Van-Tho Nguyen

Thiéry Constant

Bertrand Kerautret

Isabelle Debled-Rennesson

Francis Colin

A Machine-Learning Approach for Classifying Defects on Tree Trunks using Terrestrial LiDAR

Keywords: roundwood quality, random forests, standing tree grading

Three-dimensional data are increasingly prevalent in forestry thanks to terrestrial LiDAR. This work assesses the feasibility for an automated recognition of the type of local defects present on the bark surface. These singularities are frequently external markers of inner defects affecting wood quality, and their type, size, and frequency are major components of grading rules. The proposed approach assigns previously detected abnormalities in the bark roughness to one of the defect types: branches, branch scars, epicormic shoots, burls, and smaller defects. Our machine learning approach is based on random forests using potential defects shape descriptors, including Hu invariant moments, dimensions, and species. The results of our experiments involving different French commercial species, oak, beech, fir, and pine showed that most defects were well classified with an average F 1 score of 0.86.

Introduction

Grading standing trees and roundwoods is a critical task in a wood supply chain before harvesting or processing in the wood industry [START_REF] Fonseca | The measurement of roundwood: methodologies and conversion ratios[END_REF].

This question is especially concerned by the general trend towards digitization for forest wood-chain traceability, supply chain optimization, and transformation [START_REF] Pickens | Choosing Prices to Optimally Buck Hardwood Logs with Multiple Log-Length Demand Restrictions[END_REF][START_REF] Lin | An integrated 3D log processing optimization system for hardwood sawmills in central Appalachia[END_REF][START_REF] Gardiner | Creating the wood supply of the future[END_REF][START_REF] Müller | Digitization in wood supply -A review on how Industry 4.0 will change the forest value chain[END_REF]. After the overall shape characterization defining material yield, and wood quality information coming from the cross-sectional ends in the case of roundwood, wood quality is mainly assessed from singularities of the bark surface. The occurrence of such singularities indicates local variations of the material properties generally corresponding to decreased normal distribution of the clearwood properties and characteristics, which detrimentally impact future products and their mechanical, physical or aesthetical functions. Nevertheless, the resulting grade made by an expert corresponds to a global assessment of the quality by taking many criteria into account through grading rules. After the attribution of the grade, the original causes are often forgotten.

Alternatives using X-ray computed tomography (CT) can be considered as reference methods for such a characterization [START_REF] Li | Automated analysis of CT images for the inspection of hardwood logs[END_REF][START_REF] Zhu | A prototype vision system for analyzing CT imagery of hardwood logs[END_REF][START_REF] Aguilera | Detection of knots using X-ray tomographies and deformable contours with simulated annealing[END_REF]Colin et al., 2010b). On the one hand, CT can achieve good accuracy for defect recognition (up to 95%; [START_REF] Li | Automated analysis of CT images for the inspection of hardwood logs[END_REF]), detect the defects as small as 1 millimeter in diameter by manually placing plot markers along the tracks of knot (Colin et al., 2010b), or automatically detect knots [START_REF] Longuetaud | Automatic knot detection and measurements from X-ray CT images of wood: A review and validation of an improved algorithm on softwood samples[END_REF][START_REF] Krähenbühl | Knot detection in X-ray CT images of wood[END_REF][START_REF] Krähenbühl | Robust knot segmentation by knot pith tracking in 3d tangential images[END_REF]. Industrial solutions are proposed by several companies (Microtec, 2019;[START_REF] Elektronik | JORO-X: X-ray scanner -Detection of internal wood qualities[END_REF]. On the other hand, CT has its own limitations with investment cost and the need to fell the tree and cut it into logs. Besides the fact that grading rules are mainly defined from external observations where bark is present, recent studies confirmed a strong correlation between internal and external defects [START_REF] Thomas | Modeling the relationships among internal defect features and external Appalachian hardwood log defect indicators[END_REF][START_REF] Stängle | Clear wood content in standing trees predicted from branch scar measurements with terrestrial lidar and verified with X-ray computed tomography 1[END_REF][START_REF] Racko | Verify the accurancy of estimation the model between dimensional characteristics of branch scar and the location of the knot in the beech trunk[END_REF][START_REF] Pyörälä | Comparison of terrestrial laser scanning and X-ray scanning in measuring Scots pine (Pinus sylvestris L.) branch structure[END_REF] with coefficients of determination (R 2 ) greater than 0.6.

From these results and practices, the question arose as to the use of threedimensional (3D) technologies for describing the external envelope of trunks or logs with the objective of detecting bark surface defects.

LiDAR (Light Detection and Ranging) can measure objects in three dimensions through a technique in which a laser beam is emitted and the reflected light is received by a detector. The resulting product is a point cloud that contains the three spatial dimensions (x, y and z coordinates) of the scanned object. In forestry, terrestrial laser scanning (TLS) can provide information about an individual tree or a plot [START_REF] Dassot | The use of terrestrial lidar technology in forest science: Application fields, benefits and challenges[END_REF]. A variety of forestry applications have been developed in the last two decades.

In particular, a number of studies has taken advantage of the potential of LiDAR for the replacement of conventional methods of measuring forest inventory parameters, such as tree height, diameter at breast height (DBH, trunk diameter measured at 1.3 m above ground level) [START_REF] Hopkinson | Assessing forest metrics with a ground-based scanning lidar[END_REF][START_REF] Simonse | Automatic determination of forest inventory parameters using terrestrial laserscanning[END_REF], stand density, stand basal area, and volume for biomass assessment [START_REF] Van Leeuwen | Retrieval of forest structural parameters using lidar remote sensing[END_REF][START_REF] Yao | Measuring forest structure and biomass in New England forest stands using echidna ground-based lidar[END_REF][START_REF] Dassot | Terrestrial laser scanning for measuring the solid wood volume, including branches, of adult standing trees in the forest environment[END_REF]Astrup et al., 2014).

On standing trees, there have been attempts to estimate tree quality criteria from TLS [START_REF] Kankare | Estimation of the timber quality of scots pine with terrestrial laser scanning[END_REF][START_REF] Blanchette | Predicting wood fiber attributes using local-scale metrics from terrestrial lidar data: A case study of newfoundland conifer species[END_REF], airborne LiDAR [START_REF] Maltamo | Predicting tree attributes and quality characteristics of scots pine using airborne laser scanning data[END_REF][START_REF] Luther | Predicting wood quantity and quality attributes of balsam fir and black spruce using airborne laser scanner data[END_REF][START_REF] Kankare | Estimation of the timber quality of scots pine with terrestrial laser scanning[END_REF], or both types of LiDAR [START_REF] Van Leeuwen | Assessment of standing wood and fiber quality using ground and airborne laser scanning: a review[END_REF]. The quality parameters targeted in these works mainly concerned the overall shape of the timber: ovality, curvature, taper, and the presence of branches. Research focused on the detection of external defects are scarce [START_REF] Schütt | Approaches for recognition of wood quality of standing trees based on terrestrial laserscanner data[END_REF][START_REF] Stängle | Clear wood content in standing trees predicted from branch scar measurements with terrestrial lidar and verified with X-ray computed tomography 1[END_REF][START_REF] Thomas | Automated detection of severe surface defects on barked hardwood logs[END_REF][START_REF] Kretschmer | A new approach to assessing tree stem quality characteristics using terrestrial laser scans[END_REF]. Most of these studies were dedicated to the detection of large and very obvious defects. [START_REF] Thomas | Automated detection of severe surface defects on barked hardwood logs[END_REF]; [START_REF] Thomas | A graphical automated detection system to locate hardwood log surface defects using high-resolution threedimensional laser scan data[END_REF] detected, on red oak and yellow poplar, defects with a diameter greater than 7.5 cm and protruding by at least 2.2 cm from the bark. [START_REF] Kretschmer | A new approach to assessing tree stem quality characteristics using terrestrial laser scans[END_REF] proposed an approach to detect and manually measure the branch scars on Scots pine by highlighting them on a 3D reconstruction of the bark surface: the bark surface is colored based on the distance to a fitted cylinder surface corresponding to a trunk part. The scars, with a diameter of at least 2 cm and protruding by at least 1.5 cm from the bark, were detected. Existing research on the automated classification of defects on tree bark using TLS is even scarcer. [START_REF] Schütt | Approaches for recognition of wood quality of standing trees based on terrestrial laserscanner data[END_REF] presented a semi-automatic approach, based on a neural network, to detect and classify wood defects using both range and intensity information of TLS data.

In a previous work (Nguyen et al., 2016b), we successfully developed an algorithm to detect the defects on trunks surface. Using a suitable spatial resolution of the 3D data, the detection can segment potential defects with a dimension as small as 1 cm and small protrusion on trunks of different tree species. This important improvement was obtained from two major components. First, the definition of the most relevant trunk centerline results from a voting algorithm selecting the most frequent locations of the intersections of the inward pointing normals to the surface. Secondly, the reference distance to the centerline is computed for each individual point by taking its neighborhood into account. The computation of reference distance for each individual point allows for more precisely detecting the abnormalities on the bark than more global reference surface based on primitive fitting such as cylinder [START_REF] Schütt | Approaches for recognition of wood quality of standing trees based on terrestrial laserscanner data[END_REF][START_REF] Stängle | Clear wood content in standing trees predicted from branch scar measurements with terrestrial lidar and verified with X-ray computed tomography 1[END_REF][START_REF] Kretschmer | A new approach to assessing tree stem quality characteristics using terrestrial laser scans[END_REF] or circle [START_REF] Thomas | Automated detection of severe surface defects on barked hardwood logs[END_REF][START_REF] Thomas | A graphical automated detection system to locate hardwood log surface defects using high-resolution threedimensional laser scan data[END_REF].

Returning to the main purpose of the work presented here, once potential defects are detected, an automatic procedure must be able to assign them to a defect type and to confirm their status. The main challenge in the classification of these defects is to deal with the variability of their appearance, even for the same type of defect. In the forestry domain, the defects are often defined by the biological origin (Colin et al., 2010a) that leads to a high intra-class variability and inter-class similarity. Figure 1 (c-f) and (g-i) give examples of the intra-class variability between branch scars and burls respectively. Inter-class similarity between an epicormic shoot and a burl is shown in Figure 1 (b) and (g). Factors contributing to the intraclass variability or inter-class similarity are the tree species, often linked to the characteristics of its bark, the shape and the age of the defect and all the history of its development in connection with the environment of the tree. Facing this huge variability, a major difficulty is to build a representative database allowing the establishment of classification methods and their testing especially in studying the feasibility of such an approach as in this work. Several methods in the field of pattern recognition can be applied to classify objects, such as neural networks [START_REF] Bishop | Neural Networks for Pattern Recognition[END_REF], support vector machines [START_REF] Cortes | Support-vector networks[END_REF], random forests [START_REF] Breiman | Random forests[END_REF], Bayes classifier [START_REF] Devroye | A Probabilistic Theory of Pattern Recognition[END_REF], and deformable models [START_REF] Terzopoulos | Deformable models[END_REF]. Most approaches are based either on parametric models or on machine-learning techniques. In the remote sensing domain, the machinelearning supervised classifiers are widely used because they are more flexible in handling the high variability in object appearance and are more robust than model-based approaches [START_REF] Niemeyer | Contextual classification of lidar data and building object detection in urban areas[END_REF]. In particular, random forests are a supervised machine-learning method that is based on ensembles of classification trees. Random forests exhibits many interesting properties, such as high accuracy, robustness against over-fitting, noise or missing data in the training set [START_REF] Díaz-Uriarte | Gene selection and classification of microarray data using random forest[END_REF]. Moreover, random forests is a non-parametric method that does not require the information on the distribution of data. These advantages make random forests a successful classification method since its introduction by [START_REF] Breiman | Random forests[END_REF]. In the domain of remote sensing, random forests were used in landcover classification or urban area classification from airborne LiDAR [START_REF] Chehata | Airborne lidar feature selection for urban classification using random forests[END_REF][START_REF] Guo | Relevance of airborne lidar and multispectral image data for urban scene classification using random forests[END_REF] or Landsat data [START_REF] Yuan | Land cover classification and change analysis of the Twin Cities (Minnesota) Metropolitan Area by multitemporal Landsat remote sensing[END_REF][START_REF] Gislason | Random forests for land cover classification[END_REF]. In the forestry domain, random forests were used to accompany the forest inventory, such as for biomass assessments [START_REF] Mutanga | High density biomass estimation for wetland vegetation using worldview-2 imagery and random forest regression algorithm[END_REF], using airborne LiDAR. [START_REF] Othmani | Single tree species classification from terrestrial laser scanning data for forest inventory[END_REF] used random forests to identify the tree species from the analysis of tree bark pattern from the mesh derived from TLS data. Random forests were used to assess the timber quality of Scots pine by estimating tree properties, such as trunk diameters, tree height and branch heights using the parameters computed from TLS data [START_REF] Kankare | Estimation of the timber quality of scots pine with terrestrial laser scanning[END_REF].

The main objective of this work is to classify the potential defects detected on trunk surface by previously developed algorithms (Nguyen et al., 2016b). The other objective is to evaluate the performance of a robust and commonly used machine-learning algorithm, random forests, for the classification of bark singularities. The targeted types of defects are branch, branch scar, burl, and small defects including sphaeroblast, bud cluster, and picot. These types were chosen to represent the existing diversity of defects; nevertheless, some were grouped because of the difficulty in distinguishing them given their size or shape. We aimed to develop a method that works on the common commercial tree species, including hardwood species like sessile oak (Quercus petraea (Matt.) Liebl.), European beech (Fagus sylvatica L.), and wild cherry tree ( Prunus avium (L.) L.), or conifers such as silver fir (Abies alba Mill.), Scots pine (Pinus sylvestris L.), and Norway spruce (Picea abies (L.) H.Karst.). Here a special focus is given to the results concerning oak and European beech two hardwood species that have very different bark roughness, defect types and shapes. The first species has a furrowed bark and its most common defect types are burl and picot. The second has smooth bark and the most common defect type is branch scar with an eyebrow (or "Chinese mustache") shape.

Materials and Methods

Defects on trunk surface

Several defects on the trunk surfaces can be caused by exogenous factors depending on their environment, such as heat, frost, other trees, animals, and human beings. Our study focused on the most frequent source of defects, which arises from tree branching. Branching defects are the result of the development and growth of the tree. Their scars are associated generally with protruding regions that result from the inclusion of the defect by the radial growth of the trunk. More precise definitions of what we considered as a branching defect were as follows:

• A sequential branch was a branch that emerged after a winter's rest of the original bud.

• An epicormic branch was a branch that emerged after several winters from a latent bud.

• A branch scar was a track of a branch, either sequential or epicormic that maintains when this branch has died and has been degraded. Branch scars on hardwood were often referred to as bark distortions.

• A bud was a miniature leafy shoot protected by a covering of scales.

• A burl was a group of juxtapositional defects of one or more type, such as bud, picot, branch or branch scar. By definition, a burl could have a great variability in shape and size and composition.

• A bud cluster was a limited group of buds of less than six buds.

• A sphaeroblast was a bud whose base produces xylem that progressively covers the apical meristem of the bud (mainly on beech) [START_REF] Fink | Pathological and Regenerative Plant Anatomy[END_REF].

• A picot was a small branch with its apex naturally pruned. Picots are defined and illustrated in Colin et al. (2010b).

Typical defects on trunk surface were represented in Figure 1. These defects were characterized by a large intra-class variability in size and shape.

For instance, burls could range from a large bud cluster with at least six buds to a very extended mass of buds, picots, short or long branches with a diameter of several tens of centimeters.

The impact of defects on the wood quality depended on their type and dimension. For defects of the same type, larger defects had a more important impact than smaller ones. In general, the most penalizing defects were branch scar, branch and burls. The impact of small defects such as bud cluster, sphaeroblast and picot is small, but some had to be taken into account in the highest quality class.

Methodology

The steps of our method are presented in Figure 2. After their acquisition, the TLS data were preprocessed to obtain a smooth mesh corresponding to a trunk portion. Next, the potential defects were detected by using a segmentation algorithm, which is an improved version of the previously published work (Nguyen et al., 2016b) and is summarized in section 2.5. Then, the potential defects were classified into defect types using trained random forests.

Finally, the results were visualized by various colors on the mesh according to the defect type. The classification was validated by comparing the results with the ground-truth labels classified by an expert on the trunks before the TLS scans were carried out. Two methods were used by the expert to mark the defect type. The first method used small distinctive shape pinned in the vicinity of the defect. Thus, the defect type was recognized in the reconstruction of trunk surface. The second method measured the coordi-

(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l)

Acquisition of TLS data

The tree trunks exhibiting different defects were measured with a Faro Focus 3D X130 laser scanner in the Champenoux and Haye forests in the Grand-Est region of France. To detect small defects, we chose a high-resolution setting and put the scanner close to the trunk. The utilized resolution was one half of the maximum value and the distance from the scanner to the trunk was approximately 3-4 meters. With this setting, the angular resolution of the scan was 0.018 • in both horizontal and vertical directions, and the resulting distance between two neighboring 3D points on the trunk surface in the point cloud was around 1 millimeter. Such settings ensured a high-quality description of the defects limiting the laser beam inclination resulting from the defect height and the distance to the tree. The trees were sampled according to several criteria. Among the main commercial species, selected trees must have a sufficiently large diameter (see Table 1) and represent a variability in bark roughness, which depends on the species and the age of the trees. In agreement with these criteria, we scanned 26 trees: nine sessile oaks, eight

European beeches, three wild cherries, two Scots pines, three silver firs, and one Norway spruce. These scans were divided into 2 sets. One was used to train the random forests and another was used to test the method efficiency (Table 1). The training set contained 425 defects from 16 trees and the test set contained 183 defects from 10 trees.

During this acquisition step, the objective was to maximize the number and type of defects per scan; thus, trunks were either scanned entirely with four scans from suitable points of view or partially with one or two scans on just one side. If the trunk was scanned from multiple points of view, the scans were merged into a single file per tree to recover the 3D view of the trunk.

The registration was performed by the standard procedure available in the FARO SCENE software (Faro Technologies Inc., Lake Mary, FL), through the use of spheres.

Preprocessing of TLS data

LiDAR data are generally noisy, and the first processing step aimed to manage noise for enhancing the recognition rate. It included the reduction of noise and the smoothing of the trunk surface. Noise reduction is a difficult and complex process, due to different noise patterns from scan to scan. It depends on the condition of the scanning environment and also the characteristics of the trees. For example, we observed that when the trunk had branches or small epicormic shoots, there was much of noise caused by the multiple interceptions of the same laser beam by several branches and the bark. This is the situation when a laser beam hits both the contour of the branch and the bark resulting in a ghost point, with no reality, between the branch and the bark (Figure 3 (a)). We observed that the point density in noisy regions was often lower than in the relevant data regions. Thus, we proposed a simple approach to remove noise by clustering the point cloud by

Euclidean distance with the idea that relevant data points are in the largest cluster where the point density is highest. The choice of the threshold on the minimal distance between clusters is critical. If the threshold is too small, there is a risk that the relevant data would be removed, especially in the high part of the trunk where the resolution is lower. After testing different values, Due to the nature of a laser scan, the raw point cloud contains a certain level of error. For example, the utilized scanner had a ranging error of ±2 millimeters at 10 meters. The smoothing step was performed to reduce surface roughness caused by ranging uncertainty. However, the smoothing intensity was limited to maintain the bark roughness or defect shapes. The following steps were performed for smoothing and creating a mesh from the trunk point cloud using the Graphite software (https:

//gforge.inria.fr/frs/?group_id=1465):

1. Smooth the point cloud [START_REF] Lévy | Variational anisotropic surface meshing with voronoi parallel linear enumeration[END_REF]) using only one iteration with 30 neighbors. Only one iteration was used because with more iterations the smoothing process may erase defects with a weak relief.

2. Reconstruct the trunk surface [START_REF] Boltcheva | Surface reconstruction by computing restricted voronoi cells in parallel[END_REF] with the normal vector computed from 30 neighbors and the maximum distance used to connect neighbors of 5 millimeters. The radius value was chosen to be greater than the between-point distance in the point cloud but not too large to prevent the creation of wrong edges.

3. Smooth the created mesh by using the remesh smooth function [START_REF] Lévy | Variational anisotropic surface meshing with voronoi parallel linear enumeration[END_REF]. The used parameter was the number of points similar to the one of the original point cloud.

Segmentation of defects

Our strategy to classify the defects on trunk surface was first to detect all potentially defective areas using a segmentation algorithm. The algorithm is an enhanced version of our previously published one (Nguyen et al., 2016b) that focuses on defects with little protuberance from tree bark. In this study, we proposed a preliminary step for segmenting tree branches. The motivation for developing this approach came from the existing links between a defect present in the woody part and the impact of that defect on the bark surface, expressed by a structured, and often protruding, irregularity. To detect these irregularities, we defined the centerline of the trunk as a reference. In the evaluation of the algorithm presented in Nguyen et al. (2016b), the presence of branches was identified as an inconvenience for detecting smaller defects in a branch vicinity. Thus, in this work, the branches were first segmented by an algorithm that separates the points into two disjointed sets (illustrated in Figure 4): (1) set T contains closer points to the trunk surface, and (2) set B contains the branches according to the following algorithm.

• Estimation of the trunk radius r m , using the mode of the distance to the centerline of all points in the point cloud.

• Division of the point cloud volume into slices with a thickness of l millimeter, following the centerline direction. Each slice was then divided into angular sectors with an angle of l rm radian. The value of l should be greater than the diameter of the largest branch. In our experiment, the l parameter was set to values between 50 and 100 millimeters.

• For each angular sector, the nearest point to the center of the trunk was added to set T , and the other points of the portion were added to set B.

• For each point P in set T , we found subset S of set B, such as the distance between point S i ∈ S and P was less than or equal to √ 2l, and we moved them in set T . This algorithm assured that no point on trunk surface left on the branches set B by accepting a branch part with a length of √ 2l on the trunk set T .

After the branch segmentation, the original method (Nguyen et al., 2016b) was applied to set T as follows. (i) For each point P in set T , we estimated a reference point P from a linear regression linking the radius variation to longitudinal positions on a patch of neighboring points of P . (ii) The defect points were detected by thresholding the difference between the distance from P and P , denoted as (δ). (iii) The threshold was automatically computed on the histogram of δ using the Rosin's method [START_REF] Rosin | Unimodal thresholding[END_REF]. Then, the detected defect points were merged with set B containing the branches to The random forests [START_REF] Breiman | Random forests[END_REF] classifier is an ensemble classifier that aggregates a set of classification and regression trees (CARTs) [START_REF] Breiman | Classification and regression trees[END_REF] to make a prediction. In the training step, all trees were built with the same parameters but on different subsets of the training samples.

These subsets were generated from the training samples by a bootstrap sampling, which randomly selected the same number of vectors from the original set. The remaining "out-of-bag" (OOB) was used to compute the estimation error, which is known as the OOB error. Unlike CART, random forests does not consider all variables at each node to determine the best split threshold but a random subset of variables of the feature vector and the trees are built without pruning. The cardinality of the subset is an input parameter.

Another important parameter of the random forests classifier is the number of trees, which must be sufficiently large to capture the full variability of the training data and yields good classification accuracy. One of the advantages of the random forests classifier is that it does not overfit when increasing the number of trees at the expense of slower running time. In the classification step, random forests tested the feature vector, describing the new object with each tree in the forest. Each tree made a classification, or in other words, gave a vote for a class. The random forests classifier chose the class on which the majority of trees voted.

As mentioned above, the number of trees in the forest (nbT rees) and the number of variables (nbV ariables) used to select and test for the best split when growing the trees are two important input parameters needed to train the random forests classifier. The OOB error can be used to find the optimal value for these parameters. We ran an experiment with the nbT rees from 100 to 5,000 and the nbV ariables from 1 to the number of variables of the feature vector. For each value of nbV ariables, we could find the minimum value of nbT rees, which gave the minimum OOB error.

The random forests has been implemented in a number of free and open source libraries. In this study, we used the implementation in OpenCV-3.3 [START_REF] Bradski | The OpenCV Library[END_REF]. The advantage of OpenCV is its compatibility with the implementation of our algorithms in C++ programming language. The source code and sample data are available at the following GitHub repository:

https://github.com/vanthonguyen/trunkdefectclassification 2.6.2. Feature vector

In this step, we used the defects detected by our segmentation algorithm and constructed the feature vector based on our expertise on the defects.

Before computing the features, the point cloud of the defect was converted from Cartesian coordinate system to a custom coordinate system {l, z, d}, where l is the arc length computed from angle between the point and the plane Oxz and the distance from the point to the centerline, z is the height, and d is the difference between the distance and the reference distance from the point to the centerline (the distance between P and P as presented in section 2.5). This conversion allowed us to measure the defect diameter along the curved surface of the trunk similar to a manual measurement. To reduce the inhomogeneity of point clouds due to the superimposition of data coming from several points of view or the non-uniform by TLS, the feature vector was computed from a subsampled point cloud. The subsampled point cloud latter was computed by keeping only the closest point to the center of each voxel of a regular voxel grid of the defect point cloud. The voxel size was chosen by the average point spacing, which was 3 mm in our study. The following features were used:

1. Species: s.

2. Ratio between the number of points of the defect and the volume of its bounding box: c (equation 1)

3. Defect arc length: w = l max -l min .

4. Ratio between w and defect height: w h where h equals z max -z min .

5. Ratio between w and maximum of d: w dmax .

6. Mean of difference between the distance from P and P for all points P of the defect: d.

7. Standard deviation of the difference between the distance from P and P for all points P of the defect: σ d .

8. Hu moment invariants: I 1 , I 2 , I 3 , I 4 , I 5 , I 6 , I 7 (see equations 4-10).

9. Ratio between the eigenvalue λ 1 and the eigenvalue λ 3 : λ 1 λ 3 .

10. Ratio between the eigenvalue λ 2 and the eigenvalue λ 3 : λ 2 λ 3 .

11. Angle between the eigenvector -→ v 3 and the trunk axis at the height of defect: α.

where λ 1 is the eigenvalue associated with the eigenvector -→ v 1 of the defect having the smallest angle, with the radial vector of the trunk at the center of the intersection between the defect and the trunk. λ 2 is the eigenvalue associated with the eigenvector -→ v 2 of the defect having the smallest angle with the tangential vector of the trunk at the center of the intersection between the defect and the trunk. λ 3 is the eigenvalue associated with the eigenvector -→ v 3 of the defect having the smallest angle with the trunk axis at the height of defect.

The species was an important variable because each one had a specific bark roughness and a set of defects. For example, oak had burls but does not had sphaeroblast, which was conversely related to beech. In addition, for the same defect type, its shape could differ from one species to another.

For example, a branch scar on oak and on beech was very different.

Another relevant variable was the ratio between the number of points of the defect and the volume of its bounding box, which measured the compactness of the defect in the {l, z, d} coordinate system equation ( 1). This feature could discriminate a flat defect and a significantly protruding defect. c = number of points (l max -l min )(z max -z min )(d max -d min )

(1) By using our expertise in the domain, the dimension was an important criterion to classify defects, in particular small defects such as small burl and bud cluster. For that reason, we included the arc length w as a feature. The ratio w h allowed us to distinguish between a branch scar and a bark zone, which had a roughness higher than the local average on oak tree because the branch scars often have width greater than height and bark zones have width smaller than height. The ratio w dmax helped to distinguish a flat object, such as bark portion, branch scar and a more protruding one such as sphaeroblast and picot. The mean and standard deviation of d were also included in the feature vector because they help to distinguish between a branch scar and a burl composed only of buds.

The Hu moment invariants [START_REF] Hu | Visual pattern recognition by moment invariants[END_REF] had good characteristics for the object recognition because they were invariant with respect to translation, scale, and rotation. The Hu moment invariants {I 1 , . . . , I 7 } were computed from the normalized central moments nu ij of orders (i + j) 2 and 3 (see equations ( 3)-( 10)).

mu ij = z,l (z -z) i (l -l) j d (2) nu ij = mu ij mu (i+j)/2+1 00
(3)

I 1 = nu 20 + nu 02 (4)
I 2 = (nu 20 -nu 02 ) 2 + 4nu 2 11
(5) The eigenvectors and eigenvalues of the defect were computed from a principal component analysis (PCA) [START_REF] Wold | Principal component analysis[END_REF], which could be useful for distinguishing between the defect with a long axis (branch) and the flatter ones. Furthermore, because of the small number of branches in our dataset, we did not distinguish between sequential branches and epicormic ones. Nevertheless, the angle between the eigenvector -→ v 1 of defect and the trunk axis could be used to classify these types of branch on beech, oak and fir, as epicormic branches were quasi-perpendicular to the trunk axis, while sequential branches were more fastigiated.

I 3 = (

Construction of the training dataset

We used both manually segmented and automatically segmented defects to train the random forests. The manual segmentation was done by using a home-made software (DGTalTools-Contrib), based on the library DGTal (DGtal). The software allowed us to select the faces on the mesh to define the footprints of the defects (Figure 5). Each defect was then saved in a separate file and used for training the random forests. We also trained the random forests using the results of our segmentation algorithm, along with the verification given by the shape of paper labels set in the vicinity of the defects and identifiable in the scan. Bark (no-defect) class was introduced even though it is not a defect type; they were bark zones with a roughness higher than the local average. These bark zones are often miss detected as a defect by the segmentation algorithm. This is concordant with our approach as the detection step was built to provide all potential zones of defects assuming the risk of false positive that could be eliminated in the classification step. The training database includes the following classes and the number of defects of each class is summarized in Table 2: 1. Branch, including sequential branch and epicormic branch.

2. Branch scar.

Burl.

4. Small defects, including picot, sphaeroblast, bud and bud cluster.

5. Bark.

Performance evaluation criteria

To evaluate the performance of the classification algorithm, we used the F-measure, a performance measurement, that is frequently used for classification problems. The F-measure is the harmonic mean of precision (P R)

and recall (RE). We used the F 1 score, mixing both with equal weights on P R and RE. The precision P R is the number of correctly classified positive defects divided by the number of defects labeled by the system as positive (equation ( 11)). The recall is the number of correctly classified positive defects divided by the number of positive defects in the data (equation ( 12)).

On a binary classification problem, the F 1 is defined by equation (equation ( 13)).

P R = T P T P + F P (11)

RE = T P T P + F N ( 12
)
where T P, F P, F N are true positive, false positive and false negative respectively. Their definition is as follows:

• T P is the number of actual defects correctly classified as defect.

• F P is the number of non-defects incorrectly classified as defect.

• F N is the number of actual defects incorrectly classified as non-defect.

F 1 = 2 P R.RE P R + RE (13)
For a multi-class classification problem, the F-measure must be extended from the binary classification by an average of the F-measure of each class.

There are two approaches [START_REF] Manning | Introduction to Information Retrieval[END_REF]. One approach is the macroaveraged F-measure (equation ( 14)), which is the unweighted mean of Fmeasure for each label. The other is the micro-averaged F-measure (equation ( 15)), which considers predictions from all instances together and calculate the F-measure across all labels. Arithmetically, the micro-averaging favors bigger classes.

F m1 = n i=1 F 1i n ( 14
)
F µ1 = 2 P R µ .RE µ P R µ + RE µ ( 15
) P R µ = n i=1 T P i n i=1 (T P i + F P i ) (16) RE µ = n i=1 T P i n i=1 (T P i + F N i ) (17)
where n is the number of classes.

We also used the confusion matrix [START_REF] Provost | Glossary of terms[END_REF] to evaluate the performance for a more detailed analysis of the misclassification between classes.

Results

In this section, we present the results of the segmentation algorithm followed by the results of the classification algorithm in comparison with the ground-truth data. We first present a global analysis of the performance related to exhaustiveness independently of the defect type focused on the differences coming from tree species. Then, the analysis of the results focuses on defect types independently of the species which are nevertheless considered in the discussion.

Table 3 shows the results of the segmentation algorithm for each individual tree in the test database in terms of defect detection. We can see that the segmentation algorithm detected almost all of the defects, with 179 detected out of 183 (97.8%) in total. However, the number of false positives was very high ( 765), which will then be removed by the classification algorithm through a refined analysis of each detected areas. Moreover, Table 3 also shows that these false positives were mostly removed by the classification algorithm at the expense of some defects lost. The classification algorithm removed not only 694 (90.7%) false positives but also 28 (15.3%) actual defects.

We also observed that the segmentation algorithm produced more false positives on trees with furrowed barks, such as oak and pine, than on trees with smooth barks, such as beech and wild cherry. By contrast, the classification algorithm removed the false positives more efficiently on trees with furrowed bark than on trees with smooth-bark. For example, in Table 3, we can see that on pine the number of false positives from the segmentation and classification are 105 and 2 respectively while on Beech 2 these numbers are 70 and 12, respectively. The difference is illustrated in Figure 6. Concerning the performance according to defect types, Figure 7 illustrates classification results by coloring the mesh in agreement with the defect type.

Table 4 shows the performance criteria by defect types resulting from the classification. The overall macro-and micro-averaged scores were 0.86 and 0.73, respectively. However, the algorithm did not perform equally well on all classes of defect. The branch had the best F 1 score of 0.89, followed by the burl with an F 1 score of 0.76. The algorithm performed less well on branch scar and the small defect types with F 1 scores of 0.61 and 0.46, respectively.

For allowing a better understanding of the differences, Figure 8 is Branch type including both sequential and epicormic branches, is Branch scar, is Burl, is Small defect including bud cluster, sphaeroblast and picot. On the mesh of the Spruce, the detected defects (circled) are the paper marks and pushpins that were used by the expert to mark the defect type before the scan was carried out. These false positives were ignored in our evaluation.

ing between predicted and observed defect types and allows a finer analysis of the differences. We can see that one branch was classified as branch scar.

A more detailed analysis showed that it was a short dead stub branch of a wild cherry (the large green region in Figure 7 (c)). Another branch was classified as a burl because an epicormic branch is often originated from a small burl, and the distinction by the algorithm is difficult in young development stages. While the recall of the algorithm on the branch scar was very high (0.84), the precision was not as good (0.48) because there were 49 bark portions recognized as branch scar while there were 69 branch scars in total.

Some burls were confounded with the bark portions and small defects be- 1 (i) and (j)) or a bark portion since both are quite flat. The confusion matrix shows that the small defects were often confounded with bark portions and branch scars. It is to be noted that the number of bark portions miss-classified as small defects was 15 and the number of small defects miss-classified as bark portions was 16. There was only one branch scar miss-classified as small defect but 11 small defects miss-classified as branch scars.

Although no spruce data were used to train the random forests, the predictions on this spruce (Figure 7 (d)) were good, as 15 out of 18 were detected.

However, two branch scars were detected as small defects and two branch scars were detected as burls.

Discussion

Defect detection

In summary, our algorithms had a very good performance in defect detection, even with the small defects corresponding to a slight modification of the bark roughness. These good results are both due to the robust estimation of the trunk centerline, and the fitting on a local longitudinal patch, of the regular radius variation, allowing for the calculation a local reference distance. Our approach outperforms the detection based on a radius resulting from the fitting of geometrical primitives such as circle or cylinders proposed in other works [START_REF] Thomas | Automated detection of severe surface defects on barked hardwood logs[END_REF][START_REF] Kretschmer | A new approach to assessing tree stem quality characteristics using terrestrial laser scans[END_REF] especially for cross-sections with less circular shape as already discussed in Nguyen et al. (2016b). It is clear that several factors can impact the detection, such as scan resolution and quality and missing data resulting from occlusion. Our algorithm can detect small defects such as picot which often have a diameter between 0.5 centimeter and 1 centimeter, thus outperforming all previous works with size ranging from 7.5 centimeters [START_REF] Thomas | Automated detection of severe surface defects on barked hardwood logs[END_REF] to 2.0 centimeters [START_REF] Kretschmer | A new approach to assessing tree stem quality characteristics using terrestrial laser scans[END_REF]. Moreover, [START_REF] Kretschmer | A new approach to assessing tree stem quality characteristics using terrestrial laser scans[END_REF] only focused on the branch scars and their method was not automatic.

Because of their shapes, French and North American foresters have named large branch scars of beech and wild cherry trees "Chinese mustache" (or eyebrow). It often covers a large peripheral area, and the two parts of the mustache are often thin. This may result in an over-segmentation (Figure 9 (a)). Two or more large defects can also be close enough to form a large shape.

Although the human eye will dissociate the large shape as multiple separated defects, the algorithm saw it as a defect, which consequently created an under-segmentation (Figure 9 As the segmentation is the step preceding the classification, the perfor-mance of the classification algorithm also depends on the performance of the segmentation step. Thus, any improvement in segmentation will result in a better classification. The most important parameters were the patch size and the bin width of the histogram used to find the threshold by the Rosin's method [START_REF] Rosin | Unimodal thresholding[END_REF], and the voxel size used to compute the centerline. Their choices were described in detail in Nguyen et al. (2016a). As mentioned earlier, the over and under-segmentation can occur in the segmentation step especially through the defect clustering through a Euclidean distance filter. These errors can affect the classification, and consequently, the assessment of the tree quality. In addition to the influence of misclassification, the over-segmentation increased the number of defects and decreased their dimension. By contrast, the under-segmentation decreased the number of defects and increased their dimensions.

Defect classification

Visually, we can see that our algorithms were able to detect and classify most of the defects (Figure 7), including small defects such as picot and bud clusters. Based on Table 4, the overall classification result was good, with a micro-averaged F 1 score of 0.86 and a macro-averaged score of 0.73. The result was promising, particularly on the classification of branch and burl.

However, we did not obtain a very high F 1 score (0.46) on the small defect because, first, we could not totally remove all the false positives and, second, there was some confusion between the classes due to the very high intra-class variability and the interclass similarity.

For example, the confusion between branch scars and burls can be explained by the fact that some burls containing only buds have a shape that looks like a branch scar because both are flat. In the field, human eyes can easily distinguish these two defect types; however, in the point cloud or mesh, it could be difficult to distinguish them. For small-sized defects, the confusion between burls and small defects can merely be explained by the initial definition of burl and small defect. When a burl is composed only of buds it might have a similar shape to a bud cluster. In our database, small defect types include several biological defect types: a bud cluster with less than six buds, sphaeroblast, and picot. A bud cluster may have a shape similar to a small burl. The confusion was high, even for expert eyes.

With the objective of wood quality assessment, subclasses considering the size of defects with the same biological origin can be useful to refine the analysis in future studies but need a suitable assessment of the defect characteristics by algorithms, which is beyond the scope of this paper. More generally, it addresses the problem of a combination of defects that occurs rather frequently because they have the same origin and correspond to different stages of development or because they result from a spatial proximity,

as in examples illustrating under-segmentation in Figure 9. Improvements could be a more refined algorithm for merging close protruding areas and a detailed definition of the defect types, adding size classes linked to the resulting quality impact as already mentioned.

Influence of species and bark roughness

As a non-intuitive result (coming from the easier visual assessment of the defects on smooth bark), a lower F 1 score was observed on beech compared with oak (Table 4). In the segmentation step, on trees with furrowed bark, there were many more false positives, resulting of the misdetection of bark portions as defects. This is in agreement with our hypothesis. However, the false positives on trees with furrowed bark had a common shape created by the pattern of the rhytidome, and they were easily detectable and removed by the classification through the definition of the Bark class. In contrast, on trees with smooth bark, the false positives were created by bark portions, very similar to actual defects in terms of protrusion and spatial distribution.

Moreover, on species with smooth bark, and particularly on beech, we also observed many wrinkles or cambium alterations revealed by the elliptical shape (Nectria disease) of bark (Figure 10). These alterations were often misclassified by our algorithm as branch scars rather logically in the absence of more relevant type definition corresponding to these singularities. Thus, the classification algorithm has a higher performance on furrowed bark trees than on smooth bark trees.

Parameters of random forests and future improvements

Random forests have only two principal parameters: the number of trees in the forest (nbT rees) and the number of variables (nbV ariables) used to select and test for the best split when growing the trees. Their performance was slightly influenced by the number of trees if it was chosen sufficiently high (1,000 trees in our experiment). With the number of trees over 1,000, the performance gain was minimal. nbV ariables was chosen following the OpenCV recommendation, which was √ variables. We also noticed that random forests are very robust to over-fitting so the feature selection is less critical. Random forests can give a good performance, even with a small training dataset [START_REF] Rodriguez-Galiano | An assessment of the effectiveness of a random forest classifier for land-cover classification[END_REF]; however, it depends also on the intra-class variability of the defect class. Because burl and branch scar training data. Our test carried out with data of the most present species (beech) in our database did not clearly outperform random forests trained with all species. The F µ1 were 0.71 for random forests trained with only beech defects and 0.70 for random forests trained with all species defects.

Use for grading trunk quality

The performance of defect classification can influence the grading result of standing trees. Nonetheless, the impact of the misclassification of class on the quality assessment is difficult to assess. The most important is the classification of large defects. Once there is an occurrence of these large defects, the occurrence of smaller defects is less important. However, in the case of highest quality trunk, the classification performance is more critical because one misclassification, even of a small defect, can result in a change to a higher or lower quality class. Thus, a further development of the current method is needed to measure the defect dimension which is required to assess the impact of defects by a standard (AFNOR, 1999a(AFNOR, ,b, 2012)).

Regarding the current scanning setting, the spatial resolution does not allow for classifying between a picot and a less important small defect, such as bud cluster. Only one picot is allowed in the case of highest quality trunk.

Thus, in the case that there is only the occurrence of small defects, an additional expert inspection could be suggested to verify the classification result in the case of high commercial value. Beyond grading issues, the information about defect type and position on the log can be used to optimize the transformation, with the objective of increasing the volume of high-quality products but such exceeds the scope of this paper even if it is a real prospect.

As a common problem for the remote sensing technologies, the quality of TLS data can be limited by the occlusion, especially when there are branches on the trunk or false positive created by moss (Musci L.) or lichens. In general, scanning the tree from multiple views can reduce occlusions, as the occlusion on the high part of the tree is difficult to avoid.

Conclusions

In this paper, we have presented a random forests-based classifier to identify defects on trunk surface from TLS data. The potential defects were detected by our segmentation algorithm (Nguyen et al., 2016b). Each detected defect was then classified into one of the four defect classes or bark using the random forests classifier. Our experiment showed that from the high-density data acquired by TLS, we can detect and classify most of the defects on tree bark. The overall F µ1 score of the classification algorithm was 0.86. These preliminary results are thus very promising. We could further improve the score with the addition of more data and with the definition of defect subclasses considering not only their biological type but also their size and impact on wood quality. An interesting option will be to train the random forests separately for each tree species. The information about the defect type in addition to its dimension and position can be used to assess the quality of roundwood or standing tree. This is the first step towards developments for helping experts in the assessment of the quality of standing trees or timber logs in forests or for enhancing the knowledge coming from true shape scanners in the primary wood processing industry.

Figure 1 :Figure 2 :

 12 Figure 1: Some illustrations of the defect types considered in this study. (a, b) branches: sequential branch (a), and epicormic shoot (b); (c-f) branch scars: on oak (c), on wild cherry (d), on beech (e), and on beech (f);(g, h) burl: consisting of buds and an epicormic shoot (g), buds and short epicormic shoots (h), and buds (i); small defects: (j) bud cluster, (k) sphaeroblast, and (l) picot.

Figure 3 :

 3 Figure 3: Noise processing for a wild cherry trunk. Point cloud before (a) and after (b) noise reduction process that only keeps the biggest cluster; the minimal distance between two clusters is 5 millimeters.

Figure 4 :

 4 Figure 4: Illustration of the branch segmentation: the angular sector is defined by the volume inside planes formed by blue lines. The points in this angular sector that had a distance to P less than or equal to √ 2l were moved to the set of trunk points (T ). The set of branch points (B) is in solid grey color.

Figure 5 :

 5 Figure 5: Manual segmentation of a defect

Figure 6 :

 6 Figure 6: Defects detected by the segmentation algorithm (a, c) and refinement by the classification algorithm (b, d) for two logs: Beech 2 (a, b) and Pine (c, d).

Figure 7 :

 7 Figure 7: Examples of the classification results on the mesh of Oak 3 (a), Beech 1 (b), Wild cherry 3 (c), and Spruce (d).is Branch type including both sequential and

Figure 8 :

 8 Figure 8: Confusion matrix with the absolute value and normalized value (precision). The color of cells is a function of normalized value.

  (b)). The under-segmentation can also occur on the trunk of conifer in the case of connected branch scars (Figure 9 (c)).

Figure 9 :

 9 Figure 9: Examples of over-segmentation on beech (a), under-segmentation on beech (b)and on spruce (c). Within each image, all connected green areas belong to the same defect.

Table 1 :

 1 Number and attributes of the sample trees.

		Number of trees	Range of diameters
	Species
		Training Testing	at breast height (cm)
	Oak	6	3 35 -76
	Beech	5	3 30 -57
	Wild cherry	2	1 22 -33
	Pine	1	1 34 -57
	Fir	2	1 23 -45
	Spruce	0	1 19
	Total	16	10

  I 6 = (nu 20 -nu 02 )[(nu 30 +nu 12 ) 2 -(nu 21 +nu 03 ) 2 ]+4nu 11 (nu 30 +nu 12 )(nu 21 +nu 03 ) I 7 = (3nu 21 -nu 03 )(nu 30 + nu 12 )[(nu 30 + nu 12 ) 2 -3(nu 21 + nu 03 ) 2 ]+ (3nu 12 -nu 30 )(nu 21 + nu 03 )[3(nu 30 + nu 12 ) 2 -(nu 21 + nu 03 ) 2 ]

	(9)
	(10)

nu 30 -3nu 12 ) 2 + (3nu 21 -nu 03 ) 2 (6) I 4 = (nu 30 + nu 12 ) 2 + (nu 21 + nu 03 ) 2 (7) I 5 = (nu 30 -3nu 12 )(nu 30 + nu 12 )[(nu 30 + nu 12 ) 2 -3(nu 21 + nu 03 ) 2 ]+ (3nu 21 -nu 03 )(nu 21 + nu 03 )[3(nu 30 + nu 12 ) 2 -(nu 21 + nu 03 ) 2 ] (8)

Table 3 :

 3 Results of the segmentation (seg.) and classification (cla.) steps compared with the observed defects.

			True positive False positive False negative
	Tree name Observed
			Seg.	Cla. Seg.	Cla. Seg.	Cla.
	Oak 1	8	8	8	9	0	0	0
	Oak 2	25	24	19	147	7	1	6
	Oak 3	24	23	20	79	7	1	4
	Beech 1	30	30	24	55	19	1	6
	Beech 2	29	29	21	70	12	0	8
	Beech 3	24	22	18	47	14	2	6
	Wild Cherry	8	8	8	10	0	0	0
	Pine	4	4	4	105	2	0	0
	Fir	14	14	14	129	8	0	0
	Spruce	17	17	15	114	2	0	4
	Total	183	179	151	765	71	5	34

Table 4 :

 4 Precision, recall and F 1 score of the different defect types

	Defect type	Precision Recall	F 1
	Branch	1.00	0.80 0.89
	Branch scar	0.48	0.84 0.61
	Burl	0.73	0.81 0.76
	Small defect	0.56	0.39 0.46
	Bark	0.95	0.90 0.93
	Beech (micro avg.)	0.70	0.70 0.70
	Beech (macro avg.)	0.70	0.70 0.70
	Oak (micro avg.)	0.90	0.90 0.90
	Oak (macro avg.)	0.66	0.68 0.67
	All (micro avg.)	0.86	0.86 0.86
	All (macro avg.)	0.75	0.74 0.73
	cause a burl consisting of only buds may have a similar look to a small defect
	(see Figure

Acknowledgments

This work was supported by the French National Research Agency through the Laboratory of Excellence ARBRE (ANR-12-LABXARBRE-01) and by the Lorraine French Region. We would like to thank Florian Vast for providing technical support and for scanning and measuring the trees used in this research.

have a high intra-class variability, in future work, we would like to add more training data of these types. As the incident angle of laser beams changes with the different heights of the trunk, it is also important to have the defect data from different trunk heights.

Another suggestion to improve the performance of the classification is to remove species in the feature vector and separately train random forests for each species, considering that the information on the species is a prerequisite brought by an operator or by another identification step [START_REF] Othmani | Single tree species classification from terrestrial laser scanning data for forest inventory[END_REF]. This approach might have a better performance but requires more


Besar Asllani
email: abesar.asllani@supergrid-institute.com

Pascal Bevilacqua
email: bpascal.bevilacqua@insa-lyon.fr

Hervé Morel
email: cherve.morel@insa-lyon.fr

Dominique Planson
email: ddominique.planson@insa-lyon.fr

Luong -Viêt Phung
email: eluong-viet.phung@insa-lyon.fr

Beverley Choucoutou
email: fbeverley.choucoutou@supergrid-institute.com

Thomas Lagier
email: thomas.lagier@supergrid-institute.com

Michel Mermet-Guyennet
email: hmichel.mermetguyennet@supergrid-institute.com

Static and Switching Characteristics of 10 kV-class Silicon Carbide Bipolar Junction Transistors and Darlingtons

Keywords: 10 kV SiC BJT, 10 kV SiC Darlington, SiC BJT parallelisation, Device Processing, Electrical characterisation, Double Pulse test

This paper reports the device design, fabrication and characterisation of 10 kV-class Bipolar Junction Transistor (BJT). Manufactured devices have been packaged in single BJT, two paralleled BJTs and Darlington configurations. The static and switching characteristics of the resulting devices have been measured. The BJTs (2.4mm² active area) show a specific on-resistance as low as 198 mΩ•cm² at 100 A/cm² and room temperature for a βMax of 9.6, whereas the same active area Darlington beats the unipolar limit with a specific on-resistance of 102 mΩ•cm² at 200 A/cm² (β=11) for a βMax of 69. Double pulse tests reveal state of the art switching with very sharp dV/dt and di/dt. Turn-on is operated at less than 100 ns for an EON lower than 4mJ, whereas the turnoff takes longer times due to tail current resulting in EOFF of 17.2 mJ and 50 mJ for the single BJT and Darlington respectively when operated at high current density. Excellent parallelisation have been achieved.

Introduction

The research on Silicon Carbide (SiC) has made huge progress in the last 30 years. From the complete assessment of the material properties to the commercialisation of discrete devices a lot of efforts has been put. This has proven that the intrinsic properties of SiC can be exploited and are not just a researcher's fantasy. Nowadays the automotive markets are the ones pushing the production and devices on the range between 650 V and 1200 V have gone into mass production [START_REF]Applications | Automotive[END_REF]- [START_REF]SiC for automotive applications[END_REF]. In this range SiC Metal Oxide Semiconductor Field Effect Transistors (SiC-MOSFET) is very appealing due to their superior performance even though less costly Si counterparts exist.

For higher voltages (3.3 kV and above) and applications like High Voltage Direct Current (HVDC) converters, Medium Voltage Direct Current (MVDC) converters and Modular Multilevel Converter (MMC) submodules SiC devices cost projections place them in second position compared to Si Insulated Gate Bipolar Transistors (Si-IGBTs), which are now considered to be a mature technology in the industrial environment. In order for SiC to become interesting in that voltage range, it has to offer better electric performance than Si-IGBT, improve the system reliability, meet the current rating requirements, while not drastically increasing the global cost of the converter. This means that, SiC devices for these applications have to have much lower losses and provide advantages in terms of switching speed. This is not an advantage for MMCs, but it could be interesting for Solid-State Transformer like in traction application. Also, the current ratings require device paralleling and improved gate/base control. System reliability has to be warranted and this is usually supposed to be the case since fewer devices need to be used in series, but gate oxide issues on MOSFETs still fail to convince. One way to overcome these issues, is to completely get rid of the gate oxide by employing Junction Field Effect Transistors (JFETs) or Bipolar Junction Transistors (BJTs). JFETs are a good alternative to MOSFETs but the normally-on nature that confers them very low on resistance is unattractive to application engineers. On top of that, JFETs are unipolar devices and for high voltages (>15 kV) bipolar ones are to be preferred since they provide lower on-resistance when resistivity modulation is achieved [START_REF] Johannesson | Potential of ultra-high voltage silicon carbide semiconductor devices[END_REF].

BJTs seem to be a good alternative for high and ultra-high voltage devices since they are proven to benefit from resistivity modulation property [START_REF] Gao | Comparison of Static and Switching Characteristics of 1200 V 4H-SiC BJT and 1200 V Si-IGBT[END_REF]- [START_REF] Zhang | A 10-kV monolithic darlington transistor with βforced of 336 in 4H-SiC[END_REF]. They do not have any gate oxide which renders them free from the related issues and gives them a more compact form factor compared to MOSFETs. This means that for the same current rating, less bulk material is needed because the conduction happens fully on the volume as compared to the conduction of the channel of the MOSFETs, which can be considered as surface conduction with classical channel mobility reduction [START_REF] Okamoto | Improved Inversion Channel Mobility in 4H-SiC MOSFETs on Si Face Utilizing Phosphorus-Doped Gate Oxide[END_REF]. For both these reasons SiC BJTs can be more economical compared to same rating SiC MOSFETs. But this does not take into account the fact that the SiC MOSFET integrates a PiN diode intrinsically, whereas the BJT has to be paralleled with a diode in order to be used in converter applications. One of the drawbacks that has slowed down the development of BJTs is its control. Since one has to provide continuous current to keep the BJTs in on-state, the driver is slightly more complicated than the ones used for SiC MOSFETs [START_REF] Peftitsis | Gate and Base Drivers for Silicon Carbide Power Transistors: An Overview[END_REF], [START_REF] Tournier | SiC BJT driver applied to a 2 kW inverter: Performances and limitations[END_REF] and the losses that can be eliminated by the bipolar nature of this device can be transferred to the driver, at least partially [START_REF] Tolstoy | A Discretized Proportional Base Driver for Silicon Carbide Bipolar Junction Transistors[END_REF]. Nevertheless, the potential of BJTs has to be explored for applications such as power converters for MVDC/HVDC and also for Surge Protection.

Experimental

Device design and fabrication. The BJTs have been manufactured on 4" N+ substrates after 3 layers of epitaxy have been grown. First the collector layer (drift layer) was grown with a doping of 7•10 14 and a thickness of 110 µm. Since this layer is the one responsible for the blocking capability of the device, it is in theory able to withstand 16.8 kV for an infinite plane junction. The optimal thickness and doping of the base layer has been determined to be 1.5•10 17 cm-3 and 1.5 µm respectively. The choice for such a thick base layer is made to ensure that the remaining base thickness after etching is enough to sustain the high electric field. The main information of the doping and thickness of the base and drift layer are resumed in Fig. 1. The optimisation of the current gain is crucial for power BJTs. For this reason small and medium-sized (0.75•0.75 mm 2 2.6•2.6 mm 2 ) interdigitated devices were developed with 4 designs (geometry variations) and a cell pitch between 25 µm and 35 µm. The active area of the medium size BJTs is 2.4 mm 2 . The peripheral protection is an association of MESA and JTE that has been inherited from the 10 kV PiN diodes with same drift layer properties [START_REF] Asllani | Advanced Electrical Characterisation of High Voltage 4H-SiC PiN Diodes[END_REF]. More details on the design and optimisation process can be found in [START_REF] Choucoutou | Étude en simulation et conception d'un transistor bipolaire ( BJT ) 10 kV en 4H-SiC[END_REF].

Emitter Base Base

Collector

Packaging. After on-wafer characterisation best performing medium sized BJTs from each design have been selected and packaged in high temperature custom package ISOPLUS from DeepConcept. For testing purposes, 4 hybrid devices were packaged, where 4 samples were used to make 2 paralleled BJTs and 4 other samples were used to make 2 Darlingtons. Extra care was taken to select the highest current gain (β) and the lowest parameter spread for the hybrid devices. Fig. 2 shows the packaging layout of a single BJT (a), paralleled BJT (b) and Darlington (c) on the left and the packaged device on the right. The test bench was not capable of thermal conditioning at the time of this study. BJTs were mounted on low-side, while a 4 mH air core inductor in parallel with a custom freewheeling diode was mounted on high-side. The freewheeling diode is made of two 1.7 kV SiC Junction Barrier Schottky diodes in series. The BJTs were driven by a GA15IDDJT22-FR4 driver [START_REF]GA15IDDJT22-FR4[END_REF] able to deliver a typical continuous current of 2 A on the base. The on-state and off-state voltages delivered by the driver are 5 V and -8 V respectively. Collector-Emitter voltage was measured through a Tektronix THDP0100 high-voltage differential probe. Collector current was measured through a 25 mΩ shunt in series with the BJT emitter, whereas the base current was measured through a Tektronix CT2 current transformer coupled with a P6041 probe. Tests were carried out on 2 paralleled BJTs and Darlingtons also. For paralleled BJTs, the GA15IDDJT22-FR4 driver was employed, whereas for Darlingtons a CPWR-AN10 Rev-C SiC MOSFET Isolated Gate Driver [START_REF]SiC MOSFET Isolated Gate Driver[END_REF] was employed as the two base emitter diodes in series require at least 6 V to trigger the device.

Results and Discussion

This section reports the characterisation results divided in static and dynamic characteristic. The results will be analysed and discussed further in this section. Throughout the paper the on-resistance is calculated as the ratio between applied collector emitter voltage and the resulting collector current. On-resistance does not refer to dynamic resistance that is calculated as the slope of the output characteristic. Static characteristics. The BJTs, the paralleled devices and the Darlingtons have been extensively characterised. As shown in Fig. 3|a) the open base blocking capability of single BJTs shows a breakdown voltage of 5 kV, which is half of the targeted blocking voltage due to a faulty (higher than the optimal) implantation dose of the peripheral protection. Nevertheless, PiN diodes with same epitaxial layer have recently been designed with an optimised peripheral protection and successfully block 11 kV. This achievement can be applied to a future run of BJT to assure the targeted blocking voltage. On the other hand, the output characteristic at room temperature presented in Fig. 3 -The open base blocking capability of BJT 3#D5-3 a) and its output characteristics in b). shows a healthy BJT saturation behaviour and an infinite Early voltage. The specific on resistance is calculated to be 198 mΩ•cm² at 100 A/cm² and a β of 9.6 for device 3#D5-3. The resistivity of the 10 kV SiC BJT reported in this study is 66% higher than that of 10kV SiC MOSFET reported in [START_REF] Das | 10 kV, 120 A SiC half H-bridge power MOSFET modules suitable for high frequency, medium voltage applications[END_REF] and leaves room for improvement in a future run. However, the epitaxy of the BJT is highly oversized as its thickness is 110 µm as compared to the 85 µm epi of the MOSFET [START_REF] Das | 10 kV, 120 A SiC half H-bridge power MOSFET modules suitable for high frequency, medium voltage applications[END_REF]. This means that a good part of the resistivity is due to the oversized epitaxy.

Another aspect is the low injection due to low lifetimes in the drift region. At higher temperature the BJT might beat the unipolar limit and have a lower resistance than the MOSFET, but data on the 10 kV MOSFET at 150°C have not been found for comparison. Current gain as a function of collector current of BJTs with designs 2# and 3# have been selected and measured after packaging and are shown in Fig. 4|a). One can see the clear effect of the design (base and emitter width variations) as there are two distinct groups of β. Design 3# has the highest β, which peaks at 9.8 at just above 100 A/cm² and rapidly decreases for current densities higher than 133 A/cm². The effect of high temperature is quite high as β max goes from 8.5 at 25°C to 5.9 at 150°C for device 3#D2-3. Whereas the on-resistance increases from 201 mΩ•cm² at 25°C to 500 mΩ•cm² at 150°C. These values are far from the record-breaking βs published in literature, like βMax = 75 for a 10 kV SiC SJT [START_REF] Sundaresan | 10 kV SiC BJTs -Static, switching and reliability characteristics[END_REF], βMax=28 for a 10 kV SiC BJT [START_REF] Zhang | 10 kV, 10 A Bipolar Junction Transistors and Darlington Transistors on 4H-SiC[END_REF], βMax=139 for a 15 kV single cell SiC BJT [START_REF] Salemi | 15 kV-Class Implantation-Free 4H-SiC BJTs With Record High Current Gain[END_REF] and βMax=139 for a 21 kV single cell SiC BJT [START_REF] Miyake | 21-kV SiC BJTs with spacemodulated junction termination extension[END_REF]. The record for highest beta (β = 256 and β = 335 for (0001) and (000-1) crystal orientations respectively) is held by Miyake et al. [START_REF] Miyake | 4H-SiC BJTs with record current gains of 257 on (0001) and 335 on (000-1)[END_REF], but the base layer is so thin that the open base break down voltage is limited to 600 V, which is far targeted voltage for MVDC and HVDC applications. The performance of the tested devices gives room for improvement, but the resulting βs were consistent throughout the wafers and the yield was above 50% in terms of β only. An interesting aspect of BJTs is that they can be paralleled or used in a Darlington configuration. Parallelisation is useful when high current rating cannot be achieved with a single device, whereas Darlington is one way to lower the base current by multiplying the individual gains, but at the cost of a doubled VBE voltage and a 3 V threshold voltage. Both these configurations have been tested and the output characteristics along with βs are presented in Fig. 5. Compared to the results in Fig. 4|a) the 2 paralleled BJT are capable of doubling the current without degrading β. This is a sign that current sharing is optimal. βMax = 9 and 207 mΩ•cm² at 100 A/cm² is achieved, which is consistent with the results of a single BJT. As of the Darlington, βMax = 69 and 102 mΩ•cm² at 200 A/cm² (β=11) has been recorded. The reduction of the specific on resistance is a result of high injection happening in the Darlington. The BJT does not show a clear bipolar behaviour for base currents up to 1 A. This result is encouraging as the specific resistance is 20 % lower than that of 10kV SiC MOSFET reported in [START_REF] Das | 10 kV, 120 A SiC half H-bridge power MOSFET modules suitable for high frequency, medium voltage applications[END_REF] and lower than the unipolar limit of SiC. Experimenting with monolithic Darlingtons can yield devices with very low specific on resistance and double the current rating for the same active area. Dynamic characteristics. The 10 kV SiC BJT is meant to be used as a power switch. As such, the static characteristic is very important as it accounts for the conduction losses, but it also needs to perform when it comes to changing states (conduction to blocking and vice versa). The switching losses have to be well known, especially when the frequency is high, which is one of the main arguments in favour of SiC devices. In order to assess the switching behaviour of the studied devices the Clamped Load Inductive switching, also commonly called Double Pulse test, was carried out on single BJT Zooming in on the turn-on of these devices shows a state-of-the-art performance. As can be seen in Fig. 7, IC trise and VCE tfall are inferior to 100 ns. Very high dV/dt and di/dt are recorded on the three devices even though they were subjected to very high current density (cf. Table 1). Turn-on energy lower than 4 mJ was extracted on the 3 devices. The current peak during the turn-on phase results from the capacitance of the freewheeling diode. During the turn-off phase, reported in Fig. 8, one can notice that VCE trise is lower than 100 ns for the 3 devices. The influence of the test bench parasitic elements is noticeable, since during the fall time of the collector current some oscillation is observed. IC tfall on the other hand exhibits an exponential decaying behaviour that could be related to the recombination of electron-hole pairs that constitute the plasma during bipolar conduction, commonly referred to as the tail current. In Fig. 6|c), the collector current takes around 5 µs to decay (between 7µs and 12 µs), which results in a lifetime of 1 µs for bipolar conduction. This value is consistent with literature as some self-heating may occur in the device and produce an increase of the ambipolar lifetime that is reported to be 0.6 µs at 25°C [START_REF] Ivanov | High hole lifetime (3.8μs) in 4H-S1C diodes with 5.5 kV blocking voltage[END_REF]. Unfortunately, during these tests the test bench could not be used at higher temperatures. Bipolar conduction may be the slow decaying current that produces high turn-off losses compared to turn-on. In order to reduce this effect as much as possible, lowering the negative VBE voltage should be explored in the future. This may increase the reverse recovery current in the base-emitter junction and thus enhance the recombination. The reverse recovery current of IB is visible in Fig. 8 for the 3 devices. The bipolar degradation has not been studied in this paper and cannot be excluded since very high current densities were injected in the device. Repetitive switching tests and stress tests may be carried out in the future to investigate the potential bipolar degradation phenomenon. Other papers in literature report outstanding switching performance [START_REF] Sundaresan | 10 kV SiC BJTs -Static, switching and reliability characteristics[END_REF], [START_REF] Zhang | 10 kV, 10 A Bipolar Junction Transistors and Darlington Transistors on 4H-SiC[END_REF]. Nevertheless, comparing the actual BJTs and Darlingtons with the devices from literature would not be fair as the device in [START_REF] Sundaresan | 10 kV SiC BJTs -Static, switching and reliability characteristics[END_REF] performs only in unipolar mode and the device in [START_REF] Zhang | 10 kV, 10 A Bipolar Junction Transistors and Darlington Transistors on 4H-SiC[END_REF] is tested only at 2 kV and 30 A/cm 2 .

Turn-ON JC (A/cm²)

dV/dt (V/ns) di/dt (A/µs) EON (mJ)

Fig. 1 -

 1 Fig. 1 -Drift region doping details.

Fig. 2 -

 2 Fig. 2 -Packaging layout of a single BJT (a), paralleled BJT (b) and Darlington (c) on the left and the packaged device on the right.

Fig. 3 -

 3 Fig. 3 -The open base blocking capability of BJT 3#D5-3 a) and its output characteristics in b).

Fig. 4 -

 4 Fig. 4 -The βs of design 2# and 3# of the tested devices in a) and β of BJT 2#D2-3 at 25°C and 150°C in b).

Fig. 5 -

 5 Fig. 5 -Output characteristics of the Darlington a) and β of the Darlington as opposed to that of the two paralleled BJTs b).

( 3 #Fig. 6 -

 36 Fig. 6 -Full Double Pulse waveforms for BJT single 3#D5-3 in a), paralleled 3#P1 in b) and Darlington 3#D1 in c) at room temperature.

Fig. 7 -

 7 Fig. 7 -Hard turn on waveforms for BJT single 3#D5-3 in a), paralleled 3#P1 in b) and Darlington 3#D1 in c) at room temperature with a bus voltage of 3 kV and a turn on current of 10 A.

Fig. 8 -

 8 Fig. 8 -Hard turn-off waveforms for BJT single 3#D5-3 in a), paralleled 3#P1 in b) and Darlington in c) at room temperature with a bus voltage of 3 kV.

Table 1 -

 1 Main switching parameters of the single BJT, the paralleled BJT and the Darlington extracted from Fig.7and Fig.8.

Acknowledgement

The authors wish to acknowledge CALY Technologies for their precious help with the design, fabrication and on wafer characterisation of the BJTs. Acknowledgements are addressed to DeepConcept also for their help with packaging.

This work was supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" Program (ANE-ITE-002-01).

Summary and Conclusions

Static and switching characteristics of 2.4 mm² active are single SiC BJT, 2 paralleled SiC BJTs and SiC Darlington have been measured and reported in this study. Average βMAX of 9.5 has been achieved for the third (3#) and best design. The specific on-resistance is as low as 198 mΩ•cm² for the single BJT and102 mΩ•cm² for the Darlington. The peripheral protection has to be improved on a future run in order to block 10 kV. Turn-on is obtained for times inferior to 100 ns with very sharp dV/dt and di/dt. Turn-on energies lower than 4 mJ have been recorded. Turn-off has been successfully operated at current densities as high as 854 A/cm² and 987 A/cm² for the single BJT and Darlington respectively. This gave rise to current tail, which may be due to bipolar operation under high current injection condition. The Darlington packaging showed that a monolithic Darlington can be an interesting device for power switching applications.