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CdTe heterojunction
Thin Solid Films 515 (2007) 6179 – 6183 www.elsevier.com/locate/tsf
The analysis of current flow mechanism in CdS/CdTe heterojunction Sergiu Vatavu ⁎, Petru GaŞin Physics, Moldova State University, 60 A. Mateevici street, MD 2009, Chisinau, Moldova Available online 8 February 2007
Abstract An analysis of current–voltage dependencies of CdS/CdTe heterojunction in the 78–370 K temperature range has been carried out. According to this analysis the current flow mechanism is determined by the tunneling processes through dislocations, which penetrate the heterojunction space charge region. The concentration of dislocations has been estimated as 2 · 105 cm− 2. The number of steps necessary for tunneling varies: 2.5 · 102–1.7 · 103. The characteristic energy has a weak temperature dependence (− 0.2 meV/K) and its value vary 120–200 meV. The increase of the annealing duration results in the decrease of the characteristic energy. The multistep tunneling processes through local centres, determined by impurity centres, interface states and defects in the space charge region, predominate at reverse biases. The number of tunneling steps is 1–4 · 102. The concentration of local centres (traps) in the heterojunction have been estimated as 2.37 · 105–1.63 · 106 cm− 3. The thermal annealing in the presence of CdCl2 up to 60 min does not modify the current flow mechanism in CdS/CdTe heterojunctions. © 2007 Elsevier B.V. All rights reserved. Keywords: CdS/CdTe; Heterojunction; Current flow mechanism
1. Introduction For a photovoltaic energy conversion the maximum efficiency can be reached if a binary semiconductor with the band gap close to 1.5 eV is chosen [1]. The theoretical maximum efficiency for solar cells with a thin film CdTe absorber is 26.6% [1]. Recently, one of the most perspective heterojunction used for photovoltaic solar energy conversion is CdS/CdTe. The maximum efficiency for CdS/CdTe-based solar cells is 16.5% [2]. High photovoltaic parameters can be achieved if CdS/CdTe heterojunctions are annealed in the presence of CdCl2 for 10– 40 min at temperatures close to 400 °C [3]. As a result of deposition and annealing procedures, a layer consisting CdSxTe1 − x solid solutions is formed at the interface of CdS/ CdTe heterojunction. This fact as has been proven by different methods [4–7] such as photoluminescence, cathodoluminescence, modulation spectroscopy and other. This layer is believed to be the one influencing the electrical, photovoltaic and optical properties of the heterojunction. ⁎ Corresponding author. Tel.: +373 22 577 686 (Lab), +373 22 577 579 (Dean's office), +373 692 39063 (mobile); fax: +373 22 244 248. E-mail address: [email protected] (S. Vatavu). 0040-6090/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2006.12.086
The current flow mechanism in CdS/CdTe heterojunction is a complex one. Recently, several models, which explain more or less the experimental current–voltage dependencies, exist. CdS and CdTe lattice mismatch Da a is N 10% is causing the appearance of growth defects at the CdS/CdTe interface with a concentration of ∼ 1014 cm− 3 . The interface states related to the growth defects influenced the characterstics of the heterojunctions. The authors [8] are considering a model consisting of an anizotypic heterojunction with a high concentration of the interface states. The Schottky-like states are present on the both sides of the heterojunction. For a high concentration of the interface states with a high capture cross-section for both types of charge carriers, the current flow will be determined by the recombination through the interface states. If the captured crosssection has a low value, the redistribution of the potential between the two semiconductors plays an important role. One of the most often used mechanism for explaining the current–voltage characteristics [9,10] is the classic ShockleyNoyce-Sah model, considering the generation recombination mechanism in the space charge region. Unfortunately there are no current–voltage and saturation current vs temperature dependencies presented. It is known that the lnI ∼ T − 1 (I — the current) only for a narrow temperature interval (temperatures higher than
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300 K) and the diode quality factor has values as 2.5 up to 4. So, the classic current flow theory cannot be applied always. One of the models, satisfactorily explaining the experimental J-U plots and accepted by several authors [11–13], is the one considering the tunneling in the space charge region. This model can be used for to explain both current–voltage dependencies at forward and reverse biases. This paper is presenting the analysis of the temperature current–voltage dependencies with the consideration of tunneling of the charge carried through the space charge region of the heterojunction. 2. Experimental Thin film CdS/CdTe heterojunctions were fabricated by successive deposition of CdS and CdTe by CSS (closed spaced sublimation) technique, onto SnO2 covered glass plates (2 × 2 cm2), with a transparency of ∼80% in the visible spectral region and the resistivity ∼ 10− 3 Ω cm. The CdTe:Sb single crystals have been used as a source material for CdTe thin films deposition and vacuum annealed CdS powder has been used as CdS layers deposition. Our studies show, that the optimum temperatures for substrate and source are: 445 °C and 640 °C for CdS layers and 445 °C and 550 °C CdTe thin films respectively. The thickness of CdS and CdTe thin films was 0.3–1.6 μm and 2.3–6.6 μm respectively. As-deposited samples have low photovoltaic parameters: I sc = 0.17 mA (0.25 cm 2 ) and Uoc = 0.45 V. For, to increase the cell's efficiency a chloride annealing step followed the deposition procedure. The investigations of the influence of annealing in the presence of CdCl2 (at 390–420 °C for 15–60 min) influence on current flow mechanism in CdS/CdTe heterojunction, has been studied. The cleaning of the sample has been performed with a 350 ml 85% H3PO4 + 140 ml H2O + 4.4 ml 70% HNO3 solution or with a Brmethanol etchant. Magnetron-deposited Ni has been used as back contact to CdTe. After CdS/CdTe heterojunction annealing the open circuit voltage is Uoc = 0.70 V and the short circuitcurrent is Isc = 21.6 mA/cm2, and the fill factor ff = 0.43 at the illumination of 100 mW/cm2 were recorded. 3. Results and discussions 3.1. Current flow mechanism at forward bias For, to establish the current flow mechanism, the current– voltage (I–U) dependencies of CdS/CdTe heterojunctions have been studied in the 78–370 K temperature intervals. Their I–U plot has a diode behavior for the entire temperature interval analyzed. The built-in voltage (UD) vs temperature dependence is determined by the band gap and Fermi level variation. This dependence is a linear one with a tangent of − 1.7 · 10− 3 V/K. The I(U) plot, is minorily influenced by the heterojunction annealing duration variations from 15 to 60 min. So, all the analysis presented further is done for a 60 min annealed samples, as an example. The I(U) plot for different temperatures is presented in Fig. 1. There can be distinguished up to two linear regions, depending on the applied bias, pointing at an
Fig. 1. The current-voltage dependencies for the samples annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2).
exponential current vs voltage dependence. In the first approximation the I–U plot can be described by: I ¼ Is exp ðAU Þ:
ð1Þ
The values for A and satuation current Is, for a given voltage interval (0 b U b 0.45 V) vary: at 78 K A = 13.60 V − 1 , Is = 4.86 · 10− 11 and at 369 K A = 6.67 V− 1, Is = 4.79 · 10− 6 A (Sjunction = 0.25 cm2). The direct current vs temperature for different forward biases is given in Fig. 2. The presented data can be approximated with straight lines the slopes being equal to 0.034 K− 1, for 0.1–0.3 V biases. As it comes from the analysis of the experimental data for different biases and temperatures, the dependence on the direct current on applied voltage and on temperature can be described by the equation: Idirect ¼ I0 expðBT Þ exp ðAU Þ
ð2Þ
where I0, A and B — are constants, which do not depend on temperature. The same equation [12,14,15] is characteristic for a current flow mechanism, which considers tunneling through the interface states from CdS/CdTe heterojunctions determined by the lattice mismatch. For a direct, band to band tunneling, a charge carrier concentration of 1018–1019 cm− 3 [15] is needed, but the concentration of charge carriers in CdTe has a quite low value ∼ 1016 cm− 3. As it comes from the data presented above, the nature of the interface states and their high concentration still remain inexplicable. For, to proceed with the analysis of the experimental results, we have applied another model, presented in [16] with a further development in [17]. This model considers the tunneling process (nonhomogeneous tunneling) through the dislocation lines, which penetrate the space charge region. The I–U dependence can be described analytically by the following expression [17]: eU I ¼ Is exp −1 ð3Þ e where e — is the characteristic energy.
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Table 1 The values of m at different temperatures T, K 78 mI mII
112
136
166 190 213
229 252
294 325 336
347
2.8 2.1 2.16 1.76 1.56 1.35 1.43 1.3 1.15 1.09 1.09 1.12 1.43 1.29 1.02 1.02 0.95 0.88 0.88 0.82 0.68 0.82 0.68 0.68
value of factor B from (2) has been estimated if one admits that: eUD ðT Þ ð5Þ Is ~ exp − eðT Þ
Fig. 2. The dependence of the direct current vs temperature for different biases 1–0.1 V; 2–0.2 V; 3–0.3 V for the samples annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2).
Considering that the analyzed semiconductors are nondegenerated ones, and the space charge region width (W ∼ 0.137 μm) is much larger than the characteristic tunneling length λ ∼ 4.58 · 10− 10 m. W ≪ λ and the data presented in [18] indicate the fact that tunneling can occur in several steps through a system of levels distributed along the space charge region. The characteristic energy vs temperature dependence is a linear one with a slope of − 0.2 meV/K, the characteristic energy value varying in the range of 120–200 meV. The characteristic energy temperature dependence is given by [19]:
Nc = 2.19 · 1018 cm− 3, Nv = 5.08 · 1018 cm− 3 the effective density of state for CdS conduction band and CdTe valence band respectively. The calculations give a value of
eðT Þ ¼ e10 cth
e10 : nl kT
and the temperature variation of the built-in voltage is determined by the temperature variation of the band gap Eg = Eg(0) − αT, αCdTe = − 4.1 · 10− 4 eV/K. So, B is determined as: 1 Nc Nv B¼ a þ k ln ð6Þ e10 nn pp
ð4Þ
For high temperatures e(T) = n∞kT and considering the presented data, n∞ ≈ 2.5, for T → 0, e(0) = e10 = 222 meV. The
Fig. 3. The reverse current–voltage characteristics for the samples annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2).
Fig. 4. The reverse current vs temperature dependencies for the samples annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2) [T b 300 K (a) T N 300 K (b)].
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linear slopes I (for − 0.3 V ≤ U ≤ −1.3 V biases) and II (for − 1.5 V ≤ U ≤ − 2.25 V biases) and in the first approximation can be described by [12]: ð8Þ
I ¼ CU m
where m value is presented in Table 1. Both slopes are decreasing with the temperature increase. As it was established, there is an exponential dependency of the reverse current on temperature (Fig. 4), a characteristic for the presence of tunneling currents. For, to explain the experimental results the models presented in [15] have been used. The I–U analytic expression is given by: rffiffiffiffiffiffiffiffiffiffiffiffiffi Irev Er ln ¼ −HðEgp þ DEv Þ ð9Þ U UD −U where the multistep tunneling is considered, Er is the barrier corresponding to one tunneling step. Plotting the experimental data according to (9) one can observe two linear segments for reverse biases (Fig. 5): at U b 1.45 V and U N 1.45 V. The analysis of the plots mentioned above show, that for temperatures T b 300 K (≡ Tc) the slope is decreasing with temperature increase. For temperatures T N Tc the slope does dot suffer any changes. For higher biases (U N 1.45 V), T b Tc the slope decreases monothonically, while at futher temperature increase T N Tc, its variation is difficult to explain. The traps' concentration Nt necessary for tunneling can be calculated from [15]: I Nt exp ðg½UD −U −1=2 Þ ¼ ae2 U h
Fig. 5. The ln IUrev ¼ f
1 ffi pffiffiffiffiffiffiffiffiffi UD −U
plot for different temperatures (the samples
annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2): T b 300 K (a) T N 300 K (b) at low reverse biases (U b 1.45 V)).
B = 1.08 · 10− 2 K− 1, which is consistent with the presented experimental data. The concentration of dislocations ρ can be estimated, by using the model presented by authors of [16]:
I0 nn pp q¼ emD Nc Nv
kTe
Eg exp e
ð7Þ
where νD — is Debye frequency; ρ — is the density of dislocations; νD CdTe = 4.16 · 1012 s− 1. The calculations give a concentration of dislocations ρ ∼ 1.89 · 105 cm− 2. 3.2. Current flow mechanism at reverse biases The study of the current–voltage dependencies show that the reverse current increases with temperature increase. The reverse current vs voltage dependence at different temperatures is presented in Fig. 3 in a lnIrev = f(U ) scale. This plot shows two
ð10Þ
where: a — lattice constant, h — Planck's constant. The number of steps necessary for tunneling Θ and the trap concentration vs temperature are presented in Table 2. One can notice, that for small biases a decrease of tunneling steps is observed with temperature increase, while for U N 1.45 eV the number of tunneling steps has almost constant
Table 2 The number of tunneling steps Θ and the traps concentration Nt at different temperatures U b 1.45 V T, K 78 112 136 166 190 213 229 252 294 312 325 336 347 369
Nt, cm− 3 6
1.63 · 10 2.32 · 105 2.43 · 104 2.60 · 104 8.25 · 104 1.14 · 105 1.26 · 105 9.47 · 104 1.41 · 105 7.54 · 104 6.64 · 104 8.70 · 104 1.19 · 105 2.37 · 105
U N 1.45 V Θ 376 246 130 95 115 102 87 44 29 13 1 5 6 17
Nt, cm− 3 5
7.76 · 10 3.83 · 105 3.97 · 105 6.04 · 105 8.78 · 105 8.17 · 105 1.10 · 106 1.20 · 106 1.07 · 106 1.21 · 106 2.39 · 106 1.11 · 106 1.08 · 108 4.64 · 106
Θ 346 268 253 235 224 192 184 157 116 131 152 107 314 150
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value, about ∼ 102. For reverse biases b 0.3 V the current vs temperature dependence can be determined by leakage currents. 4. Conclusions As a result of the analysis of current–voltage characteristics at different temperatures it was established that: The current flow mechanism in the CdS/CdTe heterojunction at direct biases for the 78–370 K temperature intervals is determined by the tunneling processes through the interface states. The interface states are determined by the dislocations penetrating the space charge region. The density of dislocations is 1.89 · 105 cm− 2. The current flow mechanism at reverse biases is determined by the tunneling through local states at the interface of the heterojunction. The trap concentration by means of which the tunneling occur is 105 cm− 3 for U b 1.45 V and for higher voltages is about 106 cm− 3. The number of steps necessary for tunneling is about 1–3 · 102 for reverse biases higher than 1.45 V and have a weak temperature dependence, for voltages less than 1.45 eV and decreases along with temperature from ∼ 3 · 102 at 78 K up to unities ∼ 370 K. The current flow mechanism does not depend on the annealing time in the presence of CdCl2. References [1] J.J. Loferski, J. Appl. Phys. 27 (1956) 777. [2] X. Wu, J.C. Keane, R.G. Dhere, et al., 17th European Photovoltaic Solar Energy Conference, Munich, Germany, 22–26 October, Proceedings, 2001, p. 995.
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[3] U. Jahn, T. Okamoto, A. Yamada, et al., J. Appl. Phys. 90 (2001) 2553. [4] J. Van Gheluwe, J. Versluys, D. Poelman, et al., Thin Solid Films 480481 (2005) 246. [5] S. Vatavu, in: William Shafarman, Timothy Gessert, Shigeru Niki, Susanne Siebentritt (Eds.), Thin-Film Compound Semiconductor Photovoltaics, Mater. Res. Soc. Symp. Proc., vol. 865, 2005, p. F5.22, Warrendale, PA. [6] B.T. Boiko, G.S. Khripunov, V.P. Yurchenko, et al., Sol. Energy Mater. Sol. Cells 45 (1997) 303. [7] D.H. Levi, L.M. Woods, D.S. Albin, et al., 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion, Vienna, Austria, 6–10 July, Proceedings, 1998, p. 1047. [8] A.Ya. Schik, Yu.V. Shmartsev, Phys. Tech. Semicond. 14 (1980) 1724. [9] L.A. Kosyachenko, X. Mathew, V.V. Motoshyuk, et al., Phys. Tech. Semicond. 39 (2005) 569. [10] V.P. Singh, D.L. Linam, D.W. Dils, et al., Sol. Energy Mater. Sol. Cells 63 (2000) 445. [11] T.C. Anthony, A.L. Fahrenbruch, M.G. Peters, et al., Journal of Applied Physics 57 (1985) 400. [12] V.E. Baraniuk, V.P. Makhniy, Phys. Tech. Semicond. 25 (1991) 217. [13] H. Bayhan, C. Ercelebi, Semicond. Sci. Technol. 12 (1997) 600. [14] C. Ercelebi, A.W. Brinkman, T.S. Furlong, et al., J. Cryst. Growth 101 (1990) 162. [15] S.S. Ou, O.M. Stafsudd, B.M. Basol, Solid-State Electron. 27 (1984) 21. [16] V.V. Evstropov, Yu.V. Zhilyaev, M. Dzhumaeva, et al., Phys. Tech. Semicond. 31 (1997) 152. [17] V.V. Evstropov, M. Dzhumaeva, Yu.V. Zhilyaev, et al., Phys. Tech. Semicond. 34 (2000) 1357. [18] E. Burstein, S. Lundkvist (Eds.), Tunneling Processes in Solid State M. Mir, 1973, p. 422. [19] V.V. Evstropov, A.M. Strel'chuk, Phys. Tech. Semicond. 30 (1996) 92.
The analysis of current flow mechanism in CdS/CdTe heterojunction Sergiu Vatavu ⁎, Petru GaŞin Physics, Moldova State University, 60 A. Mateevici street, MD 2009, Chisinau, Moldova Available online 8 February 2007
Abstract An analysis of current–voltage dependencies of CdS/CdTe heterojunction in the 78–370 K temperature range has been carried out. According to this analysis the current flow mechanism is determined by the tunneling processes through dislocations, which penetrate the heterojunction space charge region. The concentration of dislocations has been estimated as 2 · 105 cm− 2. The number of steps necessary for tunneling varies: 2.5 · 102–1.7 · 103. The characteristic energy has a weak temperature dependence (− 0.2 meV/K) and its value vary 120–200 meV. The increase of the annealing duration results in the decrease of the characteristic energy. The multistep tunneling processes through local centres, determined by impurity centres, interface states and defects in the space charge region, predominate at reverse biases. The number of tunneling steps is 1–4 · 102. The concentration of local centres (traps) in the heterojunction have been estimated as 2.37 · 105–1.63 · 106 cm− 3. The thermal annealing in the presence of CdCl2 up to 60 min does not modify the current flow mechanism in CdS/CdTe heterojunctions. © 2007 Elsevier B.V. All rights reserved. Keywords: CdS/CdTe; Heterojunction; Current flow mechanism
1. Introduction For a photovoltaic energy conversion the maximum efficiency can be reached if a binary semiconductor with the band gap close to 1.5 eV is chosen [1]. The theoretical maximum efficiency for solar cells with a thin film CdTe absorber is 26.6% [1]. Recently, one of the most perspective heterojunction used for photovoltaic solar energy conversion is CdS/CdTe. The maximum efficiency for CdS/CdTe-based solar cells is 16.5% [2]. High photovoltaic parameters can be achieved if CdS/CdTe heterojunctions are annealed in the presence of CdCl2 for 10– 40 min at temperatures close to 400 °C [3]. As a result of deposition and annealing procedures, a layer consisting CdSxTe1 − x solid solutions is formed at the interface of CdS/ CdTe heterojunction. This fact as has been proven by different methods [4–7] such as photoluminescence, cathodoluminescence, modulation spectroscopy and other. This layer is believed to be the one influencing the electrical, photovoltaic and optical properties of the heterojunction. ⁎ Corresponding author. Tel.: +373 22 577 686 (Lab), +373 22 577 579 (Dean's office), +373 692 39063 (mobile); fax: +373 22 244 248. E-mail address: [email protected] (S. Vatavu). 0040-6090/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2006.12.086
The current flow mechanism in CdS/CdTe heterojunction is a complex one. Recently, several models, which explain more or less the experimental current–voltage dependencies, exist. CdS and CdTe lattice mismatch Da a is N 10% is causing the appearance of growth defects at the CdS/CdTe interface with a concentration of ∼ 1014 cm− 3 . The interface states related to the growth defects influenced the characterstics of the heterojunctions. The authors [8] are considering a model consisting of an anizotypic heterojunction with a high concentration of the interface states. The Schottky-like states are present on the both sides of the heterojunction. For a high concentration of the interface states with a high capture cross-section for both types of charge carriers, the current flow will be determined by the recombination through the interface states. If the captured crosssection has a low value, the redistribution of the potential between the two semiconductors plays an important role. One of the most often used mechanism for explaining the current–voltage characteristics [9,10] is the classic ShockleyNoyce-Sah model, considering the generation recombination mechanism in the space charge region. Unfortunately there are no current–voltage and saturation current vs temperature dependencies presented. It is known that the lnI ∼ T − 1 (I — the current) only for a narrow temperature interval (temperatures higher than
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300 K) and the diode quality factor has values as 2.5 up to 4. So, the classic current flow theory cannot be applied always. One of the models, satisfactorily explaining the experimental J-U plots and accepted by several authors [11–13], is the one considering the tunneling in the space charge region. This model can be used for to explain both current–voltage dependencies at forward and reverse biases. This paper is presenting the analysis of the temperature current–voltage dependencies with the consideration of tunneling of the charge carried through the space charge region of the heterojunction. 2. Experimental Thin film CdS/CdTe heterojunctions were fabricated by successive deposition of CdS and CdTe by CSS (closed spaced sublimation) technique, onto SnO2 covered glass plates (2 × 2 cm2), with a transparency of ∼80% in the visible spectral region and the resistivity ∼ 10− 3 Ω cm. The CdTe:Sb single crystals have been used as a source material for CdTe thin films deposition and vacuum annealed CdS powder has been used as CdS layers deposition. Our studies show, that the optimum temperatures for substrate and source are: 445 °C and 640 °C for CdS layers and 445 °C and 550 °C CdTe thin films respectively. The thickness of CdS and CdTe thin films was 0.3–1.6 μm and 2.3–6.6 μm respectively. As-deposited samples have low photovoltaic parameters: I sc = 0.17 mA (0.25 cm 2 ) and Uoc = 0.45 V. For, to increase the cell's efficiency a chloride annealing step followed the deposition procedure. The investigations of the influence of annealing in the presence of CdCl2 (at 390–420 °C for 15–60 min) influence on current flow mechanism in CdS/CdTe heterojunction, has been studied. The cleaning of the sample has been performed with a 350 ml 85% H3PO4 + 140 ml H2O + 4.4 ml 70% HNO3 solution or with a Brmethanol etchant. Magnetron-deposited Ni has been used as back contact to CdTe. After CdS/CdTe heterojunction annealing the open circuit voltage is Uoc = 0.70 V and the short circuitcurrent is Isc = 21.6 mA/cm2, and the fill factor ff = 0.43 at the illumination of 100 mW/cm2 were recorded. 3. Results and discussions 3.1. Current flow mechanism at forward bias For, to establish the current flow mechanism, the current– voltage (I–U) dependencies of CdS/CdTe heterojunctions have been studied in the 78–370 K temperature intervals. Their I–U plot has a diode behavior for the entire temperature interval analyzed. The built-in voltage (UD) vs temperature dependence is determined by the band gap and Fermi level variation. This dependence is a linear one with a tangent of − 1.7 · 10− 3 V/K. The I(U) plot, is minorily influenced by the heterojunction annealing duration variations from 15 to 60 min. So, all the analysis presented further is done for a 60 min annealed samples, as an example. The I(U) plot for different temperatures is presented in Fig. 1. There can be distinguished up to two linear regions, depending on the applied bias, pointing at an
Fig. 1. The current-voltage dependencies for the samples annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2).
exponential current vs voltage dependence. In the first approximation the I–U plot can be described by: I ¼ Is exp ðAU Þ:
ð1Þ
The values for A and satuation current Is, for a given voltage interval (0 b U b 0.45 V) vary: at 78 K A = 13.60 V − 1 , Is = 4.86 · 10− 11 and at 369 K A = 6.67 V− 1, Is = 4.79 · 10− 6 A (Sjunction = 0.25 cm2). The direct current vs temperature for different forward biases is given in Fig. 2. The presented data can be approximated with straight lines the slopes being equal to 0.034 K− 1, for 0.1–0.3 V biases. As it comes from the analysis of the experimental data for different biases and temperatures, the dependence on the direct current on applied voltage and on temperature can be described by the equation: Idirect ¼ I0 expðBT Þ exp ðAU Þ
ð2Þ
where I0, A and B — are constants, which do not depend on temperature. The same equation [12,14,15] is characteristic for a current flow mechanism, which considers tunneling through the interface states from CdS/CdTe heterojunctions determined by the lattice mismatch. For a direct, band to band tunneling, a charge carrier concentration of 1018–1019 cm− 3 [15] is needed, but the concentration of charge carriers in CdTe has a quite low value ∼ 1016 cm− 3. As it comes from the data presented above, the nature of the interface states and their high concentration still remain inexplicable. For, to proceed with the analysis of the experimental results, we have applied another model, presented in [16] with a further development in [17]. This model considers the tunneling process (nonhomogeneous tunneling) through the dislocation lines, which penetrate the space charge region. The I–U dependence can be described analytically by the following expression [17]: eU I ¼ Is exp −1 ð3Þ e where e — is the characteristic energy.
S. Vatavu, P. GaŞin / Thin Solid Films 515 (2007) 6179–6183
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Table 1 The values of m at different temperatures T, K 78 mI mII
112
136
166 190 213
229 252
294 325 336
347
2.8 2.1 2.16 1.76 1.56 1.35 1.43 1.3 1.15 1.09 1.09 1.12 1.43 1.29 1.02 1.02 0.95 0.88 0.88 0.82 0.68 0.82 0.68 0.68
value of factor B from (2) has been estimated if one admits that: eUD ðT Þ ð5Þ Is ~ exp − eðT Þ
Fig. 2. The dependence of the direct current vs temperature for different biases 1–0.1 V; 2–0.2 V; 3–0.3 V for the samples annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2).
Considering that the analyzed semiconductors are nondegenerated ones, and the space charge region width (W ∼ 0.137 μm) is much larger than the characteristic tunneling length λ ∼ 4.58 · 10− 10 m. W ≪ λ and the data presented in [18] indicate the fact that tunneling can occur in several steps through a system of levels distributed along the space charge region. The characteristic energy vs temperature dependence is a linear one with a slope of − 0.2 meV/K, the characteristic energy value varying in the range of 120–200 meV. The characteristic energy temperature dependence is given by [19]:
Nc = 2.19 · 1018 cm− 3, Nv = 5.08 · 1018 cm− 3 the effective density of state for CdS conduction band and CdTe valence band respectively. The calculations give a value of
eðT Þ ¼ e10 cth
e10 : nl kT
and the temperature variation of the built-in voltage is determined by the temperature variation of the band gap Eg = Eg(0) − αT, αCdTe = − 4.1 · 10− 4 eV/K. So, B is determined as: 1 Nc Nv B¼ a þ k ln ð6Þ e10 nn pp
ð4Þ
For high temperatures e(T) = n∞kT and considering the presented data, n∞ ≈ 2.5, for T → 0, e(0) = e10 = 222 meV. The
Fig. 3. The reverse current–voltage characteristics for the samples annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2).
Fig. 4. The reverse current vs temperature dependencies for the samples annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2) [T b 300 K (a) T N 300 K (b)].
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linear slopes I (for − 0.3 V ≤ U ≤ −1.3 V biases) and II (for − 1.5 V ≤ U ≤ − 2.25 V biases) and in the first approximation can be described by [12]: ð8Þ
I ¼ CU m
where m value is presented in Table 1. Both slopes are decreasing with the temperature increase. As it was established, there is an exponential dependency of the reverse current on temperature (Fig. 4), a characteristic for the presence of tunneling currents. For, to explain the experimental results the models presented in [15] have been used. The I–U analytic expression is given by: rffiffiffiffiffiffiffiffiffiffiffiffiffi Irev Er ln ¼ −HðEgp þ DEv Þ ð9Þ U UD −U where the multistep tunneling is considered, Er is the barrier corresponding to one tunneling step. Plotting the experimental data according to (9) one can observe two linear segments for reverse biases (Fig. 5): at U b 1.45 V and U N 1.45 V. The analysis of the plots mentioned above show, that for temperatures T b 300 K (≡ Tc) the slope is decreasing with temperature increase. For temperatures T N Tc the slope does dot suffer any changes. For higher biases (U N 1.45 V), T b Tc the slope decreases monothonically, while at futher temperature increase T N Tc, its variation is difficult to explain. The traps' concentration Nt necessary for tunneling can be calculated from [15]: I Nt exp ðg½UD −U −1=2 Þ ¼ ae2 U h
Fig. 5. The ln IUrev ¼ f
1 ffi pffiffiffiffiffiffiffiffiffi UD −U
plot for different temperatures (the samples
annealed in CdCl2 for 60 min (Sjunction = 0.25 cm2): T b 300 K (a) T N 300 K (b) at low reverse biases (U b 1.45 V)).
B = 1.08 · 10− 2 K− 1, which is consistent with the presented experimental data. The concentration of dislocations ρ can be estimated, by using the model presented by authors of [16]:
I0 nn pp q¼ emD Nc Nv
kTe
Eg exp e
ð7Þ
where νD — is Debye frequency; ρ — is the density of dislocations; νD CdTe = 4.16 · 1012 s− 1. The calculations give a concentration of dislocations ρ ∼ 1.89 · 105 cm− 2. 3.2. Current flow mechanism at reverse biases The study of the current–voltage dependencies show that the reverse current increases with temperature increase. The reverse current vs voltage dependence at different temperatures is presented in Fig. 3 in a lnIrev = f(U ) scale. This plot shows two
ð10Þ
where: a — lattice constant, h — Planck's constant. The number of steps necessary for tunneling Θ and the trap concentration vs temperature are presented in Table 2. One can notice, that for small biases a decrease of tunneling steps is observed with temperature increase, while for U N 1.45 eV the number of tunneling steps has almost constant
Table 2 The number of tunneling steps Θ and the traps concentration Nt at different temperatures U b 1.45 V T, K 78 112 136 166 190 213 229 252 294 312 325 336 347 369
Nt, cm− 3 6
1.63 · 10 2.32 · 105 2.43 · 104 2.60 · 104 8.25 · 104 1.14 · 105 1.26 · 105 9.47 · 104 1.41 · 105 7.54 · 104 6.64 · 104 8.70 · 104 1.19 · 105 2.37 · 105
U N 1.45 V Θ 376 246 130 95 115 102 87 44 29 13 1 5 6 17
Nt, cm− 3 5
7.76 · 10 3.83 · 105 3.97 · 105 6.04 · 105 8.78 · 105 8.17 · 105 1.10 · 106 1.20 · 106 1.07 · 106 1.21 · 106 2.39 · 106 1.11 · 106 1.08 · 108 4.64 · 106
Θ 346 268 253 235 224 192 184 157 116 131 152 107 314 150
S. Vatavu, P. GaŞin / Thin Solid Films 515 (2007) 6179–6183
value, about ∼ 102. For reverse biases b 0.3 V the current vs temperature dependence can be determined by leakage currents. 4. Conclusions As a result of the analysis of current–voltage characteristics at different temperatures it was established that: The current flow mechanism in the CdS/CdTe heterojunction at direct biases for the 78–370 K temperature intervals is determined by the tunneling processes through the interface states. The interface states are determined by the dislocations penetrating the space charge region. The density of dislocations is 1.89 · 105 cm− 2. The current flow mechanism at reverse biases is determined by the tunneling through local states at the interface of the heterojunction. The trap concentration by means of which the tunneling occur is 105 cm− 3 for U b 1.45 V and for higher voltages is about 106 cm− 3. The number of steps necessary for tunneling is about 1–3 · 102 for reverse biases higher than 1.45 V and have a weak temperature dependence, for voltages less than 1.45 eV and decreases along with temperature from ∼ 3 · 102 at 78 K up to unities ∼ 370 K. The current flow mechanism does not depend on the annealing time in the presence of CdCl2. References [1] J.J. Loferski, J. Appl. Phys. 27 (1956) 777. [2] X. Wu, J.C. Keane, R.G. Dhere, et al., 17th European Photovoltaic Solar Energy Conference, Munich, Germany, 22–26 October, Proceedings, 2001, p. 995.
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