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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Composition metrology of ternary semiconductor alloys analyzed by Atom Probe Tomography Enrico Di Russo, Florian Moyon, Noelle GOGNEAU, Ludovic Largeau, Etienne Giraud, Jean-François Carlin, Nicolas Grandjean, Jean Michel Chauveau, Maxime Hugues, Ivan Blum, Williams Lefebvre, François Vurpillot, Didier Christian Blavette, and Lorenzo Rigutti J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03223 • Publication Date (Web): 22 Jun 2018 Downloaded from http://pubs.acs.org on June 25, 2018

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The Journal of Physical Chemistry

Composition Metrology of Ternary Semiconductor Alloys Analyzed by Atom Probe Tomography. E. Di Russo1, F. Moyon1, N. Gogneau2, L. Largeau2, E. Giraud3, J.-F. Carlin3, N. Grandjean3, J.M. Chauveau4, M. Hugues4, I. Blum1, W. Lefebvre1, F. Vurpillot1, D. Blavette1, L. Rigutti1* 1

Normandie Univ., GPM, UNIROUEN, INSA Rouen, CNRS, 76000 Rouen, France.

2

Centre de Nanosciences et de Nanotechnologies, CNRS UMR 9001, Univ. Paris-Sud, Université

Paris-Saclay, C2N – Orsay, 91405 Orsay Cedex, France. 3

Institute of Physics, Ecole polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne,

Switzerland. 4

Université Côte d’Azur, CNRS, CRHEA, 06560 Valbonne, France.

ABSTRACT: Ternary semiconductor alloys based on the AyB1-yC stoichiometry are widely employed in electronic devices and their composition plays a key role in bandgap engineering of heterostructures. We have studied the crucial issue of accuracy in composition measurements of AlyGa1-yN and MgyZn1-yO alloys by Atom Probe Tomography. The results indicate a similar behavior for both nitride and oxide systems. A correct site fraction y is measured at low field conditions, while Ga and Zn preferentially evaporate at high field yielding an overestimation of y. Furthermore, APT datasets exhibit local biases depending on the distribution of the electrostatic field at the specimen surface. We estimate the detection efficiencies for each species and interpret the results through a model describing preferential evaporation in simple terms. 1. Introduction

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Measuring correct mole fractions in semiconductor compound allows for accurate evaluation of material properties and for an accurate design of electronic devices based on such materials systems. The alloy composition has indeed a direct influence on lattice constants, bandgap, effective masses, electron and hole mobility, and other related properties. Laser-assisted Atom Probe Tomography (La-APT) is nowadays established as one of the possible techniques that can be applied to the determination of alloy compositions in semiconductors. Among the main advantages of the La-APT one could cite the following: first, the composition can be determined by simply counting the detected ions, discriminating among the different chemical species; secondly, the composition can be determined locally, in three dimensions, in small reconstructed volumes of the order of the cubic nanometer. However, recent works have demonstrated that the technique is not exempt of compositional biases. This has been observed for a number of wide bandgap binary compound semiconductors1–7, for narrower bandgap III-V binary compounds and for several other systems8–11. It emerged that for typical conditions of analysis, the intensity of the electric field at the specimen surface during the analysis can severely affect the accuracy of the measurements. However, the composition of binary compound semiconductors is usually known a priori, as their stoichiometry is fixed. This is not the case in semiconductor alloys, where the composition can vary over a wide range, depending on the parameters adopted during the synthesis of the material. It becomes thus crucial to establish whether APT can accurately measure semiconductor alloy compositions, and if this is the case, under which conditions. Recent works have addressed this problem in specific cases. It was shown that the measurement of InGaN composition is quite robust and nearly independent of the experimental conditions12. The measurement of the III-site fraction in Al0.25Ga0.75N, on the other hand, exhibits a dependence on the electric field, with a correct composition measured


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at low field conditions only13. The importance of performing independent composition measurements has also been underlined14. In this work we address more systematically semiconductor alloys with AyB1-yC stoichiometry, where A and B are metallic elements belonging to the same group, the proportion of ([A]+[B])/[C]=1 species being imposed. In particular, we analyzed (Al,Ga)N and (Mg,Zn)O containing different site fractions of Al/Ga and Mg/Zn. Our results point out that accurate site fractions can be obtained at low surface field conditions, while the fraction of the lighter metallic element apparently increases at high field. Based on volume reconstructions as accurate as possible, we estimate the detection efficiency for each chemical species. Beyond specific losses during the analysis, the detection efficiency mapping also indicates that it is generally not possible to measure correct atomic fractions. Finally, we interpret the experimental results using a simple preferential evaporation model according to which the heavier metallic elements, more loosely bound on the specimen surface, are lost when they are field evaporated between laser pulses. The methods illustrated in this work can be straightforwardly transposed to other semiconductor alloy systems and possibly constitute a starting point for the study of metrology issues relative to dilute doping concentrations in binary or ternary compound semiconductors.

2. Experimental Details 2.1. Samples and specimen preparation Two different ternary alloy systems were analyzed in this study. Both are of the type AyB1-yC, where A and B are metallic elements, while C is either N or O. The first system is AlyGa1-yN, with the site fraction y varying from 0.07 to 0.56. The list of samples is reported in table 1. All samples were grown by MBE at LPN Marcoussis, with the exception of the sample AG3



that was grown at EPFL under the conditions described in refs.13,15 . All samples are grown along the polar c-axis. In all the composition range, AlGaN is expected to be a random alloy, exhibiting thus a nearly uniform composition on the scale of several nanometers cubed. This is an important condition that the material should fulfil for a correct evaluation of the detection efficiency, which will be dealt with in section 3.4. All these samples are multi-layer samples. With the exception of sample AG3, designed as an intersubband modulator, they have been conceived with specific geometries for this study. The composition of the AlyGa1-yN layers was determined by energy dispersive X-ray spectroscopy (EDX) and x-ray diffraction (XRD). The second material system is MgyZn1-yO. These samples are non-polar heterostructures grown along the [1-100] direction, containing ZnO quantum wells, with y ranging between 0.27 and 0.35, designed as intersubband photodetectors and grown under the conditions described in ref.7. The upper bound y=0.35 is due to the fact that MgZnO may form a mixed hexagonal wurtzite /cubic halite phase for y>~0.35-0.45 before undergoing a phase transition to the cubic halite phase typical of MgO for higher y15. In these samples, MgZnO barriers are not uniform, as alloy decomposition tends to take place driven by morphological features during the growth7. This hampers a straightforward detection efficiency analysis on these samples. However, it is still possible to analyze the dependence of the composition measured by APT by an accurate choice of the sampled regions in the reconstructed volume, as detailed in the supplementary information. Atom Probe tip specimens were obtained by standard lift-off and annular milling procedures based on focused ion beam (FIB)16. All tips were prepared with the axis coincident with the growth direction. A scanning electron microscopy image of a typical tip specimen from sample AG-1 is reported on fig. 1-(a), while a dark field transmission electron microscopy image of a tip from the same sample after APT analysis is displayed in fig. 1-(b). The first


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image yields the morphological information about tip radius and half-shank angle, while the second one can be used in order to have an independent assessment of layer thicknesses. These data are subsequently used for optimizing volume reconstruction through an adequate choice of the parameters.

AlGaN

Al III-site

Table 1 – Synopsis of analyzed systems Analyzed Description

Sample

fraction (y)

Specimens

Independent measurement of composition

AG1

0.07

2

30 periods of

Supplementary

AlGaN/GaN 15/15 nm

Information

thick layers AG2

0.16

1

300 nm thick AlGaN

Supplementary

layer with 2 GaN marker

Information

layers AG3

0.25

1

15 periods containing 25

Ref. 13

nm thick AlGaN alyers AG4

0.56

2

300 nm thick AlGaN

Supplementary

layer with 2 GaN marker

Information

layers MgZnO

Mg II-site

Sample

fraction (y)

MZ1

0.28

2

20 periods containing 8

Ref. 7

nm thick MgZnO layers MZ2

0.35

1

20 periods containing 8 nm thick MgZnO layers


Ref. 7


Fig. 1. (a) SEM image of one of the analyzed tip specimens from sample AG-1 before APT analysis. The superimposed reconstructed APT volume indicates the portion of tip analyzed by APT. (b) TEM image of a tip specimen from sample AG-1 after APT analysis. The dark and light contrasted regions correspond to GaN and AlGaN layers, respectively.

2.2. Atom Probe investigations Atom Probe analyses were performed using a Laser-assisted Wide Angle Tomographic Atom Probe (LaWaTAP), operated with femto-second laser pulses (350 fs) focused on ~60 µm diameter spot. All measurements were performed using a laser wavelength λ= 343 nm (UV) at laser repetition frequency flaser=100 kHz. During measurements the laser pulse energy Elas ranged between 5 and 40 nJ, (the pulse energy Elas = 1 nJ corresponds roughly to an average pulse intensity Ilas = 0.22 W µm−2). The specimen base temperature Tbase was set to either 50 or 80 K. The detection system was a multi-channel plate/advanced delay line detector (MCP/aDLD) with a MCP efficiency ≈ 0.617,18. The field of view of the LaWaTAP is fixed at ±18°. The role of the experimental parameters on the measured composition was investigated performing long measurements with the detection rate ϕDet fixed between 2.25-2.75x10-3 Ions/pulse and constant laser energy Elas, while the applied bias VDC is allowed to vary.


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In fig. 2 we report the typical example of an APT analysis performed on one AG-1 tip specimen. The variation of the detection rate and of the applied bias VDC are reported in fig. 2-(a). The detection rate shows oscillations between 2.25-2.75x10-3 Ions/pulse due to the alternate erosion of high field (AlGaN) layers and low field (GaN) layers. The same oscillations are visible in the VDC curve. The applied bias increases during the experiment. This counterbalances the effect of the increase of the apex radius, which would decrease the field if the bias remained constant. The mass spectrum is shown in fig. 2-(b). The main species found are Al1+, Al2+, Al3+, Ga2+, Ga1+, N2+ and N22+ (some ambiguity persists about the attribution of the peak at 14 amu, but this will not impact the following of the work). Molecular species, such as AlN2+, and GaN32+ also contribute to the determination of the composition of the sample. Parasitic species, such as hydrogen-, carbon- and water-related peaks (at 17 and 18 amu), and hydrides (containing either N or Al, at 15,16 or between 20 and 22 amu) are also present, most likely supplied by the environment, by the Pt-C soldering deposited during the preparation of the tip by focused ion beam or by some other unidentified source of impurity. The total fraction of unidentified and parasitic ions (hydrogen-related species) in the mass/charge spectrum amounts to slightly less than 8% and 2%, respectively.


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Fig. 2. Results of an APT analysis of an Al0.07Ga0.93N /GaN multilayer specimen. (a) Variation of the detection rate (set between 2.25x10-3 and 2.75 x10-3 ions/pulse) and of the voltage applied to the specimen during the analysis. (b) Mass spectrum from the whole analyzed volume. (c) Variation of the Al2+/Al+ and of the Ga2+/Ga+ charge state ratios within a 5x5x500 nm subvolume including the axis of analysis as a function of the reconstructed depth coordinate. (d) Reconstructed volume showing the distribution of Al1+ (green), Al2+ (red), Ga1+ (20% of the ions, blue) and Ga2+ (grey) ions.


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The 3D volume reconstruction, highlighting the spatial distribution of Al2+, Al1+, Ga1+ and Ga2+ is shown in fig. 2-(c). This reconstruction has been obtained by applying the “cone angle” algorithm with initial radius R0=35 nm,, projection point m+1=1.6, cone angle 4.5°, curvature factor 2, reconstruction detection efficiency =0.21. The geometric parameters are determined based on the SEM image of the tip, while the detection efficiency is adjusted so that the reconstructed layer thickness matches with that determined by TEM. The Al2+/Al1+ and Ga2+/Ga1+ charge state ratios can be considered as indicators of the field. While the accuracy of this metrics will be critically discussed in section 3.1, its trends reflect the variations in the surface electric field during the analysis. Both quantities, sampled within a 5x5x5 nm3 cube containing the axis of analysis are displayed as a function of the reconstructed depth in fig. 2-(d). They clearly indicate that the field locally increases when an AlGaN layer is evaporated, while it decreases when a GaN layer is evaporated, while the significant fluctuations are due to the small size of the sampling volume. On the average, the overall trend of the charge state ratios is a decrease. In fact, when the apex radius increases during the analysis, a larger surface is imaged onto the detector. in order to have a constant detection rate, the evaporation rate decreases. This is obtained through a decrease of the surface field. .

3. Results and discussion

3.1. Preliminary considerations about the charge state ratio metrics In this work, we adopted the so-called Me2+/Me1+ Charge State Ratio (CSR) metrics of the metallic elements. The advantages of the CSR metrics are the following: (i) The Me2+/Me1+ CSR is related to the surface field. This relationship might be made quantitative through the post-ionization statistics introduced by Kingham19. In principle,



the phenomenon of post-ionization takes place at a distance of several Å from the sample surface, and should be nearly independent of the material in which the atom was found if the evaporation takes place in the singly charged state. The charge state abundances of the evaporated ions are thus a function of the surface field. By inverting this function, it becomes possible to calculate an effective surface field Feff. The CSR-Field relationship, calculated in the framework of the post-ionization model, is explicitly shown for Al, Ga and Zn in fig. 3-(a), while the relative abundance of 1+, 2+ and 3+ charge states is reported in fig. 3-(b) for Ga and Al. However, this effective field Feff should only be considered as an estimate of the actual surface field F 20,21. (ii) The Me2+/Me1+ CSR can be defined as a local quantity, as it can be calculated within arbitrarily chosen 3D volumes. This is useful in order to map the local surface field and correlate it with the locally measured composition. (iii)

The Me2+/Me1+ CSR allows for studying the composition trends even in the

case where the tip shape significantly changes during the APT analysis. (iv) Finally, the Me2+/Me1+ charge state ratio allows comparing data generated by different instruments (LaWaTAP, FlexTAP, LEAP), analyses performed on different materials containing a metallic species in common, and by different users.


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Fig. 3. Relevant quantities calculated in the framework of the post-ionization model (ref. 19). (a) Charge state ratio Me2+/Me1+ as a function of the field at the surface of a field emitter for the metallic elements Ga (blue, dash-dotted line), Al (red, dashed line) and Zn (green, short dashed line). (b) Ionization probability of the 1+, 2+, 3+ charge states for Al (top) and Ga (bottom). (c) Correlation between the charge state ratios Ga2+/Ga1+ and Al2+/Al1+ sampled in in AlGaN at high (black symbols) and low field (orange symbols) and comparison with the prediction of the post-ionization model (red dashed line)

However, the use of the CSR metrics is not exempt of important limitations. As previously mentioned, some of them are inherent to the model of post-ionization20,21. Furthermore, the evaporation of the same element from different matrices could yield different charge state statistics for equal surface fields, as the evaporated charge state is not only the result of postionization, but also of the symmetry and strength of the chemical bonds of the atom at the surface, and these effects are not taken into account in the post-ionization model. Finally, evaporation may be related to changes of the field over time, while the CSR is determined as a time average. As an example of these limitations, we can notice the presence of Al1+, Al2+ and Al3+ in the mass spectrum in fig. 2-(b), all in significant amounts (>10% of the total



amount of Al). This result can be also shown to hold locally, on the nm scale. According to the post-ionization theory (fig. 3-(b), top) it should not be possible to observe these three species at the same time in amounts higher than 0.01% of the total of Al. The comparison of the Al2+/Al1+ and Ga2+/Ga1+ CSRs gives an indication of the consistency of the use of these metrics for estimating the surface field in AlGaN. Figure 3-(c) shows the correlation diagram between the Al2+/Al1+ and Ga2+/Ga1+ CSRs, sampled in voxels of approximately 5 nm side from two regions of interest of sample AG-3, the first region being at an average high field, the second at an average low field. The red dashed line superimposed to the experimental distribution is the prediction of the post-ionization model. The other samples yield a similar behavior. The result clearly indicates that the post-ionization model can be considered as consistent at low field conditions only, while the Ga2+/Ga1+ and Al2+/Al1+ CSRs would yield two different surface fields when the statistics is performed at high field conditions; However, we notice that the two CSRs deviate by no more than a decade from the prediction of the Kingham model. According to the results shown in fig. 3(a), this translates into an uncertainty of around 1 V/nm (~5% of relative uncertainty) in terms of surface field only for the experimental conditions typical of this work.

3.2. Dependence of the measurement of alloy composition on the surface electric field

3.2.1. AlGaN The results of the compositional analysis of the AlGaN alloy is presented in fig. 4. In this plot, each point is obtained by averaging the Ga2+/Ga1+ charge state ratio over a volume, extracted from a single layer, containing 104-105 atoms of all species. The measurements have been performed at either T=50K or T=80K. A symbol of a given shape and interior corresponds to a given tip specimen, analyzed at constant detection rate and with fixed laser intensity. The applied potential is thus the only parameter varying through the experiment, while the


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variation of the field is related to the progressive increase of the apex radius during the analysis.

Fig. 4. Correlation between the y III-site fraction in AlyGa1-yN and the Ga2+/Ga+ charge state ratio for 6 tip specimens from four different samples. The site fraction values y=7% - 56% in the label correspond to samples AG-1 – AG-4.

The measured III-site fraction is strongly dependent on the surface electric field. All samples with different content show that the measured Al III-site fraction y is close to the correct value at low field and increases as the surface field increases. This behavior is general and reproducible within the explored range of compositions. It is also interesting to notice that we could not obtain evaporation at lower fields than those giving a correct site fraction, i.e. there



are no data below the Ga CSR of 0.01, 0.02 and 0.05 for y=0.07, y=0.25 and y=0.56 respectively.

3.2.2. MgZnO APT data related to MgZnO are presented in fig. 5. The Zn2+/Zn1+ CSR was averaged over a volume containing 103-104 atoms. Due to the scarce amount of Mg1+ (see the supplementary fig. S-1-(a)), the consistency between the Zn2+/Zn1+ and the Mg2+/Mg1+ CSR could not be checked5. Furthermore, the MgZnO layers do not strictly exhibit a random alloy distribution. In fact, decomposition phenomena driven by the surface morphology occur during the growth, as reported elsewhere7. As shown in detail in the supplementary information (fig. S-1-(b,c)), the MgZnO layer composition has been sampled outside of these decomposition planes, where the metallic species are nearly randomly distributed on the II-sites of the crystal lattice. The measurements were done at T=50K. As in AlGaN, a symbol of a given shape and interior corresponds to a given tip specimen, analyzed at constant detection rate and with fixed laser intensity.


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Fig. 5. Correlation between the y II-site fraction in MgyZn1-yO and the Zn2+/Zn+ charge state ratio for 5 tip specimens from two different samples analyzed at T=50K.

The measured II-site fraction exhibits a clear correlation with the surface electric field. Both samples show that the Mg II-site fraction is close to the independently determined value at low field and it increases at higher field. As in AlGaN, a higher content of Mg has the effect of increasing the average field at which the analysis is performed. For MgZnO too, it was not possible to analyze specimens at a Zn2+/Zn1+ CSR lower than the one allowing for an accurate composition measurement. Note that this behavior, reproducible in AlGaN and in MgZnO, is counterintuitive (it should be possible to decrease the field further) and could not satisfactorily be explained. It could be tentatively related to the adsorption of parasitic molecules at low field, which would facilitate the charge transfer leading to post-ionization, but the phenomenon requires a dedicated study in order to be understood.

3.3. Dependence on temperature The dependence of the measured site fraction on the specimen base temperature has been studied in the AlGaN AG-1 sample. The data, reported in fig. 4, indicate that temperature 15 ACS Paragon Plus Environment


plays a significant role for a correct composition assessment. Comparing the Al III-site fractions measured at Tbase=50K and at Tbase=80K, they exhibit a similar behavior, with a correct composition measured at low field and an increasing III-site fraction measured at high field, but the curve at Tbase=80K is globally shifted towards lower field values. We will argue in the following that this is a consequence of preferential evaporation as a mechanism for Ga loss.

3.4. Local estimation of the specific detection efficiency (AlGaN)

3.4.1. General considerations on detection efficiencies

In APT, different detection efficiencies can be defined.

Efficiency of the detection system. The efficiency of the detection system , is mainly limited by the efficiency of the multi-channel plate detector, related to the ratio between the surface of the open micro-channels and the total detector surface. It can be considered as independent of the detected species. In the present study, = 0.618.

Reconstruction detection efficiency. The reconstruction (or global) detection efficiency

is the parameter intervening in the reconstruction algorithm. It is a weighted average of the detection efficiencies for each species as defined in the mass spectrum, and its value is generally determined a posteriori, so that the depth scale of the reconstructed volume best matches that of the analyzed volume. It is possible that a constant value of is not sufficient to ensure an accurate reconstruction throughout large datasets. In this case, if it is not possible to determine a functional relationship between reconstructed depth and , it can be convenient to perform different reconstructions on different subvolumes.


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Specific detection efficiency. The specific detection efficiency is defined as the ratio between the number of detected atoms of a certain species i and the number of atoms effectively present within a given analyzed volume. In general, it is difficult to determine the specific detection efficiency. However, it is possible to do it in specimens satisfying the following set of conditions: (i) the volume occupied by a given species within the material is a priori known; (ii) the atomic or site fractions of each species is a priori known; (iii) the reconstruction of the analyzed volume is accurate and free of distortions. These conditions are in principle satisfied by the samples analyzed in this study, because (i) the lattice parameters of AlGaN and MgZnO are known (ii) the sample compositions have been determined independently and (iii) the specimen tip radii and interlayer distances are known from SEM and TEM characterization, respectively, which makes it possible to accurately reconstruct the analyzed volumes. We will see in the following that the last condition is actually satisfied only in part, introducing uncertainty in the results. The specific detection efficiencies can therefore be determined within accurately reconstructed volumes as the ratio between the number of detected atoms of the i-th species per unit volume and the expected number of atoms of the i-th species per unit volume:

= /

(1)

Note that this quantity can be locally defined, allowing for a detection efficiency mapping within the overall reconstructed volume, and is related to the efficiency of the detection system through :

=

(2)

where corresponds to the fraction of detectable atoms, i.e. those which evaporate on-pulse as ionized species.



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3.4.2. Application to AlGaN dataset

The specific detection efficiencies (i=Ga, Al, N) for Al0.25Ga0.75N were determined in a tip specimen for which the measured composition is given in fig. 4 and in previous works

13,14

.

The 3D reconstruction was calibrated based on SEM and TEM observations of both tips and lamellae. This reference reconstruction was obtained by applying the cone angle protocol

45

[45]

, with curvature factor 1.2, a cone angle of 7°, a projection point m+1 = 1.5 and an initial

tip radius r0 = 30 nm and a reconstruction detection efficiency ηrec = 0.25. Cone angle and initial radius have been determined on the basis of the experimental SEM observation of the tip specimen, while the projection factor has been determined through the calculation of the electric field distribution on the tip apex, as detailed in the supplementary information. The ηrec factor was set in order to obtain the correct interlayer distances. Possible uncertainty on the reconstruction parameters will be critically discussed later on. Figure 6 displays the analysis of a 5 nm thick slice containing the axis of the analyzed volume. The distribution of the Ga2+/Ga1+ CSR is reported in fig. 6-(a), showing that the field is higher close to the axis of analysis (corresponding to the crystallographic [0001] axis), and that the field gradually decreases during the analysis. The specific detection efficiencies are reported in the maps of fig. 6-(b-d). These values are correctly defined for the AlGaN barrier regions only. Notice that the CSR and the detection efficiencies undergo significant and rapid variations at the interfaces. This occurs because the applied voltage changes in order to maintain a constant detection rate, while the evaporation fields of GaN and AlGaN are different. The main observations to report are the following :


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(a) The detection efficiency for Al ηAl (fig. 6-(b)) does not exhibit a significant variation from the beginning to the end of the analysis, but it varies in the radial direction. In the radial direction, ηAl is larger in low-field regions, where it also approaches the upper limit of the detector efficiency ηAl ~ηdet =0.6. (b) The detection efficiency for Ga ηGa (fig. 6-(c)) exhibits a strong correlation with the Ga2+/Ga1+ CSR both in the axial and in the radial direction. Only in low-field regions close to the end of the analysis the specific detection efficiency approaches the detector efficiency. (c) The detection efficiency for N ηN (fig. 6-(b)) is weakly dependent on the radial coordinate, while it slightly increases in the axial direction with the opposite trend of ηGa. On the average, ηN remains quite far from the upper limit, ηN = 1⁄?> is the time between two laser pulses.

9 is the number of sites

occupied by the species i on the surface. At steady state, this number is such that: A/ A

"

= A ∑$ Φ$ =

/C A

∑$ ;$ %$ &'$ , ($ ) =

(8)

it is thus proportional to the true atomic fraction. In this way, the number of detected atoms of the i-th species is proportional to the relative probability with which the atom leaves the surface through the channel 0. Only channel 0 allows indeed for its identification in the mass spectrum. The flux of detected atoms is thus

ΦD = ∑ Φ , ,

(9)

while the fraction of detectable atoms of the i –th species α (over the total number of atoms of the i –th species) is

α = ∑

AF,/

2 A2,/

.

(10)

According to this and to the expression (X) in section (A), the specific detection efficiency

η is:

η = α η

(11)

Where η is the efficiency of the detection system. The atomic fractions are measured as:

H> = ∑

AF,/

2 AF,2

(12) 25 ACS Paragon Plus Environment


A slightly different expression defines the site fraction. In AlGaN it is defined by taking into account the group III elements only (in MgZnO one would take into account the group II elements only):

I H> =

AF,JK

AF,JK LAF,MN

.

(13)

3.5.2. Application to AlGaN

In the fig. 7, the behavior of the specific fluxes of Al and Ga and of the Al III-site fraction is reported as a function of the field. Notice that it is possible to take into account the relative amounts of Al and Ga only, which simplifies the interpretation by discarding the more complex behavior of N5,25. Nitrogen is indeed most likely emitted in large amount through channel 2. On the contrary, the Arrhenius expressions for channels 0 and 1 in laser pulsed mode for Al and Ga are quite straightforward. The choice of the parameter set is reported in table II. There is actually a large uncertainty concerning parameters such as the barrier energy and the evaporation fields for the different elements in AlGaN. Concerning the barrier energies, for instance, the value of Q is quite close to the experimental values of the cohesive energy per bond reported for AlN and GaN26,27, but about one order of magnitude lower than calculated binding energy values28. For comparison, the adopted energy barriers are also lower than the value QZn~ 6eV that can be extrapolated for Zn+ field evaporating from a ZnO surface according to the density functional theoretical calculations of Xia and Kreuzer29. This means that the model still needs more accurate input in order to be quantitative, but it is at least possible to qualitatively reproduce the features found experimentally in the behavior of AlGaN. The key point is that Al is more strongly bound than Ga, as it is also observed in molecular beam epitaxy of AlGaN alloys26.


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We display the specific fluxes normalized by the number of surface sites Φ$, /9 for the channels 0 (on-pulse) and 1 (out-of-pulse) for both elements in fig. 7-(a), while the III-site fraction I H> measured at 50K and 80 K is displayed in fig. 7-(b). At low field, both Ga and Al evaporate through channel 0 (with the pulse), as shown in fig. 7-(a) and an accurate Al IIIsite fraction is measured (as shown in fig. 7-(b)). When Ga approaches its evaporation field (supposed as lower than that of Al), evaporation of Ga through channel 1 sets on, and a surplus of Al is measured. The point where equal amounts of Ga are evaporated through either channel is marked by an arrow in fig. 7-(a). When the field further increases, out-ofpulse evaporation of Al also begins: in this regime, however, too many atoms are lost and the overall detection efficiency drops to levels which would make an APT analysis not particularly meaningful. The above considerations also tend to confirm that one should be able to measure an accurate fraction by lowering the field. Finally, some critical remarks could be made: (a) The fraction of lost Ga atoms critically depends on the ratio between the opening time of the out-of-pulse channel and the in-pulse channel. While it is convenient to work with fast (ps) or ultrafast (sub-ps) laser pulses, the duration of the thermal pulse being limited by the fast relaxation mechanisms of the tip (tens of ps)30, the increase of the pulsing cadency should significantly reduce preferential field-induced uncorrelated evaporation effects. (b) The parameters used for the curves below should not be too far from reality, but the increase of the measured site fraction as a function the field is significantly steeper than the experimental behavior shown in fig. 4. The reason for this could be that the specific energy barriers and evaporation fields actually depend on the site neighborhood and on the crystallographic orientation of the surface. The latter hypothesis is also supported by a number of observations that indicate that the distribution of the surface field in GaN is far from uniform2,3,5,11. Interestingly, this is also confirmed by the observation of anisotropic growth rates in selective



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area growth of GaN31. Furthermore, it is shown in the supporting information (Fig. S-3) that the measured site fraction exhibits only a very weak dependence on the specimen temperature during the pulse. The main driving parameter of the compositional biases is thus the evaporation field: the amount of the more strongly bound species will be overestimated at higher field. It is also worth mentioning that the assumption of an evaporation field independent of the site fraction y leads to an onset of preferential losses at the same field value for the three compositions displayed in fig. 7-(b). However, the experimental results displayed in fig. 4 indicate that the onset of preferential evaporation losses increases with the Al III-site fraction. This suggests that the evaporation field of Ga increases when the amount of Al within the matrix increases. This is consistent with a dependence of the binding energy of a Ga atom on the Al site fraction, as an effect of nearest neighbors of order n>1.

Table II Parameters adopted for the preferential evaporation model Parameter

Value

Notes

Energy Barrier for Ga

Symbol in equations QGa

1 eV

Estimateda,b

Energy Barrier for Al

QAl

1.1 eV

Estimateda,b

Evaporation Field for Ga

Fev,Ga

25 V/nm

Experimental, Estimated

Evaporation Field for Al

Fev,Al

27 V/nm

Experimental, Estimated

ν0

1013 s-1

Estimated c

Base Temperature

Tbase

50K, 80K

Set in experiment

Interval between pulses

tlaser

10-5 s

Instrumental, fLawatap=105 Hz

On-pulse Temperature

Tpulse

Tbase+150K

Estimated c*

Pulse duration

tpulse

10-11 s

Instrumental + Calculation c

Arrhenius frequency pre-factor


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a

=ref.28; b =ref. 27; c=ref. 30; * effect of variation of Tpulse reported in the supplementary

information.

Fig. 7. Predictions of the preferential evaporation model. (a) Specific fluxes for Al and Ga through the two different channels out of pulse (dashed line) and on-pulse (solid line). The arrow marks the point where an equal amount of Ga evaporates through either channel. (b) Measured Al III-site fraction y from AlGaN samples with different composition as a function of the surface electric field according to the preferential evaporation model.



4. Summary The accuracy of composition measurements using La-APT in the ternary semiconductor alloys AlyGa1-yN and MgyZn1-y O alloys has been studied and modeled. The results indicate a similar behavior for both nitride and oxide systems, which can be listed as follows: (i)

A correct site fraction y is measured at low field conditions, while Ga and Zn

preferentially evaporate at high field yielding an overestimation of y; furthermore, low base temperature reduces preferential losses for a given surface field. This result is expected to hold for different APT instruments and for different detection rate conditions. However, the surface field allowing for a correct measurement should be evaluated according to the situation. (ii)

APT datasets exhibit local biases depending on the distribution of the electrostatic

field at the specimen surface. The specific detection efficiencies for Al and Ga get close to the limit value of the detector efficiency for low field conditions. (iii)

It is generally impossible to accurately determine all atomic fractions. We estimate the

detection efficiencies for each species and interpret the results through a model describing preferential evaporation in simple terms. (iv)

The observations reported can be described within a preferential evaporation model

that takes into account the difference in the surface energy barrier and the evaporation field for each metallic species. Energy barriers and evaporation fields for Ga and Al could be estimated as QGa =1 eV, QAl =1.1 eV, Fev,Ga = 25 V/nm, Fev,Al = 27 V/nm. These parameters should be further verified by a more systematic set of measurement and by dedicated theoretical calculations. However, the comparison between the model and the experimental data indicates that the evaporation fields and energy barriers should vary with the alloy composition, with both Al and Ga being more tightly bound to the surface when the matrix is


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richer in Al. The same observation can be qualitatively performed based on the measurements performed in MgZnO.

Author information: * Corresponding author: [email protected] phone: +33 2 35 14 71 82 Acknowledgements: This work has been funded through projects EMC3 Labex ASAP, ANR-13JS10-0001-01 TAPOTER, EMC3 Labex AQURATE and through the regional-EU RIN-FEDER BRIDGE. We also acknowledge the French Research Nation Agency (ANR) for having funded the acquisition of the TEMPOS NANOTEM platform (Dual-beam FEI SCIOS FIB and FEI Titan Themis TEM-STEM) within the EQUIPEX ANR-10-EQPX-50 program. Author Contributions: E.D.R. performed specimen preparation, APT analysis, interpreted the results, wrote part of the manuscript; F.M. performed TEM analysis, N.G. designed and grew the samples by MBE at LPN, L. L. characterized by TEM-EDX and X-ray diffraction the samples grown at LPN, E. G., J.-F. C. and N. G. designed and grew the samples at EPFL, J.M.C. and M. H. designed and grew the samples at CRHEA. I. B. contributed to APT data analysis and specimen preparation, W. L. supervised TEM analysis, F. V. performed electrostatics simulations and contributed to the interpretation of the APT data, D. B. contributed to APT data interpretation and supervised part of the APT experiments, L. R. designed the experiments, performed part of specimen preparation and APT analysis, contributed to data interpretation, wrote part of the manuscript. All authors discussed and approved the manuscript. Supporting Information: Supplementary data and information about MgZnO APT analysis, estimation of reconstruction parameters and preferential evaporation model are provided in a separate file. .

References 31 ACS Paragon Plus Environment


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Fig. 1. (a) SEM image of one of the analyzed tip specimens from sample AG-1 before APT analysis. The superimposed reconstructed APT volume indicates the portion of tip analyzed by APT. (b) TEM image of a tip specimen from sample AG-1 after APT analysis. The dark and light contrasted regions correspond to GaN and AlGaN layers, respectively. 214x146mm (72 x 72 DPI)



Fig. 2. Results of an APT analysis of an Al0.07Ga0.93N /GaN multilayer specimen. (a) Variation of the detection rate (set between 2.25x10-3 and 2.75 x10-3 ions/pulse) and of the voltage applied to the specimen during the analysis. (b) Mass spectrum from the whole analyzed volume. (c) Variation of the Al2+/Al+ and of the Ga2+/Ga+ charge state ratios within a 5x5x500 nm subvolume including the axis of analysis as a function of the reconstructed depth coordinate. (d) Reconstructed volume showing the distribution of Al1+ (green), Al2+ (red), Ga1+ (20% of the ions, blue) and Ga2+ (grey) ions.

442x250mm (72 x 72 DPI)


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Fig. 3. Relevant quantities calculated in the framework of the post-ionization model (ref. 19). (a) Charge state ratio Me2+/Me1+ as a function of the field at the surface of a field emitter for the metallic elements Ga (blue, dash-dotted line), Al (red, dashed line) and Zn (green, short dashed line). (b) Ionization probability of the 1+, 2+, 3+ charge states for Al (top) and Ga (bottom). (c) Correlation between the charge state ratios Ga2+/Ga1+ and Al2+/Al1+ sampled in in AlGaN at high (black symbols) and low field (orange symbols) and comparison with the prediction of the post-ionization model (red dashed line) 329x238mm (72 x 72 DPI)



Fig. 4. Correlation between the y III-site fraction in AlyGa1-yN and the Ga2+/Ga+ charge state ratio for 6 tip specimens from four different samples. The site fraction values y=7% - 56% in the label correspond to samples AG-1 – AG-4. 205x274mm (72 x 72 DPI)


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Fig. 5. Correlation between the y II-site fraction in MgyZn1-yO and the Zn2+/Zn+ charge state ratio for 5 tip specimens from two different samples analyzed at T=50K. 339x250mm (72 x 72 DPI)



Fig. 6. Analysis of the specific detection efficiency ηi for the species contained in the random Al0.25Ga0.75N alloy constituting the barriers of sample AG-3. The quantities shown in this figure are relative to a 5 nm thick slice containing the axis of the analyzed volume. (a) Map of the Ga2+/Ga1+ charge state ratio and (b,c,d) specific detection efficiencies for Al, Ga and N, respectively. The effect of the reconstruction parameters on the specific detection efficiencies is shown in (e,f). Reconstruction and specific detection efficiencies sampled at different positions in the reconstructed volume as a function of the compression factor m+1 with constant initial radius r0=30 nm (e) and as a function of the initial radius with constant compression factor m+1=1.5. (f). The grey shaded regions indicate efficiency values higher than the efficiency of the detection system η_Det. The reconstructions were performed by the cone angle algorithm and the reconstruction detection efficiency η_rec (top plots) was adapted in order to conserve the correct interlayer distances. 219x251mm (72 x 72 DPI)


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Fig. 7. Predictions of the preferential evaporation model. (a) Specific fluxes for Al and Ga through the two different channels out of pulse (dashed line) and on-pulse (solid line). The arrow marks the point where an equal amount of Ga evaporates through either channel. (b) Measured Al III-site fraction y from AlGaN samples with different composition as a function of the surface electric field according to the preferential evaporation model. 270x179mm (72 x 72 DPI)


Composition metrology of ternary semiconductor ... - ACS Publications

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