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SECTION I

Impedance spectroscopy is a technique for the electrical characterization of dielectrics by measuring the response of the material to an applied ac signal [1], [2]. According to this technique, the complex impedance of a test sample, $Z$, is expressed as $Z=Z^{,}+jZ^{\prime\prime}$ where $Z^{\prime}$ is the real part and $Z^{\prime\prime}$ is the imaginary part. The complex impedance spectroscopy allows the investigation of intrinsic material parameters such as the frequency dependence of real and imaginary parts of impedance as well as the internal structures of the device. This tool has been amply used in recent years for dye-sensitized solar cells (DSC) and organic solar cell [3] [4] [5], while there are only a few works to date on solid state devices, such as those based on nanocrystalline/amorphous Si [6] thin-film CdTe/CdS [7] and CdS/Cu(In, Ga)Se_{2} solar cells [8]. In this paper the impedance spectroscopy (IS) of ZnSe/CdTe thin film heterostructures is presented. For diminishing the lattice mismatch between the ZnSe and CdTe (∼14 %) an intrinsic layer at the interface was grown in order to form *p-i-n*-structures. The application of the ac technique of the complex impedance analysis eliminates pseudoeffects, if any, in the material electrical properties by separating out the real and imaginary parts of the material electrical properties. A Cole-Cole plot, an equivalent electrical circuit, the activation energy $\Delta{\rm E}_{\cal T}$ of the relaxation process and the bulk resistance and its activation energy is calculated and interpreted.

SECTION II

Two different types of ZnSe/CdTe heterostructures were grown with CdS and ZnTe and without interlayer at the interface by close spaced sublimation method (CSS). ZnSe thin films were obtained from specially grown ZnSe crystals doped with iodine by long term-high-temperature annealing in Zn melt. The ZnSe layers were deposited at ${\rm T}_{\rm s}\ =\ 450^{\rm o}{\rm C}$ and ${\rm T}_{\rm ev}\ =$ $900^{\rm o}{\rm C}$. ZnSe thin films obtained from such source of evaporation have conductivity $\sim \ 10^{2}$ $(\Omega\cdot{\rm cm})^{-1}$ and electron concentration $2\cdot10^{17} cm^{-3}$ at room temperature. The ZnTe and CdS layers are about 200 nm thick. The optimal growth conditions for CdS were ${\rm T}_{\rm s}=340^{\rm o}{\rm C}$ substrate temperature and ${\rm T}_{\rm ev}=\!620^{\rm o}{\rm C}$ source temperature. CdTe thin films were grown at ${\rm T}_{\rm s}=\!310^{\rm o}{\rm C}$ substrate temperature and ${\rm T}_{\rm ev}\!=\!620^{\rm o}{\rm C}$ source temperature. The ${\rm CdC}1_{2}$ chemical treatment and annealing in air at 420°C was applied. All cells were completed with a Ni contact thermally deposited in vacuum. The impedance measurements were carried out on a Wayne Kerr 6500B impedance analyzer, in the frequency range from 10 Hz to 10 MHz. Since the typical p-i-n diode is a nonlinear device, the amplitude of the applied signal should be less than thermal voltage $({\rm V}_{\rm T}\ \approx\ 26{\rm mV}\ {\rm at}\ 22\ ^{o}\ {\rm C})$. The ac signal of amplitude 10 mV was selected to ensure that the response of the system is linear piecewise to a good approximation.

SECTION III

The impedance spectrum of a circuit with resistor $({\rm R}_{\rm p})$ and capacitance in parallel is a semicircle in the fourth quadrant about the real axis touching the origin, with a radius of R/2 [1]. If the semicircle is away from the origin, it indicates the presence of series resistance. Measurements of the impedance spectra for the ZnSe/CdTe samples at ${\rm T}\!=\!300\ \ \ \ {\rm K}$ show a deviation from the perfect semicircle. The investigation of the J-V and C-V characteristics of ZnSe/CdTe and ZnSe/CdS/CdTe thin film heterostructures show the variation of shunt resistance and capacitance of herterojunctions, therefore the deviation from the perfect semicircle observed in the above named thin film heterosrtuctures may be attributed to these parameters. The impedance spectra for the ZnSe/CdTe samples should be modeled from more complicated equivalent circuits and require further investigations for interpretation. The frequency-temperature dependence of impedance for ZnSe/ZnTe/CdTe was analyzed. Fig. 1 shows the frequency dependent (a) real $({\rm Re}({\rm Z}))$ and (b) imaginary $(\rm Im({\rm Z}))$ parts of the complex impedance of ZnSe/ZnTe/CdTe heterostructure at different temperatures. It shows that $\rm Re(Z)$ and $\rm Im\!(Z)$ depend strongly on the temperature at frequencies between 20 Hz and 100 kHz, whereas at higher frequencies $\rm Re(Z)$ and $\rm Im\!(Z)$ are almost temperature independent. The peak frequency, ${\rm v}_{{\rm p}}$, of the $\rm Im(Z)$ shifts to the higher frequencies with increasing temperature. Cole-Cole plot at different temperatures is shown in Fig. 2.

In this plot the implicit variable is the frequency that increases from right to left. The plot shows a single semicircle at all temperatures and the size of the semicircle decreases abruptly with increasing temperature. This indicates that the device behavior can be modeled by using an RC circuit in combination with a series resistance $R_{s}$. The equivalent circuit of the device is shown in Fig. 3. At low frequencies, impedance of the capacitance $C_{b}$ is too high and the circuit response is mainly due to the resistances $R_{s}$ and $R_{p}$. So, the impedance at low frequencies is given by $Z(0)=R_{s}+R_{p}$. It is generally assumed that the ${\rm R}_{\rm P}{\rm C}_{\rm b}$ network simulates the response from the interface of the junction region and series resistance ${\rm R}_{{\rm s}}$ represents all ohmic contributions due to the device bulk and the ohmic contacts. The real and the imaginary components of this simple equivalent circuit (see Fig. 1) are as follows [2]; TeX Source$$\eqalignno{{\rm Re} Z=& R_{s}+{R_{p}\over 1+\omega^{2}R_{p}^{2}C_{b}^{2}}&\hbox{(1)}\cr {\rm Im} Z=&{\omega R_{p}C_{b}\over \omega^{2}R_{p}^{2}C_{b}^{2}}&\hbox{(2)}}$$

The equivalent capacitive effect $C_{h}\ =\ C_{\cal T}+C_{d}$ of this $R_{p}C_{b}$ network could possibly be assumed to be raised due to the gradient of charge density inside the device, $C_{d}$ (diffusion capacitance) and the space charge capacitance, ${\rm C}_{{\rm T}}$ (transition capacitance).

The equivalent parallel resistance, ${\rm R}_{\rm p};\ {\rm R}_{\rm d}\ \Vert$ ${\rm R}_{\rm T}$ could then be caused by the bulk resistance of the space charge region, ${\rm R}_{\rm d}$ and the resistance due to recombination of free carriers in the space charge region, ${\rm R}_{\rm T}$. The typical value of the equivalent capacitance ${\rm C}_{\rm T}\quad +{\rm C}_{\rm d}$ at a given temperature is first roughly estimated by using the value of frequency $v$ at maximum of ImZ (Fig. 2) *i. e*.,
TeX Source$$({\rm Im} Z)_{\rm max}\ ={1\over 2\pi v(C_{d}+C_{T})}\eqno{\hbox{(3)}}$$

The rough values of ${\rm R}_{\rm s}$ and ${\rm R}_{\rm s}\ +\ {\rm R}_{\rm p}$ are estimated from the low and high frequency intercepts of the semicircular variations on the ${\rm Re}\ \ {\rm Z}$ axis of complex impedance plots. The peak frequency of the semicircle satisfies the relation $\omega_{\rm p}\cdot\tau=\ 1$, where $\tau$ is the dielectric relaxation time.

To understand the temperature dependent natures of the equivalent circuit parameters, both $R_{d}\Vert {\rm R}_{\rm T}$ and $C_{T}\ +C_{d}$ values are plotted against temperature as shown in Fig. 4.

It is observed that the $R_{\rm p}$ value increases while the $C_{\rm b}$ value decreases with the increase of temperature. The dielectric relaxation time decreases with the increase of the temperature as shown in Fig. 5. This behavior can be understood as follows: as the temperature is increased, a large number of charge carriers are injected into the device resulting in a decrease in the dielectric relaxation time and hence the parallel resistance $R_{\rm p}$ of the device increases. The temperature dependence of relaxation time can be expressed as TeX Source$$\tau(T)=\tau_{o}\exp{\Delta E_{\tau}\over k_{B}T}\eqno{\hbox{(4)}}$$ where $\Delta E_{\tau}$ is the activation energy for relaxation processes and the pre-factor $\cal T_{0}$ represents the relaxation time at infinite temperature.

Two linear regions with $\Delta{\rm E}_{\tau}$ and ${\cal T}_{0}$ values are observed in this plot. The activation energy and the pre-factor were obtained from the slope and intercept of the Arrhenius plot. The values of $\Delta E_{A}$ and $\tau_{0}$ were 47.8 meV $(\rm T=300\ldots 200)$ K, 24.3 meV (200…100) K and 4.2.10^{−6} s, 2.1 10^{−5} s, respectively. The parallel resistance $R_{\rm p}$ of the device decreases rapidly with the increase of the temperature. The temperature dependent nature of $R_{p}$ can be expressed as TeX Source$$R_{p}\ =\ R_{o}\exp{\Delta E_{a}\over kT}\eqno{\hbox{(5)}}$$ where $R_{0}$ is the pre-exponential term and $\Delta E_{a}$ is the activation energy of the process. It is observed that ${\rm R}_{{\rm p}}$ is exponentially related to the measurement temperature.

Two linear regions are observed in this plot, also.

The values of $\Delta E_{a}$ and $R_{0}$ are 73 meV $({\rm T}\!=\!200\ldots 300)$ K, 35 meV (100…200) K and $2\ \ {\rm k}\Omega,\ \ 14\ \ {\rm k}\Omega$, respectively. The value ${\rm R}_{\rm d}\Vert {\rm R}_{\rm T}$ decreases with temperature because the photodiode current increases with temperature.

SECTION IV

The ac impedances of ZnSe/ZnTe/CdTe *p-i-n* heterostructures are studied for different measurement temperatures from 100 K to 300 K. Both the real and imaginary parts of impedance are frequency dependent. The Cole-Cole plots show the presence of temperature dependent electrical relaxation phenomena in ZnSe/ZnTe/CdTe thin film heterojunction. The relaxation time becomes shorter at higher temperatures due to the thermal excitation of more electrons and/or the formed dipoles.

This work has been supported by EU 7^{th} FP project FLEXSOLCELL GA-2008-230861.

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