Bombarding solid surfaces by energetic particles leads to a variety of phenomena that are closely correlated with the energy deposition processes of the incoming ions [1, 2]. At the surface, ion irradiation may result in substantial morphological changes [3], resulting in a coarsening of the surface. Eventually, prolonged ion irradiation often leads to the development of a very specific surface topography. Interestingly, these structures can exhibit highly periodic features such as ‘nanodots’ [4, 5] or ‘ripple’-like contours [6, 7], with feature sizes in the nanometer range. These self-organized nanostructures evolving due to ion bombardment on surfaces have been studied quite thoroughly in the past decade [8–14]. Generally, the formation of these structures is assumed to be related to (and caused by) the interplay between ion erosion (which roughens the surface) and transport processes which induce a smoothing [9, 10, 12]; the latter could be effected by (beam-enhanced) surface diffusion [15, 16] or viscous flow [17, 18] within the ion penetration layer.

Theoretically, a substantial degree of understanding of ripple formation is due to the pioneering model proposed by Bradley and Harper (BH) [

19] that considers the surface evolution in terms of such a dynamic balance between roughening and smoothing processes. The concept of BH combines the effects of sputtering and surface diffusion and is based on the sputtering theory of Sigmund [

20,

21]. The latter relates the rate of atom removal to the energy deposited by the incident ion in the near-surface region in a sequence of collisions. BH extended that approach and emphasized that the sputtering yield is proportional to the curvature of the surface; eventually, this may lead to a roughening. This process could be counteracted by surface relaxation processes. Combining these competitive mechanisms, BH derived an equation for the surface height

*h*(

*x*,

*y*,

*t*) [

9,

19]:

$\frac{\partial h}{\partial t}=-{v}_{0}+\frac{\partial {v}_{0}}{\partial \theta}\frac{\partial h}{\partial x}+{\nu}_{x}\frac{{\partial}^{2}h}{\partial {x}^{2}}+{\nu}_{y}\frac{{\partial}^{2}h}{\partial {y}^{2}}-K{\nabla}^{4}h$

(1)

Here, *v*_{0} is the average erosion velocity of the surface which depends on the incidence angle of the ion beam *θ*, the ion flux, and the sputtering yield. ν_{
x
} and ν_{
y
} are functions of the ion beam parameters [9] and relate the sputtering yield at any point on the surface to the local curvature. The last term in Equation 1 represents surface diffusion of mobile species and is proportional to the second derivative of the curvature [22, 23]. The parameter *K* depends on the surface energy, the diffusivity of mobile surface defects, and their average concentration. Such a diffusive process might also be triggered or enhanced by ion bombardment [8]. A similar functional form of smoothing can arise from ion-induced viscous flow in a thin surface layer [24, 25]. Several extensions and modifications of the BH model were later envisaged [12, 13, 26].

Solutions of Equation

1 would predict that each Fourier component of the surface height will grow exponentially with a rate that depends on the wavevector, and a maximum growth rate might be reached. The corresponding modulation will outgrow the others and lead to ripples with a characteristic wavelength

*λ*^{*}:

${\lambda}^{*}=2\pi \phantom{\rule{0.12em}{0ex}}\sqrt{2K/{\nu}_{\text{max}}}$

(2)

where ν_{max} is the maximum of the two values ν_{
x
} and ν_{
y
} in Equation 1. The magnitude of the latter determines the orientation of the ripple pattern with respect to the ion beam direction [19].

For binary (or, more generally, multicomponent) specimens, the situation might be complicated by the potential presence of the preferential sputtering of one of the components [1, 2]. This process will tend to modify the composition in a surface layer with a thickness of a few atomic layers for the low energies considered here. Relevant for the present context is the theoretical demonstration [27] that, apart from the formation of specific nanostructures (ripple or dots), compositional gradients may exist within individual of these features: for example, in ripple structures, one component will be enriched in the crests while being depleted in the valleys, and vice versa for the other component. Further theoretical approaches [28–31] confirmed and refined this possibility.

In a binary system A-B,

*Y*_{A} and

*Y*_{B} may denote the sputtering yields of species A and B (sputtered atoms per incoming ion). (

*Y*_{A} and

*Y*_{B} are not necessarily equal to the yields of the respective pure samples A or B.) If

*Y*_{A} ≠

*Y*_{B}, preferential sputtering will lead to steady-state

*surface* concentrations

*c*_{s} which deviate from the bulk concentrations

*c*_{b} while the fluxes of emitted species should be proportional to their bulk composition for steady-state conditions [

2]. As a consequence, a layer of altered composition

*c*_{s} is formed near the surface. Its thickness Δ will amount to a few atomic layers for the low impact energies employed in this work. For planar specimens, such ion-induced surface modifications have been studied quite extensively in the past for a large variety of (binary) systems [

1,

2]. Typically, this surface layer is found to be enriched (depleted) in the species that has the lower (higher) sputtering yield. However, segregation (diffusion) processes may lead to rather abrupt concentration gradients at the surface, that is,

*c*_{s} might not be constant over the depth Δ. In the presence of nanostructures, a height variation

*h*(

*x*,

*y*,

*t*) could be associated with a perturbation in composition,

*ζ*(

*x*,

*y*,

*t*) [

27], where

*ζ* =

*c*_{s} −

*c*_{b}. Therefore, the ion-induced enrichment (depletion) might be site specific (e.g., different for crests or valleys in ripples) leading, eventually, to a modulation in composition that can be in or out of phase with the (ripple) topography. The evolution equations, to linear order in the perturbations, were shown to take the form [

27]

$\frac{\partial \zeta}{\partial t}=A{\nabla}^{4}H+B{\nabla}^{2}\zeta -\mathit{C\zeta}$

(3)

$\frac{\partial H}{\partial t}=-A\text{'}{\nabla}^{4}H+B\text{'}{\nabla}^{2}\zeta +C\text{'}\zeta +D\text{'}{\nu}_{h}$

(4)

where *H* = *h*/Δ and ν_{
h
} gives the slope and curvature dependence of the sputtering yield [19]. The coefficients of the terms on the right-hand sides of Equations 3 and 4 are specified in [27]. A key feature of this theoretical concept is the coupling between the height and composition modulations. An experimental examination of such correlated compositional modulations within individual nanostructures (ripples or dots) formed by ion bombardment would be required to verify that approach and to elucidate the pertinent processes. Because of the small dimensions, such an investigation is quite challenging and available data are rather limited.

In order to study such possible compositional variations in individual nanodots caused by ion bombardment, atom probe tomography (APT) has been used in this work. APT is a very unique analytical tool for the elemental characterization of solid materials on nanometer spatial scales [32, 33]. In APT, ions are released via field evaporation from a tip with a very small radius of curvature (*R* less than approximately 50 nm) in the presence of a high electric field (approximately 30 to 50 V/nm). The removal of material from the tip releases atoms from continuously deeper layers of the specimen. A reconstruction of the complete data set provides ideally the original 3-dimensional distribution of the atoms in the analyzed sample volume. (A typical size would be 50 × 50 × 200 nm^{3}). Several experiments have demonstrated that in APT analyses sub-nanometer spatial resolution can be achieved [32, 33]. In fact, different types of nano-sized structures have been successfully analyzed by APT [34–36].

The objective of the present work was hence twofold: (i) to examine the formation and evolution of nanodots on InP surfaces under Ar^{+} ion bombardment and determine specific feature sizes (height, radius, and wavelength) as a function of irradiation parameters (ion fluence and ion flux) and (ii) to employ APT for a compositional analysis of *individual* nanodots with nanometer spatial resolution. This appears to constitute a completely novel approach of nanodot characterization.