Philippe Ravier
email: philippe.ravier@univ-orleans.fr

Frédéric Leclerc
email: frederic.leclerc@univ-orleans.fr

Cedric Dumez-Viou
email: cedric.dumez-viou@obs-nancay.fr

Guy Lamarque
email: guy.lamarque@univ-orleans.fr

Redefining performance evaluation tools for real-time QRS complex classification systems

Keywords: QRS complex detection, heartbeat recognition, neural network, classification, hardware implementation

In a heartbeat classification procedure, the detection of QRS complex waveforms is necessary. In many studies, this heartbeat extraction function is not considered: the inputs of the classifier are assumed to be correctly identified.

This paper aims to redefine classical performance evaluation tools in entire QRS complex classification systems and to evaluate the effects induced by QRS detection errors on the performance of a heartbeat classification processing (normal vs abnormal). Performance statistics are given and discussed considering the MIT/BIH database records that are replayed on a real-time classification system composed of the classical detector proposed by Hamilton & Tompkins, followed by a neural network classifier. This study shows that a classification accuracy of 96.72% falls to 94.90% when a drop of 1.78% error rate is introduced in the detector quality. This corresponds an increase of about 50% bad classifications.

I. INTRODUCTION

The problem of heartbeat classification has been widely explored in the literature [START_REF] Minami | Real-time discrimination of ventricular tachyarrhythmia with Fourier-transform neural network[END_REF]- [START_REF] Hu | Applications of artificial neural networks for ECG signal detection and classification[END_REF]. However, real-time classification systems often necessitate the detection of QRS complex shapes before any classification procedure.

In such classification systems, classical performance evaluation tools become irrelevant since the detection errors are not taken into account in the classification statistics. In this paper, we therefore propose to:

• redefine the classical performance evaluation tools taking the entire classification system into consideration;

• experimentally discuss the influence of the detection stage on classification results;

• give material for finding the best compromise between the quality of the detector, the quality of the classifier and the computational time in real-time classification systems.

In order to achieve these goals, we implemented a simple real-time classification system on an electronic board.

The proposed system is composed of a QRS complex extractor (detection part) followed by a normal or abnormal peak recognition step (classification part). Abnormal beats are opposed to normal beats according to their QRS waveform shapes.

For instance, a normal/abnormal classification system may be useful for Holter monitoring where only the critical parts as well as the cardiac history (i.e. peak to peak intervals) are of medical interest. It is not worth recording the healthy electrocardiographic (ECG) samples. The amount of data can therefore be drastically reduced and the entire breakdown will be shorter since the physician will devote his expertise to the critical parts of the ECG signal, while also taking into account the peak to peak intervals of the entire monitoring.

Several algorithms have been proposed in the literature for the detection and classification of ECG beats. Since our system has to be embedded with real-time processing constraints, the computation cost must be low. Various approaches (wavelets [START_REF] Li | Detection of ECG characteristic points using wavelet transforms[END_REF], [START_REF] Kadambe | Wavelet transform-based QRS complex detector[END_REF], filter banks [START_REF] Afonso | ECG beat detection using filter banks[END_REF], neural networks [START_REF] Xue | Neural-network-based adaptive matched filtering for QRS detection[END_REF]) have been investigated to improve the quality of the detectors. However, the gain obtained is generally offset by the greater complexity of the algorithms, involving higher computational costs. It is the reason why the well known Hamilton & Tompkins [START_REF] Pan | A real-time QRS detection algorithm[END_REF], [START_REF] Hamilton | Quantitative investigation of QRS detection rules using the MIT/BIH arrhythmia database[END_REF] detector has been chosen here. Similarly, many methods have been investigated for the classification part (neural networks [START_REF] Minami | Real-time discrimination of ventricular tachyarrhythmia with Fourier-transform neural network[END_REF]- [START_REF] Shyu | Using wavelet transform and fuzzy neural network for VPC detection from the Holter ECG[END_REF],

fuzzy theory [START_REF] Shyu | Using wavelet transform and fuzzy neural network for VPC detection from the Holter ECG[END_REF], [START_REF] Osowski | ECG beat recognition using fuzzy hybrid neural network[END_REF], support vector machine [START_REF] Osowski | Support vector machine-based expert system for reliable heartbeat recognition[END_REF], higher order spectral techniques [START_REF] Khadra | A quantitative analysis approach for cardiac arrhythmia classification using higher order spectral techniques[END_REF], hidden Markov models [START_REF] Andreão | ECG analysis through hidden Markov models[END_REF],

. . . ). A neural network approach has been adopted in this study because its parallel processing implementation is well adapted to real-time constraints. Finally, we tested the system on the MIT-BIH database [START_REF] Mark | MIT-BIH Arrhythmia Database Directory[END_REF] since this database is commonly used for performance evaluations of detection or classification algorithms.

The paper is organized as follows. The classification system is introduced in the second part. Such a system leads to the redefinition of the performance evaluation tools in the third part. These new tools are tested on real data in the fourth part, considering real-time classification of the MIT/BIH recordings. Discussion and conclusion finish the article.

II. NORMAL/ABNORMAL REAL-TIME BEAT CLASSIFICATION SYSTEM

After digitizing the analog ECG signal through a 16 bits Analog to Digital Converter (ADC) using a 360 Hz sampling rate, the algorithmic part is divided into two main functions (Fig. 1):

• the ECG beat extractor that detects QRS complex waveforms and extracts ECG waveform patterns after they have been normalized and centered about the fiducial point. Two versions of the Hamilton and Tompkins detector have been real-time implemented [START_REF] Pan | A real-time QRS detection algorithm[END_REF], [START_REF] Hamilton | Quantitative investigation of QRS detection rules using the MIT/BIH arrhythmia database[END_REF]: the first one includes the search back procedure (SB+)

and the second one does not (SB-).

• the neural network classifier that is fed by Fourier coefficients of the ECG waveform patterns provided by the previous stage. The classifier is a multilayer perceptron (MLP) [START_REF] Haykin | Neural networks: a comprehensive foundation[END_REF] with 16 input nodes (16 first absolute values of the 128 Fourier samples excluding the DC component), 4 neurons in the hidden layer and one output neuron. Each neuron labeled 1 to 5 has four inputs and one output with the classical associated sigmoidal activation function y j (n) = and j the neuron number. The value v j (n) is the net internal activity level of neuron j and equals v j (n) = 4 i=1 w ji x ji (n), for j = 1 to 4 and v 5 (n) = 4 i=1 w 5i y i (n). The output S(n) = y 5 (n) is compared to a threshold η = 0.5 to make the decision. The weights w ji and bias θ j are computed with the software SNNS [START_REF] Zell | SNNS, Stuttgart Neural Network Simulator, User Manual, Version 4.2[END_REF]: The two output classes separate the normal beats (expert annotations 'N' and 'A') from the abnormal beats (expert annotations 'L', 'R', 'B', 'a', 'J', 'S', 'V', 'r', 'F', 'e', 'j', 'n', 'E', '/', 'f', 'Q' and '?').

w 1i = {7.
The detector is implemented on a Digital Signal Processor (DSP TMS320VC5402, Texas Instruments). The preprocessing of the input delivered to the neural network is also computed on the DSP. The neural network is parallel processed on a Field Programmable Gate Array architecture (FPGA XC2S200, Xilinx).

III. REDEFINING PERFORMANCE EVALUATION TOOLS

Heartbeat detection consists in discriminating at any time a QRS complex from the noise. In fact, this detection problem may be formulated as a binary classification problem, in which the two classes are the noise and the QRS complex. The same statistical tools will therefore be used to evaluate the performances of both classifiers: the QRS complex/noise classifier and the normal/abnormal beat classifier. However, the statistics for the noise class will not be defined since they provide no useful information.

A. Sensitivity S and positive predictivity P +

Making the decision within the ith class may be true or false. Each right decision increments true numbers whereas each erroneous decision increments false numbers in the following statistics: the True Positive number (T P i ) stands for the right classification number among the patterns belonging to the ith class; the False Positive number (F P i ) is the number of patterns that were found to be in the ith class while they did not belong to this class; the False Negative number (F N i ) is the number of patterns that were not found to be in the ith class while they belonged to this class. Note that, with only the two classes {Normal, Abnormal}, the following relations hold:

F P N ormal = F N Abnormal and F P Abnormal = F N N ormal .
The comparison of classification performance is carried out from the values given by the sensitivity S and the positive predictivity P + . Classically, sensitivity is the percentage of patterns truly assigned to the class i among all the patterns really belonging to this class (expert decision). Positive predictivity (also named specificity) is the percentage of patterns truly assigned to the class i among all the patterns assigned to this class by the classifier (machine decision). These statistics quantify each kind of error in the decision making since S involves F N and P + involves F P . Considering the single detector or the single classifier, these definitions clearly hold. However, they are no longer valid when considering the global classifier composed of both the classifier and the detector where detection errors must be taken into account.

In particular, the detection errors lead to a number of classified beats that may be different from the number of beats presented at the input of the global classifier. This difference is due to the erroneous F N QRS and F P QRS December 3, 2007 DRAFT decisions. The F N QRS are the number of beats which have not been detected at the first stage. These beats will thus never be classified. However, these beats are known to be either normal or abnormal beats so the F N QRS number may be broken down as F N QRS = F N QRS N ormal + F N QRS Abnormal (medical expertise separation). On the other hand, the F P QRS number introduces new false QRS beats. Since these waveforms are detected, they will be classified as normal (F P QRS N ormal ) or abnormal (F P QRS Abnormal ) while they do not belong to either of these classes. So the false alarm detection rate may be broken down as F P QRS = F P QRS N ormal + F P QRS Abnormal (machine separation). The sensitivity S and the positive predictivity P + are then redefined by introducing the detection errors as:

S i = T P i T P i + F N i + F N QRS i ; P + i = T P i T P i + F P i + F P QRS i (1)
for the classes i = N ormal, Abnormal.

Regarding S i , all the beats classified by the experts as belonging to the class i may become correctly classified (incrementing the number T P i ), or become classified in the other class (incrementing the number F N i ) or even lost forever (incrementing the number F N QRS i ). Regarding P + i , all the beats classified by the machine to the class i may come from correctly classified beats (incrementing the number T P i ), from misclassified beats (incrementing the number F P i ) or from the false alarm beats generated by the detector (incrementing the number F P QRS i ).

B. Total classification accuracy T CA

The quality of the beat classification machine is classically evaluated through the Total Classification Accuracy (TCA) which corresponds to the fraction of good classifications among the number of beats to be classified.

Regarding the global classification machine, the T CA is not sufficiently pertinent since it does not take into account the false alarms generated by the detector. For example, if the classification machine is characterized by a 100% T CA rate (estimated with no detection errors), the physician will have total confidence in the classification task even if the F P QRS attains a high level. In that case, when these non existing beats are classified as abnormal beats, the machine will alert the physician without any reason. Similarly, a 100% T CA rate combined with a high level F N QRS could lead to a dramatic situation because of a lack of complexes analyses. For all these reasons, the T CA must be redefined in order to take into account not only the quality of the classifier but also the quality of the detector.

For the physician, the classification system is a black box characterized by an estimated T CA which needs to reflect the observations. In order to retrieve confidence in the T CA, we propose a novel definition of this performance evaluation tool. Let us call T CE = 1 -T CA the Total Classification Error rate expressed as:

T CE = F P N ormal + F P Abnormal + F P QRS + F N QRS N N ormal + N Abnormal (2)
The false alarm number F P QRS really stands for non-classifications. Since the classification is binary, all the F P QRS beats could be considered as misclassifications. Let us now consider the missed detections F N QRS . If all these beats could be correctly detected, the worst case that could occur would be a misclassification of all these December 3, 2007 DRAFT beats. So the F P QRS + F N QRS beats are included in the T CE definition that describes the worst case. Finally, the T CA is computed as the complementary value of the T CE.

These redefined statistics have been used to characterize the real-time classification process of 23 free records of the MIT/BIH database. In order to evaluate the influence of the detection stage on the classification performance, the results for three detectors are presented (table I): the detector is perfect (the beats are actually extracted by the cardiologist's expertise); the detector makes erroneous decisions at the mean rate of 0.85% (result for the single detector when the search back rule is implemented, label SB+); the detector makes twice as many erroneous decisions at the mean rate of 1.78% (result for the single detector when no search back rule is implemented, label SB-).

IV. DISCUSSION

From the results presented in table I, it can be seen that our system shows coherent performance values in comparison with other single detectors or classifiers [START_REF] Hu | Applications of artificial neural networks for ECG signal detection and classification[END_REF], [START_REF] Li | Detection of ECG characteristic points using wavelet transforms[END_REF], [START_REF] Afonso | ECG beat detection using filter banks[END_REF]. In fact, the only objective performance comparison that can be made is with the detector proposed by Hamilton and Tompkins. Our results (0.85% detection error rate) slightly differ from those presented in [START_REF] Hamilton | Quantitative investigation of QRS detection rules using the MIT/BIH arrhythmia database[END_REF] (0.52%) because not all the refinements suggested in [START_REF] Hamilton | Quantitative investigation of QRS detection rules using the MIT/BIH arrhythmia database[END_REF] have been implemented, in order to optimize the computation time.

A. General comments on the results

For those records where the proportion of a given class with respect to the other class is highly unbalanced, the results in percentage of S and P + are clearly not significant. This explains that specificity and positive predictivity may vary from the extreme percentages 0% to 100% or even NaN (Not a Number). This is the case for the files 100, 101, 103, 107, 209, 214 (see tables I and II where the number of expert beats in the normal or abnormal class is less than or equal to 2). Our system presents high P + values with around 96% of the classified beats that are correctly assigned. Concerning S, from a medical point of view, a high S Abnormal rate is preferable to a high S N ormal rate since the alarms are triggered on abnormal events. Our classifier shows the opposite tendency (94.02% vs 98.14%). However, at a S Abnormal = 94.02% rate, the clinician will have at his disposal a sufficient number of abnormal beats for his expertise.

The Search Back method is a rule of reduced threshold backward detection that is triggered whenever no beat is detected during more than 150% of the previous 8 beat-to-beat intervals median elapsed time [START_REF] Hamilton | Quantitative investigation of QRS detection rules using the MIT/BIH arrhythmia database[END_REF]. The analysis of the evolution of the T according to the quality of the detector (

B. Influence of the detection errors on the S and P + statistics

The quality of detection globally seems to have no influence concerning normal beats: the 1.78% detection error rate induced by the SB-detector -with respect to a perfect detector -does not really change S N ormal and P + N ormal (Table I).

On the contrary, concerning abnormal beats, the drop affecting the sensitivity becomes serious when working with imperfect detectors. The observed difference of 4.12% between S N ormal and S Abnormal with a perfect detector now drops to 8.74% when the SB-detector is used. At a reduced scale, the observed difference of 0.49% between P N ormal and P + Abnormal becomes 0.98% with the SB-detector. This bad news concerning the statistics for abnormal beats may be significant and suggests that the quality of detection should not be neglected within a classification procedure.

C. Influence of the detection errors on the T CA statistics

A coherent behavior of the T CA with respect to the quality of the detector is observed on average in table I: the T CA decreases with the deterioration of the detection performances. An error rate of 1.78% at the first detection stage produces a loss of 1.82% in the T CA ratio (Table I). However, this ratio may individually lose about 16% (record 208) or even gain about 0.7% (record 200).

In particular, the biggest deterioration is shown in record 208 with an increase from 46 (SB+) to 462 (SB-) in the F N QRS number (table II). The result is a marked decrease in the classification ratio from T CA (SB+) = 93.13% to T CA (SB-) = 79%. Note that the F N QRS number is mainly due to the contribution of abnormal beats. Indeed, the F N QRS Abnormal number at the denominator of S Abnormal makes sensitivity dramatically decrease from 91.96% (ideal detector) to 58.00% (detector with SB-procedure) whereas minor changes are observed in the other cases for S and P + . Thus the importance of having a good detection stage is once again demonstrated.

In average, this study shows that a classification accuracy of 96.72% falls to 94.90% (table I) when a drop of 1.78% error rate is introduced in the detector quality. Thus, for quite good classifiers, particular care must be taken with the quality of the first detection stage since this increases the number of bad classifications by about 50%. In this case, it is worth trying to improve the detection algorithm, provided the real-time constraint is fulfilled.

V. CONCLUSION

In this paper, we have redefined the performance evaluation tools for characterizing a complete classifier, which consists of a detector followed by a single classifier. The detection errors are introduced in these new definitions, providing more coherent statistics for the clinician. These new statistics increase safety since they now provide reliable lower limits for the performance values. We experimentally tested these new tools on the MIT/BIH database with a dedicated real-time hardware and software architecture.

The proposed tools can be applied considering other kinds of algorithms and architectures. The comparison between various implementation configurations therefore becomes objective. December 3, 2007 DRAFT Even if an exhaustive comparative study is not presented in this paper, the results obtained are quite significant.

Indeed, the MIT/BIH database presents a great diversity of pathologies, exhibiting a good panel of QRS waveforms morphologies. The results show that the detection stage has a reduced influence concerning the sensitivity for normal beats and the positive predictivity for normal/abnormal beats. This suggests that the classification system may be improved by investigating the classification stage. Nevertheless, care must be taken with the detector stage that may deteriorate the total classification error rate by about 50%, considering a drop of 1.78% error rate in the detection quality. In conclusion, the higher the performance of the classifier, the greater the impact of the detector.

Fig. 1 .

 1 Fig. 1. Normal/abnormal beat classification: the ECG beat extraction function is compounded in the first two blocks; the neural based classification function is compounded in the last two blocks.

  62, 2.98, -11.06, 1.57}, w 2i = {8.08, 1.71, 3.31, -0.5}, w 3i = {-4.4, 24.86, 4.74, 8.58}, w 4i =

	{4.56, 4.6, 19.86, 4.89}, w 5i = {-8.85, -29.81, 11.14, 10.56} and θ j = {2.15, -5.45, -3.16, -1.61, 7.21}.

  Table II) shows the efficiency of the search back rule for a few records: 106, 201, 210, 213, 214 and more particularly 208 (where F N QRS decreases from 462 to 46). Overall, the Search Back method strongly decreases the F N QRS number (821 to 182 counts) while increasing the F P QRS number (223 to 314 counts) at the same time. The influence of these detection errors on the quality of classification is discussed in the next section.

	December 3, 2007	DRAFT

TABLE I EVOLUTION

 I OF THE CLASSIFIER PERFORMANCE (S i , P + i AND T CA) WITH THE QUALITY OF THE DETECTOR AT THE INPUT STAGE: 0%, 0.85% (LABELED SB+), 1.78% (LABELED SB-) DETECTION ERRORS. FOR THOSE RECORDS WHERE T P i = F N i = 0 (RESP. T P i = F P i = 0), S i (RESP. P + i ) IS ASSIGNED TO NAN (NOT A NUMBER) BECAUSE ITS DENOMINATOR IS ZERO.

	December 3, 2007
					Sensitivity (%)				Positive Predictivity (%)			TCA (%)
		File		Normal			Abnormal			Normal			Abnormal
		#	S	S(SB+)	S(SB-)	S	S(SB+)	S(SB-)	P +	P + (SB+)	P + (SB-)	P +	P + (SB+)	P + (SB-)	T	T(SB+)	T(SB-)
		100	100.0 100.0 100.0 100.0 100.0 100.0	100.0	100.0	100.0 100.0	100.0	100.0	100.0 100.0 100.0
		101	99.36 99.19 99.36 100.0 33.33 33.33	100.0	100.0	100.0 14.29	4.55	5.26	99.36 98.77 98.93
		102	7.07	5.05	5.05	99.95 99.95 99.95	87.50	83.33	83.33 95.78	95.69	95.69	95.75 95.66 95.66
		103	100.0 100.0 100.0	NaN	0.00	0.00	100.0	100.0	100.0	NaN	NaN	NaN	100.0 99.95 99.81
		104	82.82 86.42 87.04 94.19 92.69 92.60	52.94	48.95	50.36 98.58	93.33	94.99	93.36 86.67 88.38
		105	90.58 90.96 90.44 50.00 40.32 33.87	99.00	98.83	98.65	8.81	7.76	6.65	89.85 86.74 86.70
		106	99.93 99.87 99.87 79.42 76.92 63.08	93.37	92.79	93.02 99.76	99.50	99.39	94.67 93.98 90.43
		107	NaN	NaN	NaN	99.86 99.86 99.77	0.00	0.00	0.00	100.0	100.0	100.0	99.86 99.81 99.72
		118	1.04	1.04	1.04	99.31 99.22 99.22	6.25	5.26	5.26	95.80	95.67	95.67	95.17 94.91 94.91
		119	100.0 100.0 100.0 100.0 100.0 100.0	100.0	100.0	100.0 100.0	100.0	100.0	100.0 100.0 100.0
		200	96.84 97.29 97.52 83.70 84.20 85.40	92.71	92.89	93.56 92.52	92.33	93.40	92.66 92.54 93.35
		201	99.40 100.0 100.0 84.42 71.84 60.19	97.16	96.61	96.84 96.30	100.0	100.0	97.04 95.57 93.73
		202	99.48 99.57 99.57 66.67 60.00 35.00	99.38	99.48	99.48 70.27	72.73	60.87	98.88 98.83 98.36
		205	99.92 100.0 100.0 81.71 78.57 77.38	99.42	99.42	99.46 97.10	100.0	100.0	99.36 99.32 99.28
		208	97.54 98.10 98.09 91.96 88.24 58.00	93.36	92.91	92.78 97.00	96.89	95.47	94.95 93.13 79.00
		209	99.73 99.67 99.63 100.0 100.0 100.0	100.0	100.0	100.0 11.11	8.33	7.69	99.73 99.63 99.60
		210	97.48 97.89 97.93 68.72 63.64 50.87	97.08	97.09	97.21 71.89	71.36	69.23	95.02 94.45 93.62
		212	98.16 97.72 98.16 99.07 99.07 99.12	98.16	98.26	98.37 99.07	98.85	99.07	98.76 98.62 98.80
		213	99.96 100.0 100.0 57.44 57.00 53.41	91.46	91.42	91.36 99.70	100.0	100.0	92.31 92.25 91.60
		214	NaN	NaN	NaN	93.68 90.58 89.78	0.00	0.00	0.00	100.0	99.85	99.90	93.67 90.44 89.60
		215	99.94 99.94 99.94 81.21 77.58 76.97	99.04	98.89	98.89 98.53	97.71	97.69	99.02 98.81 98.78
		217	100.0 99.59 99.59 98.07 98.01 97.81	86.52	87.10	86.79 100.0	99.84	99.90	98.28 98.10 97.92
		219	99.86 99.86 99.95 84.62 84.62 74.63	99.52	99.52	99.52 94.83	94.83	98.04	99.40 99.40 99.16
	DRAFT	all	98.14 98.27 98.27 94.02 92.73 89.53	96.88	96.56	96.58 96.39	95.41	95.60	96.72 95.89 94.90

1+e -v j (n)+θ j , where n is the number of QRS pattern to be classifiedDecember 3,

DRAFT

December 3, 2007 DRAFT

ACKNOWLEDGMENT

The authors would like to thank CRESITT Industrie for the design and realization of the DSP-FPGA hybrid electronic board (http://www.cresitt.com).

LIST OF FIGURES 1

Normal/abnormal beat classification: the ECG beat extraction function is compounded in the first two blocks; the neural based classification function is compounded in the last two blocks. . . . . . . . . . 9 December 3, 2007 DRAFT LIST OF TABLES I Evolution of the classifier performance (S i , P + i and T CA) with the quality of the detector at the input stage: 0%, 0.85% (labeled SB+), 1.78% (labeled SB-) detection errors. For those records where


Ravi Gopal

Nagaraja Mbbs
email: ravinagaraja@nhs.net

; Morven

Wilson Mbchb

; Graham

MD Bruno Marciniak

PhD Thomas Engelhardtmd

Dr Ravi Gopal Nagaraja

The anatomic relationship between the internal jugular vein and the carotid artery in children after laryngeal mask insertion. An ultrasonographic study

Keywords: Ultrasound, Laryngeal Mask Airway, Internal Jugular

Background: Central venous cannulation although challenging in children and prone to complications is frequently required for total parentral nutrition and infusion of drugs.

Aim: The aim of this study was to determine the anatomic relationship between the internal jugular vein (IJV) and carotid artery (CA) before, and after, insertion of laryngeal mask airway (LMA) in children using ultrasound.

Methods: Patients aged 2-16 yrs were recruited into this prospective study and divided into 3 groups of 20 patients each: group 1: LMA size 2, group 2:LMA size 2 and group 3: LMA size 3. Prior to, and following, LMA insertion, the position, depth and time to location of the vessels was recorded. All measurements were made at the level of the cricoid cartilage in a neutral head position in the spontaneously breathing patient during expiration. The IJV position in relation to the CA was noticed as anterior (A), anterolateral (AL), lateral (L) or medial (M).

Results:

The position of the IJV was found to be in the anterolateral (AL) or anterior (A) position to the CA in the majority of cases. The anatomic relationship changed in 10/120 (8.3%) following insertion of the LMA. The mean depth was 0.80 (±0.15) cm for the right IJV before LMA insertion and 0.84 (±0.17) cm after insertion. Similar measurements were made on the left side (0.81 (±0.14) cm and 0.83 (±0.18) cm). The diameter as well as the depth of the IJV increased with the age and weight of the patient. is often required for total parentral nutrition and infusion of drugs. Ultrasound guided central venous cannulation results in higher success rate and lower complications compared to landmark technique [START_REF] Verghese | Ultrasound-guided internal jugular venous cannulation in infants[END_REF][START_REF] Hind | Ultrasonic locating devices for central venous cannulation: meta-analysis[END_REF][START_REF] Slama | Improvement of internal jugular vein cannulation using an ultrasound-guided technique[END_REF][START_REF] Verghese | Comparison of three techniques for internal jugular vein cannulation in infants[END_REF]. The position of the internal jugular vein (IJV) in relation to the carotid artery (CA) has been studied in adults [START_REF] Denys | Anatomical variation of the internal jugular vein location: impact on central venous access[END_REF][START_REF] Troianos | Internal jugular vein and carotid artery anatomic Relation as determined by ultrasonography[END_REF][START_REF] Riopelle | Circumferential adjustment of ultrasound probe position to determine the optimal approach to the internal jugular vein: a non-invasive geometric study in adults[END_REF]. Few studies have been reported in children, with one study demonstrating a variable position of the IJV in relation to the CA following tracheal intubation [START_REF] Roth | Anatomic relationship between the internal jugular vein and the carotid artery in pre-school children -an ultrasonographic study[END_REF]. This study describes the anatomic relationship between the IJV and CA before and after laryngeal mask (LMA) insertion.

Methods

Following local ethics committee approval and parental consent, a total of 60 healthy patients aged 2-16 years were recruited into this prospective study. The children were divided into different groups depending on their weight, Group1 (LMA size 2), Group 2 (LMA size 2½) and Group 3 (LMA size 3). Exclusion criteria included emergency surgery, patients requiring rapid sequence induction, parental refusal, patients with previous IJV cannulation and patients with known or suspected anatomical abnormality.

Following inhalational or intravenous induction of anaesthesia, the child was placed supine with the head in a neutral position. Ultrasound measurements of the neck were performed by a single investigator using a Sonosite (Micromaxx R ultrasound system, Transducer SLA 13-6 MHz, 25 mm broadband linear array). The ultrasound probe was placed perpendicular to the skin and the images were obtained from the right and left side of the neck at the level of the cricoid cartilage in the spontaneously breathing patient during expiration. The positions

Results

Sixty patients were recruited into this study. Mean (±1 SD) age and weight were 3.45 (±6) years, 8 (±2) years, 12.3 (±1.4) years and 16.32 (±3.8) kg, 26.6 (±2.9) kg, 50.5 (±7.9) kg for groups 1, 2 and 3 respectively.

The mean depth overall was 0.80 (±0.15) cm for the right IJV before and 0.84 (±0.17) cm after LMA insertion and 0.81 (±0.14) cm and 0.83 (±0.18) cm on the left side. (Table 1) The position of the IJV was found to be in the anterolateral (AL) or anterior (A) position in relation to the CA in the majority of cases and the anatomic relationship changed in 10/120 (8.3%) following insertion of the LMA. (Figure 1) The diameter as well as the depth of the IJV increased with the age and weight of the patient.

Mean duration for localization of the vessels was 4.3 (±0.9) s and 4.2 (±1.0) s for the right and left IJV, respectively. The LMA was easily identified using ultrasound.

Discussion

The use of ultrasound for central venous access is associated with a lower technical failure rate; reduction in complications and faster access. The success of IJV cannulation in infants and children has been reported in different studies to vary from 77% to 97.2% [START_REF] Hayashi | Internal jugular vein catheterization in infants undergoing cardiovascular surgery; An analysis of the factors influencing successful catheterization[END_REF][START_REF] Prince | Percutaneous catheterisation of the internal jugular vein in infants and children[END_REF]. The use of ultrasound results in an 86% relative risk reduction of failure and 57% reduction in complications compared to landmark techniques (4). Verghese et al have demonstrated a 100% success rate without arterial puncture versus 77% with 25% carotid puncture in children below 12 months using ultrasound [START_REF] Verghese | Ultrasound-guided internal jugular venous cannulation in infants[END_REF]. Internal jugular vein cannulation by landmark methods is often difficult and carries a high incidence of CA puncture due to the close proximity and the small calibre of the vessels [START_REF] Prince | Percutaneous catheterisation of the internal jugular vein in infants and children[END_REF]. In addition, there are anatomic variations in the relative positions of IJV and CA [START_REF] Denys | Anatomical variation of the internal jugular vein location: impact on central venous access[END_REF][START_REF] Troianos | Internal jugular vein and carotid artery anatomic Relation as determined by ultrasonography[END_REF][START_REF] Roth | Anatomic relationship between the internal jugular vein and the carotid artery in pre-school children -an ultrasonographic study[END_REF].

The LMA is useful airway device in children for a variety of surgical procedures. It is easy and atraumatic to insert, eliciting minimal autonomic response. Mason et al have demonstrated LMA is a safe device in children and in only 2.5% of cases had to use an alternate airway [START_REF] Mason | The laryngeal mask airway in children[END_REF].

A survey by Lopez-Gil et al in the use of LMA in children concluded that LMA provides a safe and effective form of airway management in experienced trainees [START_REF] Lopez-Gil | Safety and efficacy of the laryngeal mask airway: A prospective survey of 1400 children[END_REF]. In children with difficult airway and intubation, LMA obtained a good airway in 73% of patients and an adequate airway in 27% of patients (14). LMA is a vital component of the difficult intubation trolley (15). This current study determined the relationship between IJV and CA before and after laryngeal mask airway insertion at the level of cricoid cartilage in spontaneously breathing patients. Ultrasound location of the neck vessels was easy and did not delay the procedure.

The IJV was anterolateral or anterior to the CA in the majority of patients with the head placed in the neutral position and the diameter as well as the depth of the IJV increased with the age and weight of the patient and is consistent with previous reports [START_REF] Roth | Anatomic relationship between the internal jugular vein and the carotid artery in pre-school children -an ultrasonographic study[END_REF].

LMA insertion did alter the anatomical relationship between the CA and IJV in approximately 8% of the spontaneously breathing patients. This may be of relevance when attempting IJV cannulation using a landmark technique following initial ultrasound location of the IJV. This study, therefore, provides further evidence for the use of ultrasound for IJV cannulation following LMA insertion in spontaneously breathing children.

  This study demonstrates that the IJV is anterior or anterolateral to the artery in the majority of cases and the anatomic relationship may change following the insertion of the LMA. It supports the need of using ultrasound-guided techniques for IJV cannulation following LMA insertion in spontaneously breathing children.Keywords: Laryngeal mask airway, Internal jugular vein, ultrasound.

  IntroductionCentral venous cannulation although challenging in children and prone to complications[START_REF] Hayashi | Internal jugular vein catheterization in infants undergoing cardiovascular surgery; An analysis of the factors influencing successful catheterization[END_REF][START_REF] Kua | Airway obstruction following internal jugular vein cannulation[END_REF]

  and left IJV in relation to the CA, the depth and diameter of the vein, as well as the time taken to locate the vessel were determined. Any distortion of the vein in relation to the CA, depth and diameter were noted.The IJV position in relation to the CA was noted as anterior (A), anterolateral (AL), lateral (L) or medial (M). All measurements were repeated following insertion of the LMA. Data are expressed as mean ± SD.

  RWM. The laryngeal mask airway in the difficult paediatric airway: an assessment of positioning and use in fibreoptic intubation. Pediatr Anesth 2000; 10: 53-8. 15. Difficult airway society guidelines. http://www.das.uk.com/guidelines/guidelineshome.html (accessed 18 August 2010).

Table 1

 1 Depths and diameters of the internal jugular vein before and after LMA insertion in spontaneously breathing patients. Results are mean (±SD) in mm.Relationship between internal jugular vein and carotid artery. The figures represent the total number of cases before/ after LMA insertion in each group.

	SIZE 2	(n=20)	DEPTH		DIAMETER
			RIGHT	LEFT	RIGHT	LEFT
		BEFORE LMA 0.70±0.19	0.71±0.2	1.18±0.26	1.11±0.28
		AFTER LMA 0.71±0.19	0.71±0.18	1.28±0.3	1.15±0.29
	SIZE 2.5	(n=20)	DEPTH	DIAMETER
			RIGHT	LEFT	RIGHT	LEFT
		BEFORE LMA 0.73±0.16	0.76±0.14	1.21±0.32	1.19±0.32
		AFTER LMA 0.78±0.16	0.75±0.13	1.26±0.35	1.18±0.32
	SIZE 3	(n=20)	DEPTH		DIAMETER
			RIGHT	LEFT	RIGHT	LEFT
		BEFORE LMA 0.98±0.28	0.97±0.22	1.36±0.31	1.01±0.33
		AFTER LMA 1.03±0.29	1.04±0.23	1.34±0.33	1.06±0.32


C Krzeminski

E Lampin

Solid phase epitaxy amorphous silicon regrowth : some insight from empirical molecular dynamics simulation Insight from molecular dynamics simulation on amorphous silicon re-growth

Keywords: 68, 55, A-Nucleation and growth -81, 15, Aa

The modelling of interface migration and the associated diffusion mechanisms at the nanoscale level is a challenging issue. For many technological applications ranging from nanoelectronic devices to solar cells, more knowledge of the mechanisms governing the migration of the silicon amorphous/crystalline interface and dopant diffusion during solid phase epitaxy is needed. In this work, silicon recrystallisation in the framework of solid phase epitaxy and the influence on orientation effects have been investigated at the atomic level using empirical molecular dynamics simulations. The morphology and the migration process of the interface has been observed to be highly dependent on the original inter-facial atomic structure. The [100] interface migration is a quasi-planar ideal process whereas the cases [110] and [111] are much more complex with a more diffuse interface. For [110], the interface migration corresponds to the formation and dissolution of nanofacets whereas for [111] a defective based bilayer reordering is the dominant re-growth process. The study of the interface velocity migration in the ideal case of defect free re-growth reveals no difference between [100] and [110] and a decrease by a mean factor of 1.43 for the case [111]. Finally, the influence of boron atoms in the amorphous part on the interface migration velocity is also investigated in the case of [100] orientation.

Introduction

Advanced technological research work dedicated to silicon materials process engineering needs to control the silicon recrystallisation process at the nanometer scale for nanoelectronic [1,2] or photo-voltaic devices [3,4]. The silicon film re-growth occurs during annealing when amorphous regions or layers are created by parasitic phenomena like in vapor-liquid-solid (VLS) grown silicon nanowires or intentionally, to limit diffusion effects like in advanced junction depth processing [5]. However, it is really difficult to reach a deeper understanding of the many effects taking place during regrowth. For example, the rich interplay between the nucleation rate, the interface roughening, the defects generation or dissolution and the dopant diffusion is difficult to characterise by using only experimental fabrication and characterisation techniques.

From the theoretical point of view, there is a debate on the general physical description of crystal growth [6]. The concept of a localised interface approach where the nucleation and growth process take place was first introduced by Burton, Cabrera and Frank [7]. On the other Correspondence to: christophe.krzeminski@isen.fr hand, the concept of a diffuse interface where an ordering flux is associated to the interface migration is also proposed. This flux is assumed to be generated by the counterbalance between the atomic forces interaction induced by the short-range order and the thermal motion [6]. In this framework, solid phase regrowth is often described as an thermal activated process shown by the following equation :

v SP E (T ) = v 0 exp - E a kT ( 1
)
where T is the interface temperature, v 0 is the exponential prefactor and E a is the activation energy. For silicon phase epitaxy, the debate focused on the nature of defects (dangling bonds, kink sites, vacancies, interstitials) on their location (crystal, interface, amorphous part) and on their influence on the limited growth rate [8]. The influence of interface orientation, stress or dopant is also under debate. Atomistic process modelling [9] in the framework of molecular dynamics is expected to help to clarify the physical picture. This method could probably provide more insight into the re-growth mechanisms taking place at the amorphous/crystalline interface during thermal annealing. Dopant incorporation and the as-sociated diffusion effects during re-growth are much more complex to simulate compared to the bulk case [10]. Moreover, information technology achieved significant progress and enabled the simulation of relatively large atomic configurations that could match experimental systems.

Preliminary simulation studies of the silicon solid phase epitaxy related to junction processing by molecular dynamics were performed by Mootoka et al. [11]. But many open questions remain on solid phase epitaxy like the substrate orientation influence despite clear technological interest. More knowledge is available in the case of meltinterfaces re-growth [START_REF] Grabow | Atomic Scale Calculations in Materials Science[END_REF]. This problem has also been investigated using a finite elements based method or lattice Kinetic Monte Carlo (KMC) [13] but numerous challenges are faced to take into account the complex reordering processes at the atomic level. The main objective of this paper is to present the work performed in order to investigate the influence of orientation and dopant effects on the amorphous silicon re-growth mechanisms. The first section briefly describes the computational details and the method used in this work. Some complementary tests related to the influence of the initial properties of the disordered layer are also provided. In a second part, most important results concerning the influence of the interface orientation on recrystallisation mechanisms are presented and discussed. Preliminary results on the influence of Boron atoms on the interface migration velocity are also provided. Finally, some important conclusions are drawn in the last section.

Methods

Computational details

Empirical molecular dynamic simulations have been undertaken in this work in order : i) to generate the amorphous and ii) to simulate the annealing step and the recrystallisation of an amorphous/crystalline silicon interface. In order to generate the disordered part, a melting process simulated by a thermal annealing at high temperature with a low quenching rate [14] is considered. The procedure has been repeated for the three clusters built along directions [100], [110] and [111] and containing respectively 4928, 5120 and 5184 atoms. The cell size parameters (8 × 8 × 10) is a trade-off between reasonable computational costs and a possible influence of the periodic conditions on regrowth rate. Fig 1 illustrates the various initial configurations. In order to simulate the layer re-growth, the Molecular Dynamics (MD) technique can also be applied to estimate the various atomic displacements at a given temperature in the framework of a Nosé-Hoover thermostat [15]. The two most used empirical potentials Tersoff [16] and Stillinger-Weber (SW) [17] are under study in this work. The regrowth velocity determination is based on the evolution of the c-Si/a-Si or l-Si interface. This location is estimated by using a plane structure factor as a function of the depth [18] as shown in Fig. 2. The temperature range for annealing is a function of the empirical potential and is given in Table 1. Only lateral periodic boundary conditions are considered leaving the possibility to the stack to expand or contract. In order to perform a uniform doping in the amorphous part, a specific approach has been developed. The amorphous part is sliced in various trenches of different thicknesses. Boron atoms are introduced in the amorphous lattice in a substitutional way. After the dopants introduction, the equilibration of the cluster is performed by a short annealing step leading to a final dopants distribution located in the amorphous part. Different concentration levels of boron are considered from the lowest one (0.2%) up to (5.4-6%). In the case of Molecular Dynamics with doped boron systems, only the Tersoff potential has been used. It is often claimed that no empirical potential describes properly the subtle Si-B and B-B interactions. In this work, the approach of Pérez-Martín et al. [19] is followed where boron atoms are assumed to adopt a similar behaviour in silicon like carbon atoms.

Recrystallisation velocity and disordered part properties

In a previous work, it has been shown that for the simulation of silicon solid phase epitaxy the empirical potential must be taken carefully into account with the high sensitivity to describe or preserve an amorphous structure during annealing [20]. However, there is a debate on the influence of the initial properties of the disordered part and the recrystallisation velocity obtained by molecular dynamics. In this work, the quality of the initial interface has been enhanced in comparison to previous studies where only a Wooten Winer Weaire's amorphous cluster on a crystalline box was considered. The two main usual methods for generating a virtual amorphous cluster (Monte-Carlo bond switching [21] or by melting-quench) are confronted. The melting temperature used to generate a liquid part and next the quenching rate is described in Table 1. As shown in Fig. 3 and also in table 2, large differences for the different properties (from radial and angular distribution to the mean coordination number distribution) in the disordered part can be observed. Fig. 4 reports the recrystallisation velocity of the a-Si or l-Si/c-Si interface for the two main potentials Tersoff and Stillinger-Weber (SW). For the recrystallisation velocity obtained using a Tersoff potential, Arrhenius kinetics have been observed for the two different amorphous in relative close agreement characterised with the same activation energy of ∼ 2.9 eV. The situation is completely different in the case of a simulated annealing using Stillinger-Weber. Despite the fact that in the first case, an initial a-Si/c-Si structure whereas in the second case a completely different l-Si/c-Si interface is under consideration, small differences can be observed. Clear liquid phase epitaxy characteristics with velocity re-growth of about a few ∼ m/s in a wide temperature range limited by the melting of the crystalline part is observed slightly above a temperature of 1675K. These results strengthen our previous conclusions about the major influence of the empirical potential used for the estimation of the recrystallisation velocity and on the variability of empirical potentials to preserve an amorphous structure upon annealing [20].

3 Results and discussion 3.1 Orientation effects and solid phase epitaxy

Regrowth mechanisms

The influence of the interface orientation effect on the regrowth mechanism has been investigated. The interface migration process is studied for the different crystalline orientations [100], [110] and [111]. Fig. 5 presents the a-Si/c-Si for an interface migration at 1700K during thermal annealing. For [100], the re-growth front is governed by first a diffusion process in the disordered part, then by a partial ordering at the interface and finally by a oneby-one atom incorporation. The propagation of the crystalline front proceeds in a quasi-planar a-Si/c-Si interface with some partial reordering which could extend to one or two planes.

For the orientation [110] a relative different mechanism has been observed in Fig. 6. Two silicon atoms have to be incorporated at the recrystallisation front and then to bind with each other. In order to get a second atom and to complete the crystalline plane, the recrystallisation is observed to propagate also vertically in another nucleation site. The re-growth front predicted by simulation is made of nanofacets leading to the formation of a sawtooth interface of about 3-4 atomic planes. For [110], the interface is more diffuse and characterised by a more important roughness as a partial ordering extend to several atomic planes.

For the case [111], the recrystallisation mechanisms are observed to be even more complex (Fig. 7) in comparison with [100] and [110]. The migration from a-Si to c-Si occurs by the rearrangements of complete or partial bilayers. For example, in the case of Fig. 7 incomplete bilayers form on the right and left part, while the central part is slowly rearranging (10 ns and 20 ns) letting suddenly appear several crystalline layers (25 ns). A buried defect at the top surface remains. The interface migration is made of successive plateaus whose height correspond to the distance (or a multiple of the distance) between the bilayers (111). The formation of one or more twins in planes (111) has been observed in nearly all the temperatures simulated. Other defects are observed in about 50 % of the simulations. The [111] interface recrystallisation interface is also completely different and mostly based on a bilayer process. For [111], the silicon atoms tends to organise partially in bilayer with a significant time necessary for the atomic arrangements within the the bilayer as three atoms of the bilayer are involved in the atomic process for the creation of a six-fold rings. Again, in the case [111], the recrystallisation process is not strictly planar with a large interplay between in and out of plane nucleation.

Orientation dependent recrystallisation velocity

One main open question concerns the influence of the regrowth mechanisms related to orientation effects at the a-Si/c-Si interface. Fig. 8 presents an example of the interface velocity extraction in the intrinsic case for the three orientations under study. This corresponds to the case where it was possible to define an a-Si/c-Si interface using a planar structure factor. This is not possible for in-plane and extended defects which generate too much disorder to allow a proper interface definition. All the systems considered are free from defects except for systems [111] containing only twin parallel defects. In this particular case, the orientation [111] is estimated to be kept since it is only a default in the stacking plane sequence. The results as a function of the temperature and for the three orientations are given in Fig. 8 in the temperature range that could be considered with a reasonable computing time. It can be observed that while being very close in the orientations [100] and [110], the velocity is lower along the direction [111] by a factor 1.43. For the orientation [100], the activation energy can be extracted using the classical theory of thermally activated growth [27]. Considering the fact that the interface velocity reported in the Arrhenius plot is superimposed or either parallel, there was no reason to consider a different activation energy for the cases [110] and [111].

Discussion

The theoretical picture given by molecular dynamics simulations stresses the importance of the initial interface orientation on the growth mechanisms. It has been observed that solid phase epitaxy mechanisms are strongly dependent on the interface orientation with a quasi-planar migration for the [100] interface. This propagation is compatible with most analytical modelling based on a sharp interface migration. For [110] and [111], the situation is relatively different with the formation respectively of nanofacets for [110] and a bilayer mechanism leading to the formation and the migration of a more complex and diffuse interface associated with the generation of defects. Even if the physical reality described by molecular dynamics is more complex, some connections could be made with the phenomenological model of Drosd and Washbrun [22] which described the initial recrystallisation steps [23]. The results on the interface recrystallisation velocity are more complicated to confront with experimental results. One main issue in our study is to define an interface migration velocity in the case where the a-Si/c-Si interface is more diffuse and characterised by the presence of defects. In this paper, only free-defect re-growth is considered. It corresponds to an ideal physical picture which is not observed experimentally [22]. The resulting activation energy of the process for the various orientation is 2.87 eV in accordance with the experimental range of [2.4-2.9]eV [22,24,25]. This activation energy cannot be associated with a simple active process like self-diffusion or defects migration. This energy seems rather associated with the energy barrier at the interface as suggested by Posselt et al. [26]. Since some bond breaking and exchange between the amorphous and the silicon phase and exchange are often observed in our simulation in order to allow a proper definition and propagation of the a-Si/c-Si interface. Some links could be made with the picture given by molecular dynamics and the approach of Lu et al. [27] which considered the dangling bond breaking, moving and trapping mechanism as the main process responsible for the growth rate limitation [8]. The prefactor for orientation [111] (1.2×10 7 m/s) is reduced by a factor 1.43 compared to [100] and [110] suggesting that the atomic incorporation mechanism based on three atoms at interface [111] slows down the overall interface migration compared to the other orientation. Only a small part of the velocity reduction can be explained by our molecular dynamics simulation. Since experimentally more interface recrystallisation velocity reduction is observed for [110] and [111], the role and the influence of defects on the nucleation velocity should be investigated more in depth at the theoretical level. A remaining open question that should be addressed concerns the influence of the cell size particularly in a large presence of defects. It seems to be the most plausible hypothesis to explain the reduction velocity effects.

Regrowth of a doped a-Si:B/c-Si interface

The possible influence of boron atoms in the silicon amorphous part has been investigated in the case of interface [100]. The implantation step has not been Fig. 9 presents an example of initial doped a-Si (doped)/c-Si interface [100] and illustrates the final state where the amorphous part is completely recrystallised with most of the boron atoms incorporated in substitutional positions of the crystalline matrix. This result is in agreement with a previous study on the annealing of damage generated by octodecaborane implantation [28]. The results concerning the interface recrystallisation velocity are first detailed just below and then discussed in further subsection.

Interface recrystallisation velocity

Fig. 10 reports the evolution of the interface position at 2000K 1 for different boron concentrations. In this case, it is clearly shown that the presence of boron is increasing the velocity of the interface migration. Fig. 11 summarises all the computer experiments performed in the intrinsic case and for 2 % and 6 % boron concentration configurations. Basically, for most temperatures, it can be observed that there is no significant difference between the intrinsic case and the 2 % case. The calibration by an Arrhenius law for the last case gives the same activation energy and a small difference for the prefactor (6.2 %). For a very large boron concentration (6 %), a small increase in the solid phase epitaxy velocity is observed leading to an increase in the prefactor by a ratio 1.34. 1 which would correspond to a rescaled temperature of about 1000 • C

Discussion

In this work, a complete different behaviour has been observed compared to similar previous molecular dynamics simulations performed by Mattoni et al. [29]. Using molecular dynamics in the framework of the Stillinger-Weber empirical potential, an increase of the re-growth velocity at low boron concentrations (below 1%) has been observed whereas for larger concentrations (1% up to 10%) the velocity is reduced. On the experimental side [24], it has been observed that below 0.06 %, the boron concentration has almost no influence on the recrystallisation velocity. However, around 0.2 %, a significant increase is observed up to a factor 10 at a low temperature annealing (∼ 600 • C). Our results obtained using Tersoff are much more in agreement with the experimental picture and the observed minor influence of boron at low concentration. Probably, in the case of Stillinger-Weber simulation, the mechanism is more compatible with a framework of liquid phase epitaxy with the high tendency of SW based a-Si for melting even at low temperature [20]. Compared to the experimental results, it would not be so surprising that the influence of dopant is largely underestimated by our empirical molecular dynamics simulation since the Fermi level variations in our system are not taken into account theoretically. Generalised Fermi-Level Shifting (GFLS) model and the influence of charged defects at the interface are often assumed empirically with some success to estimate the enhancement of the normalised re-growth rate defined by the ratio of the doped recrystallisation velocity in the doped with the intrinsic one v SP E v int [30] :

v SP E v int = 1 + g exp (E f -E d ) kT 1 + g exp (E f i -E d ) kT (2)
where E f and E d are respectively the Fermi level and the defect level in the band gap whereas g is the degeneracy factor. As pointed out by Johnson et al. [30] more work is needed in this direction in order to confirm the validity of the GFLS approach. First, a more refined description level which incorporates electronic structure and Fermi shift such as tight-binding or ab-initio molecular dynamics would probably be mandatory for such a purpose. Next, the ideal system under study (doped a-Si:B/c-Si interface) has probably to be improved in order to match the experimental picture since for example dopant implantation is known to generate large amounts of defects (end of range defects, interstitials ,...) and surface roughness. .

Conclusions

Empirical molecular dynamics simulation have been undertaken in order to investigate the silicon re-growth at the atomic level. Earlier results on the influence of the empirical potential and the large sensibility of the virtual silicon amorphous to the atomic force description have been again illustrated. On the other hand, it has been observed that the interface migration velocity estimated is not so sensitive to the way a virtual amorphous silicon cluster is generated provided the amorphous character is preserved during annealing. The influence of orientation effects has been investigated at the atomic level showing a large influence of the surface orientation effects on the recrystallisation mechanism. The physical picture described by molecular dynamics is more complex than the classical re-growth theory since the relation between the atomistic structure of the interface and the defects generation is clearly underlined. The concept of a sharp interface often used in the classical theory must be put in perspective as molecular dynamics suggests a more diffuse interface. More attention is probably needed to investigate more in depth the influence of defect on velocity re-growth. Concerning doping effects, a small increase in the recrystallisation velocity has been observed at large doping concentration. Further work is clearly needed in this direction to study if the influence of charged defects could be introduced empirically in molecular dynamics simulation in order to validate or not the generalised Fermi-level shifting model often assumed by the classical re-growth theory.

Fig. 1 .

 1 Fig. 1. Stick models of the different a-Si/c-Si interface for the three orientations [100], [110], [111].

Fig. 2 .Fig. 3 .

 23 Fig. 2. Example of in-plane structure factor indicating the location of the a-Si/c-Si interface. The horizontal line at SQ = 0.5 highlights the location of the a-Si/c-Si.

Fig. 4 .

 4 Fig. 4. Evolution of the [100] interface re-growth velocity as a function of the annealing temperature for the two main types : Wooten Weiner Weaire (WWW) approach and melting/quench and for the two main potentials Tersoff and Stillinger-Weber (SW). The variation remains relatively modest compared to the difference in atomic cluster size (2000 atoms for WWW) and this work (∼ 5000 atoms) and those with the initial interface structure.

Fig. 5 .

 5 Fig. 5. Evolution of the a-Si/c-Si [100] interface position during solid phase epitaxy at 1700K. The evolution is reported for respectively 2.5, 5, 10, 15 and 20 ns illustrating the recrystallisation process where a quasi-planar interface propagates by a one atom by one atom incorporation mechanism.

Fig. 6 .

 6 Fig. 6. Evolution of the a-Si/c-Si [110] interface position during solid phase epitaxy at 1700K. The evolution is reported for respectively 5, 10, 15, 20 and 25 ns illustrating the recrystallisation mechanism where the formation and the dissolution of nanofacets is observed.

Fig. 7 .

 7 Fig. 7. Evolution of the a-Si/c-Si [111] interface position during solid phase epitaxy at 1700K. The evolution is reported for respectively 5, 10, 15, and 20 ns illustrating the bilayer recrystallisation mechanism and defect formation during re-growth.

Fig. 8 .

 8 Fig. 8. Evolution of the interface recrystallisation velocity along orientation [100], [110] and [111] for the Tersoff potential.The orientation influence concerns mostly the prefactor since the activation energy of the regrowth process is observed not to be orientation dependent.

Fig. 9 .Fig. 10 .Fig. 11 .

 91011 Fig. 9. An example of an initial a-Si:B/c-Si [100] interface for a 6 % boron concentration (top panel). The next figure shows the configuration after annealing where the dopant has been incorporated during re-growth. The segregation performed by the interface and the diffusion in the amorphous part can be clearly observed.

Table 1 .

 1 Main molecular dynamics parameters for disordered part generation.

	Potential	Annealing Range	Melting (K)	Quenching
		(K)		Rate
				(K/ps)
	Tersoff	[1700-2500]	3500	1 × 10 11
	SW (Standard)	[1000-1700]	2200	5 × 10 11

Table 2 .

 2 Distribution of the mean coordination number (CN) the different initial disordered interfaces at 300K.

	Conditions	CN	2fold	3fold	4fold	5fold	6fold
	a-Si, WWW 3.63 7.6 % 19.7% 70.8 % 0.9%	0%
	a-Si, Tersoff 4.17 0.7 %	9.9%	63.4 % 24 %	1.9 %
	l-Si, SW	2.92 24. % 38.5% 25.67%	3.4	0.16 %

The authors are grateful to Jean-Michel Droulez for his regular support on information technology aspects and to Fabrizio Cleri for stimulating discussion on molecular dynamics. This work has been supported partly by the European Commission as a contribution to the project PULLNANO under contract n • IST-026828 from the Information Society Technologies Programme (IST).