Inhomogeneous Schottky Barrier Research Articles

Measurements of current-voltage-induced heating in the Al/SrTiO3−xNy/Al memristor during electroformation and resistance switching

Heating of the Al/SrTiO3−xNy/Al memristor is characterized during electroformation and switching of the resistances. The electrode with the higher voltage potential is heated to higher temperatures than the electrode with the lower potential, suggesting a reversible (nonstable) displacement of the anions in a low voltage region (|V|<±3 V). Application of a threshold voltage appropriate for resistance switching (|V|≥±3 V) facilitates migration of anions to the anode interface and increases the local anode temperature to a maximum of 285 °C. The hysteretic I-V curves are discussed taking into account tunnel barrier formation/break and inhomogeneous Schottky barrier modification at the anode interface.

A theoretical analysis together with experimental data of inhomogeneous Schottky barrier diodes

We have shown that the current at lower temperatures may exceed the current at higher temperatures using the approximation of the apparent BH in the inhomogeneous SDs, as determined by some authors in the literature. Then, in the simulated forward I–V curves of non-interactive inhomogeneous SDs using the approximation of the apparent BH, it has been showed that the current at lower temperatures does not exceed the current at higher temperatures when considering the bias voltage dependence of apparent BH. In the calculations, the parameters from the experimental forward bias I–V characteristics, in the temperature range of 60–300 K, of the Ni/ n-GaAs Schottky contacts with the inhomogeneous BH have been used by means of the thermionic emission theory of inhomogeneous Schottky contacts, considering a Gaussian distribution of barrier heights with a linear bias dependence.

The effects of the temperature on I-V and C-V characteristics of Al/P2ClAn(C2H5COOH)/p-Si/Al structure

The current-voltage ( I - V ) and capacitance-voltage ( C - V ) characteristics of metal-organic compound conductive polymer-semiconductor Al/P2ClAn(C 2 H 5 COOH)/ p -Si structures were measured in the temperature range 80–340 K. P2ClAn: the poly(2-chloroaniline). The P2ClAn emeraldine salt was synthesized chemically by using propionic (C 2 H 5 COOH) acid. The analysis of I - V characteristics based on the thermoionic emission (TE) mechanism has revealed a decrease of zero-bias barrier height and a increase of the ideality factor at lower temperatures. Temperature dependence of the barrier height (BH) has shown a disagreement with those calculated from C - V characteristics. This behaviour is attributed to Schottky barrier inhomogeneities at interface. The temperature coefficient of BH has been found to be -2.9×10 -4 eV/K for Al/P2ClAn(C 2 H 5 COOH)/ p -Si. ln( I 0 / $T^{2})$ versus 1/ T plot gives activation energy and Richardson constant $A^{\ast}$ as 0.12 eV and 3.82×10 -9 A/K 2 cm 2 , respectively.

Hydrolysis Improves Packing Density of Bromine-Terminated Alkyl-Chain, Silicon−Carbon Monolayers Linked to Silicon

Bromine-terminated alkyl-chain monolayers, bound to oxide-free Si substrates, were prepared by self-assembly. Infrared spectroscopy and atomic force microscopy imply that monolayer packing density improves after hydrolysis, despite an increase in the presence of oxide. The probable reason is that OH-mediated intermolecular H-bonding along the monolayer emerges after hydrolysis and rearranges the molecular components of the insulating layer. Current−voltage and differential capacitance measurements show that also the interfacial electronic properties of these junctions are changed by hydrolysis of the Br groups. This is expressed in an increased effective Schottky barrier height and a decreased junction ideality factor. We correlate the proposed structural changes of the monolayer with the change in the interfacial electronic properties, with the help of the inhomogeneous Schottky barrier height model. The role of oxide in the charge transport through the monolayer is discussed, as well.

Temperature-dependent current–voltage characteristics of the Au/n-InP diodes with inhomogeneous Schottky barrier height

Abstract The current–voltage (I–V) characteristics of Au/n-InP Schottky contacts have been measured in the temperature range of 70–300 K by steps of 10 K. Our data of the Au/n-InP Schottky contact strongly suggest that the temperature-dependent electron transport at the metal–semiconductor interface is significantly affected by the barrier inhomogeneity. The distribution of local effective SBHs has been modeled by a summation of existence of double Gaussian barrier heights which represents the high- and low-barrier of the full distribution in 170–300 and 70–170 K ranges.

The gaussian distribution of inhomogeneous barrier heights in PtSi/p-Si Schottky diodes

The current-voltage characteristics of PtSi/p-Si Schottky barrier diodes were investigated in the temperature range of 85-136K and their barrier height (Φb), ideality factor (n) and series resistance (Rs) were found to be strongly temperature-dependent. While n decreases, Φb increases with increasing temperature and the conventional activation energy plot deviates from linearity. These discrepancies from ideal thermionic emission theory is attributed to Schottky barrier inhomogeneities and the Schottky barrier inhomogeneities are shown to obey a single Gaussian distribution with a mean value of 0.4548eV and a standard deviation of 0.0607eV. The modified activation plot which takes into account the barrier height variations through the Gaussian distribution is acceptably linear and gives ($\overline{\phi_b}$) and A* as 0.4546eV and 31.47Acm-2K-2 respectively.

Barrier heights at the SnO 2/Pt interface: In situ photoemission and electrical properties

The SnO 2/Pt contact has been investigated using in situ photoelectron spectroscopy and electrical 2-point and 4-point conductivity measurements. A remarkable increase of barrier height from 0.4 eV to 0.9 eV is observed after annealing the as-deposited contact in 0.5 Pa oxygen atmosphere. Subsequent annealing in vacuum reduces the barrier height again. Despite the expected large barrier height, the current–voltage characteristics displays ohmic behavior. The discrepancy between photoemission and electrical behavior is attributed to the polycrystalline nature of the SnO 2 film used in this study, leading to an inhomogeneous Schottky barrier height along the surface of polycrystalline specimens.

Gaussian distribution of inhomogeneous barrier height in Al/SiO2/p-Si Schottky diodes

The forward and reverse bias current-voltage (I-V) characteristics of Al/SiO2/p-Si (metal-insulator-semiconductor) type Schottky diodes (SDs) were measured in the temperature range of 200–400 K. Evaluation of the experimental I-V data reveals a decrease in ΦB0 and Rs but an increase in n, with a decrease in temperature. To explain this behavior of ΦB0 with temperature, we have reported a modification which included n and the tunneling parameter αχ1/2δ in the expression of reverse saturation current I0. Thus, a corrected effective barrier height ΦB eff(I-V) vs T has a negative temperature coefficient (α≈−5×10−4 eV/K), and it is in good agreement with α=−4.73×10−4 eV/K of Si band gap. Such behavior of Rs estimated from Cheung’s method could be expected for semiconductors in the temperature region, where there is no carrier freezing out, which is non-negligible at low temperatures. Also, there is a linear correlation between ΦB0(I-V) and n due to the inhomogeneities of the barrier heights (BHs). The conventional activation energy (Ea) plot exhibits nonlinearity below 320 K with the linear portion corresponding to Ea of 0.275 eV. An A∗ value of 1.45×10−5 A cm−2 K−2,which is much lower than the known value of 32 A cm−2 K−2 for p-type Si, is determined from the intercept at the ordinate of this experimental plot. Such behavior is attributed to Schottky barrier inhomogeneities by assuming a Gaussian distribution (GD) of BHs due to BH inhomogeneities that prevail at the interface. We attempted to draw a ΦB0 vs q/2kT plot to obtain evidence of a GD of the BHs, and the values of Φ¯B0=1.136 eV and σ0=0.159 V for the mean BH and standard deviation at zero bias have been obtained from this plot. Therefore, the modified ln (I0/T2)−q2σ02/2k2T2 vs q/kT plot gives Φ¯B0 and A∗ values of 1.138 eV and 37.23 A cm−2 K−2, respectively, without using the temperature coefficient of the BH. This A∗ value of 37.23 A cm−2 K−2 is very close to the theoretical value of 32 A K−2 cm−2 for p-type Si. Therefore, it has been concluded that the temperature dependence of the forward bias I-V characteristics of the Al/SiO2/p-Si SDs can be successfully explained based on the thermionic emission mechanism with a GD of the BHs.

The distribution of the barrier height in Al–TiW–Pd2Si/n-Si Schottky diodes from I–V–T measurements

The forward and reverse bias current–voltage (I–V) characteristics of Al–TiW–Pd2Si/n-Si Schottky barrier diodes (SBDs) were measured in the temperature range of 300–400 K. The estimated zero-bias barrier height ΦB0 and the ideality factor n assuming thermionic emission (TE) theory show a strong temperature dependence. While n decreases, ΦB0 increases with increasing temperature. The Richardson plot is found to be linear in the temperature range measured, but the activation energy value of 0.378 eV and the Richardson constant (A*) value of 15.51 A cm−2 K−2 obtained in this plot are much lower than the known values. Such behavior is attributed to Schottky barrier inhomogeneities by assuming a Gaussian distribution of barrier heights (BHs) due to BH inhomogeneities that prevail at the interface. Also, the ΦB0 versus q/2kT plot was drawn to obtain evidence of a Gaussian distribution of the BHs, and ΦB0 = 0.535 eV and σ0 = 0.069 V for the mean BH and zero-bias standard deviation, respectively, have been obtained from this plot. Thus, the modified ln(I0/T2) − q2σ20/2k2T2 versus q/kT plot gives ΦB0 and A* as 0.510 eV and 121.96 A cm−2 K−2, respectively. This value of the Richardson constant 121.96 A cm−2 K−2 is very close to the theoretical value of 120 A K−2 cm−2 for n-type Si. Hence, it has been concluded that the temperature dependence of the forward I–V characteristics of the Al–TiW–Pd2Si/n-Si Schottky barrier diodes can be successfully explained on the basis of a thermionic emission mechanism with a Gaussian distribution of the BHs.

The behavior of the I-V-T characteristics of inhomogeneous (Ni∕Au)–Al0.3Ga0.7N∕AlN∕GaN heterostructures at high temperatures

We investigated the behavior of the forward bias current-voltage-temperature (I-V-T) characteristics of inhomogeneous (Ni∕Au)–Al0.3Ga0.7N∕AlN∕GaN heterostructures in the temperature range of 295–415K. The experimental results show that all forward bias semilogarithmic I-V curves for the different temperatures have a nearly common cross point at a certain bias voltage, even with finite series resistance. At this cross point, the sample current is temperature independent. We also found that the values of series resistance (Rs) that were obtained from Cheung’s method are strongly dependent on temperature and the values abnormally increased with increasing temperature. Moreover, the ideality factor (n), zero-bias barrier height (ΦB0) obtained from I-V curves, and Rs were found to be strongly temperature dependent and while ΦB0 increases, n decreases with increasing temperature. Such behavior of ΦB0 and n is attributed to Schottky barrier inhomogeneities by assuming a Gaussian distribution (GD) of the barrier heights (BHs) at the metal∕semiconductor interface. We attempted to draw a ΦB0 versus q∕2kT plot in order to obtain evidence of the GD of BHs, and the values of Φ¯B0=1.63eV and σ0=0.217V for the mean barrier height and standard deviation at a zero bias, respectively, were obtained from this plot. Therefore, a modified ln(I0∕T2)−q2σ02∕2(kT)2 versus q∕kT plot gives ΦB0 and Richardson constant A* as 1.64eV and 34.25A∕cm2K2, respectively, without using the temperature coefficient of the barrier height. The Richardson constant value of 34.25A∕cm2K2 is very close to the theoretical value of 33.74A∕cm2K2 for undoped Al0,3Ga0,7N. Therefore, it has been concluded that the temperature dependence of the forward I-V characteristics of the (Ni∕Au)–Al0.3Ga0.7∕AlN∕GaN heterostructures can be successfully explained based on the thermionic emission mechanism with the GD of BHs.

High spatial and energy resolution characterization of lateral inhomogeneous Schottky barriers by conductive atomic force microscopy

We present a novel approach based on conductive atomic force microscope (c-AFM) for nano-scale mapping in laterally inhomogeneous metal–semiconductors Schottky contacts. For ultra-thin (1–5 nm) metal films with resistivity exceeding by about two orders of magnitude the bulk value, the current localization under the tip (10–20 nm diameter) occurs. By spectroscopic analysis of the current–voltage characteristics for different tip positions, the 2D Schottky barrier height (SBH) distribution is obtained with ∼0.1 eV energy resolution. The method was applied to explain the experimentally observed SBH lowering in macroscopic Au/4H–SiC diodes, in the presence of a not uniform SiO 2 layer at the SiC/Au interface. Nano-scale mapping on the oxide free Au/4H–SiC contact demonstrates a SBH distribution peaked at 1.8 eV and with tails from 1.6 eV to 2.1 eV. When ∼2 nm not uniform SiO 2 layer is intentionally grown on SiC before contact formation, the Au/SiO 2/4H–SiC SBH distribution exhibits a 0.3 eV lowering in the peak and a broadening (tails from 1.1 eV to 2.1 eV), thus explaining the macroscopically observed average effect.

Effect of temperature and inhomogeneity on the yield of PtSi–n–Si photodetectors

The temperature dependence of the current-voltage characteristics of a PtSi/Si Schottky detector is investigated between 20 and 300 K, a temperature range that is much wider than what is usually reported in literature. The data is satisfactorily interpreted on the basis of a thermionic emission mechanism across an inhomogeneous barrier. The Schottky barrier inhomogeneities are shown to obey a single Gaussian distribution with a mean barrier height of 0.76 eV and a standard deviation of 30 meV at zero bias. The calculated detector's efficiency, while taking the barrier distribution into account, shows an increase with decreasing temperature that can be considered overall as marginal but becomes much more significant below 60 K and at wavelengths near the cut-off edge.

Electrical Characterization of Inhomogeneous Ni<sub>2</sub>/Si/SiC Schottky Contacts

Abstract. The electrical characterization of nickel silicide (Ni 2 Si) Schottky contacts on 4H-SiC is reported in this work. In spite of the nearly ideal behaviour observed at room temperature ( n =1.05), a deviation from the ideality was observed at lower temperatures, thus suggesting that an inhomogeneous Schottky barrier has actually formed. The experimental results were described by the Tung’s model on inhomogeneous Schottky barriers, which considers low barrier regions embedded in a uniform high barrier Ni 2 Si contact. The inhomogeneity of the barrier is responsible of the commonly observed discrepancy between the experimental values of the Richardson’s constant A ** (i.e. 2.6 A/cm 2 K 2 in our contacts) from its theoretical value of 146 A/cm 2 K 2 in 4H-SiC. Introduction Silicon carbide Schottky diodes are very attractive devices because of their capability to reach high switching frequencies under high voltage operation and with a low on-resistance when compared to analogous silicon devices [1]. In spite of the progresses already achieved in the technology of SiC Schottky diodes, obtaining a barrier with nearly ideal electrical behaviour may represent an outstanding problem. In fact, the control of the surface preparation before metal deposition affects the uniformity of the Schottky barrier height Φ

The Effect of Series Resistance on the Relationship Between Barrier Heights and Ideality Factors of Inhomogeneous Schottky Barrier Diodes

We have studied Cd/n-Si (33 dots) Schottky barrier diodes (SBDs). Si surfaces have been prepared by the usual chemical etching, and the evaporation of metal has been carried out in a conventional vacuum system. The effective Schottky barrier heights (SBHs) and ideality factors obtained from the current–voltage (I–V) characteristics differ from diode to diode although the samples were identically prepared. The SBH for the Cd/n-Si diodes ranged from 0.605 eV to 0.701 eV, and ideality factor n from 1.213 to 1.913. The reason for that the experimental data differ from diode to diode has been analyzed by applying thermionic emission theory (TET) of inhomogeneous Schottky contacts together with standard TET and thus the effect of series resistance on the relationship between barrier heights and ideality factors of the inhomogeneous SBDs has clearly been shown. A laterally homogeneous SBH value of approximately 0.770 eV for Cd/n-Si SDs has been obtained by the barrier inhomogeneity model.

Silicon carbide pinch rectifiers using a dual-metal Ti-Ni/sub 2/Si Schottky barrier

The electrical characterization of dual-metal-planar Schottky diodes on silicon carbide is reported. The devices were fabricated on both 6H- and 4H-SiC by using titanium (Ti) and nickel silicide (Ni/sub 2/Si) as Schottky metals. These rectifiers yielded the same forward voltage drop as the Ti diodes and leakage current densities comparable to those of the Ni/sub 2/Si diodes. The reduction of the reverse leakage current density, with respect to that of the Ti diodes, was about three orders of magnitude in 6H and about a factor of 30 in 4H-SiC. All that results in a consistent reduction of the device power dissipation. Electrical characterization of the devices at different temperatures provided insight into the carrier transport mechanism. In particular, the electrical behavior of the system was explained by an inhomogeneous Schottky barrier model, in which the low Ti barrier determines the current flow under forward bias, whereas the high Ni/sub 2/Si barrier dominates the reverse bias conduction by the pinchoff of the low barrier Ti regions.

Tunneling across an inhomogeneous delta-barrier

The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy \(V\left( r \right) = \left[ {\eta + \mu \left( {x^2 + y^2 } \right)} \right]\delta \left( z \right)\) (where \(\eta >0\) and \(\mu >0\) are two constants). In particular, the perpendicular incidence of an electron with a given value \(k_0 \) of the wave vector \(k_0 = \left( {0,0,k_0 } \right)\)is considered. The electron is forward-scattered into the region behind the barrier (region 2: \(z >0\)), i. e. the wave function \(\psi _2 \left( r \right)\) is composed of plane waves with all wave vectors \(k_2 \) such that \(\left| {k_2 } \right| = k_0 \) and \(k_{2z} = \sqrt {k_{_0 }^2 - q^2 >\left. 0 \right)} \)) (where \(q = \left( {k_{2x} ,k_{2y} ,0} \right),q = \left| q \right|\)). Therefore, if \(z >0\), the wave function of the electron is represented as \(\psi _2 \left( r \right) = \int {d^2 qU_2 \left( q \right)\exp \left[ {{\text{i}}\left( {q.u + \sqrt {k_{_0 }^2 - q^2 } } \right)z} \right]} \), where \(u = \left( {x,y,0} \right)\). An approximate formula is derived for the amplitude \(U_2 \left( q \right)\). The authors pay a special attention to the flow density \(J_2 \left( r \right) = \left( {\hbar /m} \right)\operatorname{Im} \psi _{_2 }^* \left( r \right)\nabla \psi _2 \left( r \right)\) and calculate this function in two cases: 1. for the plane \(z = 0\) and 2. for high values of \(R = \left| r \right|\left( {z = R{cos}\vartheta ,{i}{.e}{.}\vartheta \in \left( {0,{\pi}/2} \right.} \right)\) is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier.

Mechanism of nonideality in nearly ideal Si Schottky barriers

The origin of nonideality in an actual nearly ideal Schottky barrier is an inhomogeneous Schottky barrier height (SBH). A high density of point defects is generated in the neighborhood of the interface by the fabrication process of the metal/Si interface. Local SBH lowering by positively ionized defects close to the interface is considered the cause of inhomogeneity based on the property of the metal-induced gap states. Results of analysis by this mechanism are in excellent agreement with ballistic electron emission microscopy (BEEM) observation of low-SBH spots. A Gaussian distribution of inhomogeneous SBH explains the BEEM spectrum, as well as the temperature dependence of both effective SBH and ideality factor, i.e., the so-called T0 anomaly. The spatial distribution of the ionized donor and its variation under applied voltage are obtained. This result indicates that the origin of the ideality factor is preferential neutralization of the donor close to the interface in equilibrium with the Fermi level. Thus, the proposed mechanism explains the various properties of nearly ideal Si Schottky barriers.

Comment on “Numerical study of electrical transport in homogeneous Schottky diodes” [J. Appl. Phys. 85, 1935 (1999)

In a recent article [J. Appl. Phys. 85, 1935 (1999)], Osvald simulated forward and reverse current–voltage and capacitance–voltage characteristics of inhomogeneous Schottky barrier (SB) diodes and concluded that the currents flowing in interacting and noninteracting inhomogeneous SBs were largely identical. This Comment points out the inappropriateness of some of the conditions chosen for these simulations which likely has rendered that conclusion untenable.

Low-frequency noise in metal–semiconductor contacts with local barrier height lowering

An analytical presentation and numerical analysis of low-frequency (1/f) noise of a spatially inhomogeneous Schottky barrier contact (SBC) (with local barrier height lowering (BHL)) are given. The spectral intensity of the current fluctuation (SI) S i is analysed as a function of temperature, current and contact area for various parameters of contact inhomogeneity, such as the area ratio of low barrier height region and main part of the SBC, the BHL value, the ideality factor of the BHL region and others. It is shown that local BHL can cause an essential increase of SI with lower temperature. It manifests itself as well in a deviation of current dependence of SI from the usual square law S i ∼ I 2, and of area dependence – from the conventional S i ∼ l/ A for a homogeneous SBC. All the above peculiarities of noise characteristics have been observed in real silicon and gallium arsenide SBCs and can be explained on the basis of the local BHL model. A Gaussian barrier height distribution, used in a number of publications, doesn’t explain the above peculiarities of real SBCs.

Metal-induced gap states model of nonideal Au/Si Schottky barrier with low defect density

Temperature dependence of current–voltage characteristics was investigated on Au/n-Si Schottky barrier. The experimental current density can be represented by a modified equation of the thermionic emission, in which nearly the same ideality factors n Φ and n v appear in the temperature dependent exponential term of the barrier height Φ B and in that of the applied voltage V, respectively. Origin of n Φ is considered to be spatially inhomogeneous Schottky barrier height distribution. Origin of n v is considered to be applied bias dependence of the effective barrier height. A microscopic model of the inhomogeneity based on the MIGS model is proposed. Positively charged defects close to interface but outside the evanescent tail of MIGS produce local lowering of barrier height due to induced charge density, which depends on a distance of the defect from interface. The local barrier height lowering is restored by disappearance of the defect charge under forward bias. This model is applicable to interfaces of defect density lower than 10 14 cm −2, which has been considered to be necessary for the Fermi level pinning.