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Current transport and thermoelectric properties of very high power factor Fe3O4 / SiO2 / p-type Si (001) devices

The current transport and thermoelectric properties of Fe3O4 / SiO2 / p-type Si(001) heterostructures with Fe3O4 thicknesses of 150, 200, and 350 nm have been investigated between 100 and 300 K. We observe a sharp drop of the in-plane resistivity at 200K due to the onset of conduction along the Si / SiO2 interface related to tunneling of electrons from the Fe3O4 into the accumulation layer of holes at the Si / SiO2 interface, whose existence was confirmed by capacitance-voltage measurements and a two band analysis of the Hall effect. This is accompanied by a large increase of the Seebeck coefficient reaching +1000 {\mu}V/K at 300K that is related to holes in the p-type Si(001) and gives a power factor of 70 mW/K2m when the Fe3O4 layer thickness is reduced down to 150 nm. We show that most of the current flows in the Fe3O4 layer at 300 K, while the Fe3O4 / SiO2 / p-type Si(001) heterostructures behave like tunneling p-n junctions in the transverse direction.


Introduction
Thermoelectric materials and devices have been investigated for many decades since the conversion of heat to electricity is important for the conservation of the environment. The conversion efficiency is described by the dimensionless figure-of-merit, ZT = S 2 T / ρ κ, where S is the Seebeck coefficient or thermopower, ρ the electrical resistivity, T the temperature, and κ the total thermal conductivity. A high ZT may be achieved by reducing κ and/or by increasing the thermoelectric power factor P = S 2 / ρ; however, this is not easy due to the interdependence of S, ρ, and κ since a reduction of ρ is usually achieved by increasing the carrier density, which in turn reduces S [1]. This constraint can be relaxed via the use of low dimensional semiconductors such as quantum wells, wires, or dots [2][3][4][5][6] after Hicks and Dresselhaus [7,8]. In addition, significant reductions in κ have been attained via the use of nanostructured materials such as nanowires [9], while large power factors P have been obtained by tuning the electronic properties [10]. For instance, a huge P, of 200 mW/K 2 m, was measured by Sun et al. [11] in FeSb 2 and shown to be electronic in origin. Recently, we investigated the lateral transport and thermoelectric properties of a 200 nm Fe 3 O 4 / SiO 2 / ptype Si(001) heterostructure, which exhibited a large increase in the Seebeck coefficient up to +900 μV/K with increasing temperature and a concurrent sharp drop in the resistance giving a very high power factor of 25.5 mW/K 2 m. The sharp drop of resistance with increasing temperature was attributed to the onset of conduction along the Si / SiO 2 interface due to tunneling of electrons from the Fe 3 O 4 layer into the accumulation layer of holes suggested to exist at the Si / SiO 2 interface as a consequence of the difference in the work functions of Fe 3 O 4 and underlying p-type Si(001) [12].
Here, we have carried out a detailed investigation into the lateral and transverse current transport and thermoelectric properties of Fe 3 O 4 / SiO 2 / p-type Si (001) heterostructures having Fe 3 O 4 thicknesses of 150, 200, and 350 nm in order to gain deeper insight of the current flow distribution and origin of the high thermopower, which are critical in extracting the resistivity and power factor. We show that the sharp drop of resistance is attributed to the current that flows along the Si / SiO 2 interface for T > 200K through the accumulation layer of holes whose existence was confirmed by capacitance-voltage measurements and two band analysis of the Hall effect. However, we show that a large fraction of the current will flow along the top Fe 3 O 4 at 300K giving a power factor of 70 mW/K 2 m when the Fe 3 O 4 layer thickness is reduced down to 150 nm. In addition, we find that the heterostructures behave like p-n junctions in the transverse direction, which is responsible for the high thermopower.

Experimental methods
Fe 3-x O 4 films with different thicknesses of 150, 200, and 350 nm were grown by pulsed laser deposition (PLD) on p-type Si (001) at 210 o C. The p-type Si (001) had a native SiO 2 thickness of 2 nm, which was verified by transmission electron microscopy. Details of the growth conditions and parameters are described elsewhere [13]. The films were analyzed regarding their phase purity, stoichiometry, crystallinity, preferred orientation growth, magnetic and electrical properties, which were compared with state-of-art magnetite films [13] High quality, polycrystalline films with the crystallites randomly oriented, x = 0.01 and uniform thicknesses of 150, 200, and 350 nm, as-determined by image analysis of their crosssections observed in a scanning electron microscope, are considered in this article. Hall effect measurements were carried out in the Van der Pauw geometry between 100 and 300K using a  Finally, the in-plane Seebeck coefficient was determined by applying a thermal gradient on Fe 3 O 4 and measuring the temperature and voltage differences between two points on the surface of Fe 3 O 4 in the steady state as shown in Fig. 4. All of the above lateral and transverse current transport and thermopower measurements were carried out using a physical property measurement system (PPMS) by Quantum Design.

Results and Discussion
In order to understand in detail the transport and thermoelectric properties, it is necessary to consider the energy band diagram of the Fe 3 O 4 / SiO 2 / p-type Si (001) heterostructure in thermodynamic equilibrium shown as an inset in Fig. 1. The p-type Si (001) substrate had a thickness of 500 μm and a hole density of 10 15 cm -3 determined from Hall effect measurements at 300 K. From p ≈ 10 15 cm -3 , we find that the Fermi level resides ≈0.25 eV above the valence band edge, i.e., E F -E V = 0.25 eV. The work function of p-type Si(001) is given by φ S = + (E C -E F ) [22] i.e., φ S = 4.92 eV since the electron affinity χ Si = 4.05 eV and E C -E F = 0.87 eV. On the other hand, the work function of Fe 3 O 4 is φ M = (5.5 ± 0.05) eV [14]; so the work function difference between the metal and semiconductor φ M -φ S = φ MS = 0.58 eV is positive, which is expected to produce an upwards band bending at the Si/SiO 2 interface leading to an accumulation of holes whose existence was confirmed by capacitance-voltage (C-V) measurements and by a two-band analysis of the Hall effect described in detail later.
Consequently, the n-Fe 3 O 4 / SiO 2 / p-type Si(001) heterostructure is expected to act like a p-n junction and we find that it exhibits asymmetric I-Vs in the transverse direction as shown in Fig. 1. More specifically, the current shows an immediate increase for negatively applied voltages (V A ), i.e., negative potential on Fe 3 O 4 , but is initially zero for positive V A and then exhibits a substantial increase only for V A > + 2V. This I-V characteristic is similar to that measured in a Fe 3 O 4 / SiO 2 / n-type Si(001) heterostructure by Qu et al. [15] with an inversion layer of holes at the n-type Si/SiO 2 interface. Similarly, the 350 nm Fe 3 O 4 / SiO 2 / p-type Si(001) heterostructure also exhibits asymmetric I-Vs as shown in Fig. 2, but while the current shows an immediate increase for negative V A we observe that V A > + 4V in order to establish a current flow. In both cases shown in Figs. 1 and 2, we find that the I-Vs depend on temperature, which was varied between 100 and 300 K, and also the thickness of Fe 3 O 4 .
However, in order to understand the current transport we ought to consider the energy band diagrams under externally applied electric fields. Upon the application of an electric field, there will be an increase in band-bending at the Si / SiO 2 interface for negative potential on with the p-n heterojunction so a larger potential difference will appear across the Fe 3 O 4 upon increasing its thickness. Similarly, a reduction in temperature will lead to a gradual suppression of thermionic assisted tunneling over the SiO 2 barrier but also a decrease of the carrier density and an increase in the resistance of the Fe 3 O 4 layer since charge ordering should open a gap at the Fermi energy resulting into the metal-insulator transition below T V = 120 K [17] and a reduction in the current for a specific applied voltage. From the above, we conclude that the Fe 3 O 4 / SiO 2 / p-type Si(001) heterostructure acts like a p-n junction, which is expected to limit the ohmic return current that occurs in bulk materials during charge redistribution under a temperature gradient resulting into higher thermopower as has been shown in p-n thermal diodes [18]. However, before elaborating further on the thermoelectric properties it is necessary to consider in more detail the current flow distribution in the lateral direction since this is critical in extracting the resistivity and power factor of the In addition, the temperature dependence of the longitudinal resistance exhibits a sharp drop with increasing temperature as shown in the inset of Fig. 4. Similar temperature dependence has been reported in Fe 3 O 4 / SiO 2 / n-type Si [19], Fe 3 C / SiO 2 / n-type Si [20], and other M / SiO 2 / Si structures, where M stands for very-thin metallic films [21] but these have been investigated as spintronic not thermoelectric devices. The sharp drop in resistivity has been attributed to the onset of conduction in the Si inversion layer of holes at the Si / SiO 2 interface, which gives a positive Hall voltage despite the fact that the substrate is n-type Si(001) [19][20][21]. More importantly, it has been shown that the current flows along the Si / SiO 2 interface in these M / SiO 2 / Si structures not through the bulk Si [21]. The existence of the accumulation layer of holes at the Si / SiO 2 interface of the Fe 3 O 4 / SiO 2 / p-type Si heterostructure in our case was confirmed by capacitance voltage (C-V) measurements for the 200 nm Fe 3 O 4 / SiO 2 / p-type Si(100) heterostructure as shown in the inset of Fig. 3, which is typical of a MOS capacitor with p-type Si [22]. For V A < 0, holes are attracted to the Si / SiO 2 interface and the capacitance is essentially governed by the oxide thickness C ox . For V A > 0, holes are depleted from the interface and the capacitance starts decreasing due to the increasing capacitance of the depletion layer, which is in series with C ox . The C-V curve of Now the sheet resistance and resistivity of the two dimensional hole gas (2DHG) with a density of 10 19 cm -3 and corresponding mobility of 100 cm 2 /Vs taking a thickness of 10 nm, which is typical of the spatial extent of the 2DHG in the quasi triangular potential well at the Si / SiO 2 interface [24] is 6 kΩ / □ and 6 mΩ cm, respectively. On the other hand, the resistivity of polycrystalline Fe 3 O 4 grown on MgO by molecular beam epitaxy was found to decrease for thicknesses < 50nm according to Eerenstein et al. [25] but the resistivity did not vary significantly for Fe 3 O 4 thicknesses between 50 and 100 nm and had a value of ≈ 5mΩ cm, which is close to the room temperature resistivity of the Fe 3 O 4 / SiO 2 / p-type Si (100) structures shown in the inset of Fig. 4. A similar type of dependence has also been found in the case of Fe 3 O 4 layers grown by Li et al. using PLD [26]. The low resistivity is a direct consequence of the large density of electrons, which is of the order of 10 21 cm -3 despite the low electron mobility as measured for instance by Reisinger et al. [27], who found a carrier density of 3 x10 21 Fig. 3. We do not expect a contribution from the p-type Si(001) bulk in accordance with Dai et al. [21], who showed that conduction occurs along the Si / SiO 2 interface in Cu / SiO 2 / Si heterostructures not through bulk Si. From the above, we conclude that most of the current will flow through the Fe 3 O 4 layer since its sheet resistance is smaller than that of the 2DHG but also in view of the intervening SiO 2 . It is worthwhile pointing out that the resistance of Fe 3 O 4 alone decreases monotonically with temperature from several MΩ down to a few kΩ as shown in the inset of Fig. 3 and is close to the resistance of the 150nm Fe 3 O 4 / SiO 2 / p-type Si(001) heterostructure at 300 K. Consequently, the sharp drop of the resistivity with temperature shown as an inset in Fig. 4 occurs due to the onset of tunneling of electrons from the Fe 3 O 4 into the accumulation layer of holes at the Si / SiO 2 interface but conduction through the Fe 3 O 4 layer is significant at 300 K. We ought to emphasize that we have observed this sharp drop of resistivity at the same temperature in Ni / SiO 2 / p-type Si (001) and Cu / SiO 2 / p-type Si(001) heterostructures similar to Dai et al [21], so it is not associated with the Verwey transition of Fe 3 O 4 . The sharp drop of resistance with increasing temperature is smaller and less abrupt, i.e., broader, by increasing the thickness of the Fe 3 O 4 layer suggesting that a larger fraction of current flows through the Fe 3 O 4 since its resistance will be smaller resulting into a smaller electric field perpendicular to the Si / SiO 2 interface that will drive current through the SiO 2 barrier and along the Si / SiO 2 interface.
While the resistivity exhibited a sharp drop for T > 200 K, we find that the thermopower measured on top of the Fe 3 O 4 increased over the same temperature range as shown in Fig. 4, something that would not be observed in bulk materials where the carrier density must be reduced in order to increase the thermopower. The thermopower of single crystal magnetite [12,23] is negative over the entire measured temperature range, i.e., S = -60 μV/K. On the other hand, the thermopower of the Fe 3 O 4 / SiO 2 / p-type Si(001) structure is small and positive, remains constant up to 200K and then exhibits a large increase reaching quite large values ≈ + 1000 μV/K at 300 K. It is useful to note that the thermopower of p-type Si(001) without the Fe 3 O 4 layer was considerably higher than + 200 μV/K between 150 and 200K and reached + 900 μV/K at 300 K, which is comparable to the thermopower measured in the case of Fe 3 O 4 / SiO 2 / p-type Si(001). In addition, it is useful to point out that the thermopower decreased significantly upon increasing the thickness of the SiO 2 so clearly the large thermopower is not due to the Fe 3 O 4 or SiO 2 , which is an insulator that is void of carriers and has a large energy band gap of 9 eV. The large thermopower is clearly related to the charge redistribution of holes, which occurs in the underlying p-type Si(001). More specifically, the application of a temperature gradient along the surface will result into a transverse temperature gradient so electrons on the high temperature side will cross the barrier into the underlying Si(001), which is at a lower temperature and the quasi Fermi level in the semiconductor will be lower than that in the metallic Fe 3 O 4 similar to the energy band diagram shown as an inset in Fig. 2. At low temperatures, only a limited number of carriers will undergo tunneling from the Fe 3 O 4 into the Si(001) but for temperatures above 200K a larger number of electrons will cross into the underlying p-type Si(001), which in turn allows one to measure the potential difference that develops as a result of the charge redistribution in the p-type Si(001) due to the applied temperature gradient. We should note that hot carrier filtering through barriers with heights of many kT [28] or carrier injection using p-n thermal diodes [18] have been shown to yield high S and ZT although the precise physical mechanisms are not yet well understood. It is, therefore, possible that hot carrier filtering occurs due to the specific electronic structure of Fe 3 O 4 and the existence of the two spin down bands as shown in Fig. 2, while the formation of a p-n like junction will limit the ohmic return current which occurs upon charge redistribution under a temperature gradient.
Evidently, the current transport and thermoelectric properties of the Fe 3 O 4 / SiO 2 / p-type Si(001) heterostructure may be exploited for the realization of high thermoelectric figure ofmerit devices by reducing j and exploiting its high thermoelectric power factor. Silicon nanowires exhibit a one-hundred fold reduction in thermal conductivity compared to the bulk giving very high ZT [9] so we anticipate that Fe 3 O 4 / SiO 2 / Si core-shell nanowires are very promising for the realization of emerging devices in future integrated circuits for power generation or cooling. However, the origin of the high thermopower, thermal conductivity, and thermoelectric figure of merit will be presented in more detail elsewhere.

Conclusions
In conclusion, we have investigated the lateral and transverse current transport and