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Electronic transport of Au/(Ca1.9Pr0.1Co4Ox)/nSi structures analysed over a wide temperature range S. Alialy, A. Kaya, E. Marıl, Ş. Altındal & İ. Uslu To cite this article: S. Alialy, A. Kaya, E. Marıl, Ş. Altındal & İ. Uslu (2015) Electronic transport of Au/(Ca1.9Pr0.1Co4Ox)/n-Si structures analysed over a wide temperature range, Philosophical Magazine, 95:13, 1448-1461, DOI: 10.1080/14786435.2015.1033029 To link to this article: http://dx.doi.org/10.1080/14786435.2015.1033029
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Date: 23 January 2016, At: 08:32
Philosophical Magazine, 2015 Vol. 95, No. 13, 1448–1461, http://dx.doi.org/10.1080/14786435.2015.1033029
Electronic transport of Au/(Ca1.9Pr0.1Co4Ox)/n-Si structures analysed over a wide temperature range S. Alialya*, A. Kayab, E. Marıla, Ş. Altındala and İ. Usluc a
Faculty of Sciences, Department of Physics, Gazi University, Ankara, Turkey; bDepartment of Opticianry, Vocational School of Medical Sciences, TurgutÖzal University, Ankara, Turkey; c Department of Chemistry, Chemistry Education Department, Gazi University, Ankara, Turkey
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(Received 8 October 2014; accepted 10 March 2015) The barrier height (BH) of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure was evaluated in the temperature range of 120–360 K using current–voltage (I–V) measurements. The zero-bias BH (ΦBo) and ideality factor (n) values deduced from standard thermionic emission theory were found to be 0.35 eV and 6.30 at 120 K and 0.83 eV and 5.1 at 360 K, respectively. Because such changes in ΦBo were not in agreement with the negative temperature coefficient (α) of the Si band gap, effects of tunnelling and BH inhomogeneity were added to the analysis of junction current. With this modification, the value of ΦBef. was found to decrease with temperature at a rate of −2.4 × 10−4 eVK−1 in approximate agreement with the known α of the Si band gap. Attempts to model the inhomogeneous BH with a single Gaussian distribution were also successful, Bo ) of 0.997 eV and a standard deviation rendering a mean value of BH (U (σo) of 0.12 eV. Similar conclusions were drawn from additional analyses, employing the modified Richardson plots. Our results suggest that the analysis of electronic transport at this and possibly other MIS junctions should include both the effect of tunnelling and that of BH inhomogeneity. Keywords: (Ca1.9Pr0.1Co4Ox) interfacial layer; current-transport mechanisms; temperature dependent; Gaussian distribution (GD) of BHs
1. Introduction Metal–semiconductor (MS)-based Schottky barrier diodes (SBDs) are widely used in the optoelectronic and electronic industry. With the insertion of a thin interfacial layer between metal and semiconductor, referred to as metal–insulator/polymer–semiconductor (MIS or MPS) sandwich configuration, the junction characteristics typically remain largely those of intimate SBDs. In recent years, MIS structures have become more popular compared with MS-type SBDs because of their industrial applications. Although there are many studies both theoretical and experimental on these devices, their conduction mechanisms and the formation of barrier height (BH) at MIS interface have not been clarified yet [1–9]. At any specific, especially low-temperature and -voltage, interval several conduction mechanisms can be individually dominating or collectively operative. These mechanisms include thermionic emission (TE), thermionic
*Corresponding author. Email:
[email protected] © 2015 Taylor & Francis
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field emission (TFE), field emission (FE), generation–recombination (GR) and tunnelling via interface states or traps. The quality and performance of these devices are dependent on various parameters such as temperature, applied bias voltage or electric field, the surface process, interfacial layer native or deposited at MIS interface, the magnitude of doping concentration atoms (acceptor or donor), series and shunt resistances (Rs and Rsh ) of diode, interface traps (Dit), the formation of BH and its homogeneity [8–13]. The analysis of a device measured only at room temperature or over a narrow range of temperatures cannot yield detailed information on the conduction mechanism and the nature of BH at the M/S interface. These measurements, when carried out over a wide temperature range, better reveal various aspects on the conduction mechanism and the nature of BH [10–14]. Many previous studies have found increases in the BH and decreases in n with increasing temperature [4–8,10–16], in disagreement with the predictions of the standard TE theory of temperature-independent BH and ideality factor. In the last two decades, both the abnormal behaviour of the BH and the nonlinearity of the Richardson plot have been observed [17–22]. Explanation of the possible reason of such anomalies may be attributed to the quantum-mechanical tunnelling (QMT) including TFE and FE [18–21], image-force lowering [22], lateral distribution of BH in-homogeneities [20,23], a Gaussian distribution (GD) of the BH over the diode area [4,11]. A comparison of tunneling parameter (Eoo) with thermal energy (kT/q) determines whether thermionic emission (TE) or tunneling (TFE and FE) will be more effective near the very top of the energy barrier, i.e., whether to go over or go through the last few Eoo (or kT/q) of the BH. When Eoo > kT/q, tunnelling will be dominated because the Boltzmann distribution tail of TE drops off by a factor of exp{−1} every kT/q, which is much faster than the decrease rate of the tunnelling probability. As conclusion, we can say that tunnelling through the barrier will be dominated only for high doped semiconductors (ND or NA ≥ 1018 cm−3) and at low temperatures [1,8,11,24]. For low doped (ND or NA ≤ 1016 cm−3) semiconductors, potential “pinch off” frequently takes place leading to bias-dependent “saddle point” effective BH for any patch. In this case, the effective BH may be dependent on both voltage and temperature. In addition, when the diode has series resistance (Rs), and interfacial layer, the applied voltage (Va) on the diode will be shared by Rs, interfacial layer and depletion layer of the diode. In this study, the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure was fabricated and the possible current-transport mechanisms in this structure have been investigated in the wide temperature range of 120–360 K by using forward bias I–V measurements. Experimental results reveal an abnormal increase in the zero-bias BH (ΦBo) and decrease in n with increasing temperature. In order to adjust the BH, Io expression was modified, by the inclusion of both n and tunnelling parameters (αχ(0.5δ) in its expression. Thus, the value of the effective BH (ΦBef.) was obtained and its α value was found to be −4.73 × 10−4 eVK−1 and it was close to the α value of the Si band gap. In addition, we attempted to draw a ΦBo vs. q/2kT plot to obtain evidence of a GD of the BHs, and the Bo ) and standard deviation (σo) values were found from this mean value of the BH (U Bo and A* values were found plot to be 0.997 eV and 0.12 V, respectively. In this way, U −2 −2 to be 0.984 eV and 110.2 A cm K from the slope and intercept of the modified ln (Io/T2)−(q2σso2/2k2T2) vs. q/kT plot, respectively. The conduction mechanisms in this structure were successfully explained on the basis of a TE mechanism with a GD of the BHs.
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2. Experimental details The Au/(Ca1.9Pr0.1Co4Ox)/n-Si structures were fabricated on n-Si (phosphorus-doped) with 4.3 × 1018 cm−3 donor concentrations and ̴ 250 mm thickness. Before the fabrication process, wafer was ultrasonically cleaned in trichloroethylene and ethanol, etched in a sequence of CP4 (HNO3:HF:COOHC2H5:H2O = 3:1:2:2 weight ratio) solutions for about 30 s. After that, it was quenched in de-ionized water with 18 MΩ cm resistivity for a long time in an ultrasonic bath. Then it was etched in a sequence of H2SO4 and H2O2 20% HF, a solution of 6HNO3:1HF:35H2O, 20% HF. Finally, it was rinsed in de-ionized water. After the cleaning processes, immediately n-Si wafer was transferred into the deposition chamber and high-purity Au (99.999%) with 1500-Å thickness was thermally evaporated onto the whole back side of the n-Si wafer at about 10−6 Torr in the high-vacuum metal evaporation system. In order to perform low-resistivity ohmic back contact, wafer was annealed at about 500 °C in ambient nitrogen. After that (Ca1.9Pr0.1Co4Ox), layer was grown in front of the n-Si wafer as follows. Firstly, the 10% PVA solution was prepared with deionized water and heated at 80 °C for 3 h, and then cooled to room temperature. Then, the metal acetates and nitrate were dissolved into the ultrapure water and acetic acid and a solution was produced. Then, PVA (10% w/w) was added into this solution, so the solution which will be used the electro-spinning process was produced. Lastly, the wafer was pasted onto the metal collector, and then the solution of the PVA/metal compound was transferred onto the wafers in the form of nano-fibres for 10 min via a electro-spinning system which consisted of a direct-current high-voltage power supply. Thus, the nano-fibres were formed on the Si wafer. The distance between the wafer and the syringe (polymer hybrid solution) was adjusted to 15 cm and 17 kV was applied to the solution with 0.5 ml/h flow rate. Polyvinyl alcohol (PVA-Mw 85,000–124,000 g/mol) was used as polymeric precursor from Sigma-Aldrich. The surface morphology of nano-fibres was examined by SEM on samples sputtered with platinum and observed at an accelerating 10 kV. The SEM images for nano-fibres are shown in Figure 1 at 2 × 104 and 4 × 104 magnifications, respectively. As can be seen in Figure 1, nano-fibres have the beady, bendy, and linear structures. After growth in the (Ca1.9Pr0.1Co4Ox) interfacial layer, the high-purity Au dots with 1-mm diameter (7.85 × 10−3 cm−2) and ~1500-Å thickness were deposited on the interfacial layer in the same metal evaporation system. Thus, the fabrication processes of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structures were completed. For the forward and reverse bias I–V measurements, the samples were placed on the copper holder with the help of silver paste and the electrical contacts were also made to the upper electrodes using thin
Figure 1. SEM images of nanofibres which include the solution of metal acetates and PVA.
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silver-coated wires with silver paste. Both the forward and reverse bias I–V measurements of these structures were performed in the temperature range of 120–360 K using Keithley 2400 source meter. All measurements were performed in the Janis vpf-475 cryostat, which enabled us to make measurements in the temperature range of 77–450 K. The sample temperature was always monitored using Lake Shore model 321 auto-tuning temperature controllers with sensitivity better than ±0.1 K. The schematic diagram of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure is illustrated in Figure 2.
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3. Result and discussion For MS- or MIS-type SBDs, according to the TE theory, the relation between I and V (V ≥ 3kT/q) can be expressed as [1–3,24–31]: q qðV IR Þ s 2 1 (1) I ¼ AA T exp UBo exp kT nkT In Equation (1), the pre-factor of brackets is the reverse-bias saturation current (Io) and it can be extracted from the intercept of the linear part of the ln (I) vs. V plot at zero bias at each temperature. The other A, A*, T, ΦBo, n, k, and the term of IRs quantities are the rectifier contact area, the effective Richardson constant (112 A/cm2 K2 for n-Si), temperature in K, the zero-bias BH, ideality factor, Boltzmann constant, and the voltage drop on Rs, respectively. The value of n can also be extracted from the slope of the linear part of the ln (I) vs. V plot at each temperature as in the following relation: q n¼ kT
dV dðln IÞ
(2)
The other main parameter is ΦBo and it can be calculated by using the obtained experimental value of Io and the rectifier contact area of the diode (A) values as in the following relation: 2 kT AA T UBo ¼ ln (3) q I0
Figure 2. (colour online) Schematic diagram of the fabricated Au/Ca1.9Pr0.1Co4Ox/n-Si structure.
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Figure 3 shows the semi-logarithmic forward bias ln I–V plots of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure in the temperature range of 120–360 K. As shown in Figure 3, ln (I) vs. V plots have a straight line with different slopes in the intermediate bias range (0.1 ≤ V ≤ 0.42 V) at each temperature and the magnification of linear parts are also shown in the inset in Figure 3. On the other hand, these plots deviated from linearity at high bias voltages due to the effect of Rs and the interfacial (Ca1.9Pr0.1Co4Ox) layer. Since the voltage was applied across the diode, it will be shared by Rs, the interfacial layer and depletion layer. The effect of Rs at low forward biases, linear region, can be neglected. As can be seen from Figure 3, in the reverse bias region, there is a soft or non-saturation behaviour and it can be explained in terms of image force lowering of the BH and the interfacial layer at the M/S interface [24,25], although the rectification ratio (RR = ±IF/IR) is high especially at low temperatures. In addition, there are considerably high noises at low enough temperatures. The obtained Io, n, and ΦBo values of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure at each temperature are tabulated in Table 1. As can be seen in Table 1 and Figure 4, these parameters were a strong function of temperature especially at low temperatures. While the value of n decreases, ΦBo value increases with increasing temperature. The Io, n, and ΦBo values were found to be 2.0 × 10−11Å, 6.3, 0.35 eV at 120 K and 2.8 × 10−7Å, 5.1, and 0.83 eV at 360 K, respectively. The change in ΦBo with temperature is not in agreement with the negative temperature coefficient (α = ΔEg/ΔT = −4.73 × 10−4 eV) of the Si band gap (Eg). As seen in Figure 5 and Table 1, the change in n with inverse temperature (T−1) was found to change linearly as follows:
Figure 3. (colour online) Experimental forward and reverse bias I–V–T characteristics of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
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Table 1. Some obtained experimental parameters of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure at various temperatures. n
ΦBo (eV)
ΦBef. (eV)
nT (K)
2.00 × 10−11 3.11 × 10−10 3.00 × 10−9 1.30 × 10−8 5.00 × 10−8 8.70 × 10−8 2.20 × 10−7 2.80 × 10−7
6.30 5.82 5.57 5.39 5.27 5.22 5.14 5.10
0.35 0.44 0.52 0.60 0.68 0.71 0.79 0.83
0.787 0.796 0.776 0.779 0.757 0.747 0.732 0.749
756 932 1113 1294 1475 1566 1747 1836
0.90
6.40
0.80
6.20 6.00
0.70
Φ BO(eV)
y = 1.97E-03x + 1.23E-01 R² = 9.99E-01
0.60
5.80 5.60
0.50
5.40
0.40
5.20
0.30 100
150
200
250
300
350
5.00
T (K)
Figure 4. Temperature dependence of n and ΦBo of Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
6.50
Ideality factor n
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120 160 200 240 280 300 340 360
Ideality factor n
Io (A)
T (K)
6.00
y = 0.214x + 4.5028 R² = 0.9995
5.50
5.00
2
3
4
5
6
7
8
1000/T (K-1)
Figure 5. The plot of n vs. 1000/T for Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
9
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S. Alialy et al. nðT Þ ¼ no þ
To T
(4)
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The increase in n with decreasing temperature is known as To effect or To anomaly. The no and To values are constants and they were found from the intercept and slope of Figure 5 to be 4.5 and 214 K, respectively. It is clear that the FE and TFE mechanisms are ruled out in the whole temperature range (120–360 K) because the slope of ln (I) vs. V or nT is not constant in the whole measured temperature range. All these results show that the value of n and tunnelling factor (χ0.5δ) should also be included in the expression for Io as in the following relation [7,32]: qUBef : Io ¼ AA exp av1=2 d exp (5a) nkT Here, ΦBef. is the effective BH, δ is the thickness of the interfacial layer through which electrons move to tunnel, α = (4π/h)(2me*)0.5 is a constant that depends on the tunnelling effective mass of electron and Planck’s constant and χ is the mean tunnelling barrier presented by δ. It is well known that the thickness and the quality/homogeneity of the interfacial layer are very important for conduction mechanisms as well as temperature, the native of the BH between the metal and semiconductor, surface states or dislocations, series resistance and doping concentration atoms. The tunnelling probability across an insulator also depends on its thickness. On the other hand, tunnelling probability across the BH especially depends on the doping concentration atoms (N) and the depletion layer width (WD) also depends on the inverse of N (N−1). Tunnelling across the BH especially occurs at low temperatures. In this study, the thickness of interfacial layer (Ca1.9Pr0.1Co4Ox) was obtained (as 63 Å) from the interfacial layer capacitance (Ci = ε’εoA/δ) by assuming the value of dielectric constant as 3. On the other hand, the tunnelling probability was determined from the Figure 8 using Equation (5a). Here, the intersection point of the plot is equal to (lnðAA Þ ða v0:5 Þ) and its slope is equal to activation energy (Ea = ΦBo). In this calculation, the value of the effective Richardson constant (A*) was used its theoretical value as 112 A/cm2 K2. It is clear that the value of A* is also lower than the theoretical value of Richardson constant. The experimental results above reveal the deviation in Richardson plots due to the spatial inhomogeneous BHs. Thus, the value of (χ0.5δ) was found to be 21.90 from the linear part of the ln (Io/T2) vs. q/nkT plot (Figure 8). Thus, the modified value of the BH (=ΦBef.) can be expressed as [7,32,33]: 2 kT AA T ln UB ¼ nðT Þ ðkT =qÞ:ð av0:5 dÞ ¼ nðT Þ: UBo ðkT =qÞð av0:5 dÞ q Is (5b) After this modification, as can be seen in Table 1 and Figure 6, the modified value of ΦBef. decreases almost linearly with temperature as follows: UB ¼ UB ð0 KÞ þ a T
(6)
Here, ΦBo (0 K) is the BH at absolute temperature and α is the negative temperature coefficient of the BH and they are found to be 0.826 eV and −2.4 × 10−4 eVK−1, respectively. It is clear that this negative temperature coefficient of the BH (ΦBef.) is close to the negative temperature coefficient of the Si band gap (−4.73 × 10−4 eVK−1).
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1
0.9 y =-2.40x10-4x + 0.826 R² =0.91
ΦBo and ΦBef (eV)
0.8
0.7
0.6
0.5
y = 1.97x10-3x + 0.123
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R² =0.999
0.4
0.3 100
150
200
250
300
350
T (K)
Figure 6. Variation of ΦBo and ΦBef. in the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
The decrease in ΦBo and the increase in n with decreasing temperature are also evidence of a deviation from the standard TE theory, suggesting that the tunnelling current mechanisms such as TFE or FE possibly warrant consideration [17–19]. It is well known the TFE mechanism requires a change in the tunnelling current parameter Eo (=nkT/q) with temperature according to the following relation [17]: Eoo Eoo Eo h ND 1=2 ntun ¼ coth ; with Eoo ¼ (7) ¼ 4p me es kT kT kT Here, me* is the effective mass of electrons and εs is the permittivity of Si and the other quantities are of usual meaning. The Eoo is an important parameter in tunnelling and (kT/q)/Eoo is a measure of the relative importance of TE and tunnelling. Therefore, we attempted to draw the n(kT/q) vs. kT/q plot to obtain an evidence of the tunnelling effect and it was given in Figure 7. The value of Eoo was found as 18 meV from the intercept of this plot. Here, the value of Eoo can be compared with kT/q at low temperatures that correspond to FE. On the other hand, the carrier concentration of the doping donor atoms was calculated as 4.3 × 1018 cm−3 from the Si substrate resistivity (1 Ω cm) given by the supplier. The Eoo value was obtained as 11.32 meV from Equation (7) using me* = 0.98mo (mo = 9.1 × 10−31 kg), the permittivity of Si εs (=11.8 εo) and the permittivity of free space (8.85 × 10−12 F/m). It is clear that this experimental value of Eoo (=18 meV) is higher than the theoretical value of 11.32 meV. These results confirmed that the dominant conduction mechanism in Au/ (Ca1.9Pr0.1Co4Ox)/n-Si structure quite well obey the FE theory rather than the other
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kT/q and n.(kT/q) (eV)
0.16
y = 4.5125x + 0.0183 R² = 1
0.14 0.12 0.1 0.08 0.06
y=x R² = 1
0.04 0.02
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0 0.0075
0.0125
0.0175
0.0225
0.0275
0.0325
kT/q (eV)
Figure 7. Experimental and theoretical values of the tunnelling current parameters (nkT/q) vs. (kT/q) for the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
mechanisms. On the other hand, the high value of n for each temperature cannot be explained only in the base of TFE and FE mechanisms. Quantum mechanics tunnelling (FE and TFE) may be a predominant conduction mechanism only at low temperatures and high doping concentrations of the donor or acceptor atoms (ND, NA). For the studied semiconductor, the value of ND is 4 × 1018 cm−3 and it can be assumed high doping concentration, but degenerated case cannot occur for this values. In this case, the value of the Fermi energy level is 48.6 meV (EC–EF) at low temperatures. In other words, the value of the effective density of states in the conduction band (Nc = 2.8 × 1019 cm−3) is seven times higher than the value of ND. So, the situation is not degenerate, but due to the low value of WD, tunnelling across the BH may be dominated especially only at low temperatures. On the other hand, as can be seen in Table 1, the product of n and T or (nT) is not constant contrary to expectations for tunnelling across the barrier. In addition, as can be seen in Figure 4, the linear parts of the ln I vs. V plot is considerably different or not constant. On the other hand, substrate resistivity or series resistance of the structure is not effective in the low and intermediate bias voltages; it is effective at high enough bias voltages. Therefore, the effect of resistivity can be negligible in the linear bias region in the calculations. For the evaluation of the BH, one may also make use of the conventional Richardson plot, ln (Io/T2) vs. q/kT, of the saturation current that corresponds to the activation energy (Ea). Therefore, the pre-factor (Io) in Equation (1) can be rewritten as Io qUBo (8) ln ¼ ln ðAA Þ 2 T kT The Richardson plots ln (Io/T2) vs. q/kT and q/nkT plot of the Au/Ca1.9Pr0.1Co4Ox/n-Si structure are given in Figure 8. As can be seen from these figures, the ln (Io/T2) vs. q/kT plot shows a linear behaviour except at 120 K. However, the ln (Io/T2) vs. q/nkT plot gives a straight line. The Ea and A* values were found from the slope and intercept
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of the ln (Io/T2) vs. q/kT plot to be 0.172 eV and 9.87 × 10−8Å cm−2 K−2, respectively. The obtained Richardson constant values are quite small compared to the theoretical value of the Richardson constant of Au/(Ca1.9Pr0.1Co4Ox)/n-Si (A* = 112Å/cm2 K2). The obtained value of Ea is also very low for the forbidden band gap of n-Si. On the other hand, the ln (Io/T2) vs. q/nkT plot shows a linear behaviour in the whole temperature range and the Ea and A* values were found from the slope and intercept of this plot to be 0.77 eV and 3.43 × 10−8Å cm−2 K−2, respectively. It is obvious that the value of A* is also far lower than the theoretical value of Richardson constant (A* = 112Å/cm2 K2 for n-Si). The deviation in the Richardson plot (Figure 8) may be due to the potential fluctuations at the interface that consists of low and high barrier areas and spatial in-homogeneities of the BHs [5,20,27–33]. In addition, the low value of A* obtained from Figure 8 may be affected by the lateral inhomogeneity of the BH and the fact that it is different from the theoretical value may be connected to the value of the real effective mass that is different from the calculated one [28]. Thus, the increase in n and the decrease in ΦBo with decreasing temperature can be also explained by the lateral distribution of the BH and it has a GD of the BH values over the rectifier contact area Bo ) and standard deviation (σso) [5,10,13,16,28,32–34]. According with the mean BH (U to this theory, the GD of the apparent or zero-BH (Φap) and the apparent ideality factor (n = nap) with temperature can be expressed by the following relations [3,22,29–33]: 2 Bo rso Uap ¼ U 2kT
(9)
and 1 qq 1 ¼ q1 ðT Þ ¼ q2 3 nap ðT Þ 2kT
(10)
-25 -26 y =-0.1715x -20.978 R² = 0.9516
-27
Ln (Io/T2) (A/K2)
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-32 -33 -34
0
20
40
60
80
100
q/kT vs q/nkT (eV-1)
Figure 8. Richardson plots of ln (Io/T2) vs. q/kT and q/nkT of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure at various temperatures.
S. Alialy et al.
Here ρ1, ρ2 and ρ3 are the voltage deformation coefficients, which may depend on tem Bo perature, and they quantify the voltage deformation of the BH distribution, while U Bo , and σso represent the mean BH and σso at zero bias, respectively. The values of U σso and voltage coefficients ρ2, ρ3 should obey Equations (9) and (10), respectively. Both ΦBo and (n−1–1) vs. q/2kT plots are given in Figures 9 and 10, respectively. It is clear that both Figures 9 and 10 have a straight line in the whole temperature range. Bo and σso2 values were found from the intercept and slope of the ΦBo vs. q/2kT The U plot (Figure 9) to be 0.997 eV and 0.12 V, respectively. This low value of σso shows the Bo . It is clear existence of a homogeneous distribution of BHs or patches at around U that the BH obtained from the temperature dependent on the forward bias I–V data is always smaller than the average of the BH at low and moderate temperatures. The voltage coefficients of ρ2 and ρ3 values were also obtained from the intercept and slope of the (n−1–1) vs. q/2kT plot (Figure 10) as 0.786 V and 0.0012 V, respectively. Now the conventional Richardson plot can be modified by combining Equations (3) and (8) as Bo Io 1 qrso 2 qU ln (11) ¼ ln ðAA Þ 2 kT T2 kT The obtained modified Richardson plot using Equation (11) is given in Figure 11. As can be seen in this figure, the modified ln (Io/T2)-(q2σso2/2k2T2) vs. q/kT plot has a good Bo and A* values were linear behaviour in the whole temperature range. Thus, the U −2 −2 found to be 0.984 eV and 110.2Å cm K from the slope and intercept of this plot, Bo and A* values indicated that the conduction mechanism in the respectively. Both the U Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure can be successfully explained on the basis of a TE mechanism with a GD of the BHs. On the other hand, the high value of n at room temperature and even above the temperatures cannot be explained by TE, tunnelling, and interfacial layer thickness. It can be explained only on the basis of the GD of the BH at the M/S interface. According to GD, the carriers with low energy can be easily crossed through the patches or pinched off between the metal and semiconductor. In this case, the value of the current increases and it leads to the increase in the ideality factor. 1.00
0.80
ΦBo(eV)
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y =-0.0145x + 0.997 R² = 0.9192
0.60
0.40
0.20 10
15
20
25
30
35
40
45
q/kT (eV)-1
Figure 9. ΦBo vs. q/2kT plot for the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
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-0.8 -0.805 -0.81
1/n-1
-0.815
y =-0.0012x -0.7861 R² = 0.9982
-0.82 -0.825 -0.83 -0.835 -0.84 15
20
25
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q/kT (eV)-1
Figure 10. (1/n−1) vs. q/2kT plots for the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure. -20 -30
Ln (IO/T2)-(q2σ2/2k2T2) (A.K-2)
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Figure 11. Modified ln (Io/T2)−(q2σs2/2k2T2) vs. q/kT plot for the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
4. Conclusions The Au/n-Si (MS) structure with (Ca1.9Pr0.1Co4Ox) was fabricated and their possible conduction mechanisms have been investigated by using the forward bias I–V–T characteristics in the wide temperature range of 120–360 K. Experimental results show that the characteristic parameters of this structure were found to be a strong function of temperature. The ΦBo and n values were found to be 0.35 eV and 6.30 at 120 K and
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0.83 eV and 5.1 at 360 K, respectively. The change in ΦBo with temperature is not in agreement with the negative temperature coefficient (α) of the Si band gap. Therefore, in the calculation of the BH, the Io expression was modified, by the inclusion of both n and tunnelling parameters (αχ0.5δ) in its expression. After this modification, the value of ΦBef. decreases with increasing temperature at −2.4 × 10−4 eV K−1 which is closed to the α of the Si band gap (−4.73 × 10−4 eVK−1). In addition, we attempted to draw a Bo and σo values ΦBo vs. q/2kT plot to obtain evidence of a GD of the BHs, and the U were found from this plot to be 0.997 eV and 0.12 V, respectively. Subsequently, the Bo and A* values modified ln (Io/T2)−(q2σso2/2k2T2) vs. q/kT plot was drawn and the U −2 −2 were found to be 0.984 eV and 110.2Å cm K from the slope and intercept of this plot, respectively. All of these results confirmed that the deviation from the typical TE theory and the conduction mechanism in this sample can be successfully explained on the basis of a TE mechanism with SGD of the BHs. All of these experimental results confirmed that the main conduction mechanism in the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure can be successfully explained on the basis of a TE mechanism with SGD of the BHs. Disclosure statement No potential conflict of interest was reported by the authors.
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