Scanning Tunneling Measurements in Membrane-Based

Article Cite This: ACS Appl. Nano Mater. 2019, 2, 4655−4664

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Scanning Tunneling Measurements in Membrane-Based Nanostructures: Spatially-Resolved Quantum State Analysis in Postprocessed Epitaxial Systems for Optoelectronic Applications Barbara L. T. Rosa,† Carlos A. Parra-Murillo,‡ Thais Chagas,†,§ Ailton J. Garcia Junior,∥ Paulo S. S. Guimarães,† Ch. Deneke,∥,⊥ Rogerio Magalhães-Paniago,† and Angelo Malachias*,† †

Departamento de Física, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, Minas Gerais, Brazil Departamento de Fisica, Universidad Del Valle, A. A. 25360, Cali, Colombia § Department Physik, Universität Siegen, Walter-Flex-Straße 3, 57072 Siegen, Germany ∥ Laboratorio Nacional de Nanotecnologia (LNNano), Centro Nacional de Pesquisa em Energia e Materiais (CNPEM), 13083-970 Campinas, São Paulo, Brazil ⊥ Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Unicamp, 13083-859 Campinas, São Paulo, Brazil

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‡

S Supporting Information *

ABSTRACT: Nanoscale heterostructure engineering is the main target for the development of optoelectronic devices. In this sense, a precise knowledge of local electronic response after materials processing is required to envisage technological applications. A number of local probe techniques that address single nanostructure signals were satisfactorily employed in semiconductor epitaxial systems. In this work we show that the use of chemically etched semiconductor nanomembranes allows carrying out scanning tunneling spectroscopy (STS) measurements in a postprocessed system which was otherwise studied mainly under in situ conditions that differ from the operational regime. We were able to acquire STS spectra with energy level resolved response on InAs quantum dots grown within a 15 nm-thick GaAs single-crystalline film transferred to an Au(111) surface. The presence of a native oxide layer does not affect the result, keeping the reliability of the usual ultra high vacuum (UHV) procedures. The use of nanomembranes also opens up the possibility of tailoring properties via additional variables such as nanomembrane thickness and surface charge depletion. Our method is applicable to a broad class of postprocessed layers extracted in nanomembrane format from epitaxial systems that are potential candidates for optoelectronic applications. KEYWORDS: scanning tunneling spectroscopy, scanning tunneling microscopy, nanomembranes, epitaxial nanostructures, quantum dots, local density of states

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INTRODUCTION Semiconductor epitaxial systems have been part of the basis of modern device technology, playing a crucial role in the integration and architectural design of optoelectronic applications.1−3 As the standard layer thickness or nanostructure size used for built-in heterostructures approaches a few nanometers, spectroscopic tools that address states in a local environment become of uttermost importance.4 Systems based on low-dimensional materials such as quantum dots, nanotubes, nanowires, and two-dimensional ribbons (among others) can only be explored individually with the use of local probes.5−7 Nevertheless, the response of a practical device lies on the expression of a large number of such nanostructures, overlapped with inherent in-operando conditions such as surface oxidation, encapsulation, or environmental humidity. Suitable techniques to compare single nanostructure responses © 2019 American Chemical Society

to that of an ensemble of nano-objects are then required to operate under real conditions. In this sense, the use of radiation such as visible and infrared light, providing measurements of optical response or vibrational properties were successfully employed in a broad class of materials, making Raman, infrared, and visible spectroscopies8 the common background tools for the exploration of materials. These radiation-based techniques have been driven to the nanoscale throughout the use of near-field microscopes,9−11 where a metallic tip serves as the antenna to capture the response of the material under illumination. On the other hand, interesting properties arise when the material is charged Received: June 12, 2019 Accepted: June 24, 2019 Published: June 24, 2019 4655

DOI: 10.1021/acsanm.9b01124 ACS Appl. Nano Mater. 2019, 2, 4655−4664

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ACS Applied Nano Materials

deposition of 40 nm-thick AlAs and a 10 nm GaAs layer. Thereafter, two monolayers of InAs forming quantum dots (QDs), were deposited. In such an uncapped QD configuration, one observes a quantum dot density of 2 × 1010 cm−2 with an average size of 30 nm diameter and 5 nm height for the QDs. The MBE chamber used has a background p-doping of Na = 1 × 1016 cm−3. Capped QDs were also prepared, repeating the growth of the previously described structure, with an additional 5 nm GaAs deposition on top (see Figure 1a). For

or subjected to electronic conduction. However, local (nanometer-resolved) electronic measurements are known to depend on a number of variables such as the occurrence of contact Schottky barriers.12 Intrinsic properties of the sample material such as the existence of charge trapping mechanisms as well as the occurrence of dominant a conduction regime (hopping, Frankel−Poole, Fowler−Nordheim, etc...) also needs to be addressed. The applicability of a nanostructured semiconductor system is directly related to its local density of states (LDOS). In postprocessed epitaxial systems, the evaluation of the LDOS using local electronic probes generally lacks spatial resolution. In this work we show that a membrane-based methodology is the key to directly employing scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) in a broad class of semiconductor systems. In our method, layers with few nanometer thickness containing epitaxial nanostructures are removed from the crystalline substrate matrix and transferred to a conductive support. In such an arrangement, the operational condition of a heterostructure is maintained (an oxidized surface is produced). The reduced thickness allows for STM/STS use, taking advantage of the absence of physical contact with the electric probe due to the operation under tunneling regime. Surface maps combining topographic and conductive properties are directly measured and STS results are retrieved, producing nanometer-resolved information on the LDOS. In this work we show that nanomembranes preserve the integrity of the electronic response if compared to usual preparation procedures of epitaxial semiconductor samples for STM/STS (in situ growth, in situ cleavage),13−17 broadening the scope of these techniques, which are usually restricted to time demanding and clean ultra high vacuum (UHV) conditions (e.g., III−V growth with As or P overpressure does not coexist with STM in the same UHV chamber). In addition, buried nanostructures can be located even when the morphology of the sample surface hides its inner content. In particular, InAs islands were studied, capped, and uncapped with a 5 nm GaAs layer and were grown on top of 10 nm GaAs layers. By applying selective etching procedures, they were removed from their original substrate18 and deposited on atomically flat commercial Au (111) surfaces. STM and STS measurements were able to probe the existence of confined states, even with the presence of a thin native oxide. These states were identified by comparison with energy level calculations. The access to this information is usually carried out on systems with in situ capabilities, which can be (i) a growth apparatus, which usually restricts the type of material that is studied (preferentially with low vapor pressure if one wants to skip setups with distinct STM and growth chamber or a transfer chamber)14 or (ii) in situ etching capabilities (e.g., atomic hydrogen cleaning15), which must be chosen for each compound system, or (iii) an in situ cleavage system, which usually allows the measurement of embedded nanostructure cross sections.13,16,17 We emphasize that the method described here can be generalized for other systems grown on rigid crystalline substrates.19−22

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Figure 1. (a) Sketch of the stacking sequence of semiconductor layers used in this work, consisting of (1) uncapped and (2) capped QDs. (b) Schematic representation of a sample with regularly spaced pits created by photolithography and the wet chemical etching procedure (arrows). The underlying sacrificial (etching sensitive) AlAs layer is removed using a diluted HF solution and oats on a beaker with deionized water. (c) The released membranes are transferred to Au (111)/mica substrates. (d) Optical microscopy images of a GaAs/ InAs membrane on top of a Au substrate. all samples, the AlAs layer is etchant-sensitive, allowing the removal of top layers upon optical lithography processing and HF etching.19−22 The process consists of defining small periodic vertical pits (15 μm diameter, separated by 30 μm distance) with a photoresist, followed by an in-depth vertical etching using a HBr (50 vol %)/Kr2Cr2O7 (0.5 mol/L)/CH3COOH (100 vol %) solution (2:1:1). After this step, the AlAs layer can be accessed and removed using an etching solution of diluted HF (40 vol %)/H2O (1:800) (Figure 1b). The released nanomembrane (NM) contains the topmost films (Figure 1c) and is then lifted by a new hosting substrate. This method produces fewmillimeter-sized membranes, as shown in the optical images of Figure 1d. All NMs studied in this work were transferred to an Au (111) film

EXPERIMENTAL RESULTS

All samples used in this work were grown by molecular beam epitaxy (MBE) on epi-ready GaAs (001) substrates, using the MBE facilities of the LNNano (Karl-Eberl MBE Komponeten). The growth sequence starts with a GaAs buffer (300 nm), followed by the 4656


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ACS Applied Nano Materials deposited on mica for scanning tunneling microscopy and spectroscopy. STM/STS measurements were carried out in an Omicron GmbH VT-STM variable temperature STM system (in constantcurrent mode) using in situ prepared tungsten STM tips. STM images obtained at 300 and 20 K were similar, while all STS measurements were performed at 20 K. STS data are displayed as differential tunneling conductance spectra (dI/dV) throughout this work. For all images a voltage of V = 1.6 V and a current setpoint of Itip = 100 pA were employed (Figure 2a). Tunneling currents were easily obtained for the membrane thickness used here.

the formation of dislocated (incoherent or relaxed) islands, in which the whole three-dimensional island lattice relaxes to the InAs bulk lattice condition.27 In our case, the coverage was chosen to produce defect-free (coherent) InAs islands. Once these islands are covered with GaAs they become QDs, which in a strict sense means that they are potential wells surrounded by barriers, resulting in the appearance of confined states.28 Their shapes are slightly modified toward a truncated apex, as a result of in-plane In atoms diffusion, which is more pronounced during GaAs capping than during InAs growth.29,30 The resulting morphologies of capped QDs were measured by cross section TEM and STM, showing a shape which is an intermediate state between a lens-shaped uncapped QD and a cylindrical shape.31 The morphology of our uncapped QDs is shown in the atomic force microscopy (AFM) image of Figure 2b, with a total field of view of 1 μm2. An STM measurement carried out on this sample is shown in Figure 2d, with a field of view of 100 nm × 100 nm, showing few QDs, which appear as brighter contrast in the height scale. The QD height is compatible in both measurements, with an average value of 5 nm (other areas of the sample were also verified). On the other hand, an AFM measurement (1 μm2 field of view) on the capped sample, shown in Figure 2c, is unable to perceive height fluctuations above 1 nm. This is in clear contrast with the STM image (100 nm × 100 nm field of view) of Figure 2e. In this case, the apparent height observed differs from pure topographic methods (such as AFM) due to the interplay between topographic and electronic response from the local density of states at a given sample’s position. In such systems, the height can be obtained using the feedback option in which the current is kept constant throughout the scan and the tip position with respect to the sample surface is dynamically modified to maintain the current constant. This is an option for a sample in which the dielectric constant is the same along the whole surface (or does not vary significantly). In the case of heterostructures in which in-plane variations of the LDOS take place (due to QD nucleation in our case) with distinct composition from the substrate, the standard direct scanning probe process to probe object height is AFM. In our specific case, the differences between AFM and STM are small, and the 5 nm uncapped QD height observed for topographic STM measurements is close to the AFM results. On the other hand, the apparent weakness of STM for precise height measurements becomes its strength when buried objects are concerned (such as in our covered InAs structures). Its sensitiveness to distinct local density of states (or simply conductance in some cases) allows it to be useful when surface morphology is monotonic. Hence, buried QDs are promptly observed by this method independently of the surface morphology. STM measurements on larger areas were not fully homogeneous as the images shown in Figure 2e due to the intrinsic waviness (wrinkling) of the released nanomembrane (see the Supporting Information), implying fluctuations of the electric contact along the Au surface. In order to carry out STM/STS measurements, the tip bias has to be larger than 1.5 V (larger than the GaAs band gap at low temperatures), enabling the tunneling across the membrane. Also, in order to preserve the tip properties (shape and cleanness) the image is formed using a large frequency at the fast scanning axis, which turns the image elongated along this direction (horizontal direction in Figures 2d and e). Such fast scanning is required for a sample overview since it preserves the tip from changes caused by charge accumulation in some regions that are not in physical contact with the Au layer. These regions must be scanned quickly. Semiconductor nanomembranes present an inherent waviness due to the transfer process, causing the occurrence of these regions. Such a preliminary scanning procedure is therefore mandatory to retrieve a region where good electric contact is established with the Au substrate and does not affect the tip condition. A detailed discussion about the membrane waviness (wrinkling) is provided in the Supporting Information. Our procedures for STM/STS on membranes were initiated with quick scans (usually of 500 nm/s) over ranges of 500 nm × 500 nm. Once a region with good electric contact is found, with a stable STM map quality and stable STS results, proper STS acquisitions over a

Figure 2. (a) Sketch of STS measurement of the sample with freestanding InAs QDs. The tunneling path Itip is indicated. Images b−e were obtained by over view measurements. The STM images were obtained at 20 K. The small yellow square is zoomed in the inset and represents an area of 100 nm × 100 nm with a 40 nm scale bar (typical STM image size). (b) Atomic force microscopy image of a uncapped QD sample (the scale bar represents 400 nm). A yellow square is also represented for reference of the STM image size. (c) Atomic force microscopy image of a capped QD sample. The scale bar is 400 nm. (d) Scanning tunneling microscopy image of an uncapped QD sample acquired at a sample voltage Vs = 1.6 V and Itip = 100 pA. The scale bar is 40 nm. (e) Scanning tunneling microscopy image of a capped QD sample acquired at the same sample voltage of panel c. The scale bar is 40 nm. Elongations in panels d and e are due to the fast scanning axis (which are indicated by arrows). A summary of InAs growth in GaAs is provided in the following lines. InAs QDs are formed by MBE in GaAs (001) following the Stranski−Von Krastanow growth mode.23 The lattice parameter mismatch of about 7% with respect to GaAs is initially accommodated through a pseudomorphic relaxation of the wetting layer, which is the main structure formed to an InAs coverage of 1.6 monolayers (MLs).24,25 After this threshold, three-dimensional lens-shaped islands appear, providing a coherent crystalline registry path for relaxation, in which the deposited InAs relaxes continuously from the bottom to the top of such a nanostructure, achieving the InAs lattice parameter at their apex.26 The interval for formation of coherent (defect free) InAs islands extends up to approximately 2.3 MLs. Above such coverage an onset of plastic relaxation is observed, with 4657


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ACS Applied Nano Materials linear path on spatially restricted regions (30 nm × 30 nm) are carried out. Figure 3 shows tunneling spectroscopy results on uncapped QDs, in three different regions (measurements carried out at T = 20 K). As

Figure 3. Tunneling spectroscopy recorded on uncapped QDs. (inset) STM morphology of the regions A, B, and C where spectroscopy was measured (maximum height of color scale: 5.8 nm). The fast scanning axis is indicated by arrows. GaAs and InAs band gaps are indicated by black dashed lines. The image was obtained using Vs = 1.6 V, Itip = 100 pA, and temperature of 20 K. Horizontal dotted lines indicate zero dI/dV values for each curve. noted in the curves, the region within the GaAs band gap (including the InAs band gap) presents only a smooth oscillating signal in arbitrary positions. Previous works32 confirm the presence of local discrete states of uncapped InAs/GaAs quantum dots only if the samples are transferred in vacuum from the growth (e.g., MBE) chamber to STM, assuring a high reproducibility of dI/dV curves. The difference in vertical (y-axis) values in plots A, B, and C of Figure 3 originates from the lack of a reliable normalization procedure but also arises from the local character of STS. For the region where capped QDs present hole states (negative bias, between the InAs and GaAs gap), the curves present similar behavior. The variation of dI/dV curves outside of the GaAs gap is not associated with the quantum dot states but can be explained taking into account local variations of the height of quantum dots above the Au surface. They cannot be directly normalized or compared since STS measurements carried out on top of a region away from QDs do not behave as a steady reference due to the presence of the InAs wetting layer and a minor response component that comes from charge trapping at neighboring QDs. Additionally, our QD height/size distribution is broad enough to affect STS response in the uncapped sample, where a fraction of the QDs with heights below ∼3 nm may be fully oxidized, while others remain with an effectively shrank crystalline core. Therefore, in this uncapped sample the reduced differences between STS measurements on top of InAs islands and outside them denote that the detection of confined states is poor with respect to the capped sample. The scanning tunneling spectroscopy were also obtained in the capped membrane, and for this condition, the measurements exhibited an unexpected result, as we can see clearly in Figure 4a where the STS spectra acquired at 20 K for both capped and uncapped membranes are presented. One notices that the STS from uncapped QDs exhibits zero values along the GaAs band gap interval (black dotted curve), as previously discussed; however in the capped QD, a series of peaks outside the InAs gap interval are observed. Considering the behavior expected for the energy levels of quantum dots present in the references,17,33−35 we can ascribe the peaks to the discrete confined states of electrons (right) and holes (left) in our

Figure 4. (a) Tunneling spectra acquired in the center of both uncapped (black dotted curve) and capped (red solid curve) QDs. Dashed lines delimit the GaAs (∼1.5 eV) and InAs (∼0.4 eV) gaps. The states indicated in the valence and conduction bands are labeled as H and E, respectively (listed in Table 1). (b) I−V curves from which the dI/dV results of a were extracted. (c) Diagram of the energy band structure showing the band bending formed by the depletion region due to the nanomembrane processing (tip bias not applied, V = 0).

nanostrutrure. The hole (H) and electron (E) levels indicated in the figure were determined by calculations, as will be discussed in the following paragraphs. To explain the difference between the spectra shown in Figure 4a, we assumed that the native oxide layer and the depletion layer, formed by the presence of a surface, are responsible for blocking the direct measurements of energy levels. The characteristics of oxide layers in III−V semiconductor heterostructures have been thoroughly discussed in the literature.36,37 Such an oxide layer is naturally formed. Since there is no specific oxide layer treatment of the membranes prior to our experiments, we assume that the native oxide layer remains at the surface and has a thickness of approximately 2−3 nm,36−39 as suggested in the literature. For the samples studied in this work, we are not able to directly measure the oxide layer thickness. Nevertheless, the I−V curves measured by STS confirm that the presence of an oxide layer is responsible for washing out the QD response. This means that in this case the oxidation changes the InAs crystalline structure, creating traps for charge carries and limiting the uncapped sample response. In such a scenario, the GaAs coverage on the capped membrane creates a protection that keeps the QD preserved. 4658


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ACS Applied Nano Materials To confirm the discussion above, we analyzed the I−V curves from which the dI/dV results (Figure 4a) were extracted. The results are shown in Figure 4. Typically, the presence of an oxide layer must be able to modify the local resistivity, decreasing considerably the sample current feedback. Considering that STM/S is a technique that makes it possible to address electrically a single nano-object, we expected the oxidation consequences to be observed in a tunneling spectroscopy. Such an effect can be seen in the I−V curves, where a prominent difference in the conductivity, between the capped (red solid line) and uncapped (black circles) quantum dot samples, was detected. The most important variation is observed in the discrete energy levels region (outside of InAs gap), which means, as suggested before, that the oxide layer heavily damages the crystalline structure of a quantum dot. We also observe that, as the tip is moved away from a capped QD, the amplitude of the response of the observed STS states is consistently reduced (see the Supporting Information). Due to the inelastic electron scattering at the oxide top layer and the large density of dots, the signal observed at regions further away from QDs is a combination of the capped QD signal (which becomes faint) and a base curve which is similar to the STS of the uncapped sample (that becomes the major response). From such a combination we estimate that the radius of influence on an STS measurement for our system is of the order of ten of nanometers,33 decaying exponentially as one retreats from the QD center. Furthermore, one must consider that the presence of surfaces due to the nanomembrane system leads to a surface carrier trapping effect. Considering that the MBE system used has a known background pdoping of Na = 1 × 1016 cm3,21 described previously, the pinning of the Fermi level (EF) at the surface implies a band bending in the vicinity of the heterostructure.40 According to Lüth40 the depth of the depletion region on a doped sample surface is given by d = [Vsεε0/ eNa]1/2, where ε0 and ε are the vacuum and relative medium permittivity and Na is the density of charge carriers (with charge e) at the bulk. Vs is of the order of 0.6 eV for GaAs. For GaAs (001), the Fermi level is pinned around the midgap41 and the depth of the depletion region on a doped surface is of the order of 150 nm. This number indicates that our QDs are inside the depletion region for both capped and uncapped samples. To calculate the band bending induced by the carrier depletion, one needs to calculate the Debye length, given by L=

discuss directly the I−V derivation of our data in order to showcase the robustness of the method.

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DISCUSSION In order to determine both electronic and heavy hole energies for our system, energy calculations following the method proposed by Gangopadhyay et al.42 were carried out. The starting point of this method is the effective mass Schrödinger equations for conduction band electrons and valence band heavy holes given by ÅÄÅ ÑÉÑ ÅÅ 1 ij me yz ÑÑ z ÅÅ∓ jj∇ ·∇zzz + (V(±) ∓ e|ε ⃗|z)ÑÑÑΨ±( r ⃗) = E±Ψe( r ⃗) jj ÅÅ ÑÑ * ÅÅ 2 k m± { ÑÖ (3) Ç where m+ = me*(r ⃗ ) and m− = mh*(r ⃗ ) are the effective mass function of the particles in heterostructure, respectively. V+ = VCB and V− = VVB are the band edge profile along the growth direction of the sample under study. To simulate the STS protocol, we introduced an external longitudinal field ε⃗ which triggers the transport through the sample. This accounts for the STS measurements at fixed tip−sample distance, in which |ε ⃗| varies linearly to a maximum value of 2 × 109 V/m. We set the energy scale to Rydberg energy units (1 Ry = 13.6 eV), such that eq 1 is dimensionless. Equation 1 can be transformed into an eigenvalue problem as follows: we first compute the eigenfunctions glmn(r ⃗ ) = Rlm(r ⃗ )φm(ϕ)Zn(z), of a cylinder of radius R and length L, where R lm(r ) =

2e Na

(5)

2 ij nπ yz sinjj z zz L kL {

Zn(z) =

(6)

Here Jl(x) is the Bessel function of the first kind. The cylinder is considered to be made of the material we set as the substrate, i.e., on which the remaining structure is grown, along the crystallographic direction (001). Thereby, we expand the k ,± glmn( r ⃗) and get the wave function as Ψ±( r ⃗) = ∑lmn Clmn eigenvalue problem

(1)

where k is the Boltzmann constant and T = 20 K. Finally, the depth (z) dependence of the potential can be expressed as

eV (z) = eVsexp(− z /L)

(4)

1 exp(ilφ) 2π

ϕm(φ) =

kTεε0 2

2 i ry J jjjαlm zzz RJl + 1(αlm) l k R {

(2)

The schematic figures of the band bending for both capped and uncapped samples were evaluated using the equations above and are presented in Figure 4c. One can observe that the asymmetric shape of uncapped sample bands should be also responsible for shifting the charge carriers from the quantum dots to the GaAs layer, before the tip-QD tunneling happens, leading then to a much less effective measurement response from the discrete energy levels. One must emphasize here that the dI/dV data obtained in our experiments were extracted by two methods: (i) using a lock-in amplifier to produce a direct derivative result and (ii) by the derivative of I−V data. In both cases, for capped QDs, the discrete states observed were very pronounced and the use of a lock-in amplifier to directly produce the dI/dV data with reduced noise was not mandatory. Curves measured by both methods have shown results of identical data quality. In our membranes carrier confinement is enhanced by the depletion of the barriers, which is an intrinsic feature of the (nano)membrane methodology. The retrieved STS results are then similar to those obtained in in situ cleaved samples. Since our membranes present GaAs barriers below and atop the InAs QDs, the confined states manifest a clear signature in any of the STM configurations discussed above with reduced noise. Along this work we decided to

(((±))lmn l ′ m ′ n′ − Eδl ′ lδm ′ mδn ′ n = 0

where the characteristic matrix 42 for details): (((±))lmn l ′ m ′ n′ = ∓

∓

+

i m

(7)

( lmn l’m’n’

takes the form (see ref

i m

(8)

{

(9)

y

k

±

∫ d=jjjjj m*(er ⃗) zzzzzgl*′m′n′( r ⃗)∇2 glmn( r ⃗) k

±

y

∫ d=gl*′m′n′( r ⃗)∇jjjjj m*(er ⃗) zzzzz·∇g lmn( r ⃗)

∫ d=gl*′m′n′( r ⃗)V±( r ⃗)glmn( r ⃗)

{

(10)

As proposed in ref 42, any semiconductor heterostructure to be studied can be built as follows. We first subtract from the initial cylinder the region with the geometry of the nanostructure (quantum dot). The inserted QD, with a lensshaped profile, has properties of material of interest: InAs embedded into GaAs.43−45 In order to obtain the adequate 4659


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ACS Applied Nano Materials values which include the corrections due to the strain effects, we have followed the work by Vurgaftman et al.46,47 See also ref 43 for more details. The general procedure for the construction of the sample to be numerically studied is sketched in Figure 5 and renders the characteristic matrix: lmn sbt (lmn l ′ m ′ n′ = [(l ′ m ′ n′]cyl

+

mat ∑ ([(lmn l ′ m ′ n′]QD

i

(9a)

sbt − [(lmn l ′ m ′ n′]QDi )

i

+

mat ∑ ([(lmn l ′ m ′ n′]QWell i

i

Table 1. Theoretical and Experimental Values for the Confined States Observed on Valence and Conduction Bands

sbt − [(lmn l ′ m ′ n′]QDi )

(10a)

(11)

Figure 5. Semiconductor heterostructure model construction. As described in the text, the nanostructure of interest can be constructed by subtracting the spatial region where either a well or a quantum dot would be located from the initial GaAs cylinder and adding back properties of the desired material InAs, i.e., band edge and effective mass value, concentrations, and others. In this work a single lensshaped QD was inserted into the heterostructure, as described in the main text (cylindrical embedded objects represented in the figure are just a sketch).

where [···]material nanostructure indicates the region and the material, to be replaced as explained above. sbt and mat stand for substrate lmn and material, respectively. The full matrix ( l’m’n’ , with dimension given by dim(( ) = lmax × mmax × nmax, is numerically diagonalized using LAPACK subroutines.48 In the current case, the STM technique allows to study every quantum dot in an isolated manner. Therefore, by construction we can set a structure that preserves the azimuthal symmetry by setting a quantum dot perfectly centered in the transversal section of the cylinder. In this scenario, l becomes a good quantum number and we can diagonalize the characteristic (l)mn matrix for each l independently since (lmn l ′ m ′ n′ = ( l ′ m ′ n′δl , l′, hence dim(( ) = nmax × mmax. The calculation was done for a lens-shaped quantum dot of height h0 = 5 nm and base radius R0 = 15 nm for the nanostrutrure: WGaAs(10 nm)/WLInAs(1 nm)/QDInAs(5 nm)/ WGaAs(5 nm), where W, WL, and QD stand for quantum well, wetting layer, and quantum dot, respectively. We diagonalized the characteristic matrix with typical dimension 6000 × 6000 for l = 0, 1, 2, 3, and 4, for which the numeric evaluation presents very good convergence. The hole and electron states obtained using the calculation method described above are shown in the first column of Table 1. In the dI/dV curves of capped QDs (Figure 4), the electron states are univocally obtained by calculations, while hole states require a more detailed discussion. First, one has to consider that STS resolution is approximately 4kT49 (k is the Boltzmann constant, and T is the temperature), which in our system

calculated hole levels (eV)

merged hole levels (eV)

level no.

−0.4008 −0.4338 −0.4339 −0.4447 −0.4451 −0.4779 −0.4785 −0.4938 −0.4967 −0.4986 −0.5003 −0.5181 −0.5306 −0.547 −0.554 −0.5582 −0.5644 −0.5775 −0.5981 −0.5985 −0.6038 −0.6178 −0.6366 −0.6398 −0.6452 −0.6736 −0.699 −0.7008 −0.7223 −0.7425 −0.7428 −0.7618 −0.7803 0.572 0.667

−0.401 −0.439

H1 H2

−0.478

H3

−0.497

H4

−0.524

H5

−0.555

H6

−0.578

H7

−0.6

H8

−0.618 −0.64

H9 H10

−0.674 −0.704

H11 H12

−0.722 −0.743

H13 H14

−0.762 −0.78 0.58 0.63

H15 H16 E1 E2

represents approximately 10 meV. As listed in the first column of Table 1, the majority of hole states present a difference between them of 4 meV or less, meaning that the calculation provides values with a precision that has to be regarded carefully due to the STS resolution. For this reason, the second column (merged hole levels) was generated using the average of states from the first column within a 12 meV energy span. Additional considerations about the observed peaks must be drawn. In order to obtain reliable experimental information, we carefully investigated 20 different QDs on the capped sample. The STS results for all QDs exhibit dI/dV peaks with pronounced intensity, when compared with the uncovered QD curves, along the interval between the InAs and GaAs bandgaps. In addition, the usual difference among of QD hole states (ΔE) for our QD sizes is approximately 30 meV, leading us to attribute our results to a superposition of hole energy states. Figures 6a and b show dI/dV curves obtained in different positions (marked with open triangle, circle and square symbols at the bottom inset of Figure 6b) on the same capped QD, and a magnification of the curve of position (circle), respectively. All hole states associated with the merged values shown in Table 1 are indicated by arrows. Among all 4660


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information that can be confronted or used to broaden the scope of structural information extracted from transmission electron microscopy (TEM) (limited to very thin samples, usually prepared by destructive methods)51 or synchrotron Xray diffraction/scattering techniques with nanofocusing (with spatial resolution limited to hundreds of nanometers and reduced availability).52 Some classes of unusual samples that would profit from STM/STS measurements are discussed in the following. First, our experiment has shown that the establishment of tunneling currents through materials with a few tens of nanometers is feasible, granting the possibility of studying thin (20−50 nm) vertically aligned nanowires. Such nanostructures present unsuitable morphology but are easily transferred to conductive substrates by mechanical processes. The electronic structure of multiple-phase nanowires (e.g., III−V VLS nanowires where zincblend and wurtzite crystalline phases coexist with fewnanometer separation)53 would greatly benefit from local STS measurements, impacting the understanding of nanowire-based devices. Embedded quantum dots and quantum wells of monolithic (epitaxial) semiconductor layers,54 used for single-electron transistors,55 narrow line light emitters,56 and spintronics57 can also be grown on sacrificial layers. Thickness limitations of some devices, which can range up to 100−200 nm could be overcome by the growth of simplified (thinner) structures, where active layers would be placed in order to enhance their response under STS conditions. The membrane removal and transfer to conductive substrates would also allow study, on the nanometer scale, of variations of the electric response with respect to the presence of shallow contacts. This approach would map out conditions for the presence (or absence) of carrier traps and define device geometries with direct impact on electron-lithography based devices (in which contacts with tens of nanometers can be build). Resistive switching oxide layers integrated to semiconductor layers58 are also a suitable target for membrane based STM/ STS exploration. Very fine control of electric pulse duration and cycling is currently achievable with standard STM electronics, making STM/STS a tool that concomitantly shows structural changes (due to surface changes after the conductive filament formation inside resistive switching devices) and electric characteristics. More recently, atomically thin two-dimensional materials such as dichalcogenides and graphene have presented remarkable charge transfer and mobility changes upon direct contact with semiconductor films, such as GaAs or Ge.59 In particular, the observation of exciton states resulting in band offset alignment44 and the interface interactions that favor solar cell performance in MoS2/GaAs junctions60,61 are clearly of crucial interest for the development of novel electronics. The resulting electronic structure of such heterojunctions is easily accessible by membrane transfer STM/STS, while other techniques to map out the band structure (such as ARPES) have restricted use on exfoliated materials (with lateral sizes of a few micrometers). Other potential applications, besides those discussed above, include the study of band alignment and local bias response on light-emitting field effect transistors,62 exploration of local effects of nanoimprint lithography for device fabrication,63 and the defect electronic environment.64

Figure 6. (a) Tunneling spectroscopy recorded on capped QDs. (a) Curves of valence band correspond respectively to positions shown in the inset figure on the bottom of panel (b), marked with triangle, circle, and square symbols (with scale bar 10 nm, maximum height 5.5 nm). (b) Detailed curve of spectroscopy. The arrows indicate the hole energies relative to the values shown in Table 1. The dI/dV curve at the top inset of panel b was measured on another QD (among 20 analyzed). The scale bar of the panel b STM top inset image is 10 nm. The maximum color scale height corresponds to 5.1 nm. All spectra were obtained using Vs = 1.6 V, Itip = 100 pA, and temperature of 20 K.

energy levels observed in such magnification of the experimental curve in Figure 6, those that were previously indicated in Figure 4 are highlighted in bold in Table 1. For the whole energy span, the ΔE of energy states (difference among arrows) exhibits a well-defined value, satisfying the expected behavior for this type of QD. The enhanced peaks in a STS spectrum (which has limited resolution) are modified as a function of the relative position of tip and QD (Figure 6). This effect is explained by the spatial distribution of the wave functions and their corresponding probability density.16,32,49 Taking into account that we have a spatial superposition of wave functions with different energies, as the tip is moved over the sample, we enhance the measured signal from states which correspond to local maxima of the wave function probability density. An example of STS measurement at the center of another QD is provided for comparison in the upper inset of Figure 6b. STS energy resolution (ΔE) is inherently low since it is constrained to thermal effects on the sample and scanning tip. Even for temperatures of the order of 10 K, the ΔE is on the order of a few milli-electronvolts,49 while optical techniques such as photoluminescence are able to distinguish states which differ only by a few micro-electronvolts.50 A STM/STS built-in combination of spatial high-resolution scanning capability and electronic response is strongly desirable as complementary to other scanning techniques such as scanning near-field optical microscopy (SNOM). This energy-resolved technique strongly depends on the quantum efficiency of the studied material (for direct gap optical emissions) and/or on the cross section of active Raman states (for inelastic scattering studies).8 Other scanning probe techniques that use probes in direct contact with the sample (or in periodic contact) such as conductive atomic force microscopy (C-AFM) suffer, among other ambient operational limitations, from the setback of introducing additional Schottky barriers on the spectroscopic signal,12 avoided in the tunneling regime. Additionally, the surface morphology and electronic response mapped out by STM/STS provides partial structural 4661



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CONCLUSION

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ASSOCIATED CONTENT

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In conclusion, we have shown in this work that the release of semiconductor nanomembranes on top of conductive substrates (Au in our case) is a quick procedure to allow STS measurements with enough resolution to observe confined electron and hole energy levels in postprocessed InAs islands, preserving the quality of the electronic response of the heterostructure. The local character of the STS measurements allows one to access distinct structures on the membrane (in the case of broader QD size distributions or lithographically defined regions). It was also possible to observe throughout STM the position, shape, and size of buried quantum dots, in conditions where the surface morphology probed by AFM is flat. In systems that allow in situ heating, the diffusion of materials and its impact on buried nanostructured shapes and electronic structure can be directly studied. Hence, the methodology we propose here makes the use of STM more versatile, offering an alternative to the requirement of an in situ apparatus for epitaxially grown semiconductors. Native oxide layers, usually with 1−2 nm thickness, do not play a crucial role in the acquisition of STS data for QDs states in capped samples. Although there is a limitation for measurements on uncapped structures, the results on confined (capped) nanostructures, are as reliable as in usual in situ UHV measurements. Particularly, the use of nanomembranes opens up the possibility of tailoring properties of uttermost relevance for optoelectronic applications by using additional variables with respect to rigid systems. Therefore, NM thickness and depletion (which depend on this last parameter as well as of the overall doping or doping profile) are complementary to nanostructure size, growth of barriers, composition choice, and growth temperature, all defined along the traditional layer deposition process. The method can be extended to other material classes where UHV epitaxial growth is required but surface oxidation is well behaved and limited.

REFERENCES

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsanm.9b01124. AFM topographic profiles of waviness (wrinkles) induced in nanomembranes. STS measurement carried out on membrane area outside quantum dots. Trace and retrace STM profiles showing elongation along the fast scanning axis direction (PDF)

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. ORCID

Ch. Deneke: 0000-0002-8556-386X Angelo Malachias: 0000-0002-8703-4283 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge FAPEMIG, CAPES, FAPESP (Process no. 2016/14001-7), and CNPq (Process no. 423962/2016-7) for financial support. 4662


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