving the density of states N(E) from the Fermi energy EF upwards toward the conduction band edge, by implicitly accounting for the spatial variations of physical quantities across the thickness of the diode.

Abstract: A new algorithm is described for deriving the density of states N(E) from the Fermi energy EF upwards toward the conduction band edge. This refinement in the analysis of space‐charge‐limited currents (SCLC) enables the accurate determination of N(E) by implicitly accounting for the spatial variations of physical quantities across the thickness of the diode. SCLC is measured in NiCr/n+/a‐Si1−xGex: H/Pt diode structures. For a‐Si:H samples, SCLC values for N(EF) are compared to those derived from admittance measurements on the same diodes. The two determinations agree in samples where 1016

TL;DR: In this article, the authors observed the formation of a filamentary region in amorphous silicon devices with coplanar metallic contacts placed near each other (∼5 μm).

Abstract: Switching has been observed in a wide variety of materials and devices. Hydrogenated amorphous silicon has become one of the most important cases because of interest in neural network applications. Although there are many reports regarding this phenomenon, not all of the physical processes involved are still determined precisely. Therefore, some more experimental information is needed in order to achieve this task. Much of the behavior of the devices has been ascribed to the existence of a filamentary region which is produced after the first switching process, called forming. We observed this filamentary region in its full extension by producing forming in amorphous silicon devices with coplanar metallic contacts placed near each other (∼5 μm). The I–V characteristics, filament optical and atomic force microscopy images and chemical etching led us to correlate changes in resistance to metal inclusion into the amorphous film. There are two stages: the first is related to contact stabilization, the second to metal transport into the film bulk. Optical images show a permanent filamentary region after forming. AFM images of these filaments showed that they are formed essentially by material accumulation between the contacts. This material tends to get some atomic arrangement, becoming a polycrystalline solid. If the device was led to breakdown, such accumulation becomes either a hillock or a thin conducting channel connecting both contacts. In the case of a switching filament, the accumulation tends to be a chain of smaller hillocks along the conduction path. Metal from the contacts remains in the conduction path after forming and chemical etching indicated that it is placed near the path core. Before forming, a tunneling transport process can be ascribed to the non-ohmic behavior of the samples during the first stage of metallic inclusion.

TL;DR: In this article, the authors show that the degree of current crowding is governed by the voltage dependence of the current flowing from the n+ contact to the conducting channel, which is a space-charge-limited current whose magnitude depends on the bulk density of states in the undoped intrinsic layer.

Abstract: Amorphous silicon staggered‐electrode thin‐film transistors (TFT’s) can show current crowding near the origin in the output characteristics. The degree of current crowding is governed by the voltage dependence of the current flowing from the n+ contact to the conducting channel. This current is a space‐charge‐limited current whose magnitude depends on the bulk density of states in the undoped intrinsic layer. For a 0.5‐μm‐thick i layer, calculations predict negligible current crowding for N(E) 3×1016 cm−3 eV−1. Experimental results are consistent with N(E) in the range 1016 cm−3 eV−1–2×1016 cm−3 eV−1. This is lower than the value derived from the transfer characteristic of the TFT (∼1017 cm−3 eV−1), which is evidence for an inhomogeneous distribution of deep gap states through the 0.5‐μm film of α‐Si:H.

TL;DR: The theory of space-charge-limited currents (SCLC) is briefly reviewed and the spectroscopic character of the method is discussed in this paper, where experimental results obtained on thin films of phthalocyanines.

TL;DR: High uniform RS and a high on/off ratio of RRAM based on graphene oxide by embedding gold nanoparticles into the device allowed reliable multilevel storage and may offer a route to develop reliable digital memristors for ANNs.

Abstract: Traditional metal-oxide semiconductor devices are inadequate for use in artificial neural networks (ANNs) owing to their high power consumption, complex structures, and difficult fabrication techniques. Resistive random access memory (RRAM) is a promising candidate for ANNs owing to its simple structure, low power consumption, and excellent compatibility with CMOS. Moreover, it can mimic synaptic functions because of its multilevel resistive switching (RS) behavior. Herein, we demonstrate highly uniform RS and a high on/off ratio of RRAM based on graphene oxide by embedding gold nanoparticles into the device. This allowed reliable multilevel storage. Further, multilevel RRAM based on spike-timing-dependent-plasticity learning rules was used for image pattern recognition. These findings may offer a route to develop reliable digital memristors for ANNs.

TL;DR: In this paper, the evidence for the distribution of gap states g(E) in hydrogenated amorphous silicon (a-Si:H) is reviewed and the gap states below the gap center need further exploration.

Abstract: The evidence for the distribution of gap states g(E) in hydrogenated amorphous silicon (a-Si:H) is reviewed. In doped and defect-rich samples g(E) has near the gap center a peak that is proportional to the density of Si dangling bonds and a minimum about 0.4 eV below the electron mobility edge. g(E) below the gap center needs further exploration. The space charge limited current method can yield g(E) data for high quality undoped material which may have no peak due to dangling bond states.

TL;DR: The presence of traps not only reduces the magnitude of space-charge-limited currents, but also is likely to distort the shape of the currentvoltage curve from an ideal square law to a much higher power dependence on voltage.

Abstract: Currents, far in excess of ohmic currents, can be drawn through thin, relatively perfect insulating crystals. These currents are the direct analog of space-charge-limited currents in a vacuum diode. In actual crystals, the space-charge-limited currents are less than their theoretical value for an ideal crystal by the ratio of free to trapped carriers. Space-charge-limited currents become, therefore, a simple tool for measuring the imperfections in crystals even in the range of one part in ${10}^{15}$.The presence of traps not only reduces the magnitude of space-charge-limited currents, but also is likely to distort the shape of the current-voltage curve from an ideal square law to a much higher power dependence on voltage. The particular shape can be used to determine the energy distribution of traps.The presence of traps tends to uniformize the charge distribution between electrodes, to introduce a temperature dependence of the current, and to give rise to certain transient effects from which capture cross sections of traps may be computed.Space-charge-limited currents offer another mechanism for electrical breakdown in insulators.

Abstract: An ohmic contact between a metal and an insulator facilitates the injection of electrons into the insulator. Subsequent flow of the electrons is space-charge limited. In real insulators the trapping of electrons in localized states in the forbidden gap profoundly influences the current flow. The interesting features of the current density-voltage ($J\ensuremath{-}V$) characteristic are confined within a "triangle" in the $logJ\ensuremath{-}logV$ plane bounded by three limiting curves: Ohm's law, Child's law for solids ($J\ensuremath{\propto}{V}^{2}$) and a traps-filled-limit curve which has a voltage threshold and an enormously steep current rise. Simple inequalities relating the true field at the anode to the ohmic field facilitate qualitative discussion of the $J\ensuremath{-}V$ characteristic. Exact solutions have been obtained for an insulator with a single, discrete trap level in a simplified theory which idealizes the ohmic contact and neglects the diffusive contribution to the current. The discrete trap level produces the same type of nonlinearity discovered by Smith and Rose and attributed by them to traps distributed in energy.

TL;DR: In this article, the authors report a comprehensive study of the dynamic response of junction space-charge layers in undoped and P${\mathrm{H}}_{3}$-doped $a$-Si:H films grown by the rf-glow discharge technique.

Abstract: We report a comprehensive study of the dynamic response of junction space-charge layers in undoped and P${\mathrm{H}}_{3}$-doped $a$-Si:H films grown by the rf-glow-discharge technique. By using the numerical analysis methods discussed in the adjoining theory paper, we are able consistently to interpret a variety of transient response and ac admittance measurements in terms of a bulk density of gap states $g(E)$ which is characteristic of each sample. While the general shape of $g(E)$ seems to be a characteristic property of $a$-Si:H, the overall concentration of gap states depends on growth conditions and doping. The density of states at approximately midgap is observed to vary between values as low as about 2\ifmmode\times\else\texttimes\fi{}${10}^{15}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ e${\mathrm{V}}^{\ensuremath{-}1}$ in undoped films and as high as 1\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ e${\mathrm{V}}^{\ensuremath{-}1}$ in some P${\mathrm{H}}_{3}$-doped films. The general shape of our $g(E)$ is dominated by a deep minimum (${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ e${\mathrm{V}}^{\ensuremath{-}1}$) between 0.3 and 0.6 eV from the conduction band and a broad shoulder of states extending from the valence band up to midgap. The significant difference between this type of bulk $g(E)$ and previous models for the density of states in $a$-Si:H may be explained by the effects of states at or near the surface of the films which strongly influence the previous types of measurements. We discuss recent transport and optical measurements and show that they provide strong support for our density of states as opposed to previous models for $g(E)$.