Charge carrier transport properties in layer structured hexagonal boron nitride

Due to its large in-plane thermal conductivity, high temperature and chemical stability, large energy band gap (~ 6.4 eV), hexagonal boron nitride (hBN) has emerged as an important material for applications in deep ultraviolet photonic devices. Among the members of the III-nitride material system, hBN is the least studied and understood. The study of the electrical transport properties of hBN is of utmost importance with a view to realizing practical device applications. Wafer-scale hBN epilayers have been successfully synthesized by metal organic chemical deposition and their electrical transport properties have been probed by variable temperature Hall effect measurements. The results demonstrate that undoped hBN is a semiconductor exhibiting weak p-type at high temperatures (> 700 ◦K). The measured acceptor energy level is about 0.68 eV above the valence band. In contrast to the electrical transport properties of traditional III-nitride wide bandgap semiconductors, the temperature dependence of the hole mobility in hBN can be described by the form of μ ∝ (T/T0)−α with α = 3.02, satisfying the two-dimensional (2D) carrier transport limit dominated by the polar optical phonon scattering. This behavior is a direct consequence of the fact that hBN is a layer structured material. The optical phonon energy deduced from the temperature dependence of the hole mobility is –hω = 192 meV (or 1546 cm-1), which is consistent with values previously obtained using other techniques. The present results extend our understanding of the charge carrier transport properties beyond the traditional III-nitride semiconductors. C 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4898630]


I. INTRODUCTION
Among the members of the III-nitride material system, hexagonal boron-nitride (hBN) is the least studied and understood.2][3][4][5][6][7] Moreover, due to its complementariness and close lattice match to graphene, hBN has recently attracted considerable attention for the exploration of van der Waals heterostructures consisting of hBN/graphene with new physics and applications. 8,9The large thermal neutron capture cross-section (3840 barns) of 10 B 10,11 also makes hBN potentially a very promising material for the realization of solid-state neutron detectors. 12,13he knowledge and experimental data on the electrical transport properties of hBN are scarce due partly to its very large bandgap and highly electrical insulating nature.An improved understanding of the electrical properties of hBN is necessary to take the advantages of its excellent physical properties for significant device applications.Our present studies focus on the electrical transport properties of unintentionally doped hBN epitaxial layers (or epilayers) grown by metal organic chemical vapor deposition (MOCVD).In contrast to traditional III-nitride semiconductors, it was observed that the mobility versus temperature behavior in hBN is governed by 2D effects due to its unique layered structure.Experimental results suggest that the scattering mechanism is dominated by carrier polar optical phonon interaction at high temperatures.The optical phonon energy deduced from the temperature dependence of the hole mobility is consistent with values previously obtained using other methods.

II. EXPERIMENT AND BASIC CHARACTERISTICS OF hBN EPILAYERS
The hBN epilayer structure used in this study is schematically illustrated in Fig. 1(a).The hBN epilayers were grown on c-plane sapphire substrates by MOCVD using hydrogen as a carrier gas.MOCVD is an established technique for producing high quality crystalline materials due to its ability to precisely control the growth processes and has been widely adopted by the commercial sector for producing III-nitride wide bandgap semiconductors in large wafer scales. 14The precursors for boron and nitrogen are tri-ethyl boron (TEB) and ammonia (NH 3 ), respectively.For the growth of hBN epilayers, the typical V/III ratio employed was around 3000 and a pulsed growth scheme (alternating flows of TEB and NH 3 ) was undertaken to minimize the pre-reaction between TEB and ammonia, which is necessary for obtaining epilayers in hexagonal phase. 15Adopted from the hetero-epitaxial growth of III-nitride device structures, a low temperature BN buffer layer of about 10 nm in thickness was deposited on the sapphire substrate at about 800 • C prior to the growth of hBN epilayer.The growth temperature used to produce hBN epilayers reported in this work was around 1300 • C. The Hall effect measurements were conducted to measure the charge carrier type, concentration, mobility, and conductivity of hBN epilayers.55.06 • , and 88.00 • , respectively with no other visible peaks.The results revealed a c-lattice constant ∼6.67 Å that matches closely with the bulk c-lattice constant of hBN (c=6.66Å) and demonstrated that our MOCVD grown hBN films are single crystals in hexagonal phase. 3Figure 1(d) compares the XRD rocking curves (ω-scans) of the (0002) diffraction peaks of an hBN epilayer and AlN epilayer which has a comparable bandgap as hBN. 16Although the observed full width at half maximum (FWHM) of 380 arcsec for hBN epilayer is much broader than the typical FWHM (∼63 arcsec) of high quality AlN epilayers grown by our group, but is comparable to the typical value for GaN epilayers grown on sapphire with a similar thickness. 14The comparison XRD results between hBN and AlN are an indicative of the fact that the development of hBN epitaxial layers is in its early stage and improvements are still needed.Secondary ion mass spectrometry results also revealed that hBN epilayers have excellent stoichiometry. 3 The grown epilayers also have a good surface morphology as indicated by the AFM image shown in Fig. 1(b) as well as by an SEM image shown in the inset of Fig. 2(a) for an hBN epilayer (etched into stripes).Moreover, as shown in Fig. 2(b), the measured 10 K band edge photoluminescence (PL) emission intensity of hBN is more than 2 orders of magnitude higher than that of high quality AlN, originating from the unusually strong p → p-like transitions and its "two-dimensional" nature. 4However, the presence of stacking faults, dislocations, and native defects cannot be precluded and all could contribute to the broadening of the FWHM of the XRD rocking curve.

III. RESULTS AND DISCUSSION
Van der Pauw-Hall method 17 was employed to measure the electrical resistivity, carrier concentration, and mobility.To minimize the impact of possible sample inhomogeneity on the measured carrier type and mobility while employing the Van der Pauw-Hall method, we used four small size triangular ohmic contacts fabricated on the four corners of the sample. 16,18Ohmic contacts consist of Ni/Au (20 nm/30 nm) bilayers were deposited using e-beam evaporation followed by rapid thermal annealing at 800 • C for 10 minutes.Figure 3(a) is the microscope image of a fabricated hBN sample with four ohmic contacts on the corners.The ratio of the contact size (d) to the sample length (L) is ∼1/10, a configuration that is considered to be adequate to provide reliable measurement results. 18Ohmic behavior of Ni/Au bilayer contacts on hBN is demonstrated by the linear behavior of the I-V curve shown in Fig. 3(b).However, the estimated room temperature resistivity of undoped hBN epilayers is in the order 10 11 Ω•cm based on the I-V characteristics.Due to the high resistivity of these undoped samples, it was difficult to carry out Hall effect measurements below 700 • K.
At T >700 • K, the mobility data consistently revealed that undoped hBN epilayers are semiconductors of weak p-type, similar to the case of diamond.Figure 4  the following equation: where k B = 8.625 × 10 −5 (eV•K −1 ) is the Boltzmann's constant.The fitted value of E A = 0.68 eV is the measure of the acceptor energy level above the valence band.Since the hBN epilayer used for this study is undoped, the origin of this deep acceptors is most likely related to the presence of native defects.One possibility is the presence of boron vacancies, V B , or V B related defects, which act as acceptors, in analogous to the acceptor-like native defects in III-nitrides, namely gallium vacancy, V Ga , in GaN and V Al in AlN. 15,19,20n contrast to conventional III-nitride semiconductors, which have an isotropic wurtzite structure, hBN is a layer structured material.In wurtzite structure, the distances between the nearest and the second nearest neighbors are nearly the same in the directions of parallel and perpendicular to the c-axis.The lattice-vibration or phonon properties and hence the carrier transport properties of conventional III-nitrides therefore are isotropic (or slightly anisotropic).It is well known that the carrier mobility (µ) in an isotropic semiconductor typically decreases with an increase of temperature at high temperatures following a power-law dependence, µ ∼ T −α with the exponent α ≈ 1.5 limited by acoustic phonon scattering or α ≈ 0.5 limited by optical phonon scattering. 21he layer structured hBN on the other hand has the same crystal structure as graphite with lattice constants a = 2.54 Å and c = 6.66 Å.3][24][25][26] For instance, although hBN bulk crystals and epilayers are three-dimensional (3D) systems, the interlayer optical transitions are much weaker than those within the layers 4 and the exciton properties of 3D hBN can be described in a 2D framework. 5Due to the highly anisotropic nature of hBN, it is also expected that phonons propagate more quickly in the c-plane (⊥ c-axis) with strong B-N bonds and slower along the c-axis (// c-axis) with Van der Waals bonds.Furthermore, the free charge carriers also have higher mobility in the lateral direction (⊥ c-axis) than in the vertical direction (// c-axis).3][24][25][26] On the other hand, compared to other layered semiconductors such as GaSe, MoS 2 , MoSe 2 , and WSe 2 , [23][24][25] which typically have an energy bandgap E g ∼ 2 eV with a maximum optical phonon energyhω ∼ 60 meV, hBN is composed of light elements B and N and has a much larger bandgap (E g ∼ 6.4 eV) 5 as well as a much larger maximum longitudinal optical (LO) phonon energy ofhω ∼ 190 meV. 22,27In fact, hBN may possess the largest phonon energy among all semiconductors.These unique properties together significantly influence the carrier-phonon scattering and hence the carrier transport properties, especially at high temperatures.
It has been reported that the scattering is dominated by homopolar optical phonons in layer structured semiconductors with energy gaps around 2 eV, [23][24][25][26]  follows µ ∼ T −α with much large exponents than in 3D and isotropic semiconductors.5][26] In the weak carrier-optical phonon coupling regime, the excess carriers behave as free quasi-particles.At sufficiently high temperatures, it is well-known that the carrier-optical phonon scattering dominates in layer structured materials and the dependence of the carrier mobility on temperature can be described by [24][25][26] over a certain temperature range around a characteristics temperature T o , where and µ o is the prefactor in the carrier mobility versus temperature relation andhω is the maximum phonon energy, which dictates the carrier-phonon scattering at high temperatures.Figure 6 shows the temperature dependence of the hole mobility in a natural logarithmic plot.The solid line is the least squares fit by Eq. ( 2).The fitted value of α = 3.02, which is larger than those seen in GaSe (α = 2.1) and MoS 2 (α = 2.6).This is expected from Eq. ( 3) since α increases linearly withhω, the maximum phonon energy.The maximum phonon energy in hBN is around 196 meV, 22,27 which gives: On the other hand, the maximum phonon energy in hBN can be estimated from the experimental data.At temperatures at which k B T is much smaller than the maximum optical phonon energy, the in-plane mobility of charge carriers in layered semiconductor due to phonon scattering satisfies the 2D limit: [24][25][26] µ ∝ e In Fig. 7, the temperature dependence of the holes mobility is presented in an Arrhenius plot according to Eq. ( 4).The fitting between the experimental data and Eq. ( 4) provides the energy of the optical phononhω ≈ 192 meV (or 1546 cm −1 ), which agrees quite well with a value of 196 meV for the maximum optical phonon energy in hBN measured using Raman and infrared reflection spectroscopy. 21,27,28The maximum eigenfrequencies of LO phonons for in-plane vibration with k ≈ 0 is proportional to the constant forces between the nearest neighbors in-plane and inversely proportional to the reduced mass of boron and nitrogen. 21[26] All article content, except where otherwise noted, is licensed under a Creative Commons Attribution

IV. CONCLUSIONS
In summary, single crystal hBN epilayers have been synthesized by MOCVD and their electrical transport properties have been studied via high temperature Hall effect measurements.It was found that undoped hBN epilayers exhibit weak p-type at high temperatures (T > 700 • K) with an in-plane resistivity of ∼ 1.6 × 10 3 Ω•cm at 790 • K.The measured energy level of the p-type defects is around 0.68 eV with a possible origin attributing to boron vacancies V B , or V B related defects.It was found that the temperature dependence of the hole mobility in hBN epilayers is dominated by the polar optical phonon scattering at high temperatures, following the power law dependence of µ ∼ T −α with an unusually large exponent α (≈3.02).The observed strong optical phonon scattering is a consequence of the 2D nature or layered structure of hBN, which has a strong in-plane force and weak Van der Waals force between layers.The maximum energy (wave number) of the optical phonon deduced from the temperature dependent mobility is ∼ 192 meV (or 1546 cm −1 ), which agrees well with the previously reported values obtained via Raman and infrared reflectance spectroscopy.Further studies are required to gain improved understanding on the carrier transport mechanisms and conductivity control in hBN epilayers.

Figure 1 (
FIG. 1.(a) Schematic layer structure of the hBN epilayer used in this study; (b) AFM image of hBN epilayer over a 2 × 2 µm 2 area scan; (c) XRD θ-2θ scan of the hBN epilayer used in this study; and (d) Comparison of XRD rocking curves of the (0002) diffraction peaks of hBN and AlN epilayers.

107126- 3 Doan
FIG. 2. (a) SEM image of an hBN epilayer (etched into stripes).(b) Comparison of deep UV photoluminescence spectra of hBN and AlN epilayers measured at 10 K.The inset is an optical image of a 2-inch wafer of hBN epilayer [partially reproduced from Fig. 1 of Ref. 16].
FIG. 3. (a) Optical image of an hBN epilayer with ohmic contacts fabricated on the four corners for Hall-effect measurements.(b) Room temperature I-V characteristics of an hBN epilayer obtained by employing Ni/Au bilayer (20 nm/30 nm) as ohmic contacts.

FIG. 5 .
FIG. 5.The Arrhenius plot of the hole concentration.The open squares are the measured data and the solid line is the least squares fit of data with Eq. (1).The error bars for the measured data are indicated in the plot.

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FIG. 6. ln (µ) versus ln (T) plot of the temperature dependence of the hole mobility.The open squares are the measured data and the solid line is the least squares fit of data with Eq. (2).The error bars for the measured data are indicated in the plot.
in which the temperature dependence