This is the submitted version of the following article: Chikoidze E., Tchelidze T., Sartel C., Chi Z., Kabouche R., Madaci I., Rubio C., Mohamed H., Sallet V., Medjdoub F., Perez-Tomas A., Dumont Y.. Ultra-high critical electric field of 13.2 MV/cm for Zn-doped p-type ß-Ga2O3. Materials Today Physics, (2020). 15. 100263: - . 10.1016/j.mtphys.2020.100263, which has been published in final form at https://dx.doi.org/10.1016/j.mtphys.2020.100263 © https://dx.doi.org/10.1016/j.mtphys.2020.100263. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Ultra-High Critical Electric Field of 13.2 MV/cm for Zn-doped p-type β-Ga2O3 Ekaterine Chikoidze*1, Tamar Tchelidze2, Corinne Sartel1, Zeyu Chi1, Riad Kabouche3, Ismail Madaci1, Carles Rubio4, Hagar Mohamed 1,5, Vincent Sallet1, Farid Medjdoub3, Amador Perez-Tomas4, Yves Dumont1 1 Groupe d’Etude de la Matière Condensée (GEMaC), Université Paris-Saclay, UVSQ – CNRS, 45 Av. des Etats-Unis, 78035 Versailles Cedex, France 2 Faculty of Exact and Natural Science, Department of Physics, Ivane Javakhishvili Tbilisi State University, 3 Av. Tchavtchavadze, 0179 Tbilisi, Georgia 3 IEMN - CNRS, UMR8520, Av. Poincaré, 59650 Villeneuve d'Ascq, France 4 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain 5 Solid State Physics Department, National Research Center, El-Behooth St. 12311 Dokki, Giza, Egypt. Corresponding author: ekaterine.chikoidze@uvsq.fr Abstract Which the actual critical electrical field of the ultra-wide bandgap semiconductor β-Ga2O3 is? Even that it is usual to find in the literature a given value for the critical field of wide and ultra-wide semiconductors such as SiC (3 MV/cm), GaN (3.3 MV/cm), β-Ga2O3 (~8 MV/cm) and diamond (10 MV/cm), this value actually depends on intrinsic and extrinsic factors such as the bandgap energy, material residual impurities or introduced dopants. Indeed, it is well known from 1950’s that reducing the residual doping (NB) of the semiconductor layer increases the breakdown voltage capability of a semiconductor media ⁄ (e.g. as 𝑁𝑁𝐵𝐵−3 4 by using the Fulop’s approximation for an abrupt junction). A key limitation is, therefore, the residual donor/acceptor concentration generally found in these materials. Here, we report that doping with amphoteric Zinc a p-type β-Ga2O3 thin films shortens free carrier mean free path (0.37nm), resulting in the ultra-high critical electrical field of 13.2 MV/cm. Therefore, the critical breakdown field can be, at least, four times larger for the emerging Ga2O3 power semiconductor as compared to SiC and GaN. We further explain these wide-reaching experimental facts by using theoretical approaches based on the impact ionization microscopic theory and thermodynamic calculations. Keywords: Ultra-wide band gap; MOCVD growth; p type β-Ga2O3; Electrical properties; Critical Electrical field; 1 1. Introduction Energy and power electronics rely on the capability of semiconductor solid-state devices to sustain high electric fields [1]. Such capability itself is determined by the semiconductor’s fundamental property, band gap (Ɛg) and by the mechanism of the process leading to the breakdown. The breakdown phenomena -i.e. when highly resistive material under high electrical field start to conduct a current - is related with the process of impact ionization. It is customary to use the well-known unipolar Baliga’s Figure of Merit, 𝜇𝜇𝜀𝜀𝑟𝑟 𝐸𝐸𝑐𝑐3 to classify wide and ultra-wide bandgap semiconductors for power electronics [2],[3]. A good semiconductor for power electronics should exhibit therefore large critical electric field (𝐸𝐸𝑐𝑐 ) while keeping reasonably high free carrier mobility (𝜇𝜇) and dielectric constant (𝜀𝜀𝑟𝑟 ). In a parallel plate capacitor, containing an insulator media with no charges at the interfaces, the electric field is constant and the critical electric field is simply the breakdown voltage divided by the interplanar distance (i.e., 𝐸𝐸𝑐𝑐 = 𝑉𝑉𝐵𝐵 ⁄𝑑𝑑 ). In any semiconductor containing a certain doping (space charge), the electric field distribution is not constant anymore but it has a spatial distribution and maximum value which depend on the doping concentration itself. Already in 1966, Sze and Gibbons [4] proposed that for an abrupt (infinite) junction, the avalanche breakdown voltage (VB) of any semiconductor is related to the drift region doping level (NB) by the expression, 3/4 Ɛ𝑔𝑔 1/2 1016 𝑉𝑉𝐵𝐵 = 60 � � � � (0) 1.1 𝑁𝑁𝐵𝐵 This qualitative expression already informs us that the breakdown capability depends on the free available charges (related to native defects or dopants) but also on semiconductor’s fundamental properties (such as bandgap energy Ɛ𝑔𝑔 ) and the impact ionization parameters resulting in avalanche breakdown. Therefore, the effective critical electric field (defined as the breakdown voltage divided by the semiconductor depletion length), is actually depending on several geometrical and material quality factors. Regardless this fact, it is very usual to find in the literature values for the electrical critical field of the most popular power and wide bandgap dielectrics such as silicon (0.3 MV/cm), 4H-SiC (2.2 MV/cm), 2H-GaN (3.3 MV/cm), for β-Ga2O3 (8 MV/cm), diamond (~ 10 MV/cm) and AlN (12.7 MV/cm). To the best of the authors knowledge, in the case of β-Ga2O3, the popular value of 8 MV/cm (a value frequently given in the literature) was originally simply from an interpolation (it was indeed not calculated or measured experimentally) on the basis of a band gap energy model reported in 2012 [5]. Short after, further efforts in the theoretical front, corroborated a theoretically calculated critical electric field of 8 MV/cm (for undoped β-Ga2O3) [6]. Irudayadass and Shi [4], predicted a much larger electric field in the range of 9-17 MV/cm but it is largely anisotropic; i.e. depending on β-Ga2O3 crystallographic orientation [7]. They studied the plane directions [001], [100], [001], [-201] and observed that the theoretical maximum electric field was obtained for the [-201] crystallographic orientation. Experimentally, a record breakdown field of 5.2 MV/cm for β-Ga2O3/graphene heterostructures has been reported in 2018 while a year later it was reported up to 7 MV/cm for β-G2O3 grown on Si [8]. In this work, it is engineered, both, the out-of-plane crystallographic orientation and doping in order to maximize the blocking voltage capabilities of parallel-plane Ga2O3 capacitors grown on conductive Silicon substrates. To reduce the background impurity level of the thin-film, it is introduced Zn atoms (~0.5%) which results to be an amphoteric impurity. In short, p-type β-Ga2O3 doped by Zn 2 critically decreases the impact ionization rate which results in the ultra-high experimental effective critical field of 13.2 MV/cm. One implication of our results is a further shift of the Baliga’s figure-of- merit for the emerging ultra-wide bandgap β-Ga2O3 as compared to classical wide bandgap SiC and GaN, therefore reinforcing the enormous potential of gallium oxide for power electronics. 2. Kinetic Impact Ionization Theory (KIIT) The enhanced ultra-high critical electric field of β-Ga2O3 is believed to be due to the combined effect of the ultra-low residual concentration and the further reduction of the impact ionization rate. In the following, it is used the Kinetic Impact Ionization Theory (KIIT) framework to understand the implications of acceptor dopant species. Under a sufficiently high electric field, the impact ionization phenomenon in a (low doped) semiconductor takes place when a high energy electron in the conduction band loses some of its energy by collision. This multiplication process results in three free carriers, two electrons and a hole, in place of the initial electron. Impact ionization by a hole is a similar process by which an energetic hole yields three final current carriers, two holes and an electron [9]. If the electric field is further improved, a multiplicative avalanche process may occur. At Impact ionization process is defined by impact ionization coefficients (𝛼𝛼) which is the average number of ionizing collisions experienced by a carrier per unit distance of its travel in the direction of the electric field. . The semi- empirical Chynoweth [10] equation is often used as, 𝛼𝛼 = 𝑎𝑎𝑒𝑒 −𝑏𝑏⁄𝐸𝐸 where 𝐸𝐸 is the electric field and 𝑎𝑎 = 𝛼𝛼∞ [cm-1] and 𝑏𝑏 [V/cm] are material constants. A useful approximation is the one given by Fulop [11] or 𝑎𝑎 = 𝑐𝑐𝐸𝐸 7 (𝑐𝑐 being a constant). If one assumes the impact ionization of electron and holes to be the same, the avalanche breakdown for an abrupt junction using the Fulop’s approximation results in the ⁄ 𝑁𝑁𝐵𝐵−3 4 dependence of eq. (1). Therefore, the avalanche breakdown occurs when the carrier concentration significantly increases in comparison the semiconductor’s thermal concentration. Let’s consider the impact ionization in wide band gap semiconductors. Due to wide band gap deep native donor/acceptor centers (if any), are assumed to deliver carriers during impact ionization. In terms of the microscopic parameters, in stationary state, the number of carriers is constant and determined by the following expression [12] { } n ωi ( E , T ) − ωr ( n, E , T ) + n0 ( E , T ) = 0 (1) Where ωi and ωr are the probabilities of impact ionization and recombination, averaged over distribution function, n0 is the number of thermally ionized carriers. With increasing field ωr decreases, while ωi increases rapidly, resulting in a net carrier concentration enhancement. When ωr = ωi carrier concentration goes to infinity and breakdown takes place. In the KIIT framework, the probability of impact ionization is proportional to the probability that the electron (hole) will cover without collision a path l = ε i eE , where ε i is the activation energy of carriers from bound state of uncompensated donor or acceptor center [13]: ωi ~ exp ( − ε i elE ) (2) 3 The pre-exponential coefficient consists of concentration of neutral (filled) donor or acceptor centers from which carriers are activated - N f , the capture cross section of this center σ f , and velocity of the carrier u =ω i N f σ f u exp ( − ε i elE ) (3) One may note that the probability of impact ionization ��� 𝜔𝜔𝚤𝚤 has the same electric field dependence as the Chynoweth equation with 𝑏𝑏 = 𝜀𝜀𝑖𝑖 ⁄𝑒𝑒𝑒𝑒. The recombination coefficients also depend on concentration of ionized centers N i , the capture cross section of this center σ i , and velocity of the carrier u : ω r = N iσ i u (4) The capture cross section of ionized center σ i = π aB2 , where aB is the Bohr radius of the center, which can be estimated by means of ionization energy; the capture cross section for the neutral center σ f = 20aB k , where k is carrier wave vector [14], Therefore, the critical field at which the breakdown occurs can be estimated by means of equating ω r and ω i : εi Ecr = − (5)  π a k Ni  el ln  B  20 N   f  𝛼𝛼 𝑏𝑏 which again is functionally identical to the Chynoweth law, ln �𝑎𝑎 � = − 𝐸𝐸 . As seen from eq. 5, the critical field at which breakdown takes place depends on the ionization energy, ( ε i ) and mean free path ( l ), and the density of neutral (filled) donor or acceptor centers from which carriers are activated [15]. 3. Intrinsic and Zn-doped p-type Ga2O3, a review Here, we propose a strategy for the enhancement of the p-Ga2O3 critical electric field by shortening the mean free pass of free carriers ( l ). For achieving that in practice, we further introduce acceptor dopant atoms in Ga2O3. The selection of the dopant species is very particular: (i) a dead acceptor it should not lead to an increase of free carriers (as otherwise is the usual situation when doping a semiconductor) and (ii) while non-compensating donor it should not lead to a change of conductivity type (i.e., keeping the p-type intrinsic behavior). We chose the amphoteric deep impurity II group element Zinc (Zn) to this end. Zn doping related theoretical predications are rather controversial. Zn doping (~ 2%) does not change the basic electronic structure of β-Ga2O3, but only generates an empty energy level above the maximum of the valence band, which is shallow enough to make the Zn-doped β-Ga2O3 a typical p-type semiconductor [16]. However, for C. Zhang and coauthors, an atomic Zn concentration of ~ 4% has been estimated to introduce shallow levels above the valence band at around 0.3 eV [17]. Contrary to this statement, for ~1.5% doping, Zn has been reported to be a very deep acceptor with > 1.2 eV energy level above valence band maximum 4 [18] with low activation rate [19]. Co-doping Zn-N has been reported as well, and refereeing an acceptor with possibly 0.5 eV activation energy [20]. Even ferromagnetic order has been predicted by 3.5 wt% Zn doping leading 100% spin polarization in gallium Oxide [21]. There are some experimental works dedicated to high amount (> 1%) Zn incorporation into Gallium Oxide for different purposes (as summarized in Table I). W. Yue et al. studied the effect of Zn doping (2 wt%) by magnetron sputtering showing that with Zn doping the band gap slightly was reduced from 4.90 to 4.87 eV [22]. Similarly, it was found that with the increase of Zn dopant concentration up to ~ 3%, the crystal lattice expands, the energy band gap shrinks, and the oxygen vacancy concentration decreases [23]. Tao et al. [24] reported however that the rise in Zn doping contents is accompanied by a widening the band gap due to Burstein-Moss effect. Interestingly, in Zn-(β-Ga2O3) thin films, electrical characterization by Hall effect at room temperatures show a electron concentration decreases from 2×1014 to 6×1012 cm-3 with increasing the nominal Zn content from 0 to 7 at%, showing that Zn plays acceptor role. From cathodoluminescence measurements the acceptor level of ZnGa is estimated to be 0.26 eV above the valence band maximum [25]. Zn doping of gallium oxide was done for improvement of oxygen gas sensing properties: it was observed that n-Ga2O3 doped with Zn showed increase of resistivity at T < 450 °C [26]. p µh Year Author Zn [%] Substrate Growth Type [cm-3] [cm2/Vs] 2017 Chikoidze 0 (0001) sapphire PLD p-type 2×1013 a 0.2 2019 Chikoidze 0 (0001) sapphire MOCVD p-type 6×1014b 9.6 2003 Li Y 9.7 -24.7 a-Sid PE-ALD n-type Zn acceptore - 2012 W.Yue 2.0 Si (111) RF sputtering - - - 2013 Shrestha 0.59 Ga, GaZn alloy anodization - - - 2014 Wang 0.0 - 7.0 (0001) sapphire PLD - Ea=0.26eVf - 2016 Feng 1.3- 3.6 NWg/β-Ga2O3 CVD - Zn acceptor - 2017 Alema 10.9 (0001) sapphire MOCVD - - - 0.69 - 2017 Guo (0001) sapphire RF sputtering n-type Zn acceptore - 3.03 2020 Chikoidze 32i (0001) sapphire MOCVD p-type 2×1015b 10 (0001) sapphire 2020 This work 0.5 MOCVD p-type 1×1014b 2 Si (111) Table I. A summary of previously reported intrinsic and Zn-doped p-type Ga2O3 from the literature; measured at 300K; b measured at 850K; c low p-type resistivity attributed to charge carrier multiplication via collective excitation of aggregated excitons and/or electron-hole liquid; amorphous silicon; overall reduction of conductivity/Zn considered as an acceptor; determined by cathodoluminescence; nanowire; iZn-content stabilized in a spinel ZnGa2O3 structure. Agnitron Technology Incorporated (USA) reported β-Ga2O3 Zn doped thin films on c-sapphire by MOCVD the incorporation of 10.9% Zn XRD patterns yielded to a mono-phase polycrystalline structure with increase of lattice parameters with doping, though room temperature Hall measurements were not successful due to very high resistivity of the samples [27]. Recently, we have shown that incorporation of Zn in p-type β-Ga2O3 with more than 5% leads the transformation of orthorhombic structure into spinel ZnGa2O4 with an increased band gap (~0.2 eV) and p-type carrier densities (×10-100 cm-3) [28]. 5 Very few experimental works are reported about low doping cases, when incorporated Zn amount is less than 1%. Shrestha et al. [29] studied properties of 0.59% Zn doped Ga2O3 nano-porous layers for photo- induced hydrogen generation. It has been concluded that a presence of small amount of zinc doping in Ga2O3 can reduce trapping sites at the donor level under the conduction band, and thereby increase the mobility of electrons. On the other hand, zinc doping also creates additional trapping sites as acceptor level over the valence band, which hampers the activation of holes. An improvement of photocatalytic activity by Zn doping (up to 1 atomic % of zinc) on H2O splitting is found and associated with increase in the mobility and concentration of holes due to the formation of an acceptor level [30]. Another study on monocrystalline Zn doped β-Ga2O3 nanowires/n-type β-Ga2O3 junction, shows good rectifying behavior, suggesting that the Zn doped β-Ga2O3 nanowires are of p-type conductivity [31]. A summary of previously reported in the literature the native and Zn- acceptor centers in Ga2O3 is shown in Table.1 Zn as a II group element is expected to be an acceptor in Ga2O3, though due to its smaller atomic radius, (137 pm) in comparison to Ga (153 pm), it can occupy an interstitial position as well and acts as a donor. This amphoteric nature of Zn could be an origin of possible so-called “impurity auto- compensation” effect. The problem of auto-compensation was discussed by Kroger [32] for Li doped ZnO, while Zn amphoteric nature has already been reported in GaAs [33]. 4. Thermodynamic analyses of Zn:Ga2O3 From the thermodynamically point of view, using Kroger-Vink notations, the following equilibrium relationships with the corresponding mass action laws are considered: (i) Lattice thermal ionization ∅ ↔ e + h, K g =np (6) (ii) Substitutional Zn transfer to interstitial position [ Zn ][V ] ZnGa ↔ Zni + VGa , K Zn =i Ga (7) [ ZnGa ] (iii) Donor and acceptor impurity ionizations  ZnGa / p ZnGa ↔ Zn + h, K a =  / (8) Ga [ ZnGa ] •  Zni•  n Zni ↔ Zn + e, Kd = (9) i [ Zni ] (iv) Ionization of native acceptor, gallium vacancy VGa/  p VGa ↔ VGa/ + h, K A = (10) [VGa ] (v) Interaction with environment, gas phase: 6 [V ] 2 3 O2 ( gas ) ↔ OO + 2VGa , KVGa =Ga3 2 (11) 2 PO2 Here e and h denote electron and hole, n and p their concentrations. ZnGa and Zni denote Zn atoms in substitutional and interstitials sites, respectively, while [ ZnGa ] and [ Zni ] are their concentrations. / ZnGa and Zni• denote ionized acceptor and donor impurities, while  ZnGa/  and  Zni•  are their concentrations. VGa denotes a Gallium vacancy, [VGa ] is the Gallium vacancy concentration, VGa/ is one ionized galium vacancy and VGa/  its concentration. Equations (6)-(11) together with electro-neutrality condition  ZnGa/  + VGa/  + = e  Zni•  + p (12) and mass balance equation  ZnGa/  +  Zni•  + [ ZnGa ] + [ Zni ] = [ Ztot ] (13) establish the equilibrium concentrations of electrons and holes, as well as impurities and defects in different charge states. Electro-neutrality and mass balance depend on the total Zn concentration ([𝑍𝑍𝑡𝑡𝑡𝑡𝑡𝑡 ]), temperature (T) and pressure (𝑃𝑃𝑂𝑂2 ) in surrounding atmosphere. We calculated the concentration of these spices for fixed temperature (T = 750 0C) and total pressure (30 tor) in the chamber reactor (these are the parameters we use in experiment) versus Zn total concentration. As usual, few additional assumptions on the three hypothetical ranges of impurity concentration are considered [34]: (I) The range of intrinsic conductivity – in this range the total concentration of Zn is very low- and dominant species is one-charged intrinsic acceptor VGa/ and hole. (II) The range of impurity p-conductivity – with the increase of Zn concentration gallium vacancies might be occupied with Zn atoms; so dominant terms in eq. (12) are  ZnGa/  and p . (III) In the range of impurity auto-compensation – with further increase of Zn concentration - a fraction of Zn atoms occupies interstitial sites. In this range dominant species are  ZnGa/  and  Zni•  . Such approximations provide a clear picture of doping peculiarities and simplify the calculations. The boundaries between these ranges can be defined by means of discontinuity of concentrations charge carriers or other species. In the first region (I: intrinsic region), (K ) 12 =p = VGa/  A KV1Ga2 PO32 4 (14) In the second region (II: impurity p-type), =p = / ZnGa  [ Zntot ] (15) In the third region (III: impurity auto-compensation) 7 12  K a K g KV1Ga2 PO32 4  p=  (16)  K K  d Zn  The boundary between the first and second region corresponds to [ Zntot ]I − II = ( K A KV1 2 PO3 4 ) 12 Ga 2 (17) And the boundary between the second and the third region (18) 12  K a K g KV1Ga2 PO32 4  [ Zntot ]II − III =    K d K Zn  This boundary concentration indicates the efficiency of doping. If this concentration is very small, that is if impurity auto-compensation starts at low concentration, it is obvious that that doping cannot increase p-conductivity. In our case [ Zntot ]I − II and [ Zntot ]II − III are approximately the same ( ≈ 1014 cm-3), therefore we do not have a sizable region where impurity controls the conductivity. In fact, the concentration of holes in Zn-doped samples is even less than that in undoped samples. In general, the total hole concentrations [ Zntot ]I − II and [ Zntot ]II − III do depend on temperature. As shown in Fig. 1, the region in between [ Zntot ]I − II and [ Zntot ]II − III is further narrowing with increasing the temperature. Very relevantly, [ Zntot ]II − III remains low at the whole temperature range. This fact indicates that, in Zn-doped β-Ga2O3, auto-compensation (due to the amphoteric nature of Zn) is very strong. In practice, it is very challenging to select the optimal temperature and Zn concentration, which can provide the impurity controlled p-conductivity. 8 Figure1: Phase diagram of intrinsic I, impurity p-type II, and impurity auto-compensation III regions, with boundary curves (I-II in red, and II-III in back) versus temperature for Ptot = 30 torr. 5. p-type Ga2O3 on conductive silicon substrates 5.1. Structural Properties To evaluate the electrical breakdown voltage in vertical structure and effective critical electric field, Zn- doped β -Ga2O3 films were grown on conductive n-type Si(111) substrates. For comparison, Zn-doped β -Ga2O3 films were grown on insulating c-sapphire, to evaluate electrical transport properties (carrier, mobility). The layers were grown at low pressure (30 torr) in a horizontal MOCVD reactor. The Ga/O ratio and growth temperature were fixed to 1.4×10-4 and 775 °C respectively. Zn flux was varying between 0-3.8 µmol. By adjusting the growth parameters, the layer thickness was varying in the range of 200 - 400 nm. On sapphire, the Zn doping does not change the quality of (-2 0 1) textured layers. X-ray (Cu-Kα) diffractograms, recorded between 2θ = 10° and 130°, in θ/2θ configuration, exhibit a highly (-2 0 1) texture of undoped and Zn:β-Ga2O3 phase with monoclinic space group (C2/m) symmetry (Fig. 2-a). The new and interesting for us was deposition on Si substrate. Several studies have shown that, as well as substrate of sapphire, silicon wafer can be used for Ga2O3 growth. MOCVD is one of effective methods using for deposition of Ga2O3, it’s usually chosen for its reproducibility, film adherence [35], scalability into larger commercial systems, and applicability to current device technology [36][37][38][39][40][38][41], while another techniques such as PEALD [42], sputtering [43],[44] also were used for Ga2O3 on silicon. Obtained film quality are varying from amorphous to polycrystalline, depending on growth technique, deposition temperature and post annealing procedure. Our undoped and doped films deposited on Si (111) are of comparable quality to state-of-the art Ga2O3 films grown on 9 sapphire (0001) with [-2 0 1] preferential normal direction (Fig. 2-b). Additional tiny Bragg peaks, intensity ratio lower than 1/30) are detected with random orientations. SIMS measurements have shown that only samples grown by the maximum flux 3.8 µmol had detectable level of Zn atoms. Estimated concentrations for both substrates are very similar: [Zn] = 1.5×1019 at/cm-3 for Ga2O3 on sapphire (0001) and [Zn] = 3.2×1019 at/cm-3 for Ga2O3 on Si (111), which is about 0.5% of doping level. This value agrees very well with the value extracted from energy-dispersive X-ray spectroscopy (EDX) profile from a transmission electron microscopy (TEM) measurements performed on the Zn:Ga2O3/Si sample.. According to EDX, there is a thin SiO2 layer (2-3 nm) at the β-Ga2O3/Si interface. Fig.2-d Also on TEM image, we can see an amorphous layer (15-20 nm) on top of SiO2. EELS profiles show that there is no diffusion of Si in this upper amorphous layer, and it has the same chemical composition Zn:Ga2O3 with Zn=0.5%. (a) (b) β−Ga2O3 Al2O3 (0 0 0 6) Al2O3 (0 0 0 12) (- 4 0 2) (- 2 0 1) β−Ga2O3 (- 4 0 2) Si (111) Si (333) 105 (- 6 0 3) 1012 (- 10 0 5) Zn:Ga2O3 (- 8 0 4) (- 6 0 3) Intensity [a.u] Intensity [a.u.] Si (222) 1010 104 (-2 0 1) (- 8 0 4) (4 0 1) (002) 108 (1 1 1) (-6 0 1) (-3 1 2) (- 7 1 2) 103 (5 1 0) Zn:Ga2O3 (-3 1 3) (0 2 0) (0 2 2) (603) 106 (601) 102 20 40 60 80 100 120 20 40 60 80 100 2-theta (deg.) 2theta [deg] (c) (d) β-Ga2O3 β-Ga2O3 SiO2 Si (111) 5 nm 5 nm 5 nm Si (111) 5 nm 10 Figure2: Cu-Kα X-ray diffractograms β -Ga2O3 and β -Zn:Ga2O3films deposited by MOCVD on (a) Al2O3 (0001) and (b) Si (111) substrates ; (c) (d) Transmission electron microscopy of the film on Si (111). Amorphous natural SiO2 2-3 nm thick layer is evidenced at interface. 5.2. p-type Ga2O3 Electrical transport properties While the breakdown measurements take advantage of the conductive silicon substrate, a detailed study of the β -Ga2O3‘s electrical transport properties have been performed on the samples grown on insulating substrate (Sapphire). I-V curves showed Ohmic behavior. Hall Effect measurements in Van der Pauw configuration is used to determine the resistivity, carrier type, density and mobility. Resistivity for undoped Ga2O3 at T = 530 K (the lowest temperature for valid measurements) was found to be ρ = 2.9×105 Ω.cm; and by heating the sample up to T = 850 K resistivity decreases down to ρ = 1.2×103 Ω.cm (Fig. 3-a). ρ(T) dependence shows normal behavior of semi-insulating material, with enhancement of contribution of hopping conductivity below T < 650K (Fig. 3-a). Zn doped sample exhibits much higher resistivity up to ρ = 2×107 Ω.cm for T = 550 K. From ln(p) versus 1/T plot a conductivity activation energy were determined very close for both samples, around Ɛa = 1.24 ± 0.05 eV. The detailed Hall Effect measurements for undoped sample: carrier concentration, type and mobility (At 850 K, p = 5.6 × 1014 cm-3. mobility varies between 9.6 and 8.0 cm2/Vs in 680- 850 K temperature range) have been reported by us in Ref 11. Hall Effect measurements for Zn:Ga2O3/Al2O3 (0001) was more complicated to perform in whole temperature range. High temperature (700-850 K) Hall Effect shows slight decrease of hole concentrations, p = 1×1014 cm-3 at 850 K. indeed, if auto-compensation mechanism takes place, Zn dopant cannot increase of p -type conductivity, even more, as we see in experiment, “amphoteric” nature of Zn can lead a decrease of charge carriers. This result corresponds well to the thermodynamic calculations discussed above. As it is shown in Fig 3, undoped and Zn-doped samples reveal p-type conductivity at high temperature exhibiting both the same activation energy of Ea ~ 1.2 eV. The free hole concertation at room temperature was estimated to be <1x108cm-3. Ga2O3 Hall holes mobilities for doped sample are lower, µ = 1-2 cm2/Vs. Such decrease of hole mobility is not surprising and might be related with doping leading the increase of scattering on Zn impurities, consequently shortening of mean free pass of free carriers 11 . Figure 3 : (a) Resistivity versus temperature (b) ln(conductivity) versus 1000/T; (c) Hall hole carrier concentration versus T for undoped and 0.5% Zn-doped β-Ga2O3 thin films d) I-V curves for breakdown voltage measurements for undoped Ga2O3/Si (111) and 0.5% Zn:Ga2O3/Si (111) structures. Insert: sketch of the vertical p-n heterojunction structure. 5.3. p-type Ga2O3 Critical Electric Field Vertical parallel plane capacitors have been fabricated by depositing Ti/Au contacts onto the undoped and Zn doped p-Ga2O3 grown on the conductive Si substrates, (see inset of Fig.3-d). The vertical breakdown voltage was determined to be 124 V for the undoped p-Ga2O3/Si and 540 V for the doped p- Zn:Ga2O3/n-Si structures. A bare Si substrate with a native SiO2 (2-3 nm thick layer) has been characterized as well. The vertical breakdown voltage (around 10V) is determined to produce negligible contribution to the large experimental VBR of the p-Ga2O3/Si structure. Taking into account the experimentally (by SEM) determined thickness of 200 nm (Ga2O3) and 400 nm (Zn:Ga2O3),and extracting bare substrate related VBR the effective parallel plate critical electric field was determined to be EC = 5.7 MV/cm for Ga2O3 and EC = 13.2 MV/cm, for Zn:Ga2O3 respectively. 12 To be certain of this breakthrough value for gallium oxide, we suspected a contribution of the amorphous Zn:Ga2O3 layer (20 nm) on the top of SiO2 layer, mentioned in section 5. Although we didn’t observed Si (very efficient dopant in Ga2O3) at this interface by EDX profile, we estimated an under-value associated to the contribution of a 20nm thick layer with a 30 MV/cm critical field. So Ec=13.2 (-0.9) MV/cm. The extraordinary experimental critical electrical field value of 13.2 MV (almost twice the largest breakdown electric field of ~7 MV/cm previously reported [7] for Ga2O3 to the best of our knowledge) is believed to be due to the Zn-doped p-type nature of the β-Ga2O3; the origin of the delayed impact ionization rate are the deep and amphoteric nature of Zn-dopants and the smaller hole mean free path (i.e., Zn-dopant makes the film even more insulating). In the following we, use the KIIT framework to test this assumption (eq. (5)). It should be noticed that the experimental KIIT parameters (as carrier concentrations and mobilities) are from Hall Effect measurements performed on undoped Ga2O3 and Zn:Ga2O3 on Al2O3(0001) insulating substrates. Hall Effect measurements were not possible to carry out for the samples grown on much conducting Si substrates. As mentioned above, as determined from SIMS, the incorporation of Zn is very similar for Ga2O3 grown on Al2O3 and Si substrates. Besides, there is no critical structural and morphological differences of these films grown either on sapphire or silicon, consequently the transport properties are assumed to be comparable. Avalanche breakdown process and consequently critical electrical filed value as it is seen from formula (5) depends 𝑁𝑁𝑖𝑖 ⁄𝑁𝑁𝑓𝑓 ratio and mean free pass of carriers, 𝑙𝑙 . The concentration of ionized centers N i is assumed to be equal (when high electrical field is applied) to the free carrier concentrations, which, can be estimated from the experimental value of the current density when breakdown occurs: I = 10 µA for Ga2O3/Si and 100 µA for Zn:Ga2O3/Si. Consequently, N i ~ 1013cm-3 and N i ~ 1014cm-3 for Ga2O3 and Zn:Ga2O3, respectively. N f is a concentration of neutral (filled) defects which are a source of free carriers, thus in our case it is considered the number of gallium vacancies. It is assumed to be approximately equal to total concentration of vacancies, which approximately equals to the high temperature hole concentration 1014-1015 cm-3. Then, we estimate the mean free pass of carriers (holes) using experimentally measured values of Hall mobilities. The mean free path is given by 𝑙𝑙 = 𝑉𝑉𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 × 𝜏𝜏, where 𝑉𝑉𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 is an average thermal velocity of free carriers at low electrical field and 𝜏𝜏 is the scattering rate of free carriers. Assuming that 𝑉𝑉𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = �3𝑘𝑘𝐵𝐵 𝑇𝑇⁄𝑚𝑚ℎ∗ , the scattering rate 𝜏𝜏 can be determined from the Drude model µ = 𝑒𝑒𝑒𝑒⁄𝑚𝑚ℎ∗ . Therefore, the mean free path can be calculated as 𝑙𝑙 = 𝑒𝑒 −1 𝜇𝜇�3𝑘𝑘𝐵𝐵 𝑇𝑇𝑚𝑚ℎ∗ . At 850K, the experimental hole mobility was found to be 1 cm2 /Vs and 8 cm2 /Vs for the Zn-doped and the undoped samples, respectively. The hole effective mass value 𝑚𝑚ℎ∗ for different crystallographic orientations has been given in the literature. According to density functional theory (DFT) calculations from Mock et al [45]], the hole effective mass is fairly anisotropic in 𝑎𝑎⃗, 𝑏𝑏�⃗ and ��⃗directions 𝑐𝑐 ∗ : 𝑚𝑚ℎ,𝑎𝑎 = 1.77 𝑚𝑚0 ; 𝑚𝑚ℎ,𝑏𝑏∗ ∗ > 10 𝑚𝑚0 ; 𝑎𝑎𝑎𝑎𝑎𝑎 𝑚𝑚ℎ,𝑐𝑐 = 0.41 𝑚𝑚0 . For our estimations, we (𝑎𝑎 ) take a mean value of hole effective mass in ⃗, 𝑐𝑐⃗ plane concerning both Hall measurements and vertical Breakdown: m* = 3 x (1/ma + 1/m2b + 1/m3 )-1 =4.65 𝑚𝑚0 . We then estimate a mean free path of 𝑙𝑙 (β-Ga2O3) = 3.1 nm and 𝑙𝑙 (Zn:Ga2O3) = 0.37nm, for the undoped and Zn-doped Ga2O3 p-type semiconductors. Thus, the mean free path is eight times smaller for doped Zn: Ga2O3 when compared to the undoped case. Since breakdown was experimentally measured at room temperature, we estimated room temperature mean free path considering that in Ga2O3 mobility follows µ ~ T −3 2 law, [46]. In should be mentioned, that motilities decrease in high electrical field, when carrier velocity tends to saturate, thus in reality mean free paths should be even shorter at room temperature. Once determined the mean free path, concentration of ionized centers N i and the number of neutral gallium vacancies 𝑁𝑁𝑓𝑓 , we can revisit the 13 microscopic kinetic impact ionization theory. The critical electrical field values where given by 𝐸𝐸𝑐𝑐 = (𝐸𝐸𝑎𝑎 ⁄𝑒𝑒𝑒𝑒 ) ln�𝜋𝜋𝑎𝑎0 𝑘𝑘𝑁𝑁𝑖𝑖 ⁄20𝑁𝑁𝑓𝑓 �. According to the KIIT model the calculated critical electric field lies in the range of 2 MV/cm and 5.7 MV/cm for the undoped Ga2O3 and Zn-doped Ga2O3, respectively. The discrepancy with the experimental values (5.7 MV/cm and 13.2 MV/cm for undoped and Zn-doped Ga2O3) may come from the inaccuracy of the hole effective mass value or/and the room temperature interpolation of hole mobilities. Although quantitively inaccurate, a microscopic model of kinetic impact ionization based in hole activated impact ionization qualitatively explains the root reason of the extraordinary capability of Zn-doped p-type Ga2O3 to sustain very large electric fields. 6. Conclusions During many years, metal oxides in solid-state electronics were primarily well known for their outstanding insulating properties. Recently, due to a greater control of the conductivity and the possibility of achieving high-quality large crystals (up to 6-inch), wide and ultra-wide oxide semiconductors have attracted a lot of interest in applications such as power electronics. In this work, capability of p-type undoped Ga2O3/Si material to sustain high EC = 6.0 MV/cm critical electrical field is shown experimentally for the first time. We have demonstrated also an efficient strategy for enhancement of EC by Zn-doping up to 13.2 MV/cm, which is 65% larger than the frequent theoretical maximum value found in the literature (8 MV/cm). According with the kinetic impact ionization theory and thermodynamic calculations, doping with 0.5% amphoteric Zn a p-type Ga2O3 thin-film further reduces the free holes concertation and their mean free path, thus delaying the impact ionization phenomena. Notably, the experimental critical electric field found in this work is to be ~4 times the one from SiC and GaN and it already surpasses widely adopted theoretical value for diamond (~10 MV/cm). This result gives a clear proof of the enormous potential of gallium oxide for power electronics, and hopefully it will also stimulate researchers for calculations and measurements of impact ionization coefficients for this fascinating material. 14 7. Experimental and theoretical Methods In order to study the role of incorporated Zn (< 1%) and its effect on point defects and free carrier concentrations, the thermodynamic equilibrium in the Zn:Ga2O3 (crystal) -versus- O2 (gas) system was modeled. We have defined the dependence of point defects and charge carriers on both temperature and oxygen partial pressure in the surrounding atmosphere. The analysis was made using the Kroger method of quasi-chemical equations, described in details for undoped Ga2O3 in our previous report. [47]. Undoped and Zn doped Ga2O3 films on sapphire (0001) and n-type Si (111) substrates. The layers were grown at low pressure (30 torr) in a horizontal MOCVD reactor with separate inlets to avoid premature reactions in the manifold between di-oxygen and organometallics precursors. Tri-methyl-gallium (TMGa) and di-oxygen were used as precursors for gallium and oxygen respectively. Argon was used as carrier gas. The TMGa bubbler was fixed at -15°C in order to obtain to low growth rate around 5 nm/min. Layer’s thicknesses were varying between 200 nm and 400 nm. SEM images were recorded with a JEOL JSM 7001F electron microscope. The crystallographic structure of the films was analyzed by X-ray diffraction (XRD) with a Siemens D-5000 diffractometer using Cu-Kα radiation (λ = 1.54 Å). Secondary- ion mass spectrometry (SIMS) were used for in-depth Ga, Zn, O profiles, using a Cameca IMS 4f equipment. TEM cross-sections were prepared by conventional mechanical polishing and ion milling. Electron energy loss spectroscopy (EELS) spectrum images and profiles were obtained in high angle annular dark-field (HAADF) STEM mode with an EDAX super ultra-thin window (SUTW) X-ray detector a Gatan Quantum SE 963 imaging filter respectively. 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 80K to 880K 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 samples. A Keysight B1505A Power Device Analyzer has been used in order to carry out the vertical breakdown measurements. Bias voltages have been applied on an isolated Ohmic contact with the substrate grounded in order to access the breakdown voltage. Acknowledgments We acknowledge Dr. F. Jomard (GEMaC) for SIMS measurements. Hagar Mohammed would like to acknowledge Cultural Affairs and Massion Sector, Egyptian Ministry for Higher Education for her fellowship giving possibility work in France. APT acknowledges Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) under contract ENE2015-74275-JIN. 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