Effect of DC bias on electrical conductivity of nanocrystalline α-CuSCN

Transparent semiconductors are very promising materials for many optoelectronic applications since they allow visible region of electromagnetic spectrum to pass through but absorb ultraviolet radiations. They are used as transparent electrodes in photovoltaic cells, flat panel displays, and light emitting diodes.¹ Among the various transparent materials CuSCN is the one of the promising hole transporting solid electrolyte used in extremely thin absorber² and dye-sensitized solar cells³ because of its energy gap and valence band edge position. Solid CuSCN exits in two polymorphic forms α and β. Both the phases of CuSCN in the absence of impurities behave as a p-type semiconductor with band gap ≈ 3.6 eV.⁴ The β phase having rhombohedral crystal structure has been prepared by various methods such as successive ionic layer adsorption and reaction (SILAR),⁵ electrodeposition³ and microcrystal growth technology.⁶ But the α-CuSCN (orthorhombic) has been prepared only by wet chemical CuO precursor route.⁷ Complex impedance spectroscopy is an appropriate and effective tool to characterize the electrical conductivity and dielectric behaviour of materials as a function of the temperature, bias, and frequency.⁸ The complex representation of the data obtained by frequency dispersion measurements offers a graphical way to read the values of resistance and capacitance corresponds to the grain and grain boundary in the equivalent circuits proposed by Bauerle.⁹ In general, one can expect three semicircular arcs in the impedance spectra in the high, intermediate and low frequency regions. High, intermediate and low frequency semicircular arcs are correlated to the contributions from grain, grain boundary regions and electrode effect respectively. Mostly, the last effect leads to the monotonous increase in the resistance, which could be eliminated carefully during the analysis of data. These parameters are experimentally measurable with the help of non-linear least-squares (NLLS) fitting of the respective Z* plot. The impedance results can be analyzed using four possible complex formalisms, i.e., impedance (Z^*), modulus (M^*), permittivity (ɛ^*), admittance (Y^*) and all these formalisms are interrelated, which is the key advantage of impedance measurements.¹⁰ One of the author Ramasamy has extensively used the temperature dependent impedance spectroscopy and studied grain boundary characteristics on electrical conductivity and dielectric behaviour of various nanocrystalline materials.^{8,11,12,14–16} The DC bias dependent measurements are appropriate to elucidate the grain boundary control of electrical properties.^17–21 This is also used to study the conduction mechanism and carrier concentration.²² In order to determine materials dielectric relaxation, phase transitions and activation energy of both the grain and grain boundary contribution to conduction processes, the measurements can be made as a function of temperature and analyzed. However, up to now there is no report on impedance spectroscopic analysis of α-CuSCN. This has motivated us to study the electrical properties of nanocrystalline α-CuSCN using impedance spectroscopy as a function of DC bias voltages with the sample prepared by wet chemical CuO precursor route as reported by Yang et al.⁷ 

Powder X-ray diffraction technique was used to confirm the formation of α-phase CuSCN nanocrystals. The measurements were done using Seifert X-ray powder diffractometer with Cu-k_α1 radiation (λ = 1.5406 Å) in a wide range of Bragg angles 2θ (10° to 60°) with a scanning rate of 0.02°/sec. The microstructure of α-CuSCN was analyzed by transmission electron microscope (TEM) using a Philips CM12 machine. Impedance spectroscopic measurements were performed at room temperature in the frequency range of 1MHz to 1Hz with the applied AC potential of 50 mV using Solartron 1260 impedance/gain phase analyzer to study the electrical properties under various DC bias voltages (0 V to -2.1 V). The nanocrystalline powder was pressed into cylindrical pellets of 6 mm diameter and 1 mm thickness with the pressure of 1 ton using a hydraulic press. Poly vinyl alcohol (PVA) solution (1 wt %) was used as a binder to reduce the brittleness of the pellet. It was burnt out by sintering the pellet under nitrogen gas flow at 150°C for 15 min.

The XRD pattern of precursor material CuO and the synthesized α-CuSCN are shown in figure 1. Both the powder X-ray diffraction data were fully indexed with the JCPDS cards using XRDA 3.1 software program.²³ The analysis confirms that, they are single phase (CuO is in monoclinic and α-CuSCN is in orthorhombic) within the detection limits of X-ray diffraction (XRD) machine in the scanned region 20° to 60°. Average crystallite size 85 nm was estimated from peak broadening of the most intense X-ray diffraction peak after eliminating instrumental and strain broadening. Transmission electron microscope image of the sample is shown in figure 2. Crystallites of α-CuSCN with in nanodimension with broad distribution were evident from the image. Agglomeration of nanocrystals is also clearly seen. In this wet chemical preparation method the polycrystalline CuO was converted in to the α-CuSCN in the addition of hydrochloric acid (pH = 3). Because of crystalline nature of starting solid precursor and the reaction was in acidic environment, the size distribution is not narrow.

Cole-Cole plot is the most widely used to communicate frequency response information of a system by complex impedance function Z*(ω) = Z^′(ω) – jZ^″(ω), where Z^′ (ω) and Z^″(ω) are the real and imaginary part of Z*(ω). The Z*(ω) can be plotted in a complex plane by either a rectangular or polar co-ordinate system. The two rectangular co-ordinate values are Z^′ (ω) = |Z|cosθ and Z^″(ω) = |Z| sinθ, where ω = 2πf, ω is the angular frequency and f is the applied frequency, the phase angle (θ) is tan^-1[Z^″(ω) / Z^′ (ω)] and |Z| = [Z^′ (ω)² + Z^″(ω) ²]^1/2. If Z^″(ω) data is plotted against Z^′ (ω) then it is called Cole-Cole plot. Figure 3(a) shows the room temperature Cole - Cole plots of complex impedance data obtained at various applied bias voltages. The high frequency magnification of -0.9 V plot is shown in figure 3(b) and it clearly shows the semicircle corresponds to the grain. The maximum of Z^″(ω) occurs when ω_maxRC= 1. R is the resistance of the material and it can be obtained from the intercept of the arc with Z^′(ω) axis at the lower frequency side. Therefore, knowing the value of resistance (R) and the frequency at which Z^″(ω) is a maximum then the value of capacitance (C) can be obtained. But for the case of nanocrystalline materials both the grain and grain boundary contributions are resolved into two semicircles in Cole-Cole plot. By fitting the respective semicircles with non-linear least square (NLLS) fitting routine, grain resistance, grain boundary resistance, grain capacitance, grain boundary capacitance and the angular frequency (ω_max) were obtained. In order to get the sample capacitance value, we have to multiply it with C_o since it is geometry dependent, where C_o = ɛ_oA/d, d is the pellet thickness; A is the cross sectional area of the pellet and ɛ_o is the permittivity of free space (8.854 x 10^-14 F/cm). The resistance data is also geometry dependant. Therefore the resistivity (ρ) was calculated using the formula, ρ = RA/l where, R, A and l are respectively the resistance, area of cross section (πd²/4) and the thickness of the pellet used. The DC conductivity (σ_dc) can be estimated using the following equation,

where the l is the thickness of pellet, d is the diameter of the pellet and R is the resistance. Using the values obtained (R_g = 0.13 MΩ, R_gb = 0.51 MΩ; C_g =147 pF, C_gb =2.6 nF) from the NLLS fitting, we have drawn an equivalent circuit diagram for impedance behaviour at -0.9 V measurement and it was shown as a inset in figure 3(b). Figure 4 shows the grain and grain boundary DC conductivity of nanocrystalline α-CuSCN. The value of DC conductivity due to grain boundary contribution is dependent on DC bias voltages but grain contribution is independent. In nanocrystalline materials, grain boundaries often have significant influence on the flow of electronic current. According to the grain boundary core-space charge layer model, a grain boundary consists of a grain boundary core and two adjacent space charge layers.²⁴ The grain boundaries of a material get modified depending upon the method of preparation due to increased interfacial atomic composition, dopants segregation and/or defect distribution. It is generally accepted that localized defect states of grain boundary can trap majority carriers forming depletion zone giving rise to a potential barrier. The potential barrier formation at the grain boundary is identical to a Schottky barrier. But it is often considered to be double (or back-to-back) Schottky barrier,²⁵ because the interface is defined as being between the two grains and the boundary region. A schematic picture of grain and grain boundaries by brick layer model and the existence of double Schottky barrier at the grain boundary with adjacent grains are illustrated in figure 5. At zero bias, the two space charge layers of a grain boundary are symmetrical but while applying bias voltage, one of the space charge layers is depressed, such a situation should cause strong variations within the space charge region the populations of the interface states are considerably changed and that led suppression of potential barrier height²⁶ at the higher biased condition. Such a situation should cause strong variations in the capacitance and hence the resistance of the depletion layers.¹⁸ Voltage drop across each grain boundary that led to the raise of grain boundary conductivity was observed in the present investigation. These results demonstrate the formation of back-to-back or double grain boundary Schottky barrier in nanocrystalline α-CuSCN.

It is known that BNN (Barton-Nakajima-Namikawa) relation connects the σ_dc and ω_max as follows,¹³ 

where H_R is the Haven ratio which reflects the degree of correlation between successive hopping for the charged defects,¹⁴ ɛ_o is the permittivity of vacuum, Δɛ = (ɛ_o - ɛ_∞) is the the permittivity change from the unrelaxed baseline (ɛ_∞) to the fully relaxed level (ɛ_o) and ω_max is the relaxation frequency. Importance of the BNN relation is that, this relates the DC and AC conductivities.²⁷ Our interest is to check whether the grain boundary of α-CuSCN obeys BNN relation or not. Plot between grain boundary conductivity σ_dc and ω_max is shown in figure 6, where the values of σ_dc and ω_max were obtained from the best fits from the NLLS fitting of Cole-Cole plot for all the applied voltages. The solid line is a linear fit of the data that gives slope (0.99) almost equals to unity, implying that the DC and AC conductions are closely correlated to each other and that they are of the same mechanism. The frequency dependent conductivity (σ_ac) for various bias voltages is shown in figure. 7. It was calculated by using the following relation,

where Z^′ (ω) is the real part of Z*(ω), The conductivity is found to be frequency independent in the low frequency region (grain boundary region) and above the characteristic onset frequency of the first plateau, the conductivity increases with the increase in frequency and then collapse into a single curve followed by a second plateau. From figure 7, the grain boundary and grain contribution in DC conductivity also have been extracted from Y-axis intercept of the first and second frequency plateau of the plot respectively. The low frequency plateau shows almost two order of magnitude of variation for varying the DC bias from 0.0 to -2.1 V. These results are identical with the DC conductivities obtained from the NLLS fitting of Cole-Cole plots. The dispersion of the second plateau clearly confirms that the grain conduction is voltage independent.

The electrical conductivity of nanocrystalline α-CuSCN have been studied as a function of frequency and DC bias voltages. Impedance behaviour of the sample was analyzed with Bauerle's equivalent circuit model using NLLS fitting procedure. Two order of magnitude variation of grain boundary conductivity was observed for varying the DC bias from 0 V to -2.1 V. The observed grain boundary behaviour was analyzed using grain boundary double Schottky barrier. The correlations between grain boundary DC and AC conductions were analyzed by using Barton-Nakajima-Namikawa (BNN) relation. The bias independent behaviour of grain and dependent grain boundary conductivity clearly explain the role with the grain boundary double Schottky barrier.