Sharp ballistic p–n junction at room temperature using Zn metal doping of graphene

Ballistic graphene p–n junctions (GPNJs) are uniquely suited to develop electrical counterparts of optical circuits as the large transparency enables a better carrier modulation in their interfaces than the diffusive junctions. Here we demonstrate a low-cost and scalable method for the fabrication of ballistic planar GPNJs based on the deposition of physisorbed Zn adatoms. A detailed study of spatially resolved Raman spectroscopy through a quartz transparent substrate enables the accurate mapping of the charge doping and strain across the graphene/Zn interface and underneath the metal layer. At the same time, the electrical measurements of transistor structures with varying channel length, i.e. transfer length electrical measurements, and their modeling reveal the ballistic nature of the charge transport up to room temperature.


Introduction
The atomically thin nature of graphene and its unique range of physical properties underpin the development of conceptually novel electronic, photonics and opto-electronic applications [1][2][3]. Core to these advances is the understanding of graphene p-n junctions (GPNJs) which play a key role in several technologies across computing (e.g. transistors), imaging and lighting (e.g. photodetectors, light-emitting diodes), as well as energy harvesting (e.g. photovoltaics) [4][5][6]. In graphene, these junctions are enabling the development of unique electrical counterparts of optical circuits such as electron lensing [7][8][9], wave guiding [10] and electron beam (Klein) collimators [11,12].
A distinguishing factor of the physics of GPNJs is their electrical transport [13], with junctions falling into one of two categories: sharp GPNJ, in which the width of the junction (w)is smaller than the Fermi wavelength λ F of the graphene carriers (w/λ F < 1), and smooth GPNJ for w/λ F > 1 (λ F ≈ 10 nm for a typical graphene carrier concentration n ≈ 10 12 cm −2 ). Whilst smooth junctions have enabled the demonstration of electron beam collimators [12], sharp GPNJs are highly desirable for studies of the electron negative refraction and the development of electron Veselago lens [9]. Furthermore, sharp junctions are ideally suited for the implementation of realistic electron optic devices as the large transparency enables a better carrier modulation in their interfaces than smooth junctions [13]. Therefore, the search for reproducible and widely accessible experimental methods for the implementation of sharp GPNJs is essential to enable the full exploitation of the potential of graphene in atomic-level electronic and photonic systems.
To date, two main methods for the realization of GPNJs have been widely studied, these are based on electrostatic gating [7][8][9][10][14][15][16] and chemical doping by adsorbed or substitutional dopants [17][18][19][20][21][22]. Whilst electrostatic doping by means of local gating has been widely employed for the formation of planar graphene heterojunctions, only the use of ultra-thin top dielectric layers (e.g. 14 nm thick hBN) has recently enabled the demonstration of quasisharp p-n junctions with a characteristic width of w = 12 nm [9]. The fabrication of truly sharp GPNJs with this method remains challenging as this requires the use of atomically thin dielectric layers which are known to suffer from defects and/or direct quantum tunneling [23][24][25]. To this end, chemical doping of graphene by means of adatoms or molecules has offered a valid alternative to attain GPNJs through charge transfer [17]. This local doping induces lateral GPNJs, and in the case of metal adatoms can provide partial screening of the out-of-plane electric field at the p-n interfaces further reducing the width of the junction [13]. Whilst smooth p-n junctions (w > 200 nm) occurring at the graphene/metal interface have been extensively studied [26][27][28], sharp GPNJs (w < 5 nm) occurring at the Cu/graphene [21] and graphene/α-RuCl 3 [22] interface have only recently been observed using scanning tunneling microscopy and spectroscopy (STM-STS).
Partially filled d states of chemisorbed metal elements onto graphene are known to have a strong interaction with the graphene π states causing chemical bonds with graphene and significant modifications to its conical energy dispersion [19,29,30]. On the other hand, physisorbed metals with filled dorbitals result in the local doping of graphene purely driven by interfacial dipoles and the difference of the metal/graphene work function [29]. In this case, only the Fermi energy of graphene is shifted whilst is conical energy dispersion is preserved. For this reason, physisorbed metals are preferable for developing electron optics applications. Recent theoretical studies have shown that transition metals prefer to sit on hollow sites when chemisorbed, but on bridge or top sites when physisorbed; which is the case of atoms with d 5 and d 10 configurations [31]. Though Zn has been predicted to be the best suited element for physisorption onto graphene [32], with other elements such as silver and copper typical resulting in a mix of physisorption and adsorption, there is no systematic experimental study of the nature of the graphene/Zn interface and its transport characteristics in a field effect configuration.
In this work, we demonstrate the fabrication of sharp planar GPNJs (w ≈ 5.3 ± 0.6 nm) with high potential step (∆V ≈ 0.8 eV) in the proximity of Zn metal contacts with graphene. In order to extract the specific geometrical and electrical characteristics of the metal-induced GPNJs we develop a versatile technique based on conventional Raman spectroscopy and electrical transfer length measurements (TLMs). This can easily be applied to the study of any type of GPNJ, and it was found to exhibit high tolerance to the charged impurities of the substrate. Finally, we adopt this novel method to explore the interface between physisorbed Zn on graphene and demonstrate the ballistic nature of these junctions

Raman characterisation of Zn/graphene interface
Single layer graphene flakes were mechanically exfoliated on 500 µm thick quartz substrates, and coated by a 20 nm thick Zn film, see inset of figure 1(a). The thermal evaporation of 99.97% pure Zn is conducted in low vacuum (<10 −6 mTorr) and with a deposition rate <1 Å s −1 and total film thickness of 20 nm. To prevent the oxidation in air of this Zn layer, we have further encapsulated the film with a 50 nm thick Au layer. Raman spectroscopy was employed for the initial characterization of changes in the doping, strain and defects which may occur in graphene upon metal deposition [33][34][35]. Figure 1(a) shows representative Raman spectra of a monolayer graphene before and after Zn deposition, obtained by shining and collecting the light signal through the optically transparent quartz substrate. Both spectra display the characteristic G-and 2D-peaks with a larger 2D/G intensity ratio, with the 2D peak resonance quantitatively described by a single Lorentzian function, as expected for monolayers, see figures 1(a) and (b).
A systematic analysis of the 2D peak in a spatially resolved Raman map over the whole flake reveals that this peak is consistently described by a narrow (FWHM < 32 cm −1 ) single Lorentzian throughout the Zn-coated graphene, see figures 1(c) and (d). This observation is in stark contrast to previous reports on graphene coated by chemisorbed metals (e.g. Ti, Ni, etc) in which the complete disappearance of the 2D-peak [33] or its splitting into two Gaussian peaks [34] was reported and attributed to the substitution of carbon with metal atoms. The absence of the defect D-peak [35] and the single Lorentzian shape of the 2D-peak measured in graphene underneath Zn are consistent with Zn being physisorbed onto the carbon atoms.
To characterize the metal-induced charge doping or strain in graphene, we employ the well-established vector analysis of the G and 2D peaks measured before and after Zn deposition [36,37]. Figure 2(a) shows a plot of the 2D Raman peak position (ω 2D ) versus that of the G peak (ω G ) extracted from the Raman maps before and after the process of metallization, respectively. The distribution of the data follows two principal axes crossing the pristine (unstrained and undoped) graphene coordinates ω G = 1581.6 cm −1 and ω 2D = 2679.6 cm −1 as shown by Lee et al [36]. These axes, marked as dashed lines in the diagram, represent the iso-doping (∆ω 2D /∆ω) ε = 2.2 and the iso-strain (∆ω 2D /∆ω) n = 0.7 cases [36,37]. Prior work has demonstrated that the projections of each data point onto these dashed directions can be used to determine the doping (n h ) and strain (ε) using the conversion values of −23.5 cm −1 /% and −13.1 cm −1 /10 13 cm −2 for strain and doping, respectively [38,39]. This analysis applied to the Raman maps before and after Zn deposition reveals a normal doping distribution with peak centered at n Zn = 1.8 × 10 12 cm −2 figures 2(b) and (c), and an increase of up to 5% in strain upon coating graphene with Zn, see figure 2(d). After Zn deposition the doping distribution of graphene shows a larger full width at half maximum than that of pristine graphene on SiO 2 . This can be the consequence of clustering of metal atoms in the deposition [40] which leads to a normal distribution of the transmission probability for charges at the graphene/metal interface.

Electrical characterization
Local doping of graphene underneath the metal contacts leads to the formation of GPNJs due to the screening of the metal induced carriers. This results in electron/hole asymmetries of the electrical currents. In a two terminal device, this is quantified by the antisymmetric part of the total resistance R odd = (R e + R h )/2, where R e and R h are the total resistance of the device in the electron and hole sides, respectively [41]. A detailed study of R odd can reveal quantitative information on the GPNJ such as Klein tunneling [42,43]. To this end, we have fabricated two terminal graphene transistors with Zn (20 nm thick) contacts on n-Si/SiO2 (300 nm thick) which serves as a back gate, see figure 3(a). Figure 3(b) shows the back gate dependence of the zero-bias resistance measured at room temperature in devices with different graphene channel width (W) and length (L). In all cases, an asymmetry in the resistance between the electron and the hole side is observed, see inset in figure 3(b).
In general, R odd has two contributions, R odd = R odd_jun + R odd_ch where R odd_jun is the antisymmetric resistance of the graphene/metal interface and R odd_ch is the antisymmetric conductivity of the channel due to asymmetries of the electron/hole carrier mobility or free carrier density [41]. R odd_jun can be expressed as 2R odd_jun = ( r np − r pp ) /W (equation (1)), where r np and r pp is the specific interface resistances of the junction in the bipolar (n-p) and monopolar (p-p) cases, respectively. R odd_jun is inversely proportional to the graphene/metal interface width and it is independent of the channel length. On the other hand, R odd_ch is a function of both channel length and width and it can be expressed as 2R odd_ch = R odd_sheet L/W where R odd_sheet is defined as the odd part of the graphene sheet resistance, 2R odd_sheet = (R e_sheet + R h_sheet ), where R e_sheet and R h_sheet are the total sheet resistance of the device in the electron and hole sides, respectively. The channel contribution can easily be determined from the analysis of the two terminal resistance for devices with the different W and L (TLM analysis). Figure 3(c) shows a plot of the product R odd W for a range of back gate voltage values (0 V <V BG < 65V) and for four different devices. It is apparent that R odd W differs significantly for each device, suggesting that R odd_ch has a significant contribution. To extract R odd_jun we subtract the R odd_ch from the total antisymmetric resistance (R odd ). Figure 3(d) shows a plot of the product R odd_jun W vs V BG for various device channel length. In this case, all the curves nicely overlap as expected for a dominant Zn/graphene interface contribution.
To assess the ballistic or diffusive nature of the charge carrier transport across the graphene/Zn GPNJ we adopt the analysis first introduced by Fogler et al [44]. This relies on the dimensionless parameter β which represents the effective junction length compared to the carrier mean free path, β = n ′ (e/µh) −3/2 where n ′ is the carrier density gradient, µ is the mobility of the charge carriers underneath the contacts ∼900 cm −2 V −1 s −1 determined using advanced TLM analysis [45] (for more information see SI), e is the elementary charge and h is Planck's constant. Prior studies have shown that upon increasing the value of β, the electrical transport in a GPNJ goes from quasi-ballistic 1 < β < 10 to ballistic for β > 10 [16,42,44,46]. The carrier density was calculated taking under consideration the nonlinear screening of the metal doped graphene from the channel carriers given by the expression [20,26] where n m and E m are the carrier density (n m = 1.8 × 10 13 cm −2 from Raman spectroscopy) and the Fermi level in graphene underneath the metal, whereas n ch and E ch are the charge density and Fermi level in the graphene far away from the Zn contacts, respectively. The transition length is given by , where the κ is the effective dielectric constant κ = 2.5, ε 0 is the vacuum dielectric permittivity, v F is the Fermi velocity and x b is found using the density continuity condition: n (x = 0) = n m . Figure 4(a) shows the spatial dependence of the induced screening potential, V (x) = µ (x) + µ F , underpinning the GPNJ for two different values of V BG = 60 V and 20 V, where µ (x) is the local chemical potential and µ F is the chemical potential of graphene away from the graphene/Zn interface [26]. The width of the junction can be directly estimated considering a change from 10% to 90% of the junction potential [8,13]. This analysis reveals that the junction width at the graphene/Zn interface changes monotonously from 10.4 nm at V BG = 20 V to 5.3 nm at V BG = 60 V, see figures 4(a) and (b). At the same time, β increases monotonously upon increasing the electrostratic doping as the electrical transport crosses from the diffusive regime, i.e. β < 1 for V BG < 20 V, to the ballistic regime, i.e. β > 10 for V BG > 60 V. The uncertainty on β due to the inhomogeneous doping is ∆β = 0.1.
A quantitative description of ballistic GPNJs based on the Landauer formalism [47] can be developed considering the relation between electrical resistance due to a scatterer (R sc ) and the transmission of electrons across it (T av ), R sc = 1−Tav G0MTav (for more information see SI). In the case of a graphene device encompassing source and drain contacts, T av is a function of the individual graphene/Zn interfaces (i.e. T S,D ) expressed as [48]: where T eff is the transmission through the two junctions, θ ι and θ r are the incident and refracted angles of carriers to the interface while k i , k r are the wavevector carriers, respectively. Prior studies have highlighted that the contribution of the Wentzel-Kramers-Brillouin exponential tunneling is only present in the p-n regime, whereas the cosine prefactors fully capture the wavefunction transmission in the unipolar case [48]. Finally, the finite temperature is taken into account as G pn/pp = G 0´+ dE [48] figure 4(c) shows a plot of the experimental and theoretical values for 2R odd_jun = 1/ ( G pn − G pp ) in the ballistic regime (i.e. β ≈ 10 and V BG ⩾ 60 V). A good agreement between experimental and theoretical model is attained for a junction width of 5.4 ± 0.6 nm, consistent with the estimated value for W based on the nonlinear screening of charges induced in graphene by metal contacts, see figures 4(a)-(c).

Conclusions
In conclusion, we have fabricated and examined the features of metal-induced GPNJs in the proximity of Zn metal contacts. Raman analysis of Zn/graphene interface reveals that Zn is a physisorbed metal which induces high p-doping in graphene (n m = 1.8 × 10 13 cm −2 ) without destroying its unique electronic structure. Theoretical investigation supported by experimental results indicates that the width of the Zn-induced contact junctions in graphene is about 5.3 ± 0.6 nm and that ballistic carriers propagate across it even at room temperature despite the high metal-induced strain from the contacts. Moreover, our analysis shows that the width and consequently the electrical transport regime of the graphene junction can easily be tuned using the back gate voltage. These findings demonstrate a simple method for the practical implementation of sharp planar graphene p-n junctions.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).