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Nov 23, 2011 - Achamma John Mathai. Abstract—Ga–pWSe2 Schottky diodes were fabricated on both uncleaved and cleaved WSe2 surfaces and were ...
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 12, DECEMBER 2011

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Conduction Mechanisms and Low-Temperature Anomalies in the Electrical Characteristics of Ga–pWSe2—A Liquid Metal Schottky Structure Achamma John Mathai

Abstract—Ga–pWSe2 Schottky diodes were fabricated on both uncleaved and cleaved WSe2 surfaces and were subjected to forward current–voltage–temperature measurements. The conduction mechanisms have been studied over a temperature range of 140 K–300 K. From and above 200 K onwards, the current–voltage characteristics of both diodes obey thermionic emission (TE) theory with Gaussian barrier height distribution. At temperatures below 200 K, the presence of generation–recombination (GR) and tunneling (TN) currents becomes noticeable. The observed anomalies at low temperatures were effectively interpreted in terms of the combined influence of TE, GR, and TN currents across the interface. Furthermore, the cleaved diode with less surface inhomogeneity showed better characteristics than the uncleaved diode. Index Terms—Combined-effect model, Ga–pWSe2 , Gaussian distribution, liquid metal Schottky contact.

I. I NTRODUCTION

M

ETAL–SEMICONDUCTOR (MS) structures are one of the farthest and most widely used contacts, both as ohmic and Schottky in the electronic industry. Due to the technological importance of Schottky diodes, it is mandatory to understand on an exhaustive way their ultimate characteristics. Although numerous studies have established the relationship between Schottky barrier height (SBH) and material properties, there is still no single robust model for a priori determination of the barrier height at the MS interface [1]–[3]. Investigations regarding temperature-dependent current– voltage characteristics (I–V –T ) allow us to gain vital information about the barrier formation and conduction processes. It also sheds light on the validity of thermionic emission (TE) theory. In many cases, SBH is temperature dependent with a simultaneous increase in ideality factor with decreasing temperature [4]–[6]. This is contrary to the pure TE theory, which assumes a temperature-independent barrier height. Researchers have put forward several theories to explain this contradiction. The barrier height inhomogeneities were used many times to explain the temperature dependence of the barrier parameters Manuscript received June 20, 2011; revised July 12, 2011, July 29, 2011 and August 9, 2011; accepted September 2, 2011. Date of publication October 14, 2011; date of current version November 23, 2011. The review of this paper was arranged by Editor H. Jaouen. The author is with the Department of Applied Physics, Indian School of Mines, Dhanbad-826004, India. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2011.2167977

[7]–[10]. The existence of tunneling (TN) current [11], [12], generation–recombination (GR) current [13]–[15], a combination of thermionic and recombination currents [16], [17], etc., could be also responsible for the temperature dependence of apparent barrier height and ideality factor. However, in the fundamental studies of Schottky diodes, the use of solid metals as rectifying contacts involves many difficulties [18]. A possible solution to overcome these difficulties is to interface metals that are liquid near room temperature (RT), such as Ga or Hg, with a semiconductor rather than a solid metal. The liquid metal should deform to the semiconductor surface closely. Additionally, the liquid metals such as Hg and Ga can be simply put on a confined area on the prepared semiconductor surfaces thereby alleviating the intricacies associated with conventional vacuum deposition techniques. Moreover, since the technique does not require any sophisticated technology, the time required for the interface formation gets radically abridged and would minimize the possibility of chemical and electronic changes that may take place on the semiconductor surface. This paper reports the forward electrical characteristics of Ga–pWSe2 Schottky diode over a wide temperature range by a current–voltage (I–V ) method for the first time. In the case of Schottky diodes, the extraction of device parameters by I–V measurements based on the TE model only at RT or at a few low temperatures may not give precise values. The analysis and interpretation with few experimental data can also lead to incorrect results even if more complex models are used. On the other hand, the characteristics measured in a wide temperature range will give much more experimental data, which allows the determination of the parameters of a Schottky structure with a higher degree of precision. In addition, the I–V investigations of the diodes on a wide temperature range will be also useful in studying the dominant conduction mechanisms in different temperature regions. The layered structure and chemical inertness of the basal plane of WSe2 semiconductor material makes it ideal for Schottky barrier fabrication and to investigate the fundamental aspects of MS interactions [19], [20]. Gallium is a metal having a melting point of 302.92 K, which is very close to RT. It has a low vapor pressure and possesses a variety of interesting characteristics, including polymorphism [21]–[23]. Solidification of Ga is ice type and has a tendency to supercool below its freezing point [24]. In addition, it supercools very easily so that once melted, it may remain liquid at RT for a

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considerable time. Unlike Hg, the work function of liquid Ga does not change with time and is easily available in a very pure form. All these suggest that liquid Ga is often more convenient to use in elemental studies. Furthermore, Ga–pWSe2 is reported to be a stable system to study the band bending aspects [18]. II. E XPERIMENT Schottky barrier diodes have been prepared using p-type WSe2 (pWSe2 ) (1000) crystals, grown by a direct vapor transport technique. The carrier concentration of the crystals was on the order of 1016 /cm3 (Lakeshore 7504 Hall effect technique). The grown crystals were washed in acetone to remove the adhesive contaminants, if any, and dried at 333 K. A fixed capillary arrangement having an area of 4.81 × 10−2 cm2 was made on top of the WSe2 surface. Through the capillary, liquid gallium metal (Chittichem, 99.99%) was poured using a disposable syringe so that Ga directly comes into touch with the WSe2 surface thereby forming the Schottky contact. Conductive silver paste (Eltec-1228C) was brushed on the other side of the crystal for ohmic contact. In order to get a comprehensive idea on the influence of surface inhomogeneities on the terminal characteristics, one more type of sample was prepared with Ga on a cleaved WSe2 surface. The current–voltage–temperature (I–V –T ) data were acquired in the 140 K–300 K temperature range using a Keithley 2400 source measurement unit attached with a Lakeshore model 340 temperature controller (±0.1 K) and CCR 75014 cryostat. III. R ESULTS AND D ISCUSSION From the TE theory, for applied voltages V ≥ 3 kT/q, the I–V expression of a Schottky diode is given as [1], [2]     q(V − IRs ) I = I0 exp −1 (1) nkT with

  qφb0 . I0 = AA∗ T 2 exp − kT

(2)

Here, I0 is the reverse saturation current, Rs is the series resistance, n is the ideality factor, φb0 is the zero-bias barrier height, A is the contact area of the device, A∗ is the effective Richardson constant, q is the electronic charge, k is Boltzmann’s constant, and T is the absolute temperature. Generally, in practical Schottky diodes, the neutral region of the semiconductor between the depletion region and back ohmic contact offers series resistance Rs . Hence, external applied bias V divides up in to a voltage drop Vc across the depletion layer of the Schottky contact and an IRs drop at the series resistance of the diode. This amounts to a reduction of the voltage across the barrier region from that actually applied to the terminals of the diode such that Vc = V − IRs . This is accounted for by replacing V by V − IRs in (1). The semilogarithmic I–V characteristics of the Ga–pWSe2 Schottky diodes in the temperature range of 140 K–300 K and their best fit are shown in Fig. 1. The curve fit is done by Sigma

Fig. 1. Experimental and best fit I–V curves of the prepared Ga–pWSe2 Schottky diodes at different temperatures.

Plot 5.0 software based on (l) using I0 , n, and Rs as fitting parameters. They match the experimental data quite well at high temperature. However, at low temperatures, particularly below 200 K, each curve consists of two regions and the fit matches the experimental data well in the large bias region only. This characteristic is more prominent for the cleaved diode. The φb0 values are determined by the following equation:   AA∗ T 2 kT ln φb0 = . (3) q I0 Here, it is assumed that A∗ is equal to the known value of 27.6 A/cm2 /K2 for WSe2 [25] at any temperature. The barrier height, which decreases with decreasing temperature, obtained from (3) is called apparent or zero-bias barrier height. However, the barrier height obtained under flatband condition is called the flatband barrier height and is considered to be the real fundamental quantity. Under the flatband condition, the electric field is zero in the semiconductor, which is not the case for zerobias barrier height. This eliminates the effect of image force lowering that would affect the I–V characteristics and removes the influence of lateral inhomogeneity [10], [18]. Flatband barrier heights φbf were calculated by the following equation [26]:   NV kT ln (4) φbf = nφb0 − (n − 1) q NA where NV is the effective density of states in the valence band, and NA is the carrier concentration of the semiconductor used, which are on the order of 1018 /cm3 and 1016 /cm3 , respectively, in the present case. The values of φb0 , φbf , and n are plotted as functions of temperature in Fig. 2. At RT, the φb0 value obtained is 0.63 eV

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Fig. 4. Richardson plot of Ga–pWSe2 Schottky diodes.

the linear region, the Richardson constants obtained are 12.4 and 32.3 A/cm2 /K2 for the uncleaved and cleaved diodes, respectively. From the slope of this line, the activation energy values Ea (φb0 ) obtained are 0.05 and 0.12 eV for these diodes, respectively, which are quite low. A. Gaussian Barrier Height Distribution

Fig. 2. Zero-bias barrier height, flatband barrier height, and ideality factor of Ga–pWSe2 Schottky diodes at different temperatures.

Fig. 3. Series resistance of Ga–pWSe2 Schottky diodes at different temperatures.

with an n of 3.19 for the uncleaved diode. Meanwhile, for the cleaved one, these values are 0.60 eV and 1.74, respectively. On the other hand, as the temperature decreases, the SBH values decrease and n increases. The n values in both cases are high, particularly for the uncleaved sample. Flatband barrier height φbf is constant for the cleaved diode. In the case of the uncleaved one, it appears at first glance to be nearly constant up to 200 K from RT. Below this temperature, it is very interesting to note an almost step-like reduction in the flatband barrier height. Moreover, as usual, the flatband barrier height φbf in both cases is always larger than zero-bias barrier height φb0 [2]. In Fig. 3, with decreasing temperature, the values of Rs slowly increase from RT and then rapidly below 200 K. Fig. 4 shows the conventional activation energy (Richardson) plot of ln(I0 /T 2 ) versus 1/T according to (2). This plot also shows significant deviation from linearity below 200 K. Considering

The large diode quality factor indicates a strong deviation from pure TE and a potentially large error in the barrier height. In addition, the low-temperature anomalies in the Richardson plot are also indicative of an imprecise estimation of barrier height [27], [28]. High n values have been previously reported for low-temperature I–V measurements of MS junctions [27], [29], [30]. In such cases, the experimentally measured φb0 at low temperatures ( 300 K) systematically misapprehended the φb0 value at 300 K. Werner and Guttler [27] have proposed a model for correction of the experimentally measured values of φb0 , which assumes a Gaussian barrier height distribution. Here, the implicit assumption is that there exist a number of parallel diodes of different SBHs (low and high) on the same surface contributing to the current independently. In such situation, the Schottky contact area with mean barrier height φb and standard deviation σ0 yields the following expression [27], [31]–[33]: φap = φb0 −

qσ02 2kT

(5)

an expression already used by Song et al. [34]. The corresponding variation of the ideality factor with temperature in the Gaussian model is   1 qρ3 . (6) − 1 = −ρ2 + nap 2kT Here, φap is the apparent (experimental) barrier height, nap is the apparent (experimental) ideality factor, φb0 is the mean barrier height under zero-bias condition, and σ0 is the standard deviation. ρ2 and ρ3 are the voltage deformation on the barrier height distribution. The plots φap versus q/2kT and (1/nap − 1) versus q/2kT together are shown in Fig. 5. These plots are important since they directly give φb0 and σ0 values, which are essential to fit the theoretical solid lines to the experimental values of barrier height and ideality factor as a function of temperature.

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Fig. 7. Experimental and best fit forward I–V curves of Ga–pWSe2 Schottky diodes at 180 K, 160 K, and 140 K temperatures. Fig. 5. φap and (1/nap − 1) versus q/2kT plot of Ga–pWSe2 Schottky diodes.

their own contributions to the total current transport at the interface [2]. However, the expression containing all the four terms aforementioned remarkably deviates from the experimental observations here. It is found that omission of the leakage current in the expression has obtained an excellent fit with the experimental data. It also shows the insignificance of the leakage current in the present case. Hence, a combined-effect model has been considered, consisting only of TE, TN, and GR, which is expressed as [2], [35]      q(V − IRS ) (V − IRS ) −1 I = I0 exp + I0TN exp nap kT E0      q(V −IRS ) −q(V −IRS ) + I0GR exp × 1−exp . 2kT kT

Fig. 6. Modified Richardson plot of Ga–pWSe2 Schottky diodes.

In order to have an explanation on the nonlinearity at low temperatures in the conventional activation energy plot (see Fig. 4), a modified Richardson plot has been considered by combining (2) and (5) as     2 2   qφb0 q σ0 I0 ∗∗ ) − − = ln(AA ln (7) T2 2k 2 T 2 kT where A∗∗ is the modified Richardson constant, which is given in Fig. 6. Figs. 5 and 6 also show bending below 200 K, albeit good linear fits are obtained in the high-temperature range. These inconsistencies, even after considering the inhomogeneous barrier height, could be a sign of the presence of conduction mechanisms other than TE. The misfit in the I–V curve at low temperatures (see Fig. 1) may also be an indication of other transport phenomena such as TN current through the barrier, the recombination current in the depletion region, the leakage current, etc. All these processes may have

(8) Here, I0TN is the TN saturation current, whereas I0GR is the GR saturation current. E0 is the TN parameter described elsewhere [1], [2]. All the other terms have their usual meaning. The best fit I–V curve for 180 K, 160 K, and 140 K with (8) is shown in Fig. 7. The various parameters extracted from the fit are given in Table II. The best fit data give an excellent fit with the measured values. This confirms the validity of TN and GR current transport mechanisms at low temperatures in the present case. The new values of I0 and nap were extracted from (8), and the φap values were recalculated for these temperatures. By replacing the existing points in Figs. 5 and 6 with these new values, a straight line over the whole temperature range was obtained. From the linear fit of the φap versus q/2kT plot (see Fig. 5), the values of φb0 and σ0 were determined as 0.85 and 0.145 eV, respectively, for the uncleaved diode. Their respective ρ2 and ρ3 values were obtained as 0.551 and −0.008 eV from the linear fit of the nap versus q/2kT plot (see Fig. 6). Similarly,

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TABLE I C OMPARATIVE TABLE OF VARIOUS PARAMETERS E XTRACTED FOR THE Ga–pWSe2 S CHOTTKY BARRIER D IODES

A∗∗ and φb0 were extracted as 38.6 Acm−2 K−2 and 0.85 eV, respectively, by the linear fit of the modified Richardson plot (see Fig. 7). In the same way, for cleaved diodes, the values of φb0 , σ0 , ρ2 , and ρ3 were obtained as 0.93, 0.132, 0.079, and −0.020 eV, respectively (see Fig. 5). From Fig. 6, the respective φb0 and A∗∗ values were extracted as 0.93 eV and 29.9 A/cm2 /K2 . The percentage value of inhomogeneity calculated for the uncleaved diode is 14.6%, whereas that for the cleaved one is 14.1%, which are rather high in both cases. The large difference between the flatband barrier height and the zero-bias barrier height may be due to these inhomogeneities at the interface, which cause large interface states, that would, in turn, affect the total electric field in the semiconductor and the zero-bias barrier height. All these results are given in Table I. In both cases, the Ea (φb0 (0)) values evaluated from the normal Richardson plot are very low, but those from the modified Richardson plot (φb0 ) are more realistic. For both diodes, the φb0 values obtained from the φap versus q/2kT plot match exactly with those from the modified Richardson plot. Rather than A∗ , the A∗∗ value has come in a closer agreement with the known value of 27.6 A/cm2 /K2 for WSe2 . Of these, the A∗∗ value of the cleaved diode has come more into proximity with the reported value. The percentage value of inhomogeneity is less for the cleaved diode compared with that for the uncleaved one, which is quite natural. This is again clear from the values of standard deviation, which show less value for the cleaved diode. By comparing the I–V curves and the parameters such as A∗∗ , φb0 , ρ2 , ρ3 , φap , nap , and the percentage of inhomogeneity, it can be said that the cleavage has improved the quality of the prepared diodes. The large values of ideality factor still after cleavage may be due to the existence of large terraces of nonreactive van der Waals planes in the form of steps, which were revealed from the optical micrographs (not shown). Now, the theoretical curve of φap and nap , according to (5) and (6), using their respective φb0 , σ0 ρ2 , and ρ3 values were plotted against T along with the experimental data in the whole temperature range. They are shown in Fig. 8. The new values of φap and nap [by (8)] were chosen for temperatures below 200 K. It is shown that the theoretical curve closely pursues the experimental data. A typical I–V characteristic at 180 K for the cleaved diode is depicted in Fig. 9. Here, the contributions from TE, GR, and TN are compared with the total current. It is evident from the graph that all the three mechanisms are bias dependent. This is very large for GR than TN. TE has the smallest variation with current. Below 0.22 V, the contributions from both GR and TN are negligible and the total current is mostly from TE

Fig. 8. Barrier height and ideality factor of Ga–pWSe2 Schottky diodes based on (5) and (6) (filled data points for cleaved and unfilled data points for uncleaved diodes).

Fig. 9. Typical I–V curve depicting various conduction mechanisms (cleaved Ga–pWSe2 diode at 180 K).

only. However, due to the sharp increase in both GR and TN, the contribution from these mechanisms becomes quite appreciable from about 0.22 V. The increase is faster for TN, and the current due to TN becomes equal to that of GR at about 0.37 V. In Table II, it is shown that the values of I0TN and E0 increase, whereas the I0GR value decreases with decreasing temperature for the cleaved diodes. In the case of the uncleaved diode, the I0TN and E0 values are maximum at 160 K and are minimum at 180 K, whereas for I0GR , the value is maximum at 160 K and minimum at 140 K.

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TABLE II VALUES OF THE D IODE PARAMETERS E XTRACTED F ROM (8)

IV. C ONCLUSION

R EFERENCES

Here, a wide span of temperature-dependent forward I–V characteristics of Ga–pWSe2 Schottky barrier diodes prepared on both cleaved and uncleaved WSe2 surfaces were reported for the first time. The crystals of WSe2 were grown by a direct vapor transport technique. The forward I–V characteristics were investigated on the basis of the TE theory. The estimated zero-bias barrier height, the ideality factor, and the Richardson plot were found to exhibit two different trends over the entire temperature range of 140 K–300 K. The conduction properties from 200 K–300 K were successfully explained on the basis of the TE model with the barrier height inhomogeneity concept. The low-temperature anomalies were analyzed and interpreted with a combined-effect model of TE, GR, and TN mechanisms across the interface. The values of the Richardson constant A∗∗ from the modified Richardson plot are found to be 38.6 and 29.9 A/cm2 /K2 for the uncleaved and cleaved diodes, respectively, which are quite close to the known value of 27.6 A/cm2 /K2 for WSe2 . The inhomogeneity percentage of the uncleaved Ga–pWSe2 diode is 14.6%, whereas that of the cleaved Ga–pWSe2 is 14.1%, which in both cases are rather high. This kind of highly inhomogeneous interface may be the possible reason for the large values of ideality factor. In Table I, the cleaved diodes show better characteristics compared to the uncleaved ones. The observed deviation of the flatband barrier height for the uncleaved diode below 200 K may be assumed due to some kind of phase/structural transitions that might have occurred at the interface. Such a hypothesis is quite reasonable since a liquid metal is used here. The result demands further investigation and is worthy of future studies on other liquid metals such as mercury. In addition, the uncleaved diode with more interface inhomogeneity shows a pronounced variation than that of the cleaved one with less interface inhomogeneity. Hence, it can be concluded that surface inhomogeneity could drastically influence the terminal characteristics of Ga–pWSe2 Schottky barrier diodes. More to the point, the variation of thermionic, GR, and TN current components are bias dependent also.

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ACKNOWLEDGMENT The author would like to thank Dr. K. J. Mathai and Dr. B. K. Antony for the fruitful discussions.

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Achamma John Mathai received the B.Sc. and M.Sc. degrees in physics from Mahatma Gandhi University, Kerala, India, in 1997 and 1999, respectively, and the M.Phil. and Ph.D. degrees from Sardar Patel University, Gujarat, India, in 2002 and 2008, respectively. Her research for the M.Phil. degree was on the synthesis and characterization of ferrite systems, whereas for the doctoral research, she was focused on the crystal growth of II–IV group compounds, fabrication of Schottky devices using these compounds, and their electrical characterization. She is currently a Research Scientist with the Department of Applied Physics, Indian School of Mines, Dhanbad, India, under the project funded by Department of Science and Technology, Government of India. Her current research interest is upon the interface modification and tuning of barrier heights in Schottky devices.