Inhomogeneous Schottky Diodes Research Articles

Analysis of temperature-dependent current–voltage characteristics of Schottky diodes by the modified thermionic emission current model

We have investigated the behavior of current flow across an inhomogeneous Schottky diode (SD) as a function of temperature by numerical simulation. We have used the modified thermionic emission (TE) current expression with a Gaussian distribution of potential barrier heights. This modified TE model assumes the presence of a series of low-barrier patches at the Schottky contact and semiconductor interface. First, we have discussed the behavior of the patch current compound relative to the TE compound in the inhomogeneous SD at 300, 200, and 100 K, as a function of standard deviation and the number of circular patches N. Then, we have investigated the behavior of temperature- and bias-dependent and bias-independent current vs voltage (I–V–T) characteristics in the 75–300 K range. In bias-dependent I–V–T curves obtained for σ1=4.35×10−5cm2/3V1/3 and σ2=7.35×10−5cm2/3V1/3 at N1=1.81×106 or N2=1.81×108, an intersection behavior has been observed in the I–V curve at 75 K for σ2 at both N values; however, the same behavior has been not observed for σ1 at both N values due to σ1<σ2. That is, the current for σ2 at 75 K has exceeded the current at higher temperatures. This behavior has been ascribed to the effective BH to decrease with decreasing temperature value. In the I–V–T curves independent of bias, such an intersection has not been observed for σ1 while it has been observed for σ2 in the I–V curves at both 75 and 100 K. Thus, it has been concluded that the bias-dependeσnt I–V equations must be used to avoid this intersection behavior while fitting the experimental I–V curve of an SD to the theoretical I–V curve.

Enhanced Non-Uniformity Modeling of 4H-SiC Schottky Diode Characteristics Over Wide High Temperature and Forward Bias Ranges

A practical model, adequate for full reproduction of inhomogeneous Schottky diodes' forward characteristics over wide high-temperature and bias ranges, is proposed. According to this p-diode model, the Schottky contact current is considered to flow through m parallel-connected internal diodes, each with stable, constant barrier height and specific series resistance (both main model parameters). The value of m, required to reproduce the entire electrical forward behavior of a non-uniform Schottky contact, is directly connected to a particular model parameter (p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> ), used to define the inhomogeneity degree. The p-diode model was tested on forward characteristics measured for both Ni and commercial Ti Schottky diodes on 4H-SiC, which exhibited varying degrees of inhomogeneity. Excellent replication of experimental curves was achieved for all investigated samples, even those with obvious irregularities, such as “humps”, explained in the model by the series resistances' influence. In the case of m = 1, the proposed model does not produce identical results with the conventional model of a homogeneous Schottky contact if p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> ≠ 0. The value of this parameter indicates how much of an inhomogeneous contact's area is essentially used for current conduction.

Characterization of non-uniform Ni/4H-SiC Schottky diodes for improved responsivity in high-temperature sensing

The development of high-temperature sensors (up to 450 °C), based on SiC Schottky diodes, which are able to work in harsh conditions, requires using high-barrier Schottky contacts, such as nickel silicide. It is well known that post metallization annealing, targeting silicide formation, leads to Schottky barrier height (SBH) non-uniformity on the contact surface. On the other hand, sensor performances are intimately tied to the value and stability of SBH. This paper discusses solutions for assessing temperature sensing performances of inhomogeneous SiC Schottky diodes, particularly targeting high-temperature, harsh industrial applications where conventional solutions are unreliable. Microphysical investigations and electrical measurements are carried out on Ni/4H-SiC Schottky diodes with varying levels of non-uniformity. Devices are characterized using SEM and EDX analyses, together with electrical parameter evaluation techniques. It is demonstrated that, despite highly inhomogeneous electrical behavior, SiC-Schottky diodes exhibit stable sensitivity (up to 2.33 mV/°C) with excellent linearity (R2 > 99.9%) over wide temperature (up to 450 °C) and bias ranges (at least 100 nA–10 µA).

Modeling of Inhomogeneous 4H-SiC Schottky and JBS Diodes in a Wide Temperature Range

This paper presents a study of the Schottky barrier evolution on SBD and JBS diodes over a wide range of temperatures from 80 to 500 K. We show that inhomogeneities of the Schottky contact have a strong impact on the dependence of barrier characteristics with temperature, especially below 200 K. Analysis of the reverse bias current of such diodes at low temperature show that the barrier height depends on temperature but also on voltage.

Numerical analysis of inhomogeneous Schottky diode with discrete barrier height patches

ABSTRACTThe potential profile inside the semiconductor at the metal–semiconductor contact is simulated by numerically solving the Poisson equation and the drift diffusion equations for inhomogeneous Schottky diode. From the simulated potential and the electron and hole concentrations, the drift-diffusion current as a function of bias is calculated. The simulation is carried out for various distribution patterns of barrier height patches at the metal–semiconductor contact to study the effect of barrier inhomogeneities on the Schottky diode parameters, namely barrier height and ideality factor and their temperature dependence. It is found that barrier height decreases and ideality factor increases with increase in the deviation of discrete barrier height patches in the distribution. The resulting barrier parameters are studied to understand the effect of barrier inhomogeneities on the current–voltage characteristics of inhomogeneous Schottky contact.

New study of the abnormal behavior of the low temperature dependence of the current in inhomogeneous Schottky diode

AbstractIn this study, we show clearly why unexpected observations have been reported in the current–voltage curves of Schottky diodes, containing barrier inhomogeneities generated by using the analytical results based on a Gaussian distribution model of barrier heights. The Chand's calculations have shown that the current (saturation current) at low temperatures may exceed the current (saturation current) at high temperatures when the effective barrier height is calculated from an appropriate integral with integration limits −∞ and +∞. In this new study, we show that the method followed by Chand to remove these anomalies is not accurate enough. We prove that the origin of these anomalies stems from the nature of a proper function f(φ) that moves to the negative barrier heights and takes large value of the integral at low temperatures than at high temperatures when it has large standard deviation (σ) and the discrepancies are not due to the integration limits as Chand concluded. In order to obtain results consistent with the thermionic emission–diffusion theory, the standard deviation must have lower values. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Studying of barrier height and ideality factor relation in the nano sized Au-n type Si Schottky diodes

The results of formation of the operating potential barrier height ( Φ в) of inhomogeneous Schottky diodes (SD) in view of an additional electric field in the near contact region of the semiconductor and features of its dependence on the external applied voltage are presented. A correlation, between SD heterogeneity and dependence between potential barrier height ( Φ в) and ideality factor ( n), is presented. Using conducting probe atomic force microscope (CP-AFM) techniques, it is shown that Au/n-Si diodes consist of sets of parallel-connected and cooperating nano diodes with the contact surfaces sizes in the order of 100–200 nm. The effective Φ в and ideality factors of the SD have been obtained from the current–voltage ( I– V) characteristics, which were measured using a CP-AFM along a contact surface. It was experimentally shown that the forward and reverse part of I– V characteristics and their effective Φ в and ideality factors of the identically fabricated nano-SD differ from diode to diode. The Φ в for the nano-SD has ranged from 0.565 to 0.723 eV and ideality factor from 1.11 to 1.98. No correlation can be found between the Φ в and ideality factor. The Φ в distribution obtained from the I– V characteristics has been fitted by a Gaussian function but the ideality factor distribution could not be fitted by a Gaussian function.

Effects of barrier height inhomogeneities on the determination of the Richardson constant

Extraction of the Richardson constant and Schottky barrier height from the current-voltage-temperature (I−V−T) characteristics of Schottky barrier contacts is greatly influenced by a variety of nonideal effects. Starting with an overview of the original Richardson plot and relevant modifications of the Richardson plot, this article discusses limitations of previous analytical approaches that attempt to account for the effects of barrier height inhomogeneities on the extracted Richardson constant. A temperature-driven fundamental change in the current conduction in an inhomogeneous Schottky diode from conduction dominated by low barrier height patches to conduction dominated by high barrier height regions is identified as a likely source for the bowing of the Richardson plot, and knowledge of which regime dominates the current transport is critical for accurate determination of the Richardson constant. A simple linear relation between the effective Richardson constant and effective barrier height is described, and this recently-reported linear relation provides a consistent method for estimating the Richardson constant of inhomogeneous Schottky diodes when transport is primarily through high barrier height regions. The method is applied to I−V−T characteristics of Au/Ni/n-GaN Schottky diodes measured from 320–440 K. A homogeneous Richardson constant of 29±6 A cm−2 K−2 is extracted using the proposed approach and is in very good agreement with the theoretical value of 26.4 A cm−2 K−2.

Thermal activation of current in an inhomogeneous Schottky diode with a Gaussian distribution of barrier height

This paper investigates the thermal activation behaviour of current in an inhomogeneous Schottky diode with a Gaussian distribution of barrier height by numerical simulation. The analytical Gaussian distribution model predicted that the I-V-T curves may intersect with the possibility of the negative thermal activation of current, but may be contradictory to the thermionic emission mechanism in a Schottky diode. It shows that the cause of the unphysical phenomenon is related to the incorrect calculation of current across very low barriers. It proposes that junction voltage Vj, excluding the voltage drop across series resistance from the external bias, is a crucial parameter for correct calculation of the current across very low barriers. For correctly employing the thermionic emission model, Vj needs to be smaller than the barrier height ø. With proper scheme of series resistance connection where the condition of Vj > ø is guaranteed, I-V-T curves of an inhomogeneous Schottky diode with a Gaussian distribution of barrier height have been simulated, which demonstrate normal thermal activation. Although the calculated results exclude the intersecting possibility of I-V-T curves with an assumption of temperature-independent series resistance, it shows that the intersecting is possible when the series resistance has a positive temperature coefficient. Finally, the comparison of our numerical and analytical results indicates that the analytical Gaussian distribution model is valid and accurate in analysing I-V-T curves only for small barrier height inhomogeneity.

The theoretical and experimental study on double-Gaussian distribution in inhomogeneous barrier-height Schottky contacts

We have considered multi-Gaussian distribution of barrier-heights for non-interactive barrier inhomogeneities in the inhomogeneous Schottky diodes, and we have shown the presence of the intersecting behavior in the forward-bias current–voltage ( I– V) curves for the double-Gaussian distribution model at low temperatures. We have tried to eliminate this effect by generating I– V curves at lower temperatures with the bias-dependent barrier-height expression which leads to the ideality factors greater than unity. For this calculation, we have obtained the expressions for the barrier-height change and ideality factor, and for bias-dependency of the BH for the multi-Gaussian model by following the literature. We have shown that the experimental forward-bias I– V curves coincide with the theoretical ones using the bias-dependent inhomogeneous BH expression at low and high temperatures in the double-Gaussian distribution of BHs.

Temperature dependence of barrier height parameters of inhomogeneous Schottky diodes

We have shown by numerical simulations of I– V– T curves that the ideality factor of inhomogeneous Schottky diodes does not increase for decreasing temperature to such extent as is commonly observed for Schottky diodes in experiment. The main consequence of such a result is that in spite of the fact that the barrier height inhomogeneities fullfil the conditions for barrier height lowering for decreasing temperature they might not be a general or the only reason for occuring of this effect in experimental structures. We found out much slower ideality factor temperature dependence than reported in the literature and the dependence was even not monotonous for simulation conditions used. We conclude that some other reason as barrier inhomogeneity is responsible for ideality factor temperature dependence.

On the temperature dependence of series resistance and interface states in Al/SiO 2/p-Si (MIS) Schottky diodes

The capacitance–voltage–temperature ( C– V– T) and conductance–voltage–temperature ( G/ w– V– T) characteristics of metal–semiconductor (Al/ p-Si) Schottky diodes with thermal growth interfacial layer were investigated by considering series resistance effect in the wide temperature range (80–400 K). It is found that in the presence of series resistance, the forward bias C– V plots exhibit a peak, and experimentally shows that the peak positions shift towards higher positive voltages with increasing temperature, and the peak value of the capacitance has a maximum at 80 K. The C– V and ( G/ w– V) characteristics confirm that the N ss and R s of the diode are important parameters that strongly influence the electric parameters in (Al/SiO 2/ p-Si) MIS Schottky diodes. The crossing of the G/ w– V curves appears as an abnormality when seen with respect to the conventional behaviour of the ideal MS or MIS Schottky diode. It is thought that the presence of a series resistance keeps this intersection hidden and unobservable in homogeneous Schottky diodes, but it appears in the case of inhomogeneous Schottky diode. In addition, the high frequency ( C m) and conductance ( G m/ w) values measured under both reverse and forward bias were corrected for the effect of series resistance to obtain the real diode capacitance.

On the difference in the apparent barrier height of inhomogeneous Schottky diodes with a Gaussian distribution

The differences in the calculated apparent Schottky barrier heights as obtained from different approaches assuming a Gaussian distribution model of barrier potential are discussed. A modified theoretical expression for the saturation current and consequently a new expression for the apparent barrier height, evaluated numerically, are proposed. The current–voltage (I–V) expression obtained is subsequently used to generate I–V curves. An adequate genetic algorithm has been used to extract diode parameters. While the previous approaches used may lead to an unphysical negative apparent barrier height at low temperatures, or may suggest the existence of a lowest critical temperature up to which the apparent barrier height can be calculated, our approach presented here yields results for the apparent barrier height in good agreement with the extracted values at different temperatures. Therefore, it is concluded that the temperature dependence of the apparent Schottky barrier height can be successfully explained with the presently proposed approach, the detailed aspects of which are presented in this contribution.

Influence of lateral current spreading on the apparent barrier parameters of inhomogeneous Schottky diodes

The influence of the series resistance of inhomogeneous Schottky diodes on the apparent barrier parameters in three different arrangements was studied. It is shown that when there is a total current spreading in the semiconductor substrate the ideality factor of the diode remains unity and the extracted series resistance is equal to the real value. On the other hand a lack of current spreading in the substrate results in the different voltage drops on the particular series resistances which causes different actual voltages on the particular diodes. The ideality factor nonequal to unity and the apparent series resistance different from the real value of the resistances are then the results of the barrier parameter extraction.

Theoretical evidence for random variation of series resistance of elementary diodes in inhomogeneous Schottky contacts

The current–voltage ( I– V) characteristics of Schottky diodes measured at low temperature shows an abnormal behavior, which is attributed to the presence of spatial variation of barrier heights of Gaussian type at metal–semiconductor interface. The simulation studies assuming Gaussian distribution of barrier heights also show similar temperature dependence of diode parameters as observed in real Schottky contacts fabricated on various metal–semiconductor systems. The simulation studies performed so far on inhomogeneous Schottky contacts assumes constant series resistance ( R S) to all elementary diodes because of the complexity in programming. We have simulated I– V characteristics of inhomogeneous Schottky diodes with Gaussian distribution of Barrier heights (BHs) assuming different R S for different elementary diodes in the distribution. It is found that the simulation performed using randomly varying R S having Gaussian distribution yields I– V characteristics similar to those obtained using constant R S with its value about which variation in R S is considered for all elementary diodes. The simulation results provide theoretical evidence about the occurrence of random fluctuation of R S of Gaussian type in elementary diodes in inhomogeneous Schottky contact.

On the profile of temperature dependent series resistance in Al/Si 3N 4/p-Si (MIS) Schottky diodes

The temperature dependence of capacitance–voltage ( C– V) and conductance–voltage ( G/ w– V) characteristics of metal–insulator–semiconductor (Al/Si 3N 4/p-Si) Schottky barrier diodes (SBDs) was investigated by considering series resistance effect in the temperature range of 80–300 K. It is found that in the presence of series resistance, the forward bias C– V plots exhibit a peak, and experimentally show that the peak positions with a maximum at 260 K shift toward lower voltages with increasing temperature. The C– V and ( G/ w– V) characteristics confirm that the interface state density ( N ss) and series resistance ( R s) of the diode are important parameters that strongly influence the electric parameters of MIS structures. The crossing of the G/ w– V curves appears as an abnormality compared to the conventional behavior of ideal Schottky diode. It is thought that the presence of series resistance keeps this intersection hidden and unobservable in homogeneous Schottky diodes, but it appears in the case of inhomogeneous Schottky diode. In addition, the high frequency ( C m) and conductance ( G m/ w) values measured under both reverse and forward bias were corrected for the effect of series resistance to obtain the real diode capacitance.

Series resistance influence on intersecting behaviour of inhomogeneous Schottky diodes I– V curves

We have studied intersecting behaviour of I– V curves measured at different temperatures for inhomogeneous Schottky diodes with a common series resistance. Analytical expression for the voltage where I– T curves have their minima and the existence of which is a necessary condition for the intersection of I– V curves was derived. It is shown that this voltage remains in the low voltage region where I– V curves of Schottky diodes are commonly measured.

A comparative study of numerical and analytical methods of simulating inhomogeneous Schottky diode characteristics

The current–voltage characteristics of inhomogeneous Schottky diodes can be generated using either analytically solved equations for total current through all elementary diodes, or by numerical integration over the entire barrier height range. The simulation performed using these two methods yields current–voltage characteristics with different features. In this paper we have analysed the nature of elementary diodes representing a Gaussian distribution of barrier heights in inhomogeneous Schottky contact, and found that it is the constant series resistance considered for all elementary diodes in the distribution which makes the two methods yield current–voltage characteristics with different features. It apparently indicates that the two methods of analysing inhomogeneous Schottky contacts are inconsistent. It is shown that each elementary barrier in the distribution has a different series resistance associated with it, which has a direct correlation with its probability of occurrence in the distribution. Performing the numerical integration with varying series resistance yields current–voltage characteristics with features similar to those obtained by the analytical method. The analysis made in this paper confirms that the two methods of modelling inhomogeneous Schottky contacts yield consistent current–voltage characteristics.

Voltage dependence of effective barrier height reduction in inhomogeneous Schottky diodes

The Schottky barrier height (SBH) variation and its dependence on applied voltage for NiSi/n-Si Schottky diodes with different SBH inhomogeneities have been studied by temperature-dependent current–voltage technique. The results show that the effective barrier height is strongly dependent on the SBH inhomogeneity and the applied voltage. The reduction of effective barrier height increases as the bias varies from forward to reverse, indicating that the pinch off, or more precisely saying, the presence of saddle point in the depletion region, does strongly affect the current transport. Under low reverse bias, the SBH reduction is proportional to one-fourth power of the band bending, which indicates that strip-like SBH inhomogeneity rather than patch-like SBH inhomogeneity exists in our samples. The strip region parameter ω is determined to be 1.63 × 10 −3 and 3.21 × 10 −3 V −1/2 cm −1/2 for the two diodes respectively. Under high reverse bias, the SBH reduction shows different behaviours for diodes with different SBH inhomogeneity. For diodes with small inhomogeneity, the SBH reduction increases faster than the one-fourth power of the band bending while for diodes with large inhomogeneity, the reduction increases more slowly than in the low reverse bias region. The reason is also explained in term of pinch off.

Analysis of current–voltage characteristics of inhomogeneous Schottky diodes at low temperatures

Two approaches of Gaussian distribution of barrier heights in inhomogeneous Schottky diodes have been analyzed by comparing the results for consistency between the two. For this the current–voltage characteristics of inhomogeneous Schottky diodes have been generated by using analytically solved thermionic-emission diffusion equation incorporating Gaussian distribution of barrier heights and by direct numerical integration over a barrier height range. The differences in the results obtained in two approaches are discussed and it is shown that the two approaches yield current–voltage characteristics with slightly different features. The discrepancies in the results obtained in two approaches are attributed to the same series resistance assumed for all elementary barriers of the distribution. It is shown that assigning same series resistance to all barrier of the distribution in numerical integration approach causes current saturation at low bias and inhibits intersection of current–voltage curves from being observable which otherwise occurs in the curves obtained using analytical equation. The paper deals with these aspects in details.