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Philosophical Magazine
ISSN: 1478-6435 (Print) 1478-6443 (Online) Journal homepage: http://www.tandfonline.com/loi/tphm20
Electronic transport of Au/(Ca1.9Pr0.1Co4Ox)/n-Si structures analysed over a wide temperaturerange
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 transportof Au/(Ca1.9Pr0.1Co4Ox)/n-Si structures analysed over a wide temperature range, PhilosophicalMagazine, 95:13, 1448-1461, DOI: 10.1080/14786435.2015.1033029
To link to this article: http://dx.doi.org/10.1080/14786435.2015.1033029
Published online: 20 Apr 2015.
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Electronic transport of Au/(Ca1.9Pr0.1Co4Ox)/n-Si structures analysedover a wide temperature range
S. Alialya*, A. Kayab, E. Marıla, Ş. Altındala and İ. Usluc
aFaculty of Sciences, Department of Physics, Gazi University, Ankara, Turkey; bDepartment ofOpticianry, Vocational School of Medical Sciences, TurgutÖzal University, Ankara, Turkey;
cDepartment of Chemistry, Chemistry Education Department, Gazi University, Ankara, Turkey
(Received 8 October 2014; accepted 10 March 2015)
The barrier height (BH) of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure was evalu-ated in the temperature range of 120–360 K using current–voltage (I–V) mea-surements. The zero-bias BH (ΦBo) and ideality factor (n) values deducedfrom standard thermionic emission theory were found to be 0.35 eV and 6.30at 120 K and 0.83 eV and 5.1 at 360 K, respectively. Because such changes inΦBo were not in agreement with the negative temperature coefficient (α) ofthe Si band gap, effects of tunnelling and BH inhomogeneity were added tothe analysis of junction current. With this modification, the value of ΦBef. wasfound to decrease with temperature at a rate of −2.4 × 10−4 eVK−1 in approxi-mate agreement with the known α of the Si band gap. Attempts to model theinhomogeneous BH with a single Gaussian distribution were also successful,rendering a mean value of BH (�UBo) of 0.997 eV and a standard deviation(σo) of 0.12 eV. Similar conclusions were drawn from additional analyses,employing the modified Richardson plots. Our results suggest that the analysisof electronic transport at this and possibly other MIS junctions should includeboth 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 inthe optoelectronic and electronic industry. With the insertion of a thin interfacial layerbetween metal and semiconductor, referred to as metal–insulator/polymer–semiconduc-tor (MIS or MPS) sandwich configuration, the junction characteristics typically remainlargely those of intimate SBDs. In recent years, MIS structures have become morepopular 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 interfacehave not been clarified yet [1–9]. At any specific, especially low-temperature and-voltage, interval several conduction mechanisms can be individually dominating orcollectively operative. These mechanisms include thermionic emission (TE), thermionic
*Corresponding author. Email: [email protected]
© 2015 Taylor & Francis
Philosophical Magazine, 2015Vol. 95, No. 13, 1448–1461, http://dx.doi.org/10.1080/14786435.2015.1033029
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field emission (TFE), field emission (FE), generation–recombination (GR) andtunnelling via interface states or traps. The quality and performance of these devices aredependent on various parameters such as temperature, applied bias voltage or electricfield, the surface process, interfacial layer native or deposited at MIS interface, themagnitude of doping concentration atoms (acceptor or donor), series and shuntresistances (Rs and Rsh) of diode, interface traps (Dit), the formation of BH and itshomogeneity [8–13].
The analysis of a device measured only at room temperature or over a narrow rangeof temperatures cannot yield detailed information on the conduction mechanism and thenature of BH at the M/S interface. These measurements, when carried out over a widetemperature range, better reveal various aspects on the conduction mechanism and thenature of BH [10–14]. Many previous studies have found increases in the BH anddecreases in n with increasing temperature [4–8,10–16], in disagreement with the pre-dictions 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 ofthe Richardson plot have been observed [17–22]. Explanation of the possible reason ofsuch anomalies may be attributed to the quantum-mechanical tunnelling (QMT) includ-ing TFE and FE [18–21], image-force lowering [22], lateral distribution of BHin-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) determi-nes whether thermionic emission (TE) or tunneling (TFE and FE) will be more effectivenear the very top of the energy barrier, i.e., whether to go over or go through the lastfew Eoo (or kT/q) of the BH. When Eoo > kT/q, tunnelling will be dominated becausethe 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 dopedsemiconductors (ND or NA ≥ 1018 cm−3) and at low temperatures [1,8,11,24]. For lowdoped (ND or NA ≤ 1016 cm−3) semiconductors, potential “pinch off” frequently takesplace 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, whenthe diode has series resistance (Rs), and interfacial layer, the applied voltage (Va) on thediode 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 possiblecurrent-transport mechanisms in this structure have been investigated in the wide tem-perature range of 120–360 K by using forward bias I–V measurements. Experimentalresults reveal an abnormal increase in the zero-bias BH (ΦBo) and decrease in n withincreasing temperature. In order to adjust the BH, Io expression was modified, by theinclusion of both n and tunnelling parameters (αχ(0.5δ) in its expression. Thus, the valueof 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, weattempted to draw a ΦBo vs. q/2kT plot to obtain evidence of a GD of the BHs, and themean value of the BH (�UBo) and standard deviation (σo) values were found from thisplot to be 0.997 eV and 0.12 V, respectively. In this way, �UBo and A* values were foundto be 0.984 eV and 110.2 A cm−2 K−2 from the slope and intercept of the modified ln(Io/T
2)−(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 theBHs.
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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 fabrica-tion process, wafer was ultrasonically cleaned in trichloroethylene and ethanol, etchedin a sequence of CP4 (HNO3:HF:COOHC2H5:H2O = 3:1:2:2 weight ratio) solutions forabout 30 s. After that, it was quenched in de-ionized water with 18 MΩ cm resistivityfor a long time in an ultrasonic bath. Then it was etched in a sequence of H2SO4 andH2O2 20% HF, a solution of 6HNO3:1HF:35H2O, 20% HF. Finally, it was rinsed inde-ionized water. After the cleaning processes, immediately n-Si wafer was transferredinto the deposition chamber and high-purity Au (99.999%) with 1500-Å thickness wasthermally evaporated onto the whole back side of the n-Si wafer at about 10−6 Torr inthe high-vacuum metal evaporation system. In order to perform low-resistivity ohmicback 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 °Cfor 3 h, and then cooled to room temperature. Then, the metal acetates and nitrate weredissolved 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 theelectro-spinning process was produced. Lastly, the wafer was pasted onto the metal collec-tor, and then the solution of the PVA/metal compound was transferred onto the wafers inthe form of nano-fibres for 10 min via a electro-spinning system which consisted of adirect-current high-voltage power supply. Thus, the nano-fibres were formed on the Siwafer. The distance between the wafer and the syringe (polymer hybrid solution) wasadjusted 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 precursorfrom Sigma-Aldrich. The surface morphology of nano-fibres was examined by SEM onsamples sputtered with platinum and observed at an accelerating 10 kV. The SEM imagesfor 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 with1-mm diameter (7.85 × 10−3 cm−2) and ~1500-Å thickness were deposited on theinterfacial layer in the same metal evaporation system. Thus, the fabrication processesof the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structures were completed. For the forward and reversebias I–V measurements, the samples were placed on the copper holder with the help ofsilver 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 measure-ments of these structures were performed in the temperature range of 120–360 K usingKeithley 2400 source meter. All measurements were performed in the Janis vpf-475cryostat, which enabled us to make measurements in the temperature range of77–450 K. The sample temperature was always monitored using Lake Shore model 321auto-tuning temperature controllers with sensitivity better than ±0.1 K. The schematicdiagram of the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure is illustrated in Figure 2.
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]:
I ¼ AA�T 2 exp � q
kTUBo
� �exp
qðV � IRsÞnkT
� �� 1
� �(1)
In Equation (1), the pre-factor of brackets is the reverse-bias saturation current (Io) andit can be extracted from the intercept of the linear part of the ln (I) vs. V plot at zerobias at each temperature. The other A, A*, T, ΦBo, n, k, and the term of IRs quantitiesare 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 voltagedrop on Rs, respectively. The value of n can also be extracted from the slope of the lin-ear part of the ln (I) vs. V plot at each temperature as in the following relation:
n ¼ q
kT
dV
dðln IÞ� �
(2)
The other main parameter is ΦBo and it can be calculated by using the obtainedexperimental value of Io and the rectifier contact area of the diode (A) values as in thefollowing relation:
UBo ¼ kT
qln
AA�T2
I0
� �(3)
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/(Ca1.9Pr0.1-Co4Ox)/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 alsoshown in the inset in Figure 3. On the other hand, these plots deviated from linearity athigh 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 interfaciallayer and depletion layer. The effect of Rs at low forward biases, linear region, can beneglected.
As can be seen from Figure 3, in the reverse bias region, there is a soft or non-sat-uration behaviour and it can be explained in terms of image force lowering of the BHand 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 considerablyhigh noises at low enough temperatures. The obtained Io, n, and ΦBo values of theAu/(Ca1.9Pr0.1Co4Ox)/n-Si structure at each temperature are tabulated in Table 1. As canbe seen in Table 1 and Figure 4, these parameters were a strong function of temperatureespecially at low temperatures. While the value of n decreases, ΦBo value increaseswith 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. Thechange in ΦBo with temperature is not in agreement with the negative temperaturecoefficient (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 theAu/(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 atvarious temperatures.
T (K) Io (A) n ΦBo (eV) ΦBef. (eV) nT (K)
120 2.00 × 10−11 6.30 0.35 0.787 756160 3.11 × 10−10 5.82 0.44 0.796 932200 3.00 × 10−9 5.57 0.52 0.776 1113240 1.30 × 10−8 5.39 0.60 0.779 1294280 5.00 × 10−8 5.27 0.68 0.757 1475300 8.70 × 10−8 5.22 0.71 0.747 1566340 2.20 × 10−7 5.14 0.79 0.732 1747360 2.80 × 10−7 5.10 0.83 0.749 1836
y = 1.97E-03x + 1.23E-01R² = 9.99E-01
5.00
5.20
5.40
5.60
5.80
6.00
6.20
6.40
0.30
0.40
0.50
0.60
0.70
0.80
0.90
100 150 200 250 300 350Id
ealit
y fa
ctor
nT (K)
BO(e
V)
Φ
Figure 4. Temperature dependence of n and ΦBo of Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
y = 0.214x + 4.5028R² = 0.9995
5.00
5.50
6.00
6.50
2 3 4 5 6 7 8 9
Idea
lity
fact
or n
1000/T (K-1)
Figure 5. The plot of n vs. 1000/T for Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
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nðTÞ ¼ no þ ToT
(4)
The increase in n with decreasing temperature is known as To effect or To anomaly. Theno and To values are constants and they were found from the intercept and slope ofFigure 5 to be 4.5 and 214 K, respectively. It is clear that the FE and TFE mechanismsare 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 resultsshow that the value of n and tunnelling factor (χ0.5δ) should also be included in theexpression for Io as in the following relation [7,32]:
Io ¼ AA� exp �av1=2d� �
exp � qUBef :
nkT
� �(5a)
Here, ΦBef. is the effective BH, δ is the thickness of the interfacial layer through whichelectrons move to tunnel, α = (4π/h)(2me
*)0.5 is a constant that depends on the tun-nelling effective mass of electron and Planck’s constant and χ is the mean tunnellingbarrier presented by δ. It is well known that the thickness and the quality/homogeneityof the interfacial layer are very important for conduction mechanisms as well as tem-perature, the native of the BH between the metal and semiconductor, surface states ordislocations, series resistance and doping concentration atoms. The tunnelling probabil-ity across an insulator also depends on its thickness. On the other hand, tunnellingprobability 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). Tunnellingacross the BH especially occurs at low temperatures. In this study, the thickness ofinterfacial layer (Ca1.9Pr0.1Co4Ox) was obtained (as 63 Å) from the interfacial layercapacitance (Ci = ε’εoA/δ) by assuming the value of dielectric constant as 3. On theother 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 v0:5Þ) and its slopeis equal to activation energy (Ea = ΦBo). In this calculation, the value of the effectiveRichardson constant (A*) was used its theoretical value as 112 A/cm2 K2. It is clear thatthe value of A* is also lower than the theoretical value of Richardson constant. Theexperimental results above reveal the deviation in Richardson plots due to the spatialinhomogeneous BHs. Thus, the value of (χ0.5δ) was found to be 21.90 from the linearpart of the ln (Io/T
2) vs. q/nkT plot (Figure 8). Thus, the modified value of the BH(=ΦBef.) can be expressed as [7,32,33]:
UB ¼ nðTÞ kT
qln
AA�T2
Is
� �� ðkT=qÞ:ð� av0:5 dÞ
� �¼ nðTÞ: UBo � ðkT=qÞð av0:5 dÞ�
(5b)
After this modification, as can be seen in Table 1 and Figure 6, the modified value ofΦBef. decreases almost linearly with temperature as follows:
UB ¼ UBð0 KÞ þ a T (6)
Here, ΦBo (0 K) is the BH at absolute temperature and α is the negative temperaturecoefficient 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.) isclose to the negative temperature coefficient of the Si band gap (−4.73 × 10−4 eVK−1).
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The decrease in ΦBo and the increase in n with decreasing temperature are also evi-dence of a deviation from the standard TE theory, suggesting that the tunnelling currentmechanisms such as TFE or FE possibly warrant consideration [17–19]. It is wellknown the TFE mechanism requires a change in the tunnelling current parameter Eo
(=nkT/q) with temperature according to the following relation [17]:
ntun ¼ Eoo
kTcoth
Eoo
kT
� �¼ Eo
kT; with Eoo ¼ h
4pND
m�ees
� �1=2
(7)
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, weattempted to draw the n(kT/q) vs. kT/q plot to obtain an evidence of the tunnellingeffect and it was given in Figure 7. The value of Eoo was found as 18 meV from theintercept of this plot. Here, the value of Eoo can be compared with kT/q at low tempera-tures that correspond to FE. On the other hand, the carrier concentration of the dopingdonor atoms was calculated as 4.3 × 1018 cm−3 from the Si substrate resistivity(1Ω cm) given by the supplier. The Eoo value was obtained as 11.32 meV fromEquation (7) using me
* = 0.98mo (mo = 9.1 × 10−31 kg), the permittivity of Siεs (=11.8 εo) and the permittivity of free space (8.85 × 10−12 F/m). It is clear that thisexperimental 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
y =-2.40x10-4x + 0.826 R² =0.91
y = 1.97x10-3x + 0.123R² =0.999
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
100 150 200 250 300 350T (K)
ΦB
o and
ΦB
ef (
eV)
Figure 6. Variation of ΦBo and ΦBef. in the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
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mechanisms. On the other hand, the high value of n for each temperature cannot beexplained only in the base of TFE and FE mechanisms.
Quantum mechanics tunnelling (FE and TFE) may be a predominant conductionmechanism only at low temperatures and high doping concentrations of the donor oracceptor atoms (ND, NA). For the studied semiconductor, the value of ND is4 × 1018 cm−3 and it can be assumed high doping concentration, but degenerated casecannot occur for this values. In this case, the value of the Fermi energy level is48.6 meV (EC–EF) at low temperatures. In other words, the value of the effective den-sity of states in the conduction band (Nc = 2.8 × 1019 cm−3) is seven times higher thanthe 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 theother hand, as can be seen in Table 1, the product of n and T or (nT) is not constantcontrary to expectations for tunnelling across the barrier. In addition, as can be seen inFigure 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 effec-tive in the low and intermediate bias voltages; it is effective at high enough bias volt-ages. Therefore, the effect of resistivity can be negligible in the linear bias region in thecalculations.
For the evaluation of the BH, one may also make use of the conventional Richard-son plot, ln (Io/T
2) vs. q/kT, of the saturation current that corresponds to the activationenergy (Ea). Therefore, the pre-factor (Io) in Equation (1) can be rewritten as
lnIoT2
� �¼ ln ðAA�Þ � qUBo
kT(8)
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
y = xR² = 1
y = 4.5125x + 0.0183R² = 1
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.0075 0.0125 0.0175 0.0225 0.0275 0.0325
kT/q
and
n.(
kT/q
) (eV
)
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.
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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 theoreticalvalue of the Richardson constant of Au/(Ca1.9Pr0.1Co4Ox)/n-Si (A
*= 112Å/cm2 K2). Theobtained value of Ea is also very low for the forbidden band gap of n-Si. On the otherhand, the ln (Io/T
2) vs. q/nkT plot shows a linear behaviour in the whole temperaturerange and the Ea and A* values were found from the slope and intercept of this plot tobe 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 fluctua-
tions at the interface that consists of low and high barrier areas and spatial in-homo-geneities of the BHs [5,20,27–33]. In addition, the low value of A* obtained fromFigure 8 may be affected by the lateral inhomogeneity of the BH and the fact that it isdifferent from the theoretical value may be connected to the value of the real effectivemass that is different from the calculated one [28]. Thus, the increase in n and thedecrease in ΦBo with decreasing temperature can be also explained by the lateral dis-tribution of the BH and it has a GD of the BH values over the rectifier contact areawith the mean BH (�UBo) and standard deviation (σso) [5,10,13,16,28,32–34]. Accordingto 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]:
Uap ¼ �UBo � r2so2kT
(9)
and
1
napðTÞ � 1 ¼ �q1ðTÞ ¼ �q2 �qq32kT
(10)
y =-0.1715x -20.978 R² = 0.9516
y =-0.7702x -22.035 R² = 0.9433
-34
-33
-32
-31
-30
-29
-28
-27
-26
-25
0 20 40 60 80 100
Ln
(Io/
T2 )
(A
/K2 )
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.
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Here ρ1, ρ2 and ρ3 are the voltage deformation coefficients, which may depend on tem-perature, and they quantify the voltage deformation of the BH distribution, while �UBo
and σso represent the mean BH and σso at zero bias, respectively. The values of �UBo,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 isclear that both Figures 9 and 10 have a straight line in the whole temperature range.The �UBo and σso
2 values were found from the intercept and slope of the ΦBo vs. q/2kTplot (Figure 9) to be 0.997 eV and 0.12 V, respectively. This low value of σso shows theexistence of a homogeneous distribution of BHs or patches at around �UBo. It is clearthat the BH obtained from the temperature dependent on the forward bias I–V data isalways smaller than the average of the BH at low and moderate temperatures. Thevoltage coefficients of ρ2 and ρ3 values were also obtained from the intercept and slopeof 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
lnIoT2
� �� 1
2
qrsokT
� �2¼ ln ðAA�Þ � q�UBo
kT(11)
The obtained modified Richardson plot using Equation (11) is given in Figure 11. Ascan be seen in this figure, the modified ln (Io/T
2)-(q2σso2/2k2T2) vs. q/kT plot has a good
linear behaviour in the whole temperature range. Thus, the �UBo and A* values werefound to be 0.984 eV and 110.2Å cm−2 K−2 from the slope and intercept of this plot,respectively. Both the �UBo and A* values indicated that the conduction mechanism in theAu/(Ca1.9Pr0.1Co4Ox)/n-Si structure can be successfully explained on the basis of a TEmechanism with a GD of the BHs. On the other hand, the high value of n at room tem-perature and even above the temperatures cannot be explained by TE, tunnelling, andinterfacial layer thickness. It can be explained only on the basis of the GD of the BH atthe M/S interface. According to GD, the carriers with low energy can be easily crossedthrough 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.
0.80
1.00
0.40
0.60
10 15 20 25 30 35 40 45 50 550.20
q/kT (eV)-1
ΦB
o(eV
)
y =-0.0145x + 0.997R² = 0.9192
Figure 9. ΦBo vs. q/2kT plot for the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
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4. Conclusions
The Au/n-Si (MS) structure with (Ca1.9Pr0.1Co4Ox) was fabricated and their possibleconduction mechanisms have been investigated by using the forward bias I–V–T charac-teristics in the wide temperature range of 120–360 K. Experimental results show thatthe characteristic parameters of this structure were found to be a strong function of tem-perature. The ΦBo and n values were found to be 0.35 eV and 6.30 at 120 K and
y =-0.0012x -0.7861 R² = 0.9982
-0.845
-0.84
-0.835
-0.83
-0.825
-0.82
-0.815
-0.81
-0.805
-0.8
10 15 20 25 30 35 40 45 50 55
1/n-
1
q/kT (eV)-1
Figure 10. (1/n−1) vs. q/2kT plots for the Au/(Ca1.9Pr0.1Co4Ox)/n-Si structure.
y =-0.984x -0.145 R² = 0.9
-100
-90
-80
-70
-60
-50
-40
-30
-20
20 30 40 50 60 70 80 90 100 110
Ln
(IO/T
2 )-(
q2 σ2 /2
k2 T2 )
(A.K
-2 )
q/kT (eV)-1
Figure 11. Modified ln (Io/T2)−(q2σs
2/2k2T2) vs. q/kT plot for the Au/(Ca1.9Pr0.1Co4Ox)/n-Sistructure.
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0.83 eV and 5.1 at 360 K, respectively. The change in ΦBo with temperature is not inagreement 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 nand tunnelling parameters (αχ0.5δ) in its expression. After this modification, the value ofΦBef. decreases with increasing temperature at −2.4 × 10−4 eV K−1 which is closed tothe α of the Si band gap (−4.73 × 10−4 eVK−1). In addition, we attempted to draw aΦBo vs. q/2kT plot to obtain evidence of a GD of the BHs, and the �UBo and σo valueswere found from this plot to be 0.997 eV and 0.12 V, respectively. Subsequently, themodified ln (Io/T
2)−(q2σso2/2k2T2) vs. q/kT plot was drawn and the �UBo and A* values
were found to be 0.984 eV and 110.2Å cm−2 K−2 from the slope and intercept of thisplot, respectively. All of these results confirmed that the deviation from the typical TEtheory and the conduction mechanism in this sample can be successfully explained onthe basis of a TE mechanism with SGD of the BHs. All of these experimental resultsconfirmed that the main conduction mechanism in the Au/(Ca1.9Pr0.1Co4Ox)/n-Si struc-ture can be successfully explained on the basis of a TE mechanism with SGD of theBHs.
Disclosure statement
No potential conflict of interest was reported by the authors.
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