Figure 2 a shows the I–V curve of structures on n type conductivity silicon substrates (n-Si/In₂O₃ : Er) for room temperature and 300, 350 and 360 K. At a low positive (forward) top contact bias (0 to +0.5 V) the current through the structure is controlled by electron injection from n type conductivity silicon over a forward barrier (Φ_ef) at the Si/In₂O₃ : Er interface to the film (the so-called sub-barrier mode, Fig. 1 a). Since the barrier height decreases due to the applied bias (Φ_ef – V_Si, where V_Si is the silicon potential drop, Fig. 1 a), the current through the barrier exhibits an exponential growth depending on the bias. Furthermore, the sub-barrier current through the barrier increases with temperature (Fig. 2 a) in the 0 < V < 0.5 rang. This growth is controlled by the high-energy tail of Boltzmann’s electron distribution curve for silicon: the higher the temperature, the more electrons capable of overcoming the barrier and the higher the current, pursuant to the electron thermoemission model [41]. For a sufficiently high forward bias 0.5 < V < 2 V (Fig. 2 a) the band bending in silicon becomes greater than the barrier height (Fig. 3 a) and all the carriers, i.e., substrate electrons, can easily overcome the barrier (over-barrier mode). In over-barrier mode the current through the structure is controlled by the resistance of the space charge region (SCR) in silicon and the In₂O₃ : Er film resistance. The current vs temperature dependence in over-barrier mode is inverse to that for sub-barrier mode, i.e., the current declines with an increase in temperature. This behavior is controlled by the temperature function of the conductivity, more specifically, the carrier mobility: the higher the temperature, the lower the mobility since high-temperature carrier mobility is mainly controlled by carrier scattering at lattice phonons [36].

Figure 2.

Analysis of Si/In₂O₃ : Er/In-contact structure I–V curves for n type conductivity silicon substrates: (a) I–V curves for different temperatures for forward (+V) and reverse (–V) bias; (b) approximation of forward (+V) currents (J_f) through the barrier as per Eq. (1b); (c) corrected approximation of forward (+V_Si) currents J_f through the barrier as per Eq. (3)

Figure 3.

Barrier thermoemission model correction (Eq. (1b)) for silicon potential drop (Eq. (3)): (a) band structure calculation in electrostatic approximation (Poisson’s equation and Boltzmann’s carrier distribution [41]) for T = 360 K; (b) V_Si(V) calculation for different temperatures T (solid curves are for KEF 7.5 n type conductivity Si substrate and 200 nm In₂O₃ : Er film, dashed curves are for KDB 7.5 p type conductivity Si substrate and 60 nm In₂O₃ : Er film)

At a negative (reverse) bias applied to the top In contact, electrons are injected from the metal to the film through the backward barrier (Φ_eb) at the In/In₂O₃ : Er interface (Fig. 1 b). At sufficiently high temperatures (room and above) the backward currents have a saturated pattern (Fig. 2 a) in accordance with the barrier thermoemission model [41]:

$J=J_s\left[exp\left(\frac{V}{nkT}\right)-1\right].$ (1a)

For the forward branch V > 3kT the simplified expression (Eq. (1a)) has an exponential growth pattern:

$J=J_{s}exp\left(\frac{V}{nkT}\right),$ (1b)

where V is the bias, n is the nonideality factor, k is Boltzmann’s constant, T is the absolute temperature and J_s is the saturation backward current determined as follows:

$J_s=A^R{T}^{2}exp\left(-\frac{Ф}{kT}\right),$ (2)

where Φ is the barrier height and A^R is Richardson’s constant (A^R = 120 A/(cm² · K²) for electrons in silicon and A^R = 30 A/(cm² · K²) for holes in silicon [41]).

Figure 2 b shows an exponential approximation of the forward I–V curve branches for low bias (at the sub-barrier section) as per Eq. (1b). It can be seen from Fig. 2 b that the initial I–V curve sections can be described with exponents but the nonideality coefficients prove to be excessively large (n = 3÷5). Correct analysis requires taking into account that the n-Si/In₂O₃ : Er/In-contact structure in question is a metal/dielectric/semiconductor (MDS) or a metal/oxide/semiconductor (MOS) structure where the In₂O₃ : Er is the intermediate dielectric layer between the silicon substrate and the metallic contact. Although In₂O₃ is not a classic dielectric but rather a wide-band semiconductor (E_gIn2O3 = 2.69÷2.93 eV [38, 39]) and has a low electron injection barrier as will be shown below, its barrier current expression (Eq. (1b)) should be corrected.

To correct Eq. (1b) one should take into account that bias applied to an MDS structure drops not only in the silicon SCR but also in the dielectric, with the barrier height decreasing exactly by the magnitude of the silicon potential drop (Φ – V_Si), see Fig. 1 a and Fig. 3 a. Barrier tunneling at lower bias is still low and is therefore ignored. Then the barrier thermoemission expression (Eq. (1b)) for the MDS structure transforms as follows:

$J=J_{s}exp\left(-\frac{V_{Si}}{nkT}\right).$ (3)

The silicon potential drop V_Si as a function of the bias V was calculated by numerically solving Poisson’s equation in Boltzmann’s carrier statistics approximation [41] and is shown in Fig. 3 b for different temperatures by solid curves for the KEF 7.5 n type conductivity Si substrate. The respective calculated curves for the Si/SiO₂ system were reported in the cited work [41]. Those curves can be used with a dielectric permeability correction for In₂O₃ (ε_In2O3 = 8.9 [31, 32]) instead of SiO₂. Reconstructing the I–V curves in the silicon potential drop coordinates (V_Si) instead of the applied bias ones (Fig. 2 c) provides a good fit between the resultant I–V curves and the exponent described by Eq. (3). The nonideality coefficient is close to unity in this case (Fig. 2 c).

Thus the initial (sub-barrier) sections of the forward I–V curves for the n-Si/In₂O₃ : Er structures can be described within the barrier thermoemission model with a silicon potential drop correction of the bias.

Figure 4 a shows the I–V curve of structures on p type conductivity silicon substrates (p-Si/In₂O₃ : Er) for room temperature and 280, 300 and 400 K. These curves also demonstrate a rectifying pattern, by analogy with those for the n type conductivity silicon substrate (Fig. 2 a) but with an inverse polarity: the forward branch (negative bias) corresponds to hole injection from the p type conductivity substrate to the film through the forward barrier Φ_hf (Fig. 1 b) while the backward branch (positive bias), to hole injection from the surface metal contact to the film through the backward barrier Φ_hb (Fig. 1 a). The forward I–V curve branch also has a sub-barrier current section from 0 to –1 V and a over-barrier current section from –1 to –3 V (Fig. 4 a). By analogy with electron injection, the sub-barrier current for hole injection grows with an increase in temperature following the increase in the concentration of over-barrier energy holes in Boltzmann’s distribution. Whereas for electron injection the sub-barrier mode is at 0 to +0.5 V, for hole injection the sub-barrier mode covers a wider range, from 0 to –1 V which may indicate a higher hole injection barrier which is nevertheless lower than it follows from the valence band discontinuity (1.64 eV, see Fig. 1 b). The forward over-barrier current in the –1 to –3 V range (Fig. 4 a) drops with an increase in temperature by analogy with the case of the n type conductivity substrate since it is controlled by the same carrier scattering mechanism, i.e., at lattice phonons [36]. For a reverse bias (0 – +5 V) the currents have a saturating pattern in accordance with the barrier thermoemission model as per Eq. (1a) [41].

Figure 4.

Analysis of Si/In₂O₃ : Er/In contact structure I–V curves for p type conductivity silicon substrates: (a) I–V curves for different temperatures for forward (–V) and reverse (+V) bias; (b) approximation of forward (–V) currents (J_f) through the barrier as per Eq. (1b); (c) corrected approximation of forward (–V_Si) currents J_f through the barrier as per Eq. (3)

By analogy with the electron injection case discussed above (Figs 2 and 3), hole injection from the p type conductivity substrate through the barrier to the In₂O₃ : Er film was also analyzed within the barrier thermoemission model. Figure 4 b shows I–V curve exponential approximation in accordance with uncorrected Eq. (1b). The nonideality coefficients prove to be large (n = 5÷7). Then, by analogy with the solution of Poisson’s equation in Boltzmann’s carrier statistics approximation, the KDB 7.5 p type conductivity Si substrate / 60 nm thick In₂O₃ dielectric MOS structure (ε_In2O3 = 8.9 [31, 32]) was simulated for different bias (V = 0 ÷ –3 V) and 228, 300 and 400 K. For each bias the silicon potential drop V_Si was found. The calculated V_Si vs V curves are shown in Fig. 3 b by dashes. Figure 4 c shows the I–V curves for forward currents J_f as a function of silicon potential drop. Then the initial (sub-barrier) sections of the I–V curves can be approximated with exponents in accordance with corrected Eq. (3) and the nonideality coefficients will be close to unity (n = 1).

Thus the initial I–V curve sections for the Si/In₂O₃ : Er structures on silicon substrates, whether n or p type conductivity, can be described within the majority carrier barrier thermoemission model with a silicon potential drop correction of the bias.

To determine the forward electron injection barrier Φ_ef between n type conductivity silicon and the In₂O₃ : Er film (Fig. 1 a), we measured the forward current vs temperature functions at low bias in sub-barrier mode V = +0.2 and +0.4 V (Fig. 2 a). To determine the backward electron injection barrier Φ_eb between the metallic In contact and the In₂O₃ : Er film (Fig. 1 b), we measured the backward current vs temperature functions at saturation V = –2 V (Fig. 2 a). The resultant temperature functions were plotted in Schottky coordinates in accordance with Eqs. (2) and (3) (Fig. 5 a).

Figure 5.

Forward current vs temperature functions in Schottky coordinates at low sub-barrier bias (color dashed lines) and backward currents at saturation (gray dashed lines) for Si/In₂O₃ : Er strucrures on (a) n and (b) p type conductivity silicon substrates. Slope and barrier height analysis for electron and hole injection

For reverse bias at saturation V = –2 V (Fig. 2 a), the backward current vs temperature function in Schottky coordinates (Fig. 5 a, grey dashes) fits a line the slope of which corresponds to the backward electron injection barrier height between the metallic In contact and the In₂O₃ : Er film: Φ_eb = 0.21 eV (Fig. 1 b). At low temperatures (T < 150 K, see Fig. 5 a) the backward current no longer depends on temperature, probably due to a change of the current mechanism from thermoemision to barrier tunneling.

For low forward sub-barrier bias V = +0.2 and +0.4 V (Fig. 2 a) the current vs temperature functions in Schottky coordinates have 82 and 14 meV slopes, respectively (Fig. 5 a, red and green dashed lines) corresponding to the forward barrier height less the silicon potential drop, i.e., Φ_ef – V_Si (Fig. 1 a). Addition of V_Si = 61 and 94 mV (Fig. 3 b, blue solid line) yields the forward electron injection barrier height between silicon and the films (n-Si/In₂O₃ : Er) Φ_ef = 0.143 and 0.108 eV, respectively. However, since V = +0.4 is already close to the over-barrier mode (Fig. 3 a), barrier thermoemission is coupled with barrier tunneling and the thermoemission barrier height Φ_ef = 0.108 eV appears to be underestimated. Thus, a more correct barrier height estimate can be obtained in purely sub-barrier mode at low bias V = +0.2 V. Thus, the forward electron injection barrier between the silicon substrate and the film (n-Si/In₂O₃ : Er) is Φ_ef = 0.14 eV.

To determine the forward hole injection barrier between p type conductivity silicon and the In₂O₃ : Er film (e.g. Φ_hf in Fig. 1 b), we measured the forward current vs temperature functions at low bias in sub-barrier mode –0.5 V ≤ V < 0 (Fig. 4 a). To calculate the backward hole injection barrier between the metallic In contact and the In₂O₃ : Er film (e.g. Φ_hb in Fig. 1 a), we measured the backward current vs temperature functions at saturation for V = 2 V (Fig. 4 a). The resultant temperature functions were plotted in Schottky coordinates in accordance with Eqs. (2) and (3) (Fig. 5 b).

For reverse bias at saturation V = +2 V (Fig. 4 a), the backward current vs temperature function in Schottky coordinates (Fig. 5 b, grey dashed line) fits a line with a slope corresponding to the backward hole injection barrier height between the metallic In contact and the In₂O₃ : Er film: Φ_hb = 0.5 eV (Fig. 6 b).

Figure 6.

Schematic band diagrams of p-Si/In₂O₃ : Er heterostructure for (a) forward and (b) reverse bias with electron and hole injection barriers shown

For low forward sub-barrier bias V = –0.2, –0.3, –0.4 and –0.5 V (Fig. 4 a) the current vs temperature functions in Schottky coordinates have slopes of 0.22, 0.21, 0.206 and 0.203 meV, respectively (Fig. 5 b, color dashed lines) corresponding to the forward barrier height less the silicon potential drop, i.e., Φ_hf – V_Si (Fig. 6 a). Correction by the calculated V_Si = 0.08, 0.1, 0.12 and 0.13 V, respectively (Fig. 3 b, blue dashed line) yields the forward hole injection barrier height between silicon and the films in the p-Si/In₂O₃ : Er structures: Φ_hf = 0.3 eV (Fig. 6 a).

Thus, the temperature functions of the backward saturation currents and the forward sub-barrier currents for the In₂O₃ : Er film structures on n and p type conductivity silicon substrates (Si/In₂O₃ : Er) suggest that the forward electron injection barrier between n type conductivity silicon and the films (n-Si/In₂O₃ : Er) is Φ_ef = 0.14 eV, the backward electron injection barrier between the metallic In contact and the film (In/In₂O₃ : Er) is Φ_eb = 0.21 eV, the forward hole injection barrier between p type conductivity silicon and the films (p-Si/In₂O₃ : Er) is Φ_hf = 0.3 eV and the backward hole injection barrier between the metallic In contact and the films (In/In₂O₃ : Er) is Φ_hb = 0.5 eV.

The data on carrier injection barriers are shown in the schematic band diagrams of the Si/In₂O_{3 :} Er heterostructure in Fig. 6 for p type conductivity silicon substrate. The conduction band discontinuity between silicon E_С and the film E_СIn2O3Er – E_СSi is shown in Fig. 6 to be equal to the calculated electron injection barrier Φ_ef = 0.14 eV. This assumption was made on the basis of indirect literary data on low electron injection barriers both for Si/In₂O₃ (e.g., there are data on a negative barrier [33, 34]) and for related materials Si/In₂O₃ : Mo [35] and Si/In₂O₃ : Sn [31,32]. Judging from the calculated electron injection barrier Φ_ef = 0.14 eV, the literary data on the silicon band gap E_gSi = 1.12 eV [41] and the film band gap E_gIn2O3 = 2.69÷2.93 eV [38, 39] (we accept it to be 2.9 eV for clarity), the valence band discontinuity between silicon E_V and indium oxide E_VIn2O3Er – E_VSi appears to be excessively large, i.e., 1.64 eV (Fig. 1 b).

Despite the large calculated valence band discontinuity (ΔE_V ~ 1.64 eV), the hole injection barrier between silicon and the film proved to be but moderate: Φ_hf = 0.3 eV (Fig. 6 a). This indicates that the band gap of the synthesized films has a hole conduction channel. It is shown by the dotted line E_ds in Fig. 6.

It seems that the hole conduction channel in the band gap is associated with the defect states caused by an imperfect structure of the RF magnetron sputtered In₂O₃ : Er films. Possibly, high defect concentrations introduced by magnetron deposition form multiple defect levels in the band gap. These multiple defect levels merge to form a defect state density spreading from the valence band edge E_V to the hole conduction channel in the band gap E_ds. In Fig. 6 the defect state density in the band gap of the In₂O₃ : Er films is schematically shown by the green curve D_ds.

Thus, electron transport in the film occurs via the conduction band E_C (Fig. 1 a) and hole transport occurs inside the band gap via the conduction channel E_ds (Fig. 6 a) generated by the tails of the defect state density D_ds in the band gap. Taking into account the literary data on the silicon band gap (E_gSi = 1.12 eV [41]) and the calculated electron and hole injection barriers between silicon and the In₂O₃ : Er film, i.e., Φ_ef = 0.14 eV and Φ_hf = 0.3 eV, respectively (Fig. 6 a), the energy gap between the conduction band electrons and the band gap conduction channel holes is E_С – E_ds = 1.56 eV (Fig. 6 b).

The 400–800 nm PL spectra (Fig. 7) confirm the existence of defect levels in the In₂O₃ band gap [42–48]. These levels fall in the 1.55–3.1 eV energy range, i.e., inside the In₂O₃ band gap E_gIn2O3 = 2.69÷2.93 eV [38, 39].

Figure 7.

In₂O₃ : Er PL spectra compared against literary data on PL of In₂O₃ films synthesized using different methods [42–48]

In₂O₃ films synthesized using different methods were studied earlier [42–48]:

– metallic In sputtering followed by thermal oxidation [42];

– growth and oxidation in an argon + oxygen gas atmosphere on an InP substrate with gold as surfactant by vapor–liquid–crystal mechanism (VLS) [43];

– oxidation of 1–3 mm metallic In grains in an argon + oxygen gas atmosphere [44];

– In evaporation and transport in an argon + oxygen gas atmosphere and deposition on substrate [45];

– In evaporation and redeposition in an argon flow atmosphere in a furnace [46];

– In₂O₃ vapor phase deposition in an argon + oxygen gas atmosphere on a silicon substrate with gold surfactant [47];

– metallic indium deposition on differently oriented silicon substrates ((100), (110), (111)) and 850 °C oxidation in a wet argon flow atmosphere [48].

These methods produce completely different film structures: 400–600 nm nanocrystals consisting of agglomerated finer 40–60 nm nanocrystals [42]; square cross-section 15–150 nm thick nanowires reaching decades of microns in length [43]; 40–120 nm diam. nanowires 15–25 μm in length [44]; 20–100 nm diam. nanowires (30 nm on average) up to 100 μm in length [45]; octahedral faced crystals several microns in size [46]; 20–40 nm diam. nanowires 1 μm in length with gold drops at ends [47]; 0.1–1.0 μm sized polycrystals [48].

The 400–800 nm PL falling into the In₂O₃ band gap was attributed to the following defects in the band gap [42–48]: oxygen deficiency related defects [42]; oxygen vacancies [43]; single-ionized oxygen vacancies [V_O⁺] [44]. One of the peaks at 420 nm was attributed [45] to oxygen deficiency related defects [V_O], and the other 630 nm one, to excess oxygen atom related defects, e.g. interstitial oxygen atoms [O_I], In vacancies [V_In] or In atoms substituted for O [O_In] [45]. In another work [46] PL was attributed to interstitial In atoms [In_i³⁺] rather than oxygen vacancies, while in [47, 48], again to oxygen vacancies. Thus the defect origin is most often reported to be oxygen atom deficiency, but exceptions occur [45]. However, the specific defect type is most often reported to be oxygen vacancy, the authors not having a general consensus though.

Similar 400–800 nm PL is observed in our magnetron sputtered films (Fig. 7, blue curve). The PL absorption edge 1.55 eV (Fig. 7) is in a good agreement with the energy gap between the electrons and the holes E_С – E_ds = 1.56 eV (Fig. 6 b). The electrons are in the conduction band E_C In₂O₃ : Er, and the holes are in the conduction channel E_ds caused by the defect state density D_ds spreading from the valence band edge E_V to inside the In₂O₃ : Er band gap (Fig. 6 b). Thus, the defect state density D_ds (Fig. 6) in the band gap is confirmed by PL and accounts for the low hole injection barrier obtained for our structures.