Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX
pubs.acs.org/NanoLett
Fingerprinting Electronic Structure in Nanomaterials: A Methodology Illustrated by ZnSe Nanowires David Wisniewski,*,† Kristopher Byrne,† Carlos Fernandes,† Corey Stewart,† Christina F. de Souza,† and Harry E. Ruda†,‡ †
Centre for Advanced Nanotechnology, University of Toronto, 170 College Street, Toronto, Ontario M5S 3E3, Canada Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China
‡
Nano Lett. Downloaded from pubs.acs.org by LEIDEN UNIV on 03/19/19. For personal use only.
S Supporting Information *
ABSTRACT: Characterizing point defects that produce deep states in nanostructures is imperative when designing nextgeneration electronic and optoelectronic devices. Light emission and carrier transport properties are strongly influenced by the energy position and concentration of such states. The primary objective of this work is to fingerprint the electronic structure by characterizing the deep levels using a combined optical and electronic characterization, considering ZnSe nanowires as an example. Specifically, we use low temperature photoluminescence spectroscopy to identify the dominant recombination mechanisms and determine the total defect concentration. The carrier concentration and mobility are then calculated from electron transport measurements using single nanowire field effect transistors, and the measured experimental data were used to construct a model describing the types, energies, and ionized fraction of defects and calculate the deviation from stoichiometry. This metrology is hence demonstrated to provide an unambiguous means to determine a material’s electronic structure. KEYWORDS: Nanowires, crystal defects, II−VI semiconductors, photoluminescence, electrical resistivity, nonstoichiometry
N
on ZnSe as an example, which is a technologically important material for visible light emission and detection and has been shown to be significantly affected by native point defects. Specifically, we study ZnSe nanowires, as ZnSe nanostructures can be readily fabricated10 and offer a new class of exciting optoelectronic applications.11−13 The concentration of point defects in a ZnSe sample depends strongly on the growth conditions.14 For a specific set of conditions, one type of defect is typically dominant due to the exponential dependence1 of the defect concentration on the defect formation energy.15 Pöykkoö16 has shown that doubly charged cation vacancies, V −− Zn , are favored in undoped, n-type ZnSe. Furthermore, the resistivity of ZnSe nanowirebased devices has been observed to range between tens of mΩ·m12,17,18 to over 1000 Ω·m.19,20 This wide discrepancy is attributed to the presence of point defects that compensate21 and scatter22 carriers and to the position of the Fermi level, which determines the fraction of ionized defects implicated in transport.
ative point defects play a critical role in the utility of optical and electronic devices such as Schottky diodes, LEDs, laser diodes, and transistors, specifically those based on transition metal chalcogenides such as selenides1 and oxides2 and other technologically important binary compounds like GaAs3 and nitrides.4 These defects, and complexes associated with these defects, can often have undesired effects on device performance, acting as recombination and scattering centers, compensating free carriers, and introducing long-lifetime trap states.5,6 However, they can also have a positive impact, serving as luminescent emission centers,4 scattering phonons,7 and acting as donors and acceptors.8 Therefore, it is of utmost importance to characterize and understand how such defects affect the electronic structure of a material. Typically, defects are studied using electrical, magnetic, or optical methods, including photocapacitance measurements, deep level transient spectroscopy (DLTS), and electron paramagnetic resonance (EPR).9 These methods alone provide information about the energy levels and types of defects but cannot typically measure the occupation of intrinsic and extrinsic electronic states. In this paper, we use a combination of photoluminescence (PL) spectroscopy, current−voltage measurements, and information obtained from traditional defect studies in the existing literature to provide a complete fingerprint of the electronic structure of a material. We focus © XXXX American Chemical Society
Received: November 17, 2018 Revised: January 30, 2019
A
DOI: 10.1021/acs.nanolett.8b04646 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. (a) Measured PL spectra of ZnSe nanowire array (scanning electron micrograph of array, inset) at room temperature and 4.2 K. Intensity-dependent analysis of DAP emission in (b) the 2.273 eV band and (c) the 1.991 eV band.
impurity species may be copper, depending on the trace elements present in the ZnSe source material. To realize efficient devices, it is necessary to understand the nature of the crystallographic defects that limit performance. Therefore, the primary objective of this paper is to develop a model that describes the types, energies, and concentrations of deep level states present in as-grown ZnSe nanowires. This will be achieved by using intensity-dependent low-temperature PL (LTPL) spectroscopy to determine the relative defect concentrations, and gate-dependent current−voltage measurements from single ZnSe nanowire field effect transistors (NWFETs) to fully identify the electronic structure, including the occupation of DL states and Fermi level position. By demonstrating this analysis using ZnSe NWFETs, this method can be applied to other nanostructured material systems. ZnSe nanowires were grown by the vapor phase growth method, catalyzed by Au-droplets based on the vapor−liquid− solid mechanism.35 The growth conditions and NWFET fabrication techniques were reported previously.36 The current−voltage characteristics of three terminal (source, drain, gate) NWFETs were studied using a HewlettPackard (HP) 4140B picoammeter to bias the source contact
Even in high-purity growth conditions, native defects arising from stoichiometric deviations exist, which can be observed by studying the low-temperature photoluminescence (PL) spectrum.23 The deep level (DL) emission from ZnSe crystals is well-recorded in the literature; however, the radiative recombination mechanisms remain disputed. There exists two DL emission bands: red (1.95−2.00 eV) and green (2.20−2.30 eV), with the origin of the former having been studied in more detail. Optically detected magnetic resonance (ODMR) experiments24,25 have shown that this emission arises from donor−acceptor pair (DAP) recombination between a distant donor impurity, +R , and an acceptor-like ++ Frenkel pair composed of native point defects (V −− Zn · Zn i ). This assignment has been proven accurate through systematic growths26 coupled with positron annihilation spectroscopy measurements.27−29 The 2.20−2.3 eV band is often labeled as copper-green emission,30 but the emission need not include copper.31−34 Rather, a more correct assignment would be DAP-emission between a distant donor, +G , and an acceptorlike complex (A-center), composed of a zinc vacancy and ++ impurity donor, e.g. (V −− Zn · DZn ). One or more of these B
DOI: 10.1021/acs.nanolett.8b04646 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 2. (a) Schematic and (b) scanning electron micrograph of three-terminal NWFET, and measured electron transport analysis, including (c) Ids−Vds measurements, and (d) transfer curve for NWA.
and measure the current at the drain while sweeping the global back-gate voltage. LTPL spectroscopy measurements were performed on an array of as-grown nanowires at 4.2 K, using the frequencydoubled output of a Coherent MIRA-900F Ti:sapphire oscillator (with pulse width of 200 fs, excitation wavelength of 390 nm, and repetition rate of 76 MHz) as the excitation source. The spectra were collected by placing a fiber optic cable directly above a microscope objective lens (Mitutoyo M Plan Apo SL 50) and dispersing the signal using a spectrometer (Jobin-Yvon TRIAX 320) for detection using a liquid-nitrogen cooled Si-based CCD detector (Horiba Spectrum One CCD-3000). Optical Characterization. Arrays of nanowires (having diameter 105 ± 35 nm and lengths of 8 ± 2 μm) studied by PL spectroscopy showed spectra dominated by two deep level emission peaks, which were very well-defined at low temperatures (Figure 1 (a)). The peak at 1.991 eV corresponds to red emission; the peak at 2.273 eV corresponds to green emission, and nearly no near band edge emission was observed. The excitation intensity dependence of the LTPL spectra was used to confirm that the deep level emission originated from DAP recombination. As the laser excitation power, L, was changed, the integrated PL intensity, I, of each peak varied
according to the power-law relationship37 given by I ∝ Lk (where the coefficient k reflects the type of radiative transition). For 0 ≤ k ≤ 1, the emission peak saturates upon increasing excitation, indicating DAP-related transitions, which arise from a finite number of defects in the sample. When 1 < k < 2 , the recombination involves free and bound excitons because excitons form independently of defects.38 For the green and red deep level peaks in the as-grown array of nanowires, it was found that k was equal to 0.480 and 0.467, respectively, thus confirming that the deep level emission originated from DAP-related transitions. To determine the donor and acceptor energies, the peak energy, hνm , was measured as a function of the excitation power. The DAP peak energy is given39 by ij yz e2 zz hνm = Eg − jjjEd + Ea − zz j 4 πε R ZnSe { k
(1)
where Eg is the bandgap energy14 (2.822 eV at 4.2 K), Ed and Ea are the ionization energies of donors and acceptors, respectively, εZnSe is the dielectric constant (equal to εsε0 using40 εs = 8.66), and R is the distance between donor and acceptor. C
DOI: 10.1021/acs.nanolett.8b04646 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters As the pump power was increased, emission from DAPs located at large separation distances saturated due to the lower transition probability of these pairs. The closely separated pairs became preferentially excited, as observed by a shift to higher energies due to the stronger Coloumbic interaction. Zacks and Halperin41 proposed a model relating the excitation intensity to the DAP peak energy: Iexc = I0
ij 2(hνb − hν∞) yz (hνm − hν∞)3 zz expjjj− hνb + hν∞ − 2hνm jk hνm − hν∞ zz{
Table 1. Summary of Room Temperature Electron Transport Parameters for NWA and NWB conductivity, σ transconductance, g threshold voltage, Vth mobility, μ carrier concentration, n
e2 4πεZnSeRB
Optical Characterization. The nanowires were dominated by DL emission, which arises from DAP recombination in the form + o + (o → ++ + (− + hν , where hν is the energy of the emitted photon. The species involved in the red emission ++ − −− ++ − + are ++R + (V −− Zn · Zn i ) , while +G + (V Zn · DZn ) are involved in the green emission. Using the results from the intensitydependent LTPL, the donor and acceptor energies levels were determined. For the red emission, it is well-documented that the ++ − (V −− Zn · Zn i ) acceptor level exists 0.7 ± 0.04 eV above the valence band edge.46−48 From (Ed + Ea)R = 0.849 eV, the donor level is approximately 0.15 eV below the conduction band edge, which agrees well with Iida,49 Besomi,50 and Meneses47 who attributed the donor to a metal impurity, ++ − possibly indium. For the green emission, the (V −− Zn · DZn ) 46,51,52 acceptor level is approximately 0.58 ± 0.03 eV above the valence band edge, giving a donor energy level 0.03 eV below the conduction band edge, which is within the error of the shallow donor value given by the hydrogen model,53
.
The results of this analysis for the green and red DL peaks are shown in Figures 1(b) and (c), respectively. From the fitting parameter hνb, the binding energy of the DAPs was calculated. For the green emission, E BG = 90 meV, while for the red emission, E BR = 99 meV. These binding energies correspond to impurity Bohr radii values of 1.83 and 1.66 nm, respectively. The sum of the ionization energies for the donors and acceptors involved, (Ed + Ea), were calculated from hν∞, and it was found that for the green emission, (Ed + Ea)G = 0.584 eV, while for the red emission, (Ed + Ea)R = 0.849 eV. Electrical Characterization. A schematic of the device architecture and a scanning electron micrograph of a completed device are shown in Figure 2 (a) and (b), respectively. Ids−Vds measurements were performed on two devices, NWA and NWB. The diameters, d, of NWA and NWB were 140 and 72 nm, respectively, and the channel lengths, L, were 6.3 and 4.2 μm, respectively. A set of typical Ids−Vds curves are shown in Figure 2(c) for NWA. The measured current increases with the gate voltage, Vg , confirming n-type conduction. Devices did not reach saturation, as a sufficiently high Vds was not applied, which could damage the nanowires. The channel conductance, dI G = dVds , was calculated for each Ids−Vds curve near Vds = 0.
me*e 4 2
2ℏ (4πεsε0)2
I(R ) = C0(R )W (R )f (R )P(R )
(3)
where C0(R ) contains the terms involved in changing variables from atomic spacing, R, to energy, E, as well as normalization constants. Colbow et al.57 showed that this condition requires C0 to scale linearly with the minority impurity concentration, i.e. the acceptor concentration, Na , in n-type nanowires. The transition probability, W (R ), is given by 5 8 W (R ) = W0exp( −2R /RB) where W0 is the radiative transition probability, which depends on the wave function of the donor, and RB is the Bohr radius of the shallower impurity, determined by intensity-dependent PL. The fraction of DAPs excited is given by f (R ), which under pulsed (fe mtosecond) excitation, is given 5 8 by f (R ) = (1 − exp(−gAR2)), where g is the excitation intensity and A is the capture cross section (assuming R2 -dependent capture cross section). The pair distribution function, P(R ), including next-available nearest neighbor interactions is given59 by P(R ) = 4πNdR2/(1 + 4πR3Nd /3)2 , where Nd is the total donor concentration. Figure 3 shows a three-parameter fit to the green (G) and red (R) emission line shapes was performed for R > 0.64RB (because no bound hole states exist60 below 0.64RB) using free parameters ζ ≡ 4πC0W0Nd , α ≡ gA , and Nd .
ds
g
the direct transconductance method,42 from which the electron dG L2 . dVg C
= 30.8 meV.
The concentration of vacancies was estimated by fitting the PL line shape function, I(E). Following refs 54−56, the emission line shape is given by
The relationship between conductance and gate voltage was found from its transfer curve, shown in Figure 2(d), also for dG NWA. The transconductance, g = dV , was calculated using mobility was calculated using μ =
NWB 9.1 mS/cm 2.3 nS/V −1.0 V 0.8 cm2/V·s 9.2 × 1016 cm−3
(2)
where Iexc is the excitation intensity, I0 is a scale factor, hν∞ is the emission energy at infinite separation, e.g. hν∞ = Eg − (Ea + Ed), and the term hνb is defined by hνb = E B + hν∞ where E B is the binding energy, which is a function of the impurity Bohr radius RB given by
EB =
NWA 12.7 mS/cm 5.0 nS/V −3.1 V 2.7 cm2/V·s 9.9 × 1016 cm−3
Here, C is the gate
capacitance, estimated using a cylinder-on-a-plate model, given 2πε ε L d by the expression C = cosh−1((t 0 eff+ r) / r) , where r = 2 is the ox
nanowire radius, εeff = 2.2 is used as the effective permittivity43 of SiO2, and tox is the oxide thickness, equal to 100 nm for the substrates used in this study. The carrier concentration, n, was calculated from the charge (Vg − VT)C
, where VT is the threshold control model,44 using n = eπr 2L voltage, which was calculated using the linear extrapolation method.45 The results from the electron transport studies are summarized in Table 1. D
DOI: 10.1021/acs.nanolett.8b04646 Nano Lett. XXXX, XXX, XXX−XXX
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The donor and acceptor concentrations in eq 4 refer to the ionized fractions, which includes all acceptor states,65 because the Fermi level must lie above the midgap. The total number of ionized acceptors is therefore given by Na− = NaR + 3.5NaR . The total number of ionized donors is the sum of specific donor levels i having energy Ei below the conduction band, found using Fermi statistics:66 ij
i Ef − Edi yzyzz zzzz zz k kT {{
∑ Nd+ = ∑ Nd jjjj1 + β expjjjj 2
Nd+ =
2
i
i=1
i
i=1
k
−1
(5)
where β is the degeneracy, equal to 2 for the singly ionized donor states considered, and Ef is the Fermi level position. In this paper, positive Ef and Ed values refer to energies below the conduction band edge. The degree of compensation between ionized donors and N− acceptors is tracked by the compensation ratio, θ = Na+ . d
Curves showing the variability of n and μ with θ are readily available,22 which suggest that the nanowires studied have very strong compensation, θ > 0.96. MBE-grown ZnSe films are known to have θ as high as 0.94,65 and our CVD growth process involves higher growth temperatures. Therefore, the impurities have an increased solubility and diffusivity, confirming that compensation should be very high. For this self-consistent model, θ = 0.98 was selected. Using values of Ndi = {NdR , NdG} determined through the line shape fit, the donor energy levels from LTPL spectroscopy, and θ = 0.98, the values of NaR and Ef were solved explicitly. The results for NWA and NWB were in good agreement, Ef = 47 a n d 4 8 m e V , Nd+ = (4.8 ± 0.3) × 1018 a n d (4.7 ± 0.3) × 1018 cm−3, respectively. The total ionized acceptor concentration, Na−, was (4.7 ± 0.3) × 1018 cm−3, which is the average value for the nanowire array. Nonstoichiometry in ZnSe NWs. The information calculated in the above defect model is useful for determining the homogeneous phase diagram boundaries. Because cation vacancies are involved in the defect complexes studied, the deviation from stoichiometry, Zn 0.5 − δSe0.5 + δ (δ > 0), was estimated, with the goal of improving the growth conditions to produce less-defective wires. The acceptor complex (VZn ·Zn i ) is composed of two defects that negate their respective effects on stoichiometry. Each vacancy makes the lattice deficient in zinc by one atom, while a zinc interstitial makes it equally zinc-rich. Therefore, it was not necessary to consider this complex in the calculation of δ. The donor species +R and +G also need not be considered, as these are shallow impurity atoms residing on zinc lattice sites, which behave as a zinc atom otherwise would.67 The defects associated with green emission involve the acceptor-like complex (VZn ·D), which were necessary to consider as it contains a zinc vacancy that is uncompensated by the substitutional impurity donor D. Therefore, the VZn from the acceptor-like complex is the only species that contributes to δ. The relationship between the concentration of defect complexes and the constituent defects is given68 by
Figure 3. Fit to measured optical emission from a ZnSe NW array using the photoluminescence line shape function, I(E).
The donor concentrations obtained through fitting were NdR = (4.5 ± 0.3) × 1018 cm−3 and NdG = (2.2 ± 0.3) × 1018 cm−3. Because the DAP transitions responsible for green and red emission saturated at approximately the same rate (similar k values), it was assumed that the radiative transition coefficient, W0 , was equivalent between the two processes. Because both sets of data were analyzed from the same spectra, the only parameter within ζ that differed between the fits was Na , which is linear57 with C0 and therefore ζ. Therefore, the relative acceptor concentration was found from the result ζ G = 3.5ζ R , giving NaG = 3.5NaR . Electrical Characterization. NWA and NWB had conductivity values (at Vg = 0) of 12.7 and 9.13 mS/cm, respectively, which agree well with many of the published results on ZnSe nanowires.61,62 There was a significant size difference between the two asgrown nanowires studied, which had a noticeable effect on the observed mobility and carrier concentration. The diameter of NWB was half that of NWA, while the channel length was over 2.5 times smaller. A higher density of surface states on the smaller wire led to stronger screening and therefore poorer coupling between the gate and the wire viz. a lower transconductance and higher threshold voltage. These states also gave a higher density of scattering centers, which in turn lowered the carrier mobility.36 The effect of inhomogeneities in the wire63 were more noticeable through the shorter channel as well, to which we attribute nonlinearities in the Ids−Vds curves. It can be noted that because the capacitance has an inverse dependence on the nanowire geometry, the net carrier concentrations remain consistent between devices. Defect Model. For the defects considered, the electroneutrality condition can be written27,64 as + − −− +− + + n + [(V −− Zn · D ) ] + [(V Zn · Zn i ) ] = p + [+G] + [+ R ]
(4)
where the square brackets represent the concentrations of the respective species, n is the free electron concentration, and p is the free hole concentration, given by p = intrinsic carrier concentration.
ni2 n
where ni is the
[AZ −·BZ +] = [A ][B] E
Nconfig Nsites
iE y expjjj b zzz k kT {
(6) DOI: 10.1021/acs.nanolett.8b04646 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters where Z is the charge of the defect species, Nconfig = 1, 22
−3
studied concurrently with suitable optical and transport characterization. Though LTPL measurements of our devices were attempted, the emission was too weak to permit a statistically significant intensity-dependent study. For devices comprising multiple nanostructures or different geometries, a simultaneous optical-electrical characterization may be possible. Such a study would provide very precise insight into the relationship between DAP processes and carrier transport, without relying on the ensemble measurements provided in this paper. Our proposed model therefore gives a means for improved characterization, leading to the realization of nextgeneration devices. Point defects play an important role in the optical and electronic performance of nanostructure-based devices. By combining results from photoluminescence spectroscopy and carrier transport measurements, we develop a self-consistent methodology to explicitly identify the types, energy levels, concentrations, and ionized fractions of donors and acceptors, considering intrinsic ZnSe nanowires as an example. Two recombination processes involving VZn complexes were observed, with a total ionized donor concentration of 4.8 × 1018 cm−3 and acceptor concentration of 4.7 × 1018 cm−3, agreeing with measured free carrier concentrations and mobilities. These concentrations represent the limit of stoichiometric ZnSe, with the deviation from stoichiometry approximated to be Zn(0.5 − 6.7 × 10−6)Se(0.5 + 6.7 × 10−6). Our methodology may be applied to other materials to improve the characterization and understanding of the role of deep level states in the performance of next-generation devices.
69
Nsites = 2.2 × 10 cm for ZnSe, and E B is the binding energy, which was estimated by E b = Ze 2 /4πεR (with R as the distance between the defects). The vacancy-interstitial distance R follows a distribution, having most probable distance, R̅ . Typically, vacancy complexes in ZnSe have binding energies on the order of 0.35 eV,70 corresponding to R̅ = 1.67a0 . Using this value, it was found that [VZn] = 3 × 1017 cm−3 which, using the density of bulk ZnSe, gave Zn(0.5 − 6.7 × 10−6)Se(0.5 + 6.7 × 10−6), correspond-
ing to an excess selenium mole fraction, xSe , of 1.3 × 10−5. On a typical phase diagram of ZnSe, the homogeneous region (50 atom % Zn) has a nonzero area, with the shape and width of this region accounting for nonstoichiometric compounds. The borders of this nonstoichiometric region describe the effective solubility limits of native defects. Using the ZnSe existence curves from ref.,71 the excess Se mole fraction was compared to the expected solubility limits of VZn in ZnSe. The extraction technique72 was used to correlate the melting temperatures from the ZnSe liquidus curve to the existence curve, for different xSe values, avoiding the tedious calculation of activity coefficients. The excess mole fraction of xSe = 1.3 × 10−5 was found to be at the Se-rich boundary for our growth temperature (675 °C), using the existence curve proposed by Brebrick.71 This means that at higher Se partial pressures, Se-rich precipitates are likely to form, which is indeed observed in nodules on nanowires intentionally grown with an additional selenium source.27 To improve the stoichiometry of our nanowires, a postgrowth anneal treatment in a zinc-rich atmosphere, analogous to zinc firing used in industrial processes,73 has been shown to improve near bandedge emission74 and the transport properties.36 Additionally, placing the growth substrate in a cooler zone of the furnace may help to reduce the excess selenium concentration, due to the exponential dependence of partial pressure with temperature. To demonstrate the utility of our model, we consider the transport characteristics of an n-type GaN nanowire FET fabricated by Huang et al.75 Specifically, we used our model to determine the deep level occupation and Fermi level for a NW FET having n = 2 × 1018 cm−3 and μ = 300 cm2/V·sec, which is consistent with a compensation ratio76 of θ = 0.3. Because Huang et al. did not perform intensity-dependent PL, data from ref 77 were used. GaN is doped n-type using silicon, which acts as a shallow donor (Ed = 30 meV below the conduction band edge) and forms an acceptor-like complex, (VGa ·Si ), having energy 1.08 eV above the valence band edge. DAP recombination between these defects produces characteristic yellow emission,77 from which the line shape was fit. For a nominal doping density of NSi = 1.1 × 1019 cm−3, it was found that Nd+ = 2.86 × 1018 cm−3, Na− = 8.6 × 1017 cm−3, and Ef = 39 meV. In ref 77, the degree of self-compensation, KD, was estimated to be 0.07, where KD is defined as KD =
NA NSi
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.8b04646.
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Detailed derivation of line shape analysis and a discussion regarding single nanowire measurement limitations (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
David Wisniewski: 0000-0002-4430-663X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Ontario Centres of Excellence (OCE).
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REFERENCES
(1) Neumark, G. F. Mater. Sci. Eng., R 1997, 21, iii−46. (2) Selim, F.; Weber, M.; Solodovnikov, D.; Lynn, K. Phys. Rev. Lett. 2007, 99, 085502. (3) Baraff, G.; Schlüter, M. Phys. Rev. Lett. 1985, 55, 1327. (4) Neugebauer, J.; Van de Walle, C. G. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 8067. (5) Morkoc, H.; Strite, S.; Gao, G.; Lin, M.; Sverdlov, B.; Burns, M. J. Appl. Phys. 1994, 76, 1363−1398.
(and is different from θ used
earlier). Nonetheless, we find excellent agreement using the results from our model, with KD = 0.078. This methodology could similarly be applied to Si FinFETs,78 ZnO thin film FETs,79 and other such devices based on optoelectronic nanomaterials, but few have been F
DOI: 10.1021/acs.nanolett.8b04646 Nano Lett. XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.nanolett.8b04646 Nano Lett. XXXX, XXX, XXX−XXX
