BALET

Most modern III-V heterostructure devices require a high level of control over the quality of their interface structures due to their large impact on many physical properties like, for example, the electron mobility in quantum wells or the tunneling behavior of sophisticated heterostructures like quantum cascade lasers. Therefore, a comprehensive interface characterization is necessary to allow the development of novel III-V compound semiconductor devices. In general, heterostructure interfaces are characterized by two fundamental properties: the physical roughness and the chemical intermixing. These properties are typically described by the root mean square (RMS) value of the interface roughness and the lateral and vertical correlation lengths as well as the chemical width of the interface.

Unfortunately, experimental tools to measure these quantities in the case of buried interfaces are fairly limited. X-ray scattering methods are able to deliver detailed information about surfaces and interfaces on large scales, and, complementary, spatially resolved methods like scanning probe microscopy are used to observe local variations providing, however, two-dimension- al (2D) images. Conventional transmission electron microscopy (TEM) in combination with the site-specific focused ion-beam (FIB) sample preparation allows to investigate interfaces in cross-sectional samples down to the atomic level. TEM micrographs are projections of samples with a thickness of up to several nanometers that make it typically difficult to distinguish between the physical roughness and the chemical width without further information.

In this contribution, a novel method is proposed to obtain a comprehensive, quantitative three-dimensional (3D) analysis of III-V heterostructure interfaces. This method is based on electron tomography using the chemical sensitive high-angle annular dark- field (HAADF) imaging mode in scanning transmission electron microscopy (STEM). The complete 3D interface characterization was performed on an (Al,Ga)As/GaAs multi-heterostructure. Figure 1(a) shows a HAADF STEM micrograph of a FIB lamella giving an overview of this sample. The structure is a multi-layered (Al,Ga)As sample with pure GaAs barriers (bright contrast) between each (Al,Ga)As layer (dark contrast). The composition x of the consecutive Al_xGa_1-xAs layers is 25 %, 50 %, 75 %, 80 %, 85 %, 90 %, 95 % and 100 %, respectively [layers marked by red arrows in

Fig. 1(a)]. An atomically resolved HAADF STEM micrograph of one interface is depicted in Fig. 1(b) identifiying each column position of Ga, mixed Al/Ga and As atoms. The corresponding intensity profile is shown in Fig. 1(c) indicating a broad transition between (Al,Ga)As and GaAs, i.e. the intensity gradient extends over the entire length of the micrograph. Due to the signal averaging along the projection direction of conventional TEM micrographs it is not possible to make a robust statement about the origin of this broad transition. For the following tomography measurement, a needle-shaped specimen was fabricated from a lamella using a specialized FIB preparation technique. A series of HAADF STEM images of the needle was recorded

with 2° tilt steps between each micrograph using an aberration-corrected JEOL ARM- 200F microscope in combination with a double-tilt tomography holder. An iterative reconstruction algorithm was applied to obtain the 3D reconstruction of the tomography needle. Figure 2 summarizes the results of the tomography measurement including the procedure of creating topographic maps of buried interfaces. A 3D representation of the reconstructed tomogram is depicted in Fig. 2(a) revealing the complete multi-layered structure. The reconstructed voxel intensities are reflecting the local material density because the HAADF image intensity is primarily dependent on the thickness t and mean atomic number Z (IHAADF = t⋅Zα, with α between 1 and 2, so-called Z-contrast). Therefore, the thin slice cut out from the center of the 3D tomogram, cf. Fig. 2(b), emphasizes the internal structure visualizing the different material components.

The voxel intensity profile in Fig. 2(c), Fig. 1(a)]. An atomically resolved HAADF STEM micrograph of one interface is depicted in Fig. 1(b) identifiying each column position of Ga, mixed Al/Ga and As atoms. The corresponding intensity profile is shown in Fig. 1(c) indicating a broad transition between (Al,Ga)As and GaAs, i.e. the intensity gradient extends over the entire length of the micrograph. Due to the signal averaging along the projection direction of conventional TEM micrographs it is not possible to make a robust statement about the origin of this broad transition. For the following tomography measurement, a needle-shaped specimen was fabricated from a lamella using a specialized FIB preparation technique. A series of HAADF STEM images of the needle was recorded

pixel of this array is thereby reproducing the average height of the mesh points above the pixel. In this way, a topographic map of the interface is generated. This procedure – called rasterization – is schematically illustrated in Fig. 2(f) and the final topographic map of interface C is exemplary given in Fig. 2(g). A background intensity, which is shown as inset, was subtracted to counter- act tilts of the surfaces with regard to the projection plane avoiding systematic errors during the analysis. Figure 3(a) represents the results of the topographic mapping of the top four interfaces between AlAs and GaAs (labeled A, B) as well as between Al_0.95Ga_0.05As and GaAs [labeled C, D, see also Fig. 2(b)] visualizing the spatial distribution of the physical roughness. Strong differences in the magnitude of the physical roughnesses are visible between normal (Al,Ga)As-on-GaAs and inverted GaAs-on-(Al,Ga)As interfaces, cf. line profile of interface A and B shown in Fig. 3(b).

Smooth interface structures with height variations in the order of a few Ångstrom are detected for the normal interfaces, whereas the height variations of inverted interfaces are more than an order of magnitude higher. For more precise quantification of the roughness the RMS value σRMS is calculated as follows: N is the number of pixels, zn the height value of the n-th pixel and the average height. RMS values have been determined for each interface over the whole (120 nm x 120 nm) area of the topographic maps with the result of 1.02 nm and 0.96 nm for the inverted and 0.15 nm and 0.12 nm for the normal interfaces, respectively. In agreement with the topographic maps, the RMS values are

significantly higher for the inverted compared to the normal interfaces. On the oth- er hand, the RMS value is not sufficiently meaningful to describe the characteristic lateral length scale defining the average spacings between interfacial steps. The height-height correlation function (HHCF) is used to extract this characteristic length by evaluating the in-plane correlation length. The one-dimensional HHCF for discrete pixels is defined as: where m = τ/Δx , Δx is the discrete sampling interval (pixel distance), M and N are the number of pixels in x-direction and the perpendicular direction, respectively. The HHCF can be phenomenologically described by:

where σx is the one-dimensional RMS value, Λx the correlation length and hx the Hurst parameter. The HHCF function is plotted for the interfaces C and D along the two crystallographic directions [110] and [110] in Fig. 3 (c) and (d), respectively. After fitting the curve according to equation (3), the fit parameters reveal a lateral correlation length of 14 nm for interface C along both, the [110] and [110] direction, and 3.6 nm and 5.8 nm for interface D along the [110] and [110] direction, respectively. The results show that the one-dimensional roughness values σx obtained by the HHCF fit agree with the previously determined RMS value σRMS. It can also be deduced from the results that measurements of the interface width by conventional TEM will give accurate values if the sample thickness is in the same range or smaller than the in-plane correlation length. In the case of the inverted interface B this would require a sample thickness below 14 nm.

In a final step, electron tomography was used to determine the chemical intermix- ing at each interface position in order to obtain a comprehensive picture of the 3D structural interface property. As schematically shown in Fig. 4(a), any III-V interface has a gradient in composition and hence several iso-concentration surfaces at different voxel intensities can be created. Accordingly, the height difference of isosurfaces of the same interface corresponding to different concentration values are used to evaluate changes in the interface width. Here, isosurfaces corresponding to 30 % and 70 % of the total compositional difference were generated and then rasterized as shown schematically in Fig. 4(b). Subsequently, the topographic height maps of the 30 %-isosurfaces were subtracted from the height maps of the 70 %-isosurfaces. As a result, height-difference-maps are obtained which spatially measure the interface distance L30 %–70 %. On the other hand, the interface width W is typically defined in the literature by the distance at which the concentration changes from 10 % to 90 % of the total difference.

These specific isosurfaces were not created due to the larger influence of noise on isosurfaces corresponding to these compositions. Instead, a sigmoidal profile of the concentration change across the interface was assumed so that the width L30 %–70 % can be extrapolated to the interface width W by using the factor 2.6. The spatially resolved interface width maps of interface A, B, C and D are depicted in Fig. 4(c) showing a random distribution of the spatial change of the interface width. The maps reveal higher average interface widths W for the inverted interfaces A and C (i.e. 6.60 nm and 3.06 nm) compared to the normal interfaces (i.e. 2.44 nm and 2.48 nm). The magnitude of the variations measured by the standard deviation of the width within the full area of the maps is significantly larger for the inverted (1.3 nm and 0.91 nm) compared to the normal interfaces (0.42 nm and 0.44 nm). These results also emphasize very clearly the strength of the electron tomography interface characterization in comparison to conventional TEM, in particular for interfaces with large variations in the physical and/or chemical width.

In summary, it was demonstrated that a comprehensive determination of interface properties can be achieved by using electron tomography. For this purpose, a method was developed to extract topographic height maps and interface width maps out of the reconstruction of a III-V heterostructure specimen. This methods allows the quantitative 3D characterization of interfaces. The strength of this method is that all important interface characteristics can be extracted at once. In addition, the analysis is site-specific due to the

FIB preparation technique and therefore allows the investigation on specific regions of a sample. Anisotropic features can be revealed due to the spatially resolved maps and the difficulties caused by the signal averaging in conventional TEM can be circumvented. This work was partially supported by the European Union and the State of Berlin within the frame of the European Regional Development Fund (ERDF) project "Applikationslabor Elektronentomographie", project number 2016011843.