Low Resistance TiO2/p-Si Heterojunction for Tandem Solar Cells

Niobium-doped titanium dioxide (Ti1−xNbxO2) films were grown on p-type Si substrates at low temperature (170 °C) using an atomic layer deposition technique. The as-deposited films were amorphous and showed low electrical conductivity. The films became electrically well-conducting and crystallized into the an anatase structure upon reductive post-deposition annealing at 600 °C in an H2 atmosphere for 30 min. It was shown that the Ti0.72Nb0.28O2/p+-Si heterojunction fabricated on low resistivity silicon (10−3 Ω cm) had linear current–voltage characteristic with a specific contact resistivity as low as 23 mΩ·cm2. As the resistance dependence on temperature revealed, the current across the Ti0.72Nb0.28O2/p+-Si heterojunction was mainly determined by the band-to-band charge carrier tunneling through the junction.


Introduction
The successful development of a monolithic perovskite/silicon tandem solar cell has attracted considerable attention during past few years [1][2][3][4][5][6][7]. The interest in this field is motivated by the rapid development of power conversion efficiency of a perovskite solar cell, from less than 3.8% to above 22% during the last decade [8][9][10][11][12][13][14][15][16]. A monolithically integrated two-terminal (2-T) perovskite/silicon tandem solar cell consists of a top perovskite subcell being deposited onto a bottom silicon subcell. The two subcells are then electrically connected in a series through a recombination layer or a tunnel junction [5]. The tunnel junction consisting of two heavily doped p + and n + silicon regions was used in the first demonstration of a 2-T perovskite/silicon tandem solar cell [1]. However, the tunnel p + -n + silicon junction can potentially contribute to parasitic optical absorption [7]. Aiming to lower the parasitic optical absorption, Shen et al. proposed to use a recombination junction formed between p-Si and atomically deposited TiO 2 , thus enabling to produce a high efficiency monolithic perovskite/silicon tandem solar cell [7].
The electrical properties of TiO 2 thin films grown by atomic layer deposition (ALD) on crystalline silicon substrates were studied recently [17]. It was found that a heterojunction was formed between the deposited TiO 2 and silicon substrate demonstrating nonohmic and asymmetric current-voltage characteristics. Usually, TiO 2 is treated as an n-type semiconductor with a wide bandgap reaching 3.4 eV, 3.2 eV, 3.02 eV and 2.96 eV for amorphous, anatase, rutile and brookite phases, respectively [17,18]. Therefore, nondoped, high quality TiO 2 has a high resistivity and may serve as an insulator for capacitors [19,20]. The electrical conductivity of nondoped TiO 2 films can be changed by variations of oxygen concentration during the TiO 2 reduction [17,18]. The O 2 deficiency creates defects such as oxygen vacancies, titanium vacancies, and Ti 3+ and Ti 4+ interstitials, which may act either as acceptors or donors of electrons [21,22]. TiO 2 is an amphoteric semiconductor, therefore creation of high conductivity nondoped TiO 2 films is hindered.
High conductivity semiconductors are needed to produce low resistivity TiO 2 /p-Si contact. Furubayashi et al. showed that Nb-doped anatase TiO 2 film is an optically transparent electrically conducting oxide [23]. The resistivity of TiO 2 films with a Nb concentration exceeding 6% was less than 2.3 × 10 −4 Ω·cm at room temperature. Furthermore, Ti 1−x Nb x O 2 films with x ≥ 0.01 showed a metallic behavior. This paper deals with details of fabrication of a highly conducting TiO 2 /p-Si heterojunction. Transparent TiO 2 films were grown by ALD and doped with Nb.

Materials and Methods
Thin Ti 1−x Nb x O 2 (mixed titanium niobium oxide) layers were formed on glass, low resistivity p + -type and low conductivity p-type silicon substrates, using a "Fiji F200" atomic layer deposition reactor (Cambridge Nano Tech, Waltham, MA USA). A modular ALD system was used for layer formation in a moderate vacuum. First, glass and silicon substrates (University Wafer, Inc., Boston, MA, USA) were cleaned in ethanol and acetone in an ultrasonic bath for 20 min. Then the silicon surface was thermally oxidized in a quartz tube furnace "SDO-125/3" (Termotron, Bryansk, USSR) at 1150 • C in air for 3 h. The thickness of the silicon oxide layer was measured by a profilometer "Dektak 6M" (Veeco Metrology LLC, Plainview, NY, USA); it was 150 nm. Round 100-µm diameter holes were formed in SiO 2 by means of a photolithography technique. Thin Ti 1−x Nb x O 2 layers were deposited using tetrakis dimethylamido titanium (TDMAT, 99.9%, STREM Chemicals Inc.) and niobium ethoxide (Nb(OEt) 5 , 99.9%, STREM Chemicals Inc.) as precursors for titanium and niobium oxides. Deionized water was used as an oxygen source for both processes. The reactions for both processes are presented below.
Partial surface reactions for TiO 2 : The reaction chamber was evacuated up to 3 × 10 −2 mbar before the deposition process. The substrates and the reaction chamber were heated up to 170 • C. A constant flow of 100 sccm of pass-thru and 40 sccm of carrier gas (argon) was used during the deposition process. This kept the reaction chamber at~0.18 mbar working pressure. To reach the desired vapor pressure, TDMAT and Nb(OEt) 5 were heated up to 80 • C and 170 • C, respectively. According to the authors of the paper [24], Ti 1−x Nb x O 2 films deposited at temperatures around 170 • C have maximum electrical conductivity. Deionized water, which was used as an oxidizer, was kept at room temperature. The mixed oxide was formed by inserting a monolayer of niobium oxide after a few consecutive monolayers of titanium oxide (number of TiO 2 monolayers was selected depending on desired Ti:Nb ratio) and the process was repeated until the desired thickness was achieved. Fabrication of every monolayer consisted of four steps: precursor pulse/purge/water pulse/purge. Timings used for titanium oxide and niobium oxide were 0.2 s/10 s/0.06 s/5 s and 0.2 s/5 s/0.06 s/5 s, respectively. Four hundred monolayers were deposited to achieve an approximately 25 nm-thick coating.
Morphology and composition of Ti 1−x Nb x O 2 layers were examined by a scanning electron microscope (SEM) "Helios NanoLab 650"(FEI, Hillsboro, OR, USA) equipped with energy dispersive X-ray spectrometer (EDX) "INCAEnergy" (Oxford Instruments, Abingdon, UK). Thin Film ID software (Oxford Instruments) was used to estimate the Ti/Nb ratio with a 3% relative error. A relatively low accelerating voltage (7 kV) was used to achieve higher surface sensitivity. For 5:1 titanium oxide and niobium oxide monolayers deposition the resulting atomic ratio was 72 at.% titanium and 28 at.% niobium. For 10:1 titanium oxide and niobium oxide monolayers deposition the ratio was 84 at.% Ti and 16 at.% Nb.
Crystallographic structure of Ti 1−x Nb x O 2 layers was studied by X-ray diffraction (XRD) using SmartLab HR-XRD diffractometer (Rigaku, Tokyo, Japan) with an X-ray tube equipped with 9 kW Cu rotating anode. Grazing incidence diffraction geometry was used with the incidence angle of Cu Kα beam set to 0.5 • which enabled investigation of thin films and reduced influence of the substrate. The resistivity of Ti 1−x Nb x O 2 layers was measured using a four-point probe method.
The Si substrates with as-deposited films were divided into two parts, and one part was annealed in the tube furnace at 600 • C in H 2 atmosphere for 30 min. 500 nm-thick aluminum layer was thermally evaporated using"VAKSIS PVD Vapor-5S_Th" (Vaksis, Ankara, Turkey) on the p-type Si immediately after its rear side treatment in HF to remove the unnecessary SiO 2 . To complete the heterojunction devices, ohmic contacts to the n-type TiO 2 were fabricated by thermal evaporation of Ti:Au metal layers with respective thicknesses of 20 nm and: 500 nm onto a photo-resistive mask, and contact patterns were formed using the lift-off technique. Schematic cross-sections of the TiO 2 /p-Si heterojunction device and microphotograph of the contacts on the top of TiO 2 are presented in Figure 1. Morphology and composition of Ti1−xNbxO2 layers were examined by a scanning electron microscope (SEM) "Helios NanoLab 650"(FEI, Hillsboro, OR, USA) equipped with energy dispersive X-ray spectrometer (EDX) "INCAEnergy" (Oxford Instruments, Abingdon, UK). Thin Film ID software (Oxford Instruments) was used to estimate the Ti/Nb ratio with a 3% relative error. A relatively low accelerating voltage (7 kV) was used to achieve higher surface sensitivity. For 5:1 titanium oxide and niobium oxide monolayers deposition the resulting atomic ratio was 72 at.% titanium and 28 at.% niobium. For 10:1 titanium oxide and niobium oxide monolayers deposition the ratio was 84 at.% Ti and 16 at.% Nb.
Crystallographic structure of Ti1−xNbxO2 layers was studied by X-ray diffraction (XRD) using SmartLab HR-XRD diffractometer (Rigaku, Tokyo, Japan) with an X-ray tube equipped with 9 kW Cu rotating anode. Grazing incidence diffraction geometry was used with the incidence angle of Cu Kα beam set to 0.5° which enabled investigation of thin films and reduced influence of the substrate. The resistivity of Ti1−xNbxO2 layers was measured using a four-point probe method.
The Si substrates with as-deposited films were divided into two parts, and one part was annealed in the tube furnace at 600 °C in H2 atmosphere for 30 min. 500 nm-thick aluminum layer was thermally evaporated using"VAKSIS PVD Vapor-5S_Th" (Vaksis, Ankara, Turkey) on the p-type Si immediately after its rear side treatment in HF to remove the unnecessary SiO2. To complete the heterojunction devices, ohmic contacts to the n-type TiO2 were fabricated by thermal evaporation of Ti:Au metal layers with respective thicknesses of 20 nm and: 500 nm onto a photo-resistive mask, and contact patterns were formed using the lift-off technique. Schematic cross-sections of the TiO2/p-Si heterojunction device and microphotograph of the contacts on the top of TiO2 are presented in Figure  1. Measurements of direct current (DC) current-voltage characteristics of the point-contact TiO2/p-Si heterojunction were performed using a E5270B Precision IV Analyzer (Keysight Technologies, Inc., Santa Rosa, CA, USA). The point-contact electrical resistance dependence on temperature was measured in a liquid nitrogen vapor atmosphere from 78 K up to 350 K. The temperature of the sample was controlled using K-type Nickel-Chromium/Nickel-Aluminum thermocouple (Thermometrics Corporation, Northridge, CA, USA).
Optical transmission spectra of the Ti1−xNbxO2 films were measured in the 300-1300 nm wavelength range using AvaSpec ULS2048XL spectrometer and AvaLight-DH-S deuterium-halogen Measurements of direct current (DC) current-voltage characteristics of the point-contact TiO 2 /p-Si heterojunction were performed using a E5270B Precision IV Analyzer (Keysight Technologies, Inc., Santa Rosa, CA, USA). The point-contact electrical resistance dependence on temperature was measured in a liquid nitrogen vapor atmosphere from 78 K up to 350 K. The temperature of the sample was controlled using K-type Nickel-Chromium/Nickel-Aluminum thermocouple (Thermometrics Corporation, Northridge, CA, USA).
Optical transmission spectra of the Ti 1−x Nb x O 2 films were measured in the 300-1300 nm wavelength range using AvaSpec ULS2048XL spectrometer and AvaLight-DH-S deuterium-halogen light source (both from Avantes, Apeldoorn, the Netherlands). A 50 ms integration time and an averaging of 100 measured spectra were used for the measurements. Figure 2 presents the XRD patterns of the Ti 0.72 Nb 0.28 O 2 film before (as-deposited) and after annealing in an H 2 atmosphere. It was seen that the as-deposited film had an amorphous structure (a broad feature with maxima at 2Θ angle of about 21.6 • ) along with a crystalline TiO 2 of anatase structure. The lattice parameters of anatase tetragonal structure of the film (a = 0.3819 nm and c = 0.9541 nm) were increased in comparison to those presented in ICDD data base card #01-075-2545 (a = 0.3799 nm and c = 0.9509 nm). The increase in lattice parameters should be a result of insertion of Nb ions into crystalline lattice of anatase. After the annealing, the XRD peaks of anatase became sharper as a result of an increase in a crystallite size. The XRD pattern of the annealed film presented one additional peak at 2Θ angle of 27.17 • , which could be attributed to niobian rutile Ti 0.712 Nb 0.288 O 2 (#01-072-7371).

Results and Discussion
During the annealing, the amorphous phase transformed into an anatase crystalline phase, as XRD measurements confirmed. No characteristic peaks of Nb 2 O 5 were observed in the Nb-doped TiO 2 thin film as indicated previously [25].
Materials 2020, 13, x FOR PEER REVIEW 4 of 10 light source (both from Avantes, Apeldoorn, the Netherlands). A 50 ms integration time and an averaging of 100 measured spectra were used for the measurements. Figure 2 presents the XRD patterns of the Ti0.72Nb0.28O2 film before (as-deposited) and after annealing in an H2 atmosphere. It was seen that the as-deposited film had an amorphous structure (a broad feature with maxima at 2 angle of about 21.6) along with a crystalline TiO2 of anatase structure. The lattice parameters of anatase tetragonal structure of the film (a = 0.3819 nm and c = 0.9541 nm) were increased in comparison to those presented in ICDD data base card #01-075-2545 (a = 0.3799 nm and c = 0.9509 nm). The increase in lattice parameters should be a result of insertion of Nb ions into crystalline lattice of anatase. After the annealing, the XRD peaks of anatase became sharper as a result of an increase in a crystallite size. The XRD pattern of the annealed film presented one additional peak at 2 angle of 27.17, which could be attributed to niobian rutile Ti0.712Nb0.288O2 (#01-072-7371).

Results and Discussion
During the annealing, the amorphous phase transformed into an anatase crystalline phase, as XRD measurements confirmed. No characteristic peaks of Nb2O5 were observed in the Nb-doped TiO2 thin film as indicated previously [25]. Annealing of the Ti0.72Nb0.28O2 films in H2 atmosphere also resulted in a substantial decrease of its electrical resistivity from 5.0  10 2 to 1.2  10 -3  cm. In spite of high conductivity, the annealed Ti0.72Nb0.28O2 film was highly transparent in the measured 400-1300 nm spectral region (Figure 3) with more than 93% transmittance within the 800-1000 nm range. Transmittance of the annealed and asdeposited Ti0.72Nb0.28O2 films was significantly higher than that of Ti0.8Nb0.2O2 film [23]. High conductivity and transmittance values suggest the annealed Ti0.72Nb0.28O2 film is a suitable candidate for transparent electrical interconnection for perovskite/silicon tandem solar cells. Annealing of the Ti 0.72 Nb 0.28 O 2 films in H 2 atmosphere also resulted in a substantial decrease of its electrical resistivity from 5.0 × 10 2 to 1.2 × 10 −3 Ω cm. In spite of high conductivity, the annealed Ti 0.72 Nb 0.28 O 2 film was highly transparent in the measured 400-1300 nm spectral region (Figure 3) with more than 93% transmittance within the 800-1000 nm range. Transmittance of the annealed and as-deposited Ti 0.72 Nb 0.28 O 2 films was significantly higher than that of Ti 0.8 Nb 0.2 O 2 film [23]. High conductivity and transmittance values suggest the annealed Ti 0.72 Nb 0.28 O 2 film is a suitable candidate for transparent electrical interconnection for perovskite/silicon tandem solar cells.  It is worth noting that the I-V characteristics were linear; it was another valuable property for the above-mentioned application. The resistance of such TiO0.72Nb0.28O2/p + -Si heterojunction device decreased as the sample was cooled down. Dependencies resistance-vs.-temperature for TiO1-xNbxO2/p-Si heterojunction devices with different content of x and formed on different Si substrates are depicted in Figure 5. It was seen that the resistance of TiO0.72Nb0.28O2/p + -Si heterojunction (substrate Si = 10 −3  cm) linearly increased with temperature. Such linear dependence was an inherent feature of the tunnel diode at small bias voltage.   It is worth noting that the I-V characteristics were linear; it was another valuable property for the above-mentioned application. The resistance of such TiO0.72Nb0.28O2/p + -Si heterojunction device decreased as the sample was cooled down. Dependencies resistance-vs.-temperature for TiO1-xNbxO2/p-Si heterojunction devices with different content of x and formed on different Si substrates are depicted in Figure 5. It was seen that the resistance of TiO0.72Nb0.28O2/p + -Si heterojunction (substrate Si = 10 −3  cm) linearly increased with temperature. Such linear dependence was an inherent feature of the tunnel diode at small bias voltage. It is worth noting that the I-V characteristics were linear; it was another valuable property for the above-mentioned application. The resistance of such TiO 0.72 Nb 0.28 O 2 /p + -Si heterojunction device decreased as the sample was cooled down. Dependencies resistance-vs.-temperature for TiO 1-x Nb x O 2 /p-Si heterojunction devices with different content of x and formed on different Si substrates are depicted in Figure 5. It was seen that the resistance of TiO 0.72 Nb 0.28 O 2 /p + -Si heterojunction (substrate ρ Si = 10 −3 Ω cm) linearly increased with temperature. Such linear dependence was an inherent feature of the tunnel diode at small bias voltage. In general, when the interband carrier tunneling takes place, the tunnel current across a p-n junction can be expressed as [26,27]: where A is a constant, Ec and Ev represent the conduction and the valence band edges, respectively, and k is the Boltzmann constant. Expression (7) shows that the resistance of a tunnel pn junction at low bias was a linear function of temperature. The Hall effect measurements indicate that electron density in TiO0.72Nb0.28O2 is 3.5 × 10 21 cm −3 and therefore it can be regarded as a degenerate semiconductor [24,28,29]. Low resistivity p + -Si ( = 10 −3  cm) is also a degenerate semiconductor. The hole concentration determined from Hall effect measurements in p + -Si was 1.3 × 10 20 cm −3 The energy band diagram of mutually heavily doped n + -TiO2/p + -Si heterojunction in equilibrium condition is shown in Figure 6. It is seen that electrons from TiO2 conduction band could tunnel through the gap to the empty sites of the p + -Si valence band under a small forward bias. Linear dependence of the resistance on temperature supports the assumption that the interband tunneling current took place in the investigated TiO0.72Nb0.28O2/p + -Si heterojunction. The specific contact resistivity of TiO0.72Nb0.28O2/p + -Si heterojunction was 23 mΩ·cm 2 at room temperature which was better than 30 mΩ·cm 2 achieved in [7]. In general, when the interband carrier tunneling takes place, the tunnel current across a p-n junction can be expressed as [26,27]: where A is a constant, E c and E v represent the conduction and the valence band edges, respectively, and k is the Boltzmann constant. Expression (7) shows that the resistance of a tunnel p-n junction at low bias was a linear function of temperature. The Hall effect measurements indicate that electron density in TiO 0.72 Nb 0.28 O 2 is 3.5 × 10 21 cm −3 and therefore it can be regarded as a degenerate semiconductor [24,28,29]. Low resistivity p + -Si (ρ = 10 −3 Ω cm) is also a degenerate semiconductor. The hole concentration determined from Hall effect measurements in p + -Si was 1.3 × 10 20 cm −3 . The energy band diagram of mutually heavily doped n + -TiO 2 /p + -Si heterojunction in equilibrium condition is shown in Figure 6. It is seen that electrons from TiO 2 conduction band could tunnel through the gap to the empty sites of the p + -Si valence band under a small forward bias. Linear dependence of the resistance on temperature supports the assumption that the interband tunneling current took place in the investigated TiO 0.72 Nb 0.28 O 2 /p + -Si heterojunction. The specific contact resistivity of TiO 0.72 Nb 0.28 O 2 /p + -Si heterojunction was 23 mΩ·cm 2 at room temperature which was better than 30 mΩ·cm 2 achieved in [7].
Materials 2020, 13, x FOR PEER REVIEW 6 of 10 In general, when the interband carrier tunneling takes place, the tunnel current across a p-n junction can be expressed as [26,27]: where A is a constant, Ec and Ev represent the conduction and the valence band edges, respectively, and k is the Boltzmann constant. Expression (7) shows that the resistance of a tunnel pn junction at low bias was a linear function of temperature. The Hall effect measurements indicate that electron density in TiO0.72Nb0.28O2 is 3.5 × 10 21 cm −3 and therefore it can be regarded as a degenerate semiconductor [24,28,29]. Low resistivity p + -Si ( = 10 −3  cm) is also a degenerate semiconductor. The hole concentration determined from Hall effect measurements in p + -Si was 1.3 × 10 20 cm −3 The energy band diagram of mutually heavily doped n + -TiO2/p + -Si heterojunction in equilibrium condition is shown in Figure 6. It is seen that electrons from TiO2 conduction band could tunnel through the gap to the empty sites of the p + -Si valence band under a small forward bias. Linear dependence of the resistance on temperature supports the assumption that the interband tunneling current took place in the investigated TiO0.72Nb0.28O2/p + -Si heterojunction. The specific contact resistivity of TiO0.72Nb0.28O2/p + -Si heterojunction was 23 mΩ·cm 2 at room temperature which was better than 30 mΩ·cm 2 achieved in [7]. As a rule, there are three main components of current in a tunnel diode: the tunnel current (I t ), the excess current (I x ) and the diffusion current (I d ). The diffusion current is responsible for the current rise under high forward biases [26]. Therefore, I d should be negligible in comparison with the tunnel current at low bias. The excess current at low bias was mainly determined by the multistep tunneling recombination process via surface states at the TiO 2 /p + -Si interface [7,30]. Substantial density of localized surface states was determined by a large number of defects, N s~7 .0 × 10 13 cm −2 , at the TiO 2 /p + -Si interface resulting from significant lattice mismatch between the heterojunction components [30]. These interfacial states can facilitate the band to band tunneling and act as generation-recombination centers at all bias voltages [7,31]. As the generation-recombination centers, the interface states had substantial influence on charge transport through TiO 2 /p + -Si tunnel heterojunction. At reverse bias, every recombination center becomes a source of carrier generation, and high electrical conductivity can be reached by thermally generated carriers [7]. Since the carrier generation-recombination strongly depends on the thermal energy, the multistep tunneling recombination process via surface states resulted in a substantial increase of the heterojunction resistance at lower lattice temperature. Such dependence of the resistance on temperature was observed in TiO 0.72 Nb 0.28 O 2 /p-Si heterojunction on low conductivity (ρ Si = 1 Ω cm) p-type silicon substrate (see Figure 5, black circles). The band-to-band tunneling was impossible in this case, therefore the current through the TiO 0.72 Nb 0.28 O 2 /p-Si heterojunction was mainly determined by the multistep tunneling recombination process via the surface states.
I-V characteristic of the TiO 0.72 Nb 0.28 O 2 /p-Si heterojunction was not linear (see Figure 7, solid black line) with forward current larger than the reverse one, as observed in other works [7,17,30]. Similar character demonstrated the I-V dependence of the TiO 0.84 Nb 0.16 O 2 /p + -Si device formed on the low resistivity substrate (Figure 7, blue long-dotted line). Electron density in the TiO 0.84 Nb 0.16 O 2 film as determined from the Hall effect measurements was 1.9 × 10 21 cm −3 . Therefore, the TiO 0.84 Nb 0.16 O 2 film could be also regarded as a degenerate semiconductor [24,28,29], and the band to band tunnel current could be present in the investigated TiO 0.84 Nb 0.16 O 2 /p + -Si heterojunction. Since electron density in the TiO 0.84 Nb 0.16 O 2 was less than in the TiO 0.72 Nb 0.28 O 2 layer, the tunnel current in TiO 0.84 Nb 0.16 O 2 /p + -Si heterojunction became of the same order of magnitude as the excess current due to multistep tunneling recombination process via the surface states at the TiO 2 /p + -Si interface. This consideration was supported by the dependence of the resistance of the TiO 0.72 Nb 0.28 O 2 /p-Si heterojunction device on temperature depicted in Figure 5 (blue squares). Very weak temperature dependence of the resistance was an inherent feature of the tunnel current consisting of two components, I t and I x [32].
Materials 2020, 13, x FOR PEER REVIEW 7 of 10 Figure 6. Energy band diagram of n + -TiO2/p + -Si tunnel heterojunction in an equilibrium condition.
As a rule, there are three main components of current in a tunnel diode: the tunnel current (It), the excess current (Ix) and the diffusion current (Id). The diffusion current is responsible for the current rise under high forward biases [26]. Therefore, Id should be negligible in comparison with the tunnel current at low bias. The excess current at low bias was mainly determined by the multistep tunneling recombination process via surface states at the TiO2/p + -Si interface [7,30]. Substantial density of localized surface states was determined by a large number of defects, Ns  7.0  10 13 cm -2 , at the TiO2/p + -Si interface resulting from significant lattice mismatch between the heterojunction components [30]. These interfacial states can facilitate the band to band tunneling and act as generation-recombination centers at all bias voltages [7,31]. As the generation-recombination centers, the interface states had substantial influence on charge transport through TiO2/p + -Si tunnel heterojunction. At reverse bias, every recombination center becomes a source of carrier generation, and high electrical conductivity can be reached by thermally generated carriers [7]. Since the carrier generation-recombination strongly depends on the thermal energy, the multistep tunneling recombination process via surface states resulted in a substantial increase of the heterojunction resistance at lower lattice temperature. Such dependence of the resistance on temperature was observed in TiO0.72Nb0.28O2/p-Si heterojunction on low conductivity (Si = 1  cm) p-type silicon substrate (see Figure 5, black circles). The band-to-band tunneling was impossible in this case, therefore the current through the TiO0.72Nb0.28 O2/p-Si heterojunction was mainly determined by the multistep tunneling recombination process via the surface states.
I-V characteristic of the TiO0.72Nb0.28O2/p-Si heterojunction was not linear (see Figure 7, solid black line) with forward current larger than the reverse one, as observed in other works [7,17,30]. Similar character demonstrated the I-V dependence of the TiO0.84Nb0.16O2/p + -Si device formed on the low resistivity substrate (Figure 7, blue long-dotted line). Electron density in the TiO0.84Nb0.16O2 film as determined from the Hall effect measurements was 1.9  10 21 cm −3 . Therefore, the TiO0.84Nb0.16O2 film could be also regarded as a degenerate semiconductor [24,28,29], and the band to band tunnel current could be present in the investigated TiO0.84Nb0.16O2/p + -Si heterojunction. Since electron density in the TiO0.84Nb0.16O2 was less than in the TiO0.72Nb0.28O2 layer, the tunnel current in TiO0.84Nb0.16O2/p + -Si heterojunction became of the same order of magnitude as the excess current due to multistep tunneling recombination process via the surface states at the TiO2/p + -Si interface. This consideration was supported by the dependence of the resistance of the TiO0.72Nb0.28O2/p-Si heterojunction device on temperature depicted in Figure 5 (blue squares). Very weak temperature dependence of the resistance was an inherent feature of the tunnel current consisting of two components, It and Ix [32].   7 also shows the I-V characteristic of the TiO 0.84 Nb 0.16 O 2 /p + -Si heterojunction device with as-deposited titanium oxide layer (red short-dotted line). As mentioned above, the as-deposited TiO 0.84 Nb 0.16 O 2 film had an amorphous structure and therefore its conductivity was low. As a result, the I-V characteristic of the TiO 0.84 Nb 0.16 O 2 /p + -Si heterojunction device was nonohmic and asymmetric, as observed in other works [7,30].

Conclusions
Two different (x = 0.16 and x = 0.28) niobium composition containing heavily doped Ti 1-x Nb x O 2 thin films were ALD-deposited on p-type Si substrates. Reductive post-deposition annealing was required to crystallize amorphous titanium dioxide into the anatase structure and to increase its electrical conductivity. The current-voltage characteristic of the TiO 0.72 Nb 0.28 O 2 /p + -Si heterojunction device is found to be ohmic, and the junction resistance linearly depends on temperature. In this case the current across the heterojunction is mainly stipulated by the interband charge carrier tunneling. When the highly conductive titanium dioxide is deposited on low conductivity (ρ Si = 1 Ω cm) p-Si substrate, the current across the TiO 0.72 Nb 0.28 O 2 /p-Si heterojunction is mainly determined by the multistep tunneling recombination process via the surface states. The contact resistivity of the TiO 0.72 Nb 0.28 O 2 /p-Si heterojunction is higher than that of the TiO 0.72 Nb 0.28 O 2 /p + -Si heterojunction. The formed titanium dioxide films also demonstrate excellent transparency with absorption less than 10% in the visible region. Therefore, the TiO 0.72 Nb 0.28 O 2 /p + -Si heterojunction could be a suitable candidate as transparent interconnection in 2-T perovskite/silicon tandem solar cells.