Enhancing the intrinsic p-type conductivity of the ultra-wide bandgap Ga 2 O 3 semiconductor

Strongly compensated Ga2O3 is shown to be an intrinsic (or native) p-type conductor with the largest bandgap for any reported p-type transparent semiconductor oxide which may shift the frontiers in fields such as power electronics and photonics.


Introduction
Recently, ultra-wide band gap gallium oxide (Ga 2 O 3 ) is receiving a lot of renewed attention as a transparent semiconducting oxide (TSO) champion owing to its unusual material properties 1-3 large tuneable conductivity [4][5] , extremely high breakdown field 6-8, unique optoelectronic properties [9][10][11] and low cost. 12 TSOs are a class of key enabling material in increasingly high demand because of the immediate applications they can find in a variety of new technologies, ranging from thin-film coatings and sensor devices, to transparent electronics and optoelectronics in telecommunications [13][14] . Some TSOs are indeed the standard choice for use in transparent electrode applications 15 and are also hugely important for information and communication technologies such as displays, touch screens, solar cells or light emitting diodes 13 . Another key factor in the adoption of oxide semiconductors is that they are compatible with the strict manufacturing requirements of large-scale, largevolume, flexible, low cost and disposable/reusable devices [16][17] . The arising TSO technology based in ultrawide bandgap gallium oxide (~4.8eV) holds the promise of extending many optoelectronic applications further into the deep ultraviolet range, overpassing the conventional wide bandgap TSO's near ultraviolet limit (~3.5 eV) (e.g. ZnO, SnO 2 or In 2 O 3 ).
However, to exploit the full potential of any emerging ultra-wide bandgap transparent optoelectronic technology, both, n-type and p-type conductivity (i.e. bipolarity), should be attained. Intrinsic wide bandgap transparent semiconductor oxides are predominately n-type due to their ability to form oxygen vacancies [18] . Depositing or annealing in reduced oxygen partial pressure can increase the conductivity of the oxide by introducing more carriers. In contrast, there are few predominantly p-type oxide semiconductors due to cation vacancies such as Cu 2 O, SnO or NiO 19,20 . The majority of oxides have fundamental thermodynamic constrains, making their p-type doping difficult. More specifically, the formation of compensating intrinsic defects when lowering the Fermi energy towards the valence band has been identified as a main impediment to p-type doping in many oxides 21 . In any case, oxides generally exhibit an important doping asymmetry and bipolar oxide semiconductors 22 represent only a small subset (e.g. CuInO 2 23 , SnO 24 , Ni x Cd 1−x O 1+δ 25 , SnNb 2 O 6 26 , ZrOS 27 ). Bipolar electronic features are also extremely interesting for Ga 2 O 3 ultra-wide bandgap power electronics to define the main blocking p-n junctions 28-29 . Here, we provide stronger experimental supporting our previous report 30 underlying that the Ga 2 O 3 is a p-type native (or intrinsic) semiconductor. In addition, we report a route for the enhancement of the native p-type conductivity in undoped Ga 2 O 3 by annealing in oxygen atmosphere. While high n-type conductivity in β-Ga 2 O 3 can be efficiently achieved by impurity doping with Sn, Si, Ge, F or Cl 31,32 (and even metallic conductivity due to charge accumulation on the surface in undoped β-Ga 2 O 3 . 3,33 ), p-type conductivity is still controversial. Remarkably we corroborate that, thanks to the β-Ga 2 O 3 particular point defect chemistry and the large formation energy of oxygen vacancies 5 (the native donor which can play role of compensators for holes), it is possible the realization of a p-type conductivity even in undoped layers 30 .

Thermodynamic analyses
Thermodynamic analyses of point defects and charge carriers have been carried out to determine the best conditions for growing highly compensated p-type β-Ga 2 O 3 thin-films. By using the Kroger method of quasichemical equations 34 , the thermodynamic equilibrium in the β-Ga 2 O 3 (crystal) -O 2 (gas) system was established to define the dependence of point defects and charge carriers on temperature (T) and oxygen partial pressure (P hole ). In general, high oxygen pressures are required to achieve p-type conductivity triggered by native (or intrinsic) acceptors, which are associated to gallium vacancy (V Ga ). The thermodynamic analysis show that high oxygen pressures guarantee the appearance of uncompensated hole conductivity effectively suppressing the compensation by native donors, which are associated primarily to oxygen vacancies (V O ). The growth conditions (oxygen partial pressure and temperature) in which acceptors become dominant species, (i.e., the compensating donor defects are suppressed), can be determined by means of the following expression: Please do not adjust margins Please do not adjust margins Where K S , K D , K i and K V are the reaction constants of creation of Schottky pair, ionization of native donor, lattice thermal ionization and creation of oxygen vacancy respectively. Details about the method were reported in Ref. 30. As shown in the map of Fig. 1 (a), the pressure required for intrinsic p-type conductivity increases sharply with T. If the growth conditions are located in the upper part of the map, it should be expected rather uncompensated Ga 2 O 3 (i.e., low p-type conductivity), whereas if growth conditions are located in the lower part, highly compensated samples should be obtained (higher p-type conductivity). Wang and coauthors has suggested also that the high the high temperature and high oxygen partial pressure are in favor of p-type doping in β-Ga 2 O 3 crystal by weakening the self-compensation effect. 35 Therefore, to achieve larger intrinsic p-type conductivities, strongly compensated -Ga 2 O 3 layers should be grown, as it is demonstrated by metalorganic chemical vapour deposition (MOCVD) on sapphire substrates. Growth details are given in the experimental details section. It is worth mentioning that the Ga 2 O 3 p-type conductivity has been consistently measured in eight different samples (under varying growth conditions) but, in the following, the discussion is restricted for simplicity to the most illustrative one.

Sample preparation and Physical Properties
β-Ga 2 O 3 high quality thin films have already been grown by MOCVD using commercial metalorganic precursors such as trimethyl-gallium (TMGa), and pure oxygen [36][37][38][39] . MOCVD is an industrial technique which allows the growth of large-area, uniform semiconductor layers (e.g. III-V compounds) with excellent control of the purity. In the case of β-Ga 2 O 3 , we thus expect high resistivity of the grown material due to a very low concentration of impurities. In agreement with that point, Almena et al 36 observed highly resistive electrical properties as no measurable conductivity was observed by Hall measurements, and Sbrockey el al 40 reported insulating films with sheet resistivity >10 10 Ohms/square, beyond the measurement range of their four-probe equipment.
The modes with A g and B g symmetry are Raman active, while those with odd parity (index u) are infrared active. The Raman spectrum for the (-201) textured -   Fig.2 (d)), which is also in agreement with previous reports 30

Electrical properties
Here, a detailed study of the electrical transport properties of strongly compensated -Ga 2 O 3 has been performed (while others were unsuccessful) thanks to home developed high temperature and high impedance set-up. Van der Pauw Hall Effect measurements were employed to determine the resistivity, carrier type, density and mobility. I-V characteristic for Ohmic contacts at 700K is shown in insert of Figure 2(a).Resistivity at T = 530 K (the lowest temperature for valid measurements) was found to be  = 2.9×10 5 Ω·cm. By heating the sample up to T = 850K, the resistivity decreases down to  = 1.2×10 3 Ω·cm as shown in Fig. 2(a). The resistivity dependence on T -(T), shows the typical behaviour of semiinsulating material, with a hopping conductivity enhancement above 650K (see Fig.2 (b)). The determination of the majority carrier type is not trivial in practice when the sample is of high resistance ( > 10 7 Ω) due to the difficulty in correctly extracting the Hall voltage (V H ) from the total measured voltage. To further validate the sign of majority carriers, the Hall voltage dependence on the applied magnetic field was measured at different temperatures. Hall voltage measurements were carried out at varying magnetic fields (0-1.6 T) in the temperature range of 650K -850K. In a non-magnetic material, V H is linearly proportional to the applied magnetic field and a positive sign indicates that the majority charge carriers are p-type (holes). As shown in Fig. 2(c), the positive V H linearly increase with perpendicularly applied magnetic field. This confirms that the layer was p-type. The temperature dependence for Hall hole concentration is shown in Fig. 2(d). At the largest available temperature of 850 K, the free hole concentration is p = 5.6×10 14 cm -3 . Hall hole mobilities varies between µ= 9.6 -8.0 cm 2 /Vs in 680-850 K temperature range. A carrier activation energy of E a = 1.24 eV ±0.05 eV has been determined from the ln(p) versus 1/T plot. For a p-type semiconductor, the general description of the hole concentration at a temperature T (K) is given by the neutrality equation: Where k is Boltzmann's constant (m 2 kg s -2 K -1 ), g D is the acceptor degeneracy , N A is the acceptor concentration (cm -3 ) and N D is the compensating donor concentration (cm -3 ). M V is the hole density of states in the valence band. If p << N A -N D and p << N D , in the strong compensation regime, the neutrality equation (2) becomes : Thus, the experimental activation energy of E a = E i = 1.24 eV should correspond to the ionization energy of the acceptor centre (E i ). This ionization energy value agrees well with two-times of the activation energy Please do not adjust margins Please do not adjust margins estimated (0.56 eV) for a previously reported arguably p-type weakly compensated Ga 2 O 3 thin-films grown by pulsed laser deposition (PLD) 30 A gallium vacancy acceptor level V Ga located at ~1.2 eV above the valence band has been already reported by several groups by deep-level transient spectroscopy (DLTS) 46,47 .

Oxygen Annealing
Annealing in an oxygen rich (i.e. Ga deficient) atmosphere should lead to an increase of acceptor V Ga centres. As many other metal oxides, gallium oxide is a well-known material for gas sensing 48 and, therefore, the effect of oxygen annealing at high temperatures on the conductivity of insulating bulk -Ga 2 O 3 have been intensively investigated previously 49,50 . For  -Ga 2 O 3 , it has been reported a conductivity activation temperature onset of around ~700 o C. Annealing above 700 o C in air or oxygen ambient would lead to the creation of oxygen vacancies (V O ) due to the outdiffusion of oxygen atoms from the Ga 2 O 3 lattice. This generation of V O leads to an additional source of freeelectrons and to a n-type conductivity enhancement. The ionization energy of V O in case of ceramic β-Ga 2 O 3 samples has been estimated to be ~1.5 eV from the conduction band 51 . The effect of oxygen annealing leading decrease of background n type carrier concentrations for diodes annealed in O2 ambient and for annealed substrate have been demonstrated. 33,[52][53][54] . Therefore, to enhance hole conductivity while not creating additional oxygen vacancies, post annealing in pure oxygen atmosphere at a reduced temperature of 600° have been carried out in a condition of weak compensation (blue spot in Fig. 1(a)). It is worth to be mentioned that, after annealing, neither X-ray diffractograms nor Raman spectroscopy evidenced any change so the gallium oxide films would remain structurally unaffected. Electrical transport measurements showed that oxygen annealing leads the decrease of resistivity from  = 1.2x10 3 ·cm to  = 1.7 x10 2 ·cm at T= 850K while, at room temperature, the resistivity was determined to be  = 1x10 4 ·cm (Fig. 3(a)). We have not detected any "electrical inhomogeneity"performing I-V characterization and resistivity measurements, which could be in case of surface conductivity resulting bilayered structure. A double-slope conductivity curve with two different activation energies has been determined with (high temperature) Ea 1 = 0.56 eV and (low temperature) Ea 2 = 0.17 eV (Fig. 3(b)). In the high temperature range, the activation energy (Ea 1 = 0.56eV) is similar to the half of the activation energy of the same acceptor centre but in highly compensated conditions (E i = 1.24eV). The low temperature activation energy (Ea 2 ) might be related with another shallow acceptor centre created after annealing in the oxygen atmosphere.
As in the as-grown samples, Hall Effect measurement methodology (measure Hall voltage with different applied magnetic field) the same as for grown sample, was applied showing that the annealed sample is ptype as well (See Fig. 3(c)). In this case, the Hall hole concentration was significantly increased up to p = 5.6x10 17 cm -3 (T = 850 K), when compared with available free-hole concentration before annealing (p = 5.6x10 14 cm -3 ). Nevertheless, the Hall mobility is lower, µ = 0.4cm 2 V/s (µ ~ 8.0 cm 2 /Vs before annealing), probably due to an increased number of scattering centers. It must be mentioned that to perform Hall Effect at entire temperature range was complicated owing to this low mobility. Though still, it was actually measured in a narrower temperature range, it appears that the hole mobility does not change significantly with temperature. Therefore, it is concluded that the conductivity activation energy is mainly determined by the activation of free carriers with temperature ( Fig.3(d)). Therefore, we could assume that the conductivity activation energy of Ea 2 = 0.17 eV is the acceptor level energy with an ionization energy of around this value.

Fig.3 a) Resistivity temperature dependence b) ln() versus T dependence c)Hall voltage VH versus applied external magnetic field at T=850K d) Hall hole concentrations versus temperature for as grown and annealed in O 2 at 600°C β-Ga 2 O 3 thin films.
A potential origin of this shallow level may be further elucidated by considering several theoretical assumptions. It is well-known that, close to the stoichiometry, oxide's oxygen vacancies tend to be preferentially in a double charged (V O ++ ) state then as single charge(V O + ) state. 55 In off-stoichiometry state, when hole concentration are important, the compensating donor defects are expected to be even more abundant in double charged state. Taking this fact into account, we attribute the shallower acceptor centre with Ea 2 = 0.17eV activation energy to be due to the creation of a V Ga --V O ++ complexes. Indeed, the high probability of creation of such vacancy complexes has been studied in detail by Ingebrigtsen et al 56 In the case of oxygen annealed strongly compensated -

because of the Coulombic interactions between V Gaand V O ++
, the V O ++ donor centre has a tendency to be located in the vicinity of charged acceptor centre, forming V Ga --V O ++ complexes. Consequently, the energy of electron localized on V Ga ' decreased by amount where is distance between V Gaand V O ++ , is static dielectric constant of Ga 2 O 3 . If V O ·· defect is located in the first coordination spheres, its proximity can reduce electronic level of V Ga ' (1.24eV) by  1 eV, which is in a good agreement with Ea 2 = 0.17eV activation energy observed in experiment.

Fig.4 (a) X-ray photoelectron spectroscopy of the Ga 2 O 3 valence band for a commercial Si-doped (n-type) reference and the p-type as-grown/annealed of this work (calibrated with respect to Ga3d). (b) A zoom of the valence band region, which in the case of stoichiometric Ga 2 O 3 , has a O2p character. Investigation of the valence band tail states for (c) n-type (Si-doped), (d) p-type (as-grown) and (e) p-type (annealed) evidencing the presence of states in the lower part of the bandgap.
X-ray photoelectron spectroscopy (XPS) is a fine chemical method to investigate a material's valence band characteristic and brings additional evidence of the presence of states within the bandgap [57][58][59] When used in high resolution in the valence band vicinity (i.e., for the lowest binding energies), it is possible to directly detect whether there are states in the lower Please do not adjust margins Please do not adjust margins part of the bandgap (those responsible of the p-type character) 60 As shown in Fig. 4, it was found a clear correlation within the amount of states in the lower half of the bandgap and the p-type character in the sequence, ntype (Si-doped) commercial reference, p-type (undoped) and p-type (annealed). The n-type control sample is a commercial (Novel Crystal Technology, Inc.) nominally n-type Si-doped β-Ga 2 O 3 (N D -N A = 1.3 × 10 18 cm −3 ) epitaxy (500 nm) grown on a single crystal β-Ga 2 O 3 (labelled "n-type (Si-doped)"). For our samples, the valence band edge is shifted towards more p-type using the Ga3d peak as the calibration peak (smaller Fermi level implies more p-type character), see Fig. 4

Comparison with the state-of-the-art
In any case, for the majority of oxides, to achieve sizable p-type conductivity is challenging because their valence band maximum consists of strongly localized O 2p-derived orbitals. In other words, the valence band of most oxides is rather flat, resulting in deep acceptor levels (lower free hole concentration at room temperature) and larger hole effective masses (lower mobilities) 61-62, During many years the possibility of doping p-type Ga 2 O 3 has been considered "out of question" due to the particular flatness of the computed valence band resulting in a high hole effective mass (see e.g. 63 ). A Ga 2 O 3 valence band being governed by O 2p orbitals with arguably very low hole mobility and having very small dispersion in the wave vector-energy space has been routinely reported 5,[64][65][66] . In addition, a strong localization of holes at specific sites in bulk Ga 2 O 3 by a self-trapping effect, has also been predicted by first-principles calculations 67 Nevertheless, it has been also recently reported that the hole conduction mass in Ga 2 O 3 is, indeed, fairly anisotropic and can be as low as ~0.4 m 0 for certain orientations (while larger than 10 m 0 in others) 68 . Fig.5 (a,b).Thus, challenging current thinking, we have found experimentally a sizable hole mobility of at least ~10 cm 2 /Vs together with an outstanding transparency in the visible of above 80%. What is more important is the significant "shift of the native p-type conductivity" up to the ~5 eV region (~250 nm) when compared with previous p-type conductive oxides such as NiO, SnO, Cu-based delafossites (CuAlO 2 , CuGaO 2 , SrCu 2 O 2 ) or oxychalcogenides, all of them lying in the range of ~2.5-3.7 eV 61,62,69-71 as shown in Fig.  5(c).

Conclusions
In this work, we corroborate, via electrical Hall effect and chemical XPS measurements, that the ultra-wide band gap Ga 2 O 3 oxide is an "native" ptype semiconductor oxide even in the case of strong compensation by donor defects. This unusual native p-type nature is due to the Ga 2 O 3 particular point defects chemistry, mainly the large formation energy of oxygen donor vacancies, allowing the realization of a p-type. This confirms, in practice, that Ga 2 O 3 is the p-type TSO with the largest band gap and also is potentially bipolar. The corroboration of this fact might have deep implications in optoelectronic, thanks to the shifting the optical band gap onset, and in power electronics in regard of the device's breakdown voltage range. Notably, the p-type nature was determined in samples grown by MOCVD, differently to the only previously reported native p-type conductivity for the samples grown by PLD 30 . Such reproducibility reinforces our claim of possible realization of native hole conductivity in Gallium Oxide. Annealing in oxygen results in much improved (three-orders of magnitude) free hole concentration p(Ox-anneal) = 5.6x10 17 cm -3 vs. p(as-grown) = 5.6x10 14 cm -3 ) (T = 850 K) and resistivity  (Ox-anneal) =1.7 ·cm vs.  (asgrown) =  = 1.2×10 3 Ω·cm (T = 850 K). However, the mobility µ = 0.4cm 2 V/s (µ ~ 8.0 cm 2 /Vs before annealing) is reduced probably due to a greater number of acceptor scattering centres. The origin of such improved p-type conductivity is preliminary ascribed to the formation of V Ga --V O ++ complexes, as a shallow acceptor centre.

Experimental Details
Ga 2 O 3 growth details. Undoped -Ga 2 O 3 sample was grown in a RF-heated horizontal MOCVD reactor with separate inlets to avoid premature reactions in the manifold between oxygen and organometallics precursors. The reactor can operate at low pressure, between 30 and 760 torr, and at high growth temperature, up to 1000°C. Trimethylgallium (TMGa) and 5.5N pure oxygen were used as gallium and oxygen sources, respectively. Argon was used as carrier gas. The TMGa bubbler temperature was fixed at -15°C in order to obtain a low vapour pressure, and consequently a moderate growth rate near 5nm/min. The -Ga 2 O 3 layer was grown on C-oriented sapphire substrate using Ga/O ratio, growth temperature and reactor pressure set at 1.4×10 -4 , 775°C, and 30 torr respectively. The layer's thickness was measured at 450nm.
Raman spectra were recorded using a Renishaw Invia Reflex micro-Raman spectrometer at room temperature. The samples were excited using a cw Modu-Laser Stellar-REN laser emitting at 514.5nm with a power of 2-4mW. The reflecting microscope objective was 50X with a NA 0.75; the excitation spot diameter was 1μm. The back-scattered light was dispersed by a monochromator with a spectral resolution of 1.4cm -1 . The light was detected by a charge coupled device. The typical accumulation time was 30s. Raman shifts were calibrated using an optical phonon frequency (520.5 cm -1 ) of silicon monocrystal. Several reference Raman spectra for beta-Ga 2 O 3 single crystal substrates and sapphire c-cut substrates have been also measured.
Hall Effect measurement set-up. Ohmic contacts were prepared by silver paint at the four corners of the sample. Hall Effect measurements were performed in a Van der Pauw configuration in the temperature range of 300K to 850K and for magnetic fields perpendicular to the film plane varying from -1.6 T to 1.6 T, using a high impedance measurement set-up which was custom designed for measurement of high resistance.