ZnO1-xTex and ZnO1-xSx semiconductor alloys as competent materials for opto-electronic and solar cell applications:a comparative analysis

    Corresponding author: Partha P. Pal, phys.ppal@gmail.com
  • 1. Department of Electronics, Calcutta University, Kolkata-700009, India
  • 2. St. Mary's Technical Campus Kolkata, Kolkata-700126, India

Key words: VBAC modelsemiconductor alloysband gapspin-orbit splitting energystrainsolar cell

Abstract: ZnO1-xTex ternary alloys have great potential to work as a photovoltaic (PV) absorber in solar cells. ZnO1-xSx is also a ZnO based alloy that have uses in solar cells. In this paper we report the comparative study of various parameters of ZnO1-xTex and ZnO1-xSx for selecting it to be a competent material for solar cell applications. The parameters are mainly being calculated using the well-known VCA (virtual crystal approximation) and VBAC (Valence Band Anti-Crossing) model. It was certainly being analysed that the incorporation of Te atoms produces a high band gap lower than S atoms in the host ZnO material. The spin-orbit splitting energy value of ZnO1-xTex was found to be higher than that of ZnO1-xSx. Beside this, the strain effects are also higher in ZnO1-xTex than ZnO1-xSx. The remarkable notifying result which the paper is reporting is that at a higher percentage of Te atoms in ZnO1-xTex, the spin-orbit splitting energy value rises above the band gap value, which signifies a very less internal carrier recombination that decreases the leakage current and increases the efficiency of the solar cell. Moreover, it also covers a wide wavelength range compared to ZnO1-xSx.

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1.   Introduction
  • A high percentage of present research works are aimed on renewable energy sources as the extant of non-renewable energy sources are at stake. Amongst the renewable energy resources, solar cells are always considered as the front runners. Till now, most of the solar cell fabrications are based on silicon. But silicon is quite labour-intensive and needs a high temperature to process too, thus making its cost comparatively high. So the desideratum of the hour is to make efficient solar cells which are cost effective as well as having less negative impact on the environment. Highly mismatched semiconducting alloys are a new class of materials[1] that are being used in solar cell fabrications. ZnO, a wideband gap n-type semiconducting material has great potential for applications as optoelectronic devices to operate in the violet and blue region[2-4]. With that, it has a great potential for applications in photovoltaic solar cells[5-7]. Till now it has been used on PV cells as a transparent conductor, but the tuning of the bandgap of ZnO up to the near infrared region, makes it suitable for application as an absorber in photovoltaic cells[7]. For the reduction in bandgap, ZnO based alloys are the most promising candidates for solar cell applications. The ternary alloys like ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x\thinspace }}$have recently been found to be quite useful as a PV absorber, which works in the wavelength region 350 to 450 nm. Although, work on these ternary alloys has recently been started, already there are some good works on these materials[8-13]. A comparative study of these materials has yet to be done. In this way, our paper is the first to discuss the bandgap reduction in ZnO$_{{1-x}}$Te$_{{x\thinspace }}$with respect to solar cell applications with a comparative study with ZnO$_{{1-x}}$S$_{{x}}$. All the related parameters are mainly being calculated using the well-known VCA and VBAC model[14-16]. VCA is mainly used for disordered alloys. It considers a virtual atom in a potentially disordered site which helps in interpolating the behaviour of the atoms in the parent compound. The VBAC model explains the interaction between the extended valence band states of the host material (ZnO) and the resonant states of replaced atoms (Te, S) thereby reconstructing the valence band and lowering the effective band gap of the alloy.

    In our work, we study the effect of Te and S in the host material ZnO. It is certainly being found that there is a high amount of bandgap reduction in the case where a few of the Oxygen atoms of ZnO are replaced by small amount of Te and S, thereby forming the alloy ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x}}$. The band gap reduction is found to be higher for Te incorporation than that of S in the host material. Thus it can be stated that ZnO$_{{1-x}}$Te$_{{x\thinspace }}$will cover a wide range of wavelength compared to ZnO$_{{1-x}}$S$_{{x}}$ for optoelectronic applications. The spin orbit splitting energy due to Te is higher than that of S due to which it can be proposed that the internal recombination will be lower in the case of ZnO$_{{1-x}}$Te$_{{x}}$ than that of ZnO$_{{1-x}}$S$_{{x}}$. Thus the light emission efficiency will be increased more in ZnO$_{{1-x}}$Te$_{{x\thinspace }}$than ZnO$_{{1-x}}$S$_{{x}}$. At the same time, leakage current will be higher for ZnO$_{{1-x}}$S$_{{x\thinspace }}$than that of ZnO$_{{1-x}}$Te$_{{x.\thinspace }}$ On the other hand, the compressive strain is higher in the case of ZnO$_{{1-x}}$Te$_{{x\thinspace }}$than that of ZnO$_{{1-x}}$S$_{{x\thinspace }}$because of the fact that the atomic radius of Te is higher than that of S, which may cause some arousal of defects in the material.

2.   Theoretical approach
  • The incorporation of Te or S atoms in the host material ZnO causes an arbitrary replacement of some of the oxygen atoms by Te and S, forming ZnO$_{{1-x}}$Te$_{{x\thinspace }}$and ZnO$_{{1-x}}$S$_{{x}}$ respectively. This causes change in the band gap related parameters in the host material. This phenomenon can be well explained using the VBAC model. But for understanding the strain related effects and the band gap lowering effects, the more perfect approach will be the combination of the VCA and VBAC models.

    Although the effect of the incorporation occurs significantly in the valence band, the position of the conduction band (CB) is modelled as per the VCA approximation for ZnO$_{{1-x}}$Te$_{{x\thinspace }}$and ZnO$_{{1-x}}$S$_{{x}}$ and is given by,

    where ${ E}_{\rm CB}^{ \rm{ZnTe}}$, $E_{\rm CB}^{ \rm{ZnS}}$ and $E_{\rm CB}^{ \rm{ZnO}}$ are the absolute conduction band positions for ZnTe, ZnS and ZnO respectively and $x$ denotes the mole fraction of the alloy. The CB position for the ZnO ($E_{\rm CB}^{\rm{ZnO}})$ is defined as,

    where $E_{\rm g}$ represents the unstrained band gap of the host material; $a_{\rm c}$ and $ a_{\rm v}$ represent the conduction and valence band deformation potentials respectively; $c_{11}$ and $c_{12}$ represent the elastic stiffness constants; $a_{\rm s} a_{\rm w}$ represent the substrate and well layer lattice constants.

    Similarly, the absolute position for the valence bands can be obtained but it must include a band gap bowing term for both ZnO$_{{1-x}}$Te$_{{x\thinspace }}$and ZnO$_{{1-x}}$S$_{{x\thinspace }}$which can be mentioned as,

    where $b_{\text{ZnO}_{{1-x}}{\text{Te}}_{{x}}}$ and $b_{\text {ZnO}_{{1-x}}\text{S}_{{x}}}$are considered to be 2.7 eV[17] and 2.91 eV[2] representing the bowing parameter for ${\text{ZnO}}_{{1-x}}{\text{Te}}_{{x}}$ and ${\text{ZnO}}_{{1-x}}\text{S}_{{x}}$ respectively.

    The valence band of the host material is mainly having three sub-band effects namely heavy hole (HH), light hole (LH) and split off (SO) band. The absolute position of these valence sub-bands can be well defined by the following equations,

    where $b$ represents the shear deformation potential and $\Delta $ represents the spin-orbit splitting energy of the host material.

    The lattice constant for the ternary alloys (ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x}})$ can be determined by the well known Vegard's law[18],

    where $a_{\text{ZnO}_{1-x}\text{Te}_x}$ and $a_{\text{ZnO}_{1-x}\text{S}_x}$ are the lattice constants of ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x}}$ respectively.

    Thus,

    and considering, ${a}_{\rm {ZnTe}}=6.101$Å[19], ${a}_{\rm {ZnS}}=5.41$Å[20] and ${a}_{\rm {ZnO}}=4.47$Å[21].

    The incorporation of Te or S in ZnO causes a change in its band structure as well as in the band parameters[7, 12]. This phenomenon can well be analyzed by the well-known VBAC (Valence Band Anti-Crossing) model[22]. This model presumes that the Te or S atoms substitute randomly some of the oxygen atoms in the host material ZnO, thereby perturbing the Hamiltonian matrix of ZnO. Thus, the VBAC Hamiltonian at $k=0$ is given by,

    where $E_{\rm HH}^{\rm ZnO} $, $E_{\rm LH}^{\rm ZnO} $ and $E_{\rm SO}^{\rm ZnO} $represent the positions of heavy hole (HH), light hole (LH) and split off (SO) band respectively for the host material (ZnO). $E_{\rm HH}^{\rm\left( {Te/S} \right)} $, $E_{\rm LH}^{\rm\left( {Te/S} \right)} $, and $E_{\rm SO}^{\rm\left( {Te/S} \right)} $ represent the Te or S related positions in the bands. $C_{\rm \left( {Te/S} \right)HH} $, $C_{\rm \left( {Te/S} \right)LH} $, and $C_{\rm \left( {Te/S} \right)SO} $ represent the coupling constants of Te or S due to interaction of the valence sub-bands, whereas $x$ represents the atomic mole fraction of Te or S substituting randomly the host material group VI atoms. Thus, the interaction of these Te or S related energy levels with the host material valence sub-bands leads to the splitting of the sub-bands for HH, LH and SO bands separately and given by the equations,

    The above equations signify the split bands formed after interactions of Te or S with the host valence sub-bands.

    Thus, the band gap of ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x}}$ is defined by:

    The wavelength range for ${\text{ZnO}}_{{1-x}}{\text{Te}}_{{x}}$ and ${\text{ZnO}}_{{1-x}}{\text{S}}_{{x}}$ is defined as:

    The strain parameters for ${\text{ZnO}}_{{1-x}}{\text{Te}}_{{x}}$ and ${\text{ZnO}}_{{1-x}}\text{S}_{x}$ can be defined by using the formula,

    The values of the parameters for ZnO that are considered for the calculations are summarized in Table 1. Apart from the values of ZnO, the values of the other input parameters that are used for calculations are summarized in Table 2.

3.   Results and discussion
  • Fig. 1 shows the variation of band gap of ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x\thinspace }}$depending upon the mole fraction variation of Te and S respectively. As oxygen atoms in the host material are replaced by Te and S, the difference in electronegativity due to Te is found to be higher than that of S, thus the band gap lowering occurs higher in the case of ZnO$_{{1-x}}$Te$_{{x}}$ than ZnO$_{{1-x}}$S$_{{x}}$. It has been observed, for a value of mole fraction($x$) greater than 0.3, the rate of reduction of the band gap is lowered for ZnO$_{{1-x}}$S$_{{x}}$ as compared to ZnO$_{{1-x}}$Te$_{{x}}$. The band gap value for a standardized highly efficient solar cell is about 1.5 eV[23], which can be achievable by tuning the molar fraction (x) of ZnO$_{{1-x}}$Te$_{{x}}$ to 0.31.

    Fig. 2 shows the variations of the spin-orbit splitting energy gap of ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x\thinspace }}$depending upon the mole fraction variation of Te and S respectively. It is observed that the spin-orbit split-off energy ($\Delta_{\rm {so}})$ for ZnO being very low, the incorporation of a small amount of Te causes an effective enhancement in spin-orbit splitting energy of the alloy ZnO$_{{1-x}}$Te$_{{x}}$. The same effect can be observed for ZnO$_{{1-x}}$S$_{{x, \thinspace }}$where a small amount of S causes a significant enhancement in spin-orbit splitting energy. The noticeable increase in $\Delta_{\rm {so\thinspace }}$ can be well explained by the large atomic mass of Te and S due to which the interaction between electron spin and angular momentum increases[24]. The increase in $\Delta_{\rm {so\thinspace }}$ is larger for ZnO$_{{1-x}}$Te$_{{x}}$ compared to that of ZnO$_{{1-x}}$S$_{{x}}$, $_{\rm {\thinspace }}$which is well expected due to the larger atomic mass and radii of Te over S.

    Fig. 3 is laid down by the combination of Figs. 1 and 2, but with a higher range of mole fraction. It shows, both the band gap reduction and spin-orbit splitting effect are higher in the case of ZnO$_{{1-x}}$Te$_{{x\thinspace }}$than ZnO$_{{1-x}}$S$_{{x}}$. It also depicts a phenomenal result where the band gap ($E_{\rm {g}})$ of ZnO$_{{1-x}}$Te$_{{x\thinspace }}$becomes equal to its spin-orbit splitting energy ($\Delta )$ at a mole fraction ($x)$ of 0.41. As the mole fraction of Te in the ternary alloy is gradually being increased, it is found that the spin-orbit splitting value goes higher than the band gap of the material (i.e., $\Delta $ > $E_{\rm {g}})$, which is a very significant effect for a solar cell material as it signifies that the distances between the valence sub-bands will be higher compared to the band gap. Thus, it signifies that the internal carrier recombination effect is lowered in the case of ZnO$_{{1-x}}$Te$_{{x\thinspace }}$compared to ZnO$_{{1-x}}$S$_{{x}}$, thereby confirming a better performing ability of the material in the solar cell. Due to the low carrier recombination factor, the leakage current decreases, thereby increasing the efficiency of the solar cell.

    Fig. 4 shows the variation of compressive strain of ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x\thinspace }}$depending upon the mole fraction variation of Te and S respectively. In our case, oxygen in the host material is replaced by Te and S, both of which have a very high atomic radii compared to Oxygen, due to which the incorporation of both the elements (i.e., Te and S) causes a compressive strain effect in the host material. But it is certainly being found that as Te has a high atomic radii compared to S, the ZnO$_{{1-x}}$Te$_{{x\thinspace }}$has a higher compressive strain than that of ZnO$_{{1-x}}$S$_{{x}}$.

    Fig. 5 shows the variation in wavelength of ZnO$_{{1-x}}$Te$_{{x}}$ and ZnO$_{{1-x}}$S$_{{x\thinspace }}$depending on Te and S mole fraction respectively. As the band gap reduction in ZnO$_{{1-x}}$Te$_{{x\thinspace }}$is found to be much higher than ZnO$_{{1-x}}$S$_{{x}}$ shown in Fig. 1, the variation in wavelength also covers a wide range for ZnO$_{{1-x}}$Te$_{{x}}$ compared to ZnO$_{{1-x}}$S$_{{x}}$ as explained by Eqs. (17) and (18). The above calculated parameters are summarized in Table 3.

4.   Conclusion
  • Our paper gives a comparative study of two most promising ZnO based ternary alloys ZnO$_{{1-x}}$Te$_{{x\thinspace }}$and ZnO$_{{1-x}}$S$_{{x}}$. The spin orbit splitting values are calculated corresponding to the band gap values. The bandgap lowering with increasing Te mole fraction for ZnO$_{{1-x}}$Te$_{{x\thinspace }}$is much higher than that for ZnO$_{{1-x}}$S$_{{x}}$. The most significant result is the increase of split off energy value of ZnO$_{{1-x}}$Te$_{{x}}$ than the corresponding bandgap value with further increasing the Te mole fraction. The result indicates a high performing ability of ZnO$_{{1-x}}$Te$_{{x\thinspace }}$as PV absorber as the internal carrier recombination and therefore the leakage current will be the least in such cases. Moreover, as the band gap lowering is higher, the wavelength range covered by ZnO$_{{1-x}}$Te$_{{x}}$ is wide compared to ZnO$_{{1-x}}$S$_{{x}}$. The only drawback of ZnO$_{{1-x}}$Te$_{{x\thinspace }}$is that the compressive strain is also quite a bit higher than that of ZnO$_{{1-x}}$S$_{{x}}$. But, if all the results are compared between these two promising ternary alloys, the ZnO$_{{1-x}}$Te$_{{x\thinspace }}$properties are quite amazing. Apart from that, these two alloys are excellent opto-electronic materials.

Figure (5)  Table (3) Reference (24) Relative (20)

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