Atom Probe Tomography: a Local Probe for Chemical Bonds in Solids

Abstract

Atom probe tomography is frequently employed to characterize the elemental distribution in solids with atomic resolution. Here the potential of this technique to locally probe chemical bonds is reviewed and discussed. Two processes characterize the bond rupture in laser‐assisted field emission, the probability of molecular ions (PMI), i.e., the probability that molecular ions are evaporated instead of single (atomic) ions, and the probability of multiple events (PME), i.e., the correlated field‐evaporation of more than a single fragment upon laser‐ or voltage pulse excitation. Here it is demonstrated that one can clearly distinguish solids with metallic, covalent, and metavalent bonds based on their bond rupture, i.e., their PME and PMI values. These findings open new avenues in understanding and designing advanced materials, since they allow a quantification of bonds in solids on a nanometer scale, as will be shown for several examples. These possibilities would even justify calling the present approach bonding probe tomography (BPT).

The metallic, covalent, and metavalent solids can clearly be distinguished based on their bond bond‐breaking behavior, i.e. their probability of multiple events (PME) and probability of molecular ions (PMI) values. These findings open new avenues in understanding and designing advanced materials since they allow quantification of bonds in solids on a nanometer scale.

1. Introduction

Atom probe tomography (APT) is a well‐established nano‐analytical technique enabling the determination of the spatial distribution of atoms in a solid with Angstrom resolution. It can characterize a broad spectrum of materials, ranging from metals to biological materials in three‐dimensions^{[ 1} , ² , ³ , ⁴ , ⁵ , ^{6 ]} Interesting physical phenomena such as impurity segregation,^{[ 7} , ^{8 ]} solute clustering,^{[ 9} , ¹⁰ , ¹¹ , ¹² , ^{13 ]} diffusion,^{[ 14} , ^{15 ]} and intermixing at hetero‐interfaces,^{[ 16} , ¹⁷ , ¹⁸ , ^{19 ]} etc. can be evaluated thanks to its unique capabilities. Some of these studies even led to the discovery of phenomena such as the snowplow effect,^{[ 20 ]} strain‐induced asymmetric line segregation,^{[ 21 ]} linear complexions,^{[ 22 ]} and Janus nano‐precipitation.^{[ 23 ]}

In this review, we summarize the present understanding of the role of chemical bonds on laser‐assisted bond rupture in atom probe tomography. It will be demonstrated that APT is suitable to probe the bond rupture and hence chemical bonds in solids on the nanometer scale. The high electric field of ≈10 V nm⁻¹ in conjunction with the pulsed femtosecond laser applied on the apex of a very small needle of ≈60 nm in diameter allows for the so‐called laser‐assisted field evaporation.^{[ 24 ]} Upon laser‐assisted field evaporation, atoms at the surface of the needle's apex are dislodged by breaking bonds to their neighbors. Hence, with APT well‐characterized bond rupture experiments are conducted, potentially justifying the acronym (BPT), i.e., bonding probe tomography. We are not seriously suggesting to use of the acronym BPT, but want to stress in this review that APT has tremendous potential to probe chemical bonds on a very local scale. Here we want to demonstrate that this is the case and provide arguments why this is so. Finally, it will be shown how APT can be employed to provide crucial insights to understand and tailor materials.

Studies on bond strength and bond‐breaking behavior with APT have so far been performed on ceramics,^{[ 25 ]} biological materials,^{[ 26 ]} and phase change materials.^{[ 27} , ^{28 ]} However, only for phase change materials (PCMs), which can also be used as excellent thermoelectric compounds,^{[ 29 ]} a very unusual bond rupture has been observed that will be described in detail next. In the subsequent section, the unusual bond rupture will be related to an unconventional type of bonding. There, it will be shown that the bond rupture in atom probe tomography differs significantly for solids that employ metallic, covalent, and metavalent bonds. In conjunction with the high spatial resolution of atom probe tomography, this allows the bonding mechanism to be determined at the local level, which would justify the abbreviation BPT. In Section S4 (Supporting Information), a pertinent question will be discussed: How can these differences in bond rupture for the different bonding mechanisms be explained? In Section S5 (Supporting Information), we will finally argue how these differences can be utilized to understand and design advanced functional materials.

1.1. Quantities Characterizing the Bond Rupture in Atom Probe Tomography

The principle of APT is based on the field evaporation of charged atoms (ions) from the surface under a high electric field of ≈10¹⁰ V m⁻¹.^{[ 24 ]} Under this high electric field, the atoms on the surface are restrained in a partial ionic state with a reduced energy barrier. For field evaporation to take place, the ions must overcome this energy barrier, which is facilitated by a voltage or a laser pulse. It is well‐accepted that not only atomic ions but also molecular ions are field‐evaporated and registered by a position‐sensitive detector during an atom probe experiment.^{[ 30 ]} Interestingly, the probability that fragments are dislodged from the tip as molecular ions is material‐specific. Thus, the probability that molecules rather than atoms are released during laser‐assisted field evaporation is one characteristic of bond breakage. Subsequently, we will abbreviate this probability as the PMI (Probability of Molecular Ions, schematically depicted in Figure 1a). Metals are typically field evaporated as single ions, thus exhibiting very low PMI values. Yet, field evaporation from covalent or ionic materials often leads to the emission of molecular ions (see Figure 1b), i.e., a high PMI. Typical covalent or ionic materials with such high PMI values are oxides, nitrides, and carbides.^{[ 31} , ³² , ^{33 ]} Interestingly, many chalcogenides including selenides, tellurides, and sulfides exhibit a high PMI value, too.^{[ 6} , ³⁴ , ³⁵ , ^{36 ]}

Figure 1.

Graphic presentation of the “Probability of Molecular Ions” (PMI) and the Probability of Multiple Events” (PME). Sketch of a bond‐breaking experiment for a sequence of successful pulses (pulses for which one or several events took place) exhibiting a) high PMI as well as b) high PME. SI stands for an ion that consists of a single ion, while SE stands for a single event (fragment) to be dislodged upon bond rupture.

Such molecular ions can dissociate on their flight path to the detector. Hence, it is possible that for the same laser or voltage pulse more than one ion reaches the detector, even though only a single molecular ion left the tip. The dissociation of molecular ions is based on the phenomenon of bond softening, which occurs in a molecular ion in a high electric field. This process has been studied thoroughly since the 1970s.^{[ 37 ]} More specifically, in the absence of an electric field the charge of the binding electron is distributed symmetrically around the ion cores. Yet, this situation changes in the vicinity of a positively charged APT tip surface, where the molecular ion AB^[2+] is found in a high electric field (see Figure 2a). Then, the probability of finding the electron adjacent to the tip surface is much larger than near the ion core B (i.e., a polarization effect occurs). This polarized molecule vibrates with a certain frequency (e.g., 10¹³ s⁻¹ for a H₂ ⁺ molecule).^{[ 37 ]}

Figure 2.

Field dissociation of molecular ions. a) Schematic presentation of the dissociation mechanism of an AB²⁺ ion in a high electric field. b) Representation of the potential curve of a molecular ion consisting of two atoms. Superposition of the potential V_i of the polarized molecular ion as shown in a) and of potential V_F of the molecular ion under the external field. Hence, E_b is the dissociation energy in the absence of a high field, while E_b’ is the dissociation energy in the presence of a high field. Ion correlation histogram of c) rhombohedral GeTe showing the weak dissociation tracks such as the dissociation a) Ge₂Te₃ ²⁺ → GeTe₂ ⁺ + GeTe⁺ and b) Ge₃Te₃ ²⁺ → GeTe₂ ⁺ + Ge₂Te⁺ as well as of d) (La_0.5,Sr_0.5)MnO₃ oxide showing strong dissociation tracks such as the dissociation a) LaMnO₂ ²⁺ → LaO⁺ + MnO⁺ and b) LaMnO₃ ²⁺ → LaO⁺ + MnO₂ ⁺ _. Figures in a) and b) were adapted from ref. [37].

During a vibration, work has to be done against the intramolecular forces. However, now the potential energy is lowered due to the high electric field (Figure 2b). This effect is easily quantified if the two ion cores A and B have the same mass. Then, the potential energy is lowered by $-\frac{1}{2}\mathrm{eF}(\mathrm{r}-{\mathrm{r}}_0)$, where e is the elementary charge (C), F is the field (V/nm), r is the distance between ions A and B and r₀ is the equilibrium distance of ions A and B as displayed in Figure 2b. Thus, for a sufficiently high field strength, the maximum of the potential curve vanishes, i.e., the dissociation energy E_b’ becomes 0, and the dissociation of the molecular ion takes place immediately.

A very elegant way of observing such molecular dissociation processes has recently been proposed by utilizing the ion correlation histogram.^{[ 38} , ^{39 ]} Examples of ion correlation histograms are given in Figure 2c,d for laser‐assisted field evaporation of rhombohedral GeTe and (La_0.5,Sr_0.5)MnO₃. Here combinations of ions m₁ and m₂ are used to construct these 2D histograms. The opposite ordering of each pair is also considered resulting in a histogram that is symmetric to the diagonal axis, i.e., m₁ = m₂ . The dissociation of molecular ions leads to tracks emanating from this diagonal axis to the ion‐pair coincident point (m₁, m₂). In this process, a larger ionic fragment (parent ion) with a given kinetic Energy (E_kin) breaks apart into two smaller fragments (daughter ions) under the high electric field. As shown in detail in ref. [38] a daughter fragment with a smaller mass‐to‐charge ratio will arrive later than expected on the detector due to the relatively slower flight speed of its parent ion. On the contrary, the other fragment with a higher mass‐to‐charge ratio will arrive earlier than expected. The result is that the ion pair moves away from the diagonal, forming characteristic tracks as seen in the dissociation histogram. In Figure 2c for example, very weak dissociation tracks are visible for the GeTe compound (most visible are a) Ge₂Te₃ ²⁺ → GeTe₂ ⁺ + GeTe⁺ and b) Ge₃Te₃ ²⁺ → GeTe₂ ⁺ + Ge₂Te⁺), while on the contrary strong dissociation tracks are visible for (La_0.5,Sr_0.5)MnO₃.

Such molecular dissociation processes also lead to an increase in the number of multiple events. This probability of multiple events (PME) describes the probability that a laser (or voltage) pulse creates more than a single fragment registered on the detector. Having a low probability of multiple events−i.e., having a high probability that only a single ion is detected per successful laser pulse is usually considered to be the signature of a high‐quality APT dataset. This is because a high PME may lead to “incorrect” positional information of an ion^{[ 40 ]} and/or compositional inaccuracies.^{[ 41} , ⁴² , ^{43 ]}

There are various possible mechanisms or even artifacts that cause high PME values, as discussed in the literature (see Table 1 ). The earliest one studied is the molecular ion dissociation mechanism presented above. Here molecular ions dislodged from the tip dissociate on the flight path to the detector, leading to a high PME. As mentioned above, this mechanism leading to high PMEs can be separated from other mechanisms leading to a high PME due to its distinct correlation histogram. Molecular dissociation is typically observed in nitrides, oxides, and other materials prone to field evaporation, producing molecular fragments such as GaSb.^{[ 31} , ³² , ³³ , ^{44 ]} Several other effects that lead to the detection of multiple events are in fact typical artifacts observed in APT. These processes include atomic migration on the apex of the tip before evaporation (observed for example for C atoms in Fe‐C alloys)^{[ 45 ]} and pile‐up effects (as seen for example in carbides^{[ 46 ]} and borides).^{[ 42 ]} For most of the compounds in Table 1, multiple events were found to be correlated in space and time (see supplementary information), leading to inaccuracies in the overall atom probe composition determination.^{[ 41} , ⁴² , ^{43 ]} Spatial correlation describes the probability of finding a certain distance of ions identified by the 2D detector, which were created by a single (laser or voltage) pulse. Temporal correlation instead describes the probability that there is a certain number of pulses n_p between two successful pulses (pulses for which at least one ion is detected) for which no ion evaporation took place (called null pulses). If the multiple events are correlated in time, then the number n_p decreases strongly so that the evaporation of multiple events for one successful pulse leads to the evaporation of other multiple events within the next successive pulses.

Table 1.

Summary of all material classes (except metavalent solids) that show a higher PME and their corresponding PME values.

Sample		PME [%]	Mechanism for multiple events formation	Refs.
Nitrides	Ti‐Si‐N	59	Molecular Dissociation	[41]
	AlGaN	27–57	–	[47]
	FeN	–	Isotopic effect due to either surface diffusion or field evaporation	[48, 49]
	GaN	40	Molecular Dissociation	[38, 40, 50]
Oxides	Y1Ba2Cu3O7−δ	28–40	Molecular Dissociation	[40]
	ZnO	40	Molecular Dissociation	[31, 51]
	Cr2O3/TiO2	>45	Molecular Dissociation	[52]
	Al2O3	>50	Molecular Dissociation	[53]
Others	GaSb	6–45	Molecular Dissociation	[43]
	NiSiPt	14–42	Unclear; probably differences in the evaporation field	[54]
Carbides	Fe‐C alloys	–	Artifact: C surface migration before field evaporation	[45]
	WC	52–60	Artifact: detector pile‐up and dead time (the time spread between two ions of the same mass‐to‐charge ratio coming from the same pulse is smaller than the dead time of ≈3 ns).	[46]
	Ti(C,N)	55
	Ti2AlC	41
	SiC	45
	M23C6	30
Borides	BN	80	Artifact: pile‐up effect or preferential field evaporation	[42]
	Boron	64
	LaB6	51.5	continuous evaporation of B	[55]

Surprisingly, there is one class of materials that behaves very differently. In this class of solids, high PME values of more than 50% are characteristic of an unconventional bond rupture.^{[ 27 ]} In this class of materials which includes crystalline GeTe, Sb₂Te_3, and elemental Bi, a PME larger than 50% has been observed. Such a high value has also been observed for PbSe in recent work by Hughes et al.^{[ 56 ]} In total, more than 50 solids have been identified,^{[ 29} , ⁵⁷ , ^{58 ]} for which the high PME values cannot be explained by the molecular dissociation mechanism or the artifacts described above. We note here that no change is observed in terms of PME between the crystallographic pole and the neighboring region proving that the crystallographic atomic arrangement of the atoms of the apex of the tip does not impact the PME values. This proves that we deal here with another phenomenon than the standard “co‐evaporation phenomenon” described in the past^{[ 59 ]} and we called it the “enhanced co‐evaporation phenomenon”.

Among those solids, there is an interesting series of samples, which range from GeTe to GeSe, but also include compounds such as GeSe_0.25Te_0.75, GeSe_0.5Te_0.5 and GeSe_0.75Te_0.25. These five compounds are isoelectronic but change significantly in their material properties.^{[ 60 ]} Two of these crystalline solids behave in their properties and bond rupture like ordinary covalent compounds (GeSe and GeSe_0.75Te_0.25), while the three others show an unusual bond rupture (GeTe, GeSe_0.25Te_0.75 and GeSe_0.5Te_0.5). An example is crystalline GeSe_0.5Te_0.5, which reveals a PME value of 55% but exhibits no molecular dissociation. This statement can be derived both from the correlation histogram (data such as shown for GeTe in Figure 2c) and the frequency diagram shown in Figure S1 (Supporting Information). Interestingly, for the rhombohedral GeSe_0.75Te_0.25 characterized by a very high PME value only one peak was observed in the blue curve, i.e., the one associated with correlated evaporation. Surprisingly, the peak intensity of the red curve for the rhombohedral GeSe_0.75Te_0.25 compound (Figure S1a, Supporting Information) is almost 10 times lower than the peak intensity of the blue curve, proving that the multiple events are not strongly correlated in time (no burst evaporation). Even more astonishing is that the peak intensity of the red curve for the rhombohedral GeSe_0.75Te_0.25 compound (characterized by a very high PME value of 58%) is 2 times lower than that of its amorphous counterparts (characterized by a low PME value), proving that the multiple events are weakly correlated in time despite their very high proportion. Yet, the very high peak intensity of the blue curve for both compounds (Figure S1a, Supporting Information) suggests a strong spatial correlation between multiple events as expected.

We note here that the PME values given were obtained for a laser energy of 5–20 pJ (laser energy for which the stoichiometry of PCMs was preserved). These PME values can be slightly reduced if the laser energy is increased (reduced electric field at the tip) as was shown recently.^{[ 27 ]} However, distinct differences between the non‐PCMs and PCMs have always been detected independently of the laser energy applied.

Comparing the field evaporation behavior of rhombohedral GeSe_0.75Te_0.25 with one of the metals like Al (Figure S1b) reveals that correlated evaporation is the evaporation mechanism responsible for both systems. The only difference between Al and rhombohedral GeSe_0.75Te_0.25 (and extrapolated to metals and crystalline PCMs in general) is that the PME value for rhombohedral GeSe_0.75Te_0.25 and crystalline PCM in general (PME>55%) is well above than that measured for Al or other metals (PME<15%). Hence, this high PME value is attributed to an unconventional mechanism named ″enhanced‐correlated field evaporation mechanism’27. It is an intrinsic property of crystalline PCMs.^{[ 27 ]} Interestingly such enhanced‐correlated field evaporation mechanism cannot be applied for the amorphous counterparts where low PME values (below 30%) were measured. This shows that the bond rupture in amorphous and crystalline phase change materials of the same stoichiometry differs significantly. This striking observation requires an explanation, which will be presented in Section S5 (Supporting Information).

One can hence conclude that three different bond rupture scenarios have been found in APT as summarized in Figure 3 below. Solids like Al, Au, Ag, Cu, W, and NiAl show a very low PMI and a low PME. This bond rupture scenario is apparently characteristic of metals. Covalent semiconductors like GaAs, GaSb, or InSb, on the contrary, have a much higher PMI but a low PME. Hence, solids that employ metallic or covalent bonding can be distinguished in atom probe tomography by analyzing the bond rupture. Finally, a significant number of crystalline chalcogenides show yet another characteristic bond rupture. These solids have unusually high PME values of above 50%, which can be attributed to enhanced correlative field evaporation. They also have PMI values much higher than metals. Crystalline solids like GeTe, Sb₂Te₃, PbTe, or Bi are characterized by this bond rupture. These solids possess an unusual property portfolio which has been attributed to an unconventional bond type, named metavalent bonding.^{[ 27} , ^{61 ]} As a consequence, the bond rupture in APT can distinguish between metallic, covalent, and metavalent bonds. What is even more striking, the bond rupture in materials like GeTe differs between the crystalline and the amorphous state. While crystalline Ge₂Sb₂Te₅ has a high PME of 65%, amorphous Ge₂Sb₂Te₅ shows a much lower PME of 22%.^{[ 27 ]} This implies that the crystallization of amorphous Ge₂Sb₂Te₅ leads to a change of bonding from covalent to metavalent bonding. This change of bonding can explain the pronounced property changes that accompany crystallization in such chalcogenides,^{[ 62 ]} which are utilized in phase change materials for data storage.^{[ 63 ]} To understand the origin of these differences in bond rupture, we need to look at the different properties that characterize the different bond types in solids.

Figure 3.

Interdependence between the electrical conductivity of the solids and two quantities that characterize the bond rupture, a) the PME, b) the PMI, and c) PMI versus PME. Several classes of materials can be distinguished based on their bond breaking in the atom probe: metals (in blue), metavalent solids (in green), and covalently bonded compounds (in red). Please note that some of the amorphous phase change materials show a bond rupture which is characteristic for covalently bonded solids. Parts of this figure, i.e., most of the PME values are taken from previous studies.

1.2. Bonding Classification and its Relation to Bond Rupture (PMI and PME)

It has recently been shown that it is possible to distinguish different classes of chemical bonds in solids due to the different portfolios of properties these compounds possess.^{[ 61} , ^{64 ]} Metals, for example, are characterized by a vanishing band gap, a large effective coordination number (ECoN), high values of the electrical conductivity (σ > 5 × 10⁴ S cm⁻¹), moderate Grüneisen parameters for transverse optical mode (γ_TO, a measure of the anharmonicity of the lattice), and vanishing values of the Born effective charge Z*, which characterizes the bond polarizability.^{[ 61 ]} Solids, which employ covalent bonding instead, are characterized by a band gap, a coordination number that usually follows the 8–N rule, a much lower electrical conductivity if the crystals are not doped, and a γ_TO which is usually close to 2. The crystalline chalcogenides and related compounds discussed here, which show an unusual bond rupture, are also characterized by a unique property portfolio. Typical physical properties such as the optical dielectric constant ε_∞, Z*, and γ_TO are much larger for these solids than for metals and covalent solids. This peculiar property portfolio as well as the unusual bond‐breaking behavior are indicative of this novel class of chemical bonds termed “metavalent bonding”.^{[ 27} , ^{61 ]} It is striking that amorphous solids of the same chalcogenides neither show these properties nor this unconventional bond rupture, which is further evidence of significant changes in bonding upon crystallization.^{[ 62 ]}

This raises the question of how the differences in bond rupture observed for the different solids can be explained. Ideally, we would like to understand, if there is a single material property that governs or is at least closely related to the bond rupture. Previous work has shown that no single parameter can distinguish all different bonding mechanisms.^{[ 61} , ^{64 ]} Instead, a portfolio of five different properties has been shown to enable a classification of different bonds. Nevertheless, the one quantity that has the highest predictive power concerning bond breaking in the atom probe is the electrical conductivity of the solids. Figure 3a shows that semiconductors with covalent bonding (in red) and metals (in blue) exhibit low PME values, as expected. Yet, only crystalline PCMs (in green) show exceptionally high PME values above 55%. On the contrary, amorphous PCMs (covalently bonded compounds) like amorphous In₃SbTe₂, amorphous GeSe, amorphous GeSe_0.25Te_0.75 and GeSe_0.5Te_0.5 show PME values below 30%.^{[ 27 ]} Hence, metavalent solids are characterized by a distinct bond rupture. It is striking that this unusual bond rupture is observed in the transition region between metallic bonding, where electrons are highly delocalized, and covalent bonding, where electrons are localized between the ion cores. This leads to a pronounced maximum in the transition region, i.e., a “volcano”‐shaped curve, confirming the notion that metavalent bonds are located in the competition zone between metallic and covalent bonds.

The second relevant parameter employed here to distinguish different solids is the PMI. This quantity is close to zero for metals. Only for solids with a conductivity below 5 × 10⁴ S cm⁻¹, significant non‐zero values of the PMI are observed. Again, a volcano‐like curve is observed, where exceptionally high values of the PMI are found for metavalent solids, i.e., in the transition region between metallic and covalent solids. Yet, Figure 3b also offers two other important insights. The highest PMI value displayed is found for Sb₂S₃, a covalent semiconductor where a PMI of 99.9% is found. For this compound, up to 42% of the ions are dislodged as Sb₃S₄ ⁺ ions. This shows that the PMI alone cannot distinguish the different bonding mechanisms, we need both the PME and the PMI to distinguish all three different bonding mechanisms, as demonstrated in Figure 3c. Furthermore, visual inspection of Figure 3 also shows that the electrical conductivity is insufficient to distinguish different types of bond rupture. In the region ≈10² S cm⁻¹, both metavalent and covalent solids are found which differ in PME and PMI. This raises the question of what role electrical conductivity plays in the breaking of the bond, a topic that will be addressed in the following, in particular concerning the “volcano” plot depicted in Figure 3, which will be discussed in more detail in Section S5 (Supporting information). Here we only want to stress one feature. Different samples of GaAs have been studied which differ significantly in electrical conductivity, i.e., vary between 10–8 and 200 S cm⁻¹. Yet, they do not differ in terms of their PME (and PMI) values. This shows that doping does not lead to a change in bond rupture, as expected from chemical intuition. We will return to this context in conjunction with the “volcano” plot for the PME.

1.3. Relating the Bond Rupture to the Field Penetration Depth

So far, we have presented evidence that the bond rupture differs significantly for different types of solids. Yet, no explanation for these differences has been offered. To understand why the materials analyzed by APT respond differently under the applied field, we recall the working principle of atom probe tomography, which is based on field evaporation.^{[ 24 ]} Field evaporation requires an electric field large enough to break the bonds between a surface atom and its neighbor(s) and can thus remove it from the sample surface. On this surface, there is a density of electrons that can respond to the external field. For conductors like metals, these surface charges shield the electric field. In metals, the charge density at the metallic surface is so large that an external electric field can penetrate only a very short distance into the material. This effect is called “field repulsion” or “field screening”.^{[ 65 ]} The situation is quite different for semiconductors since in this case the charge density at the surface is significantly smaller. Hence, the electric field can penetrate over larger distances, i.e., into the solid. One possible explanation for the high PMI values shown in Figure 3 is the field penetration depth. Thomas‐Fermi screening and an approach developed by Tsong have been utilized here to calculate the field penetration depth for a vast variety of materials. This is explained in the supplementary materials, section B, where also shortcomings of the present explanation are discussed.

Figure 4 illustrates the field penetration depth versus the conductivity for various covalent (red), metavalent (green), and metallic (blue) solids. The field penetration depth also has a maximum in the transition region between metallic and covalent bonding. This can be explained by the functional dependence of the screening length/penetration depth on the conductivity (for metals) as well as the dielectric constant and the effective masses (for semiconductors). The screening length/penetration depth is closely related to the probability of forming molecular ions. For metallic samples, molecular ions are hardly ever detected. For these solids, the screening length is much shorter than a typical interatomic spacing of ≈2.5 Å. This screening length is so efficient that molecular ions are not formed upon laser‐assisted field evaporation. For all other solids, including covalent and metavalent solids, the screening length is larger than an interatomic spacing. This is sufficient to create molecular ions, as demonstrated clearly for the two semimetals Sb and Bi. They have a screening length exceeding the interatomic spacing, but only by a factor of ≈2 to 4. Yet, this is sufficient to create a large PMI.

Figure 4.

Field penetration depth versus conductivity for various covalent (red), metavalent (green), and metallic (blue) solids.

Possibly more interesting is the functional dependence of the PME on electrical conductivity and bonding. Again, we observe particularly high values in the transition region between metals and covalent solids, i.e., the region where metavalent solids are located. This is further evidence that the PME is indeed another bond indicator, besides the characteristic property portfolio discussed in Section S3 (Supporting information). Yet, it is remarkable that we find solids in the same range of electrical conductivities of ≈10²–10³ S cm⁻¹, which differ significantly in PME. This can be seen by comparing doped InSb, GaAs, and GaSb with metavalent solids like Sb₂Te₃ or GeTe. While InSb, GaAs, and GaSb have modest PME values below 15%, metavalent solids like Sb₂Te₃ or GeTe have PME values well above 50%. This finding re‐emphasizes two conclusions, different solids that employ different bond types differ in bond rupture and material properties. Yet, the electrical conductivity alone is insufficient to distinguish different types of bonding. In several recent publications, it has been argued that two quantum chemical bonding descriptors can be employed to distinguish different types of bonding, i.e., metallic, covalent, ionic, and metavalent bonding.^{[ 66 ]} These two bonding descriptors are derived from the localization and delocalization indices calculated for solids within the QTAIM (quantum theory of atoms in molecules).^{[ 67 ]} From these quantities, we determine the electron transfer between adjacent atoms and the number of electrons shared between them. The resulting map is shown in Figure 5 . The colors of the different solids characterize the different properties. These different material properties are located in different regions of the map, in line with the argument that there is a close link between these quantum‐chemical bonding descriptors and certain material properties, as discussed in detail in ref. [64]. In Figure 5, a z‐axis has been added which characterizes the PME. Systematic changes of the PME are discernible in the map. This implies that there is indeed a close relationship between bond rupture in atom probe tomography and different types of chemical bonding.

Figure 5.

PME as a function of the bonding mechanism. High PME values are a characteristic of metavalent solids, while metallic and covalent solids possess much smaller PME values. This figure also shows that the two quantum‐chemical bonding descriptors are the best property predictors for the unusual bond rupture that characterizes metavalent solids. Reproduced under terms of the CC‐BY license,^{[ 29 ]} Copyright 2020.

There is another fascinating aspect that can be derived from comparing Figures 3 and 5. The unique bond rupture that characterizes metavalent solids is located in a well‐defined range between ≈5 × 10² S cm⁻¹ and 5 × 10⁴ S cm⁻¹. This is the range of (room temperature) conductivities, where a transition between metals and insulators occurs in most solids. It is also the conductivity range, where Mooij has found a change in the sign of the temperature coefficient of the electrical conductivity in many metals.^{[ 68 ]} Please note that we now use the term metals and insulators to describe the 0K limit of the electrical conductivity and not the type of chemical bonding. Doped semiconductors, for example, can turn metallic in terms of the electrical conductivity if doped sufficiently high to become degenerate semiconductors, but do not change their bonding type, i.e., change their atomic arrangement. This metal‐to‐insulator transition (MIT) upon doping has been well‐studied for many semiconductors such as Si and GaAs.^{[ 69 ]} Our data show that for GaAs this transition is not accompanied by a significant change of the PME, while this happens for metavalent solids. In particular, we have investigated three samples of GaAs, which differ by almost 10 orders of magnitude in electrical conductivity due to very different levels of doping, ranging from 10⁻⁷ S cm⁻¹ to 5 × 10² S cm⁻¹. These samples do not differ at all in terms of bond rupture (identically low PME value, and identical moderately low PMI value). Hence, in GaAs, the MIT caused by doping is not accompanied by a change of bond rupture. In metavalent solids, instead, an MIT is realized which differs significantly from electronic MITs attributed to either the Mott‐type (correlation)^{[ 70 ]} or the Anderson‐type (disorder)^{[ 71 ]} MIT in doped semiconductors. This is another interesting research opportunity for atom probe tomography to clarify, which MITs are accompanied by changes of bond rupture.

2. Utilizing the Bond Rupture as a Local Probe of Chemical Bonding

So far, a close relationship between different types of bonding and the bond rupture in atom probe tomography has been established. One can now contemplate, how this characteristic of APT can be utilized to understand and tailor functional materials. At present, there is only a limited number of examples that demonstrate how APT can be employed to tailor functional materials based on an in‐depth understanding of bond rupture. This can be partly attributed to the novelty of the conclusions presented above. Yet, it seems easy to sketch the promise this approach offers. One key advantage of atom probe tomography is the high spatial resolution since APT offers high, i.e., atomic resolution in three dimensions. One can now ponder which spatial resolution can be reached to locally determine the bond rupture and hence type of bonding employed. A determination of the PME and PMI requires reasonable statistics. Hence, ideally, 1000 successful laser pulses should be analyzed to determine those two quantities. With a detection rate of 50%, this corresponds to 2000 laser pulses and corresponds to a cube of 40 Å × 40 Å × 40 Å. This would indeed be very interesting for various material design approaches.

In phase change materials, for example, a pronounced change of bonding upon crystallization has been identified by atom probe tomography. This is depicted in Figure 6 (left), where the change of the bonding descriptors determined by APT, i.e., the PMI and PME values are displayed for a number of crystalline and amorphous (glassy) solids. As can be seen from this figure, for solids like Si, Ge, and GeSe, crystallization does not lead to a significant change in bond rupture. On the contrary, for a number of chalcogenides like Ge₂Sb₂Te₅, GeSe_0.25Te_0.75, and GeSe_0.5Te_0.5 a very different behavior is found. Here, crystallization leads to a pronounced change of bond rupture, in particular a very significant change in PME. While the crystalline phases have a very high PME, their amorphous counterparts have a much lower PME. This provides clear evidence for a change of bonding upon crystallization. Indeed, amorphous phase change materials typically are characterized by larger band gaps, a different atomic arrangement, characterized by a larger Peierls distortion, a smaller chemical bond polarizability (Born effective charge Z*), and a smaller maximum of the imaginary part of the dielectric function ε₂(ω) (i.e., weaker optical absorption). All of these changes are consistent with a change of bonding from covalent bonding (in the amorphous state) to metavalent bonding (in the crystalline phase). Hence atom probe tomography and the change of material properties provide a coherent view.

Figure 6.

a) Changes of bonding upon crystallization (arrows). Crystals are characterized by diamonds, glasses by circles. Bonding is characterized by two parameters (PMI and PME). Figure taken from ref. [62]. b) 2D map classifying chemical bonding in crystals and glasses. The map is spanned by the number of electrons shared (left y‐axis) between adjacent atoms and the electron transfer renormalized by the formal oxidation state (x‐axis). Different colors characterize different material properties and have been related to different types of bonds. The glasses of three solids are characterized by a bonding mechanism that closely resembles the crystal (GeSe₂, SiO_2, and GeSe). On the contrary, for GeTe, Sb₂Te₃, and GeSb₂Te₄, pronounced changes in bonding occur upon crystallization. While crystalline GeTe, Sb₂Te₃, and GeSb₂Te₄ employ metavalent bonding, their glasses are covalently bonded. Metavalent crystals show characteristic features of quantum materials, i.e., they show a pronounced change of properties upon external stimuli like pressure or temperature. These materials change their bonding mechanism upon vitrification, while this is not the case for any other bonding mechanism in solids. Figure 6b Reproduced under terms of the CC BY‐NC‐ND license,^{[ 62 ]} Copyright 2024.

Figure 6b shows another facet of the striking change of bonding upon crystallization, a map that shows the two chemical bonding descriptors ES and ET for a variety of crystalline and amorphous solids. This figure reveals that only crystalline solids in the green region, which we have coined metavalent solids, show a striking difference between the crystalline phase (hexagon) and amorphous state (circle). Ordinary glass formers (Zachariasen glasses) on the contrary employ the same bonding mechanism in the glassy and the crystalline state, as already suspected more than 90 years ago by W. Zachariasen.^{[ 72 ]} A change in bond rupture upon crystallization can hence be utilized as another identifier of phase change materials, which are accompanied by a pronounced change of properties upon crystallization. Yet, there are other methods that might be faster and less demanding to identify novel phase change materials. Nevertheless, one should ponder if a crystalline material that is characterized by a high PME could potentially behave very differently in terms of bond rupture in its amorphous phase. Hence, a high PME for a certain crystalline phase might point toward an interesting glassy state upon the vitrification of such a crystal. It seems rewarding to validate or falsify this hypothesis.

Even more attractive is the idea of employing APT to locally study crystallization. In recent years, significant differences in the crystallization speed of phase change materials have been attributed to clear changes of bonding within the map shown in Figure 6b. In particular, it has been shown that crystallization in the green region of the map is fastest for compounds with the smallest possible Peierls distortion, i.e., close to the dashed green line in Figure 6b.^{[ 73 ]} Subsequently, the high crystallization speed has been separated into two contributions, nucleation and growth. The fast crystallization speed close to the dashed green line has been attributed to a very high nucleation rate, which showed a pronounced stoichiometry dependence. A much weaker stoichiometry dependence was observed for the growth rate.^{[ 74 ]}

Now, it would be highly attractive to study the initial nucleation stage with atom probe tomography. As mentioned above, a region of less than 4 nm in diameter should be sufficient to determine the PME locally. This is also the expected diameter of a critical nucleus, i.e., the precondition to form a crystalline phase. Hence, APT could be employed to study the initial stage of crystallization and could even be utilized to characterize actual devices. The combination of bonding and stoichiometry information is particularly attractive since it seems plausible that the crystalline nucleus might even differ in stoichiometry from the surrounding amorphous matrix. APT should be able to confirm or refute such a hypothesis.

In recent years, atom probe tomography has also been employed frequently to help understand and design thermoelectrics. The unique property portfolio of MVB solids is conducive to high thermoelectric performance.^{[ 29} , ^{75 ]} By utilizing APT, different chemical bonding mechanisms at different microstructures of a compound can be discerned. This has enabled the design of high‐performance GeSe^{[ 76} , ^{77 ]} and SnSe‐based^{[ 78 ]} thermoelectrics by transforming the chemical bonding mechanism from covalent to metavalent, as directly proven by the distinctive PME values. Very recently, the power of probing local chemical bonds of APT has provided valuable insights into the role of grain boundaries^{[ 79} , ^{80 ]} and phase boundaries^{[ 81 ]} in tailoring thermoelectric properties. APT has become a very useful tool to facilitate the development of thermoelectric materials not only because of its high spatial and chemical resolution but also owing to its unique capability of probing chemical bonds of defects locally.^{[ 82} , ^{83 ]}

Another exciting area is transitions between the metallic and the insulating state^{[ 71} , ⁸⁴ , ^{85 ]} As shown in Figure 3 and Figure 5, a striking change of bond rupture is identified upon the transition between metallic and non‐metallic states. So far, we have only found metavalent solids with conductivities between 5 × 10²–5 × 10⁴ S cm⁻¹ to have particularly high PME values. Ordinary doped semiconductors with electrical conductivities in the same range, such as doped GaAs or InSb instead were characterized by very low PME values. This indicates that the conductivity range that characterizes the transition between metallic and covalent bonding is a necessary but not sufficient condition to lead to high PME values. An unusual bonding mechanism in the transition regime between metallic and covalent bonding, i.e., between delocalized and localized bonding seems to be the second necessary condition for high PME values. Understanding the transition between a metallic and an insulating state (metal‐insulator transition) and the underlying electronic mechanism is one of the grand challenges of solid‐state physics. Now, it seems as if atom probe tomography can help us to understand potential pathways between these two states. Metavalent bonding apparently lies on one of these pathways. Nevertheless, it seems plausible, or even likely that other pathways should exist as well. This hypothesis makes studies of other classes of materials at the border between localized and delocalized bonds interesting for atom probe characterization, too. This is intriguing since one can ponder how the transition from the metallic to the insulating state will be reflected in these classes of materials if characterized by atom probe measurements.

3. Conclusion

In this review, the potential of atom probe tomography to locally probe chemical bonds is presented and discussed. Two processes are shown to characterize the bond rupture in laser‐assisted field emission. These are the probability of molecular ions (PMI), i.e., the probability that molecular ions are evaporated instead of single (atomic) ions, and the probability of multiple events (PME), i.e., the correlated field‐evaporation of more than a single fragment upon laser‐ or voltage pulse excitation. Here we demonstrate that one can clearly distinguish solids with metallic, covalent, and metavalent bonds based on their bond rupture, i.e., their PME and PMI values. These differences are largely attributed to differences in the field penetration depth. These findings open new avenues in understanding and designing advanced materials since they allow the quantification of bonds in solids on a nanometer scale. In this review, various examples of bonding quantification down to the nanoscale are described. These examples even seem to justify calling the present approach bonding probe tomography (BPT). Yet, it seems much more important to use APT to locally characterize chemical bonding than to introduce a novel acronym. Hence, we hope that the present review will motivate more scientists and engineers to employ the power of the technique to design and better understand functional materials from a local chemical bonding perspective.

4. Experimental Section

Crystal Preparation

Most crystalline samples were synthesized from the elements in a vacuum‐sealed quartz ampoule. The amorphous samples were deposited on Si substrates by sputtering employing an alloy target of 99.99% purity. Annealing these amorphous specimens enabled the preparation of crystalline samples, too. The stoichiometry of the resulting samples was obtained from energy dispersive spectroscopy (EDS).

Experimental Investigations

APT analyses were conducted using a CAMECA LEAP‐5000 XS (local electrode atom probe). For APT measurements, the specimen was maintained at 50 K, and laser pulses (wavelength 355 nm) of 5–25 pJ energy were used for field evaporation. A detection rate of 1 ion per 500 pulses was chosen to obtain a 250 kHz pulse repetition rate. Moreover, the APT needle‐shaped samples were prepared by standard lift‐out procedure, using a dual‐beam focus ion beam (FEI Helios Nanolab 650). It is noted that the APT needle‐shaped samples were fabricated using very gentle milling conditions such as 16 kV and 50–23 pA. Moreover, a low‐kV cleaning (2 kV cleaning) procedure was applied to reduce the thickness of the amorphized layer from the tip apex down to below 5 nm as explained in ref. [86]. This very careful sample preparation procedure led to no Ga detection in the mass spectrum neither at the beginning nor during the APT experiments. Therefore, no Ga‐induced modifications of the PMI or PME were expected.

Both the LEAP 4000X Si and the LEAP 5000 XS employ a laser with a wavelength of 355 nm. In both APT systems, very similar results were obtained, proving that the high PME was not a system or parameter‐dependent property, but rather a material‐dependent property. No APT investigations with deep UV or IR laser had been performed yet. However, we have studied in a separate set‐up how materials respond to solids upon fs‐laser excitation. In these experiments, it was observed, in line with other studies,^{[ 87 ]} that in 0.1 ps the photo‐excited electrons relax to the bottom of the conduction band, independent of the laser wavelength (as long as the laser wavelength exceeds the band gap, which was fulfilled for the materials studied here). Hence, no dependence on the laser wavelength was expected for the solids studies here.

Theoretical Investigations

The first principle calculations were based on the Vienna Ab initio Simulation Package (VASP).^{[ 88 ]} The interaction between ions and valence electrons was described by Projected Augmented Wave (PAW),^{[ 89 ]} and the exchange‐correlation interaction was described by the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE‐GGA).^{[ 90} , ^{91 ]} The cut‐off energy was set as 400 eV, and the convergence criteria for self‐consistent electronic energy and residual force were respectively assumed to be 10⁻⁶ eV atom⁻¹ and 0.01 eV Å⁻¹. The k‐points were set up 4 × 4 × 4 based on Monkhorst‐Pack grids. The VASPKIT was employed to generate the Brillouin zone pathway and extract the band gap and effective mass of all structures.^{[ 92 ]}

The static dielectric constants have been computed using Density Functional Perturbation Theory including local field effects.^{[ 93 ]}

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

O.C.M. and M.W. have designed and developed this study. Y.Y., J.K., T.G., C.‐F.S., S.H. and C.Z. have obtained the experimental and theoretical data presented here. O.C.M. and M.W. wrote the present publication with input from all co‐authors.

Supporting information

Supporting Information

Biographies

Oana Cojocaru‐Mirédin received her Ph.D. degree in physics in 2009 from the University of Rouen, France, within the “Group Physique des Matériaux”. Afterward, she worked as a postdoc till 2012 at Max‐Planck‐Institut für Eisenforschung GmbH in Düsseldorf, Germany. By winning the “NanoMatFutur” competition organized by Federal Ministry for Education and Research in Germany, she became in 2013 the head of “Interface design in solar cells” group. In 2015, she moved to RWTH Aachen University within the I. Institute of Physics where she lead the “Nanocharacterization of Advanced Functional Materials” group. Since 2022, she is a professor for “Cross‐scale Material Characterization” at INATECH, University of Freiburg. Her research interests include the characterization and processing of compound semiconductors for energy applications using correlative microscopy, i.e. a combination of the atom probe tomography with other microscopy techniques. Dr. Cojocaru‐Mirédin has more than 100 ISI‐recorded articles and contributions to more than 60 conferences.

Yuan Yu is a group leader at the I. Physikalisches Institut of RWTH Aachen University. He completed his Bachelor's and Ph.D. degrees in Materials Science and Engineering at Hefei University of Technology in 2012 and 2017, respectively. Afterward, he joined RWTH Aachen in 2018 as a postdoctoral researcher under Prof. Matthias Wuttig. Since 2022, Dr. Yu has been leading a research group as a principal investigator. His research primarily focuses on the innovative design of thermoelectric and phase‐change memory materials utilizing metavalent bonding and its interplay with microstructures. He has published more than 90 peer‐reviewed papers in prestigious journals such as Science, Nature Materials, and Advanced Materials. He is recognized for his expertise in using advanced tools like atom probe tomography and correlative microscopy to study material properties at the atomic level.

Jan Köttgen received his Bachelor's and Master's degrees in Materials Science from RWTH Aachen University, Germany. He is currently pursuing his Ph.D. in Physics at the I. Institute of Physics (IA) at RWTH Aachen University. His research focuses on atom probe tomography (APT) of chalcogenides and integrates correlative microscopy by combining electron microscopy techniques with APT.

Carl‐Friedrich Schön received his Ph.D. in physics at the RWTH Aachen University, Germany. He is currently working at the I. Institute of Physics (IA), RWTH Aachen University and has spent semesters at the University of Tokyo (東京大学), Japan and the Nanyang Technological University (NTU) in Singapore. His research interests are Density Functional Theory (DFT), Quantum Theory of Atoms in Molecules (QTAIM) and Machine Learning (ML).

Shuai Han is currently pursuing a doctoral degree in the School of Materials Science and Engineering at Northwestern Polytechnical University in China. He primarily concentrates on the first principles calculation of semiconductor materials and machine learning potential function molecular dynamics studies.

Chongjian Zhou, professor in the State Key Laboratory of Solidification Processing & Key Laboratory of Radiation Detection Materials and Devices, MIIT, School of Materials Science and Engineering, Northwestern Polytechnical University. He received his Ph.D. degree from the School of Materials Science and Engineering, Xi'an Jiaotong University, in 2016, and worked as a postdoc at Seoul National University in 2017–2021. He focuses on designing functional solid‐state materials with extreme thermal properties.

Min Zhu, Professor of the Shanghai Institute of Microsystems and Information Technology (SIMIT). He received his B.S. degree from Hubei University in 2009 and Ph.D. degree from the SIMIT in 2014. Then he worked in SIMIT for one year as an assistant professor. From September 2015 to November 2017, he was a Humboldt Scholar at RWTH Aachen University in Germany. He rejoined the SIMIT as an associate professor since December 2017, and he became a Professor after January 2021. Min Zhu focuses on ovonic threshold switch and phase change memory. As the first author or corresponding author, he has published 33 papers SCI journals, including Science, Nature Communications (5 papers) and Advanced Materials (2 papers) etc.

Matthias Wuttig studied physics at the Universität zu Köln, Germany and received a doctorate in solid state physics in 1988 from RWTH Aachen / Forschungszentrum Jülich. After postdocs at Lawrence Berkeley Laboratory and Bell Labs (Murray Hill, USA) and several years as a staff scientist at Forschungszentrum Jülich, he was appointed as full professor at RWTH Aachen in 1997. He served as Dean of the Faculty of Mathematics, Informatics and the Natural Sciences as well as Speaker of the Strategy Board at RWTH Aachen. At present, the design of advanced functional materials is the focus of his research agenda. This goal is reached by combining concepts of quantum chemistry (‚quantum‐chemical bonding descriptors) with concepts of solid‐state physics and material science. He has published 450 papers with ≈32.000 citations (ISI Web of Science). From 2011 until 2023 he was spokesperson of the Collaborative Research Center 917.

Cojocaru‐Mirédin O., Yu Y., Köttgen J., Ghosh T., Schön C.‐F., Han S., Zhou C., Zhu M., Wuttig M., Atom Probe Tomography: a Local Probe for Chemical Bonds in Solids. Adv. Mater. 2024, 36, 2403046. 10.1002/adma.202403046