Mohammad Mohammadamini
email: mohammad.mohammadamini@univ-avignon.frsandipana.dowerah

Driss Matrouf
email: driss.matrouf@univ-avignon.frsandipana.dowerah

Jean-Franc ¸ois Bonastre
email: jean-francois.bonastre@univ-avignon.frsandipana.dowerah

Sandipana Dowerah

Romain Serizel
email: romain.serize@loria.fr

Denis Jouvet
email: denis.jouvet@inria.fr

Learning noise robust ResNet-based speaker embedding for speaker recognition

Keywords: Speaker recognition, ResNet, Additive noise, Reverberation, Robustness

The presence of background noise and reverberation, especially in far distance speech utterances diminishes the performance of speaker recognition systems. This challenge is addressed on different levels from the signal level in the front end to the scoring technique adaptation in the back end. In this paper, two new variants of ResNet-based speaker recognition systems are proposed that make the speaker embedding more robust against additive noise and reverberation. The goal of the proposed systems is to extract x-vectors in noisy environments that are close to their corresponding x-vector in a clean environment. To do so, the speaker embedding network minimizes the speaker classification loss function and the distance between pairs of noisy and clean x-vectors jointly. The experimental results obtained by our systems are compared with the baseline ResNet system. In different situations with real and simulated noises and reverberation conditions, the modified systems outperform the baseline ResNet system. The proposed systems are tested with four evaluation protocols. In the presence of artificial noise and reverberation, we achieved 19% improvement of EER. The main advantage of the proposed systems is their efficiency against real noise and reverberation. In the presence of real noise and reverberation, we achieved 15% improvement of EER.

Introduction

A speaker recognition (SR) system authenticates the identity of a claimed user from a speech utterance. The state-of-the-art systems mainly rely on Deep Neural Networks (DNN) for speaker modeling. From their emergence until now, numerous DNN architectures have been introduced in the speaker recognition realm in which TDNN [START_REF] Snyder | X-vectors: Robust dnn embeddings for speaker recognition[END_REF] and ResNet [START_REF] Xie | Voxceleb: Large-scale speaker verification in the wild[END_REF] systems are among the well-known and efficient systems. Although DNN-based SR systems have shown a degree of robustness in the presence of background noise and reverberation, their performance reduces in severe conditions [START_REF] Mohammad | Data augmentation versus noise compensation for x-vector speaker recognition systems in noisy environments[END_REF].

The problem of noise and reverberation is addressed at different levels of speaker recognition systems, including signal level [START_REF] Glass | Voiceid loss: Speech enhancement for speaker verification[END_REF], feature level [START_REF] Novotný | Analysis of dnn speech signal enhancement for robust speaker recognition[END_REF], speaker modeling level [START_REF] Ma | Pl-eesr: Perceptual loss based end-to-end robust speaker representation extraction[END_REF], x-vector level [START_REF] Mohammadamini | Compensate multiple distortions for speaker recognition systems[END_REF] and scoring technique adaptation [START_REF] Wang | A generalized framework for domain adaptation of plda in speaker recognition[END_REF]. Data augmen-tation is another approach to making the speaker recognition systems robust against noise. Researches show that data augmentation brings a degree of robustness to the speaker recognition system [START_REF] Snyder | X-vectors: Robust dnn embeddings for speaker recognition[END_REF][START_REF] Mohammad | Data augmentation versus noise compensation for x-vector speaker recognition systems in noisy environments[END_REF], but still, their performance degrades in noisy environments because there is no constraint on the speaker embedding system to extract identical or close x-vectors for pairs of noisy-clean version of the same signal.

Noise compensation in x-vector level, the estimation of clean x-vector from its corresponding noisy version, by doing a transformation between pairs of noisy/clean x-vectors is another approach that performed well in the compensation of artificial noise and reverberation [START_REF] Matrouf | Denoising xvectors for robust speaker recognition[END_REF][START_REF] Mohammad | Data augmentation versus noise compensation for x-vector speaker recognition systems in noisy environments[END_REF]. Although this approach performs well in some cases [START_REF] Mohammadamini | Compensate multiple distortions for speaker recognition systems[END_REF], it doesn't bring a significant improvement with all speaker embedding systems [START_REF] Mohammadamini | Le comportement des systèmes de reconnaissance du locuteur de l'état de l'art face aux variabiliés acoustiques[END_REF] and in all environments. The behavior of different speaker embedding systems is different because they just consider the speaker classification accuracy (inter-speaker and intra-speaker distance) during optimization and they don't put an explicit constraint on the noise impact. This characteristic makes noise compensation more difficult in some speaker embedding systems. To overcome this challenge, in the current paper, we propose two training strategies of ResNet-based speaker recognition systems that impose on the speaker embedding to extract x-vector for noisy signals that are close to their corresponding version in the clean environment.

In the first approach, the objective is to optimize the speaker embedding in a manner that converges toward the same point for the pairs of noisy/clean samples. In this system, two loss functions are used. The cross-entropy loss function is minimized for speaker classification and at the embedding layer, the mean square error (MSE) between noisy and clean x-vectors is optimized. Although the system improves for noise and reverberation, its performance is lower than the baseline system for clean environments.

To solve this problem, we propose a second system. In the second system firstly an optimal x-vector extractor for the clean environment is trained. After that, another speaker embedding is trained that jointly reduces the cross-entropy of the speaker classifier and mean square error (MSE) between the output of the embedding layer and an optimal clean x-vector extracted with the pretrained system. Since it is imposed on the output of the embedding layer to converge toward an optimum clean space, the performance of the speaker embedding is preserved for clean environments. Our proposed approaches, in all cases with different types of simulated and real noises, outperforms the baseline ResNet system. For the sake of readability in the next parts of the paper, we call the first proposed system ResNet-MSE1 and the second system named ResNet-MSE2.

The rest of the paper is organized as: the related works are reviewed in section 2, in section 3 the architecture of the proposed systems is described, the experiment's setup is described in section 4, the results are discussed in section 5.

Related works

Noise and reverberation are treated in the different parts of speaker recognition systems. Here we just review works in the speaker modeling level (x-vector extractor) and speaker embedding level (x-vector), which are directly related to our work.

In several works, the researchers tried to make the speaker embeddings robust to noise and reverberation. In [START_REF] Lin | Multi-level deep neural network adaptation for speaker verification using mmd and consistency regularization[END_REF] a domain adaptation technique is proposed that uses mean discrepancy distance (MMD) as a regularizer with speaker embedding that performs the adaptation between source and target domain. In this paper the proposed method is tested on language adaptation and its efficiency for noise and reverberation adaptation is not examined. In [START_REF] Zhou | Training multi-task adversarial network for extracting noise-robust speaker embedding[END_REF] an adversarial strategy was proposed to make the speaker embedding more robust against noise. In the standard x-vector extractors, after the embedding layer, a DNN speaker classifier is optimized. In this work, a second classifier is trained adversarially that accepts the type of noise in the output. In another work, a GAN-based speaker embedding was proposed that uses a binary discriminator to discriminate the noisiness of the x-vector alongside the speaker recognition classifier [START_REF] Zhou | Extraction of noise-robust speaker embedding based on generative adversarial networks[END_REF]. The main deficiency of adversarial speaker embedding systems is the labels that should be used in the discriminator. Another important point is that the training of the network in a manner that can not be able to discriminate the type of noise or the noisiness of an x-vector doesn't guarantee that noisy x-vectors are close enough to their clean version.

Some works are done at the x-vector level to reduce the impact of noise and reverberation in SR systems. In [START_REF] Matrouf | Denoising xvectors for robust speaker recognition[END_REF] several denoising autoencoders (DAE) are proposed to remove the impact of additive noise from x-vectors. In [START_REF] Mohammad | Data augmentation versus noise compensation for x-vector speaker recognition systems in noisy environments[END_REF] the impact of data augmentation alongside noise compensation is explored. Despite having good results for simulated noises this work doesn't include real noise and reverberation. In another work two configurations are proposed to denoise different kinds of distortions such as noise, early reverberation, and late reverberation [START_REF] Mohammadamini | Compensate multiple distortions for speaker recognition systems[END_REF]. In this paper also the capability of doing noise compensation is not explored in real environments. Also, in all of them, denoising is done with TDNN-based speaker embedding. In another work, it is shown that noise compensation doesn't bring a significant gain with x-vectors extracted from ResNet SR systems [START_REF] Xie | Voxceleb: Large-scale speaker verification in the wild[END_REF].

In the current paper, we introduce two training strategies that impose on the speaker embedding network to extract xvectors for a noisy/reverberated signal that is close to its the corresponding clean version.

Proposed system

In this section, the architecture of the baseline ResNet system and the proposed variants are described.

Baseline system

The baseline embedding extractor used in this paper is a variant based on ResNet [START_REF] He | Deep residual learning for image recognition[END_REF]. The ResNet model for extracting em- • The statistics-level component is an essential component to convert a variable-length speech signal into a single fixed-dimensional vector. The statistics level is composed of one layer: the statistics-pooling, which aggregates over frame-level output vectors of the DNN and computes their mean and standard deviation.

• The segment-level component maps the segment-level vector to speaker identities. The mean and standard deviation are concatenated together and forward to additional hidden layers and finally to the softmax output layer.

The detailed topology of the used ResNet is shown in Table 1. Batch-norm and ReLU layers are not shown. The dimensions are (Frequency×Channels×Time). The input is comprised of 60 filter banks from speech segments. During training, we use a fixed segment length of 400. The speaker ResNet system is trained with Cross Entropy loss function (Eq. 1):

LCrossEntropy = - N c=1 yo,c log(po,c) (1)
where N is the number of speakers, o is a speech signal, yo,c is the truth label of o, and po,c is the output of the softmax activation function.

ResNet-MSE1

In this subsection, the first proposed system is described (Fig. 1). In the proposed system a noisy signal and its corresponding clean version are given to the network. At the embedding layer the mean square error (MSE) between the noisy and clean xvectors is calculated at each minibatch (Eq. 2): where B is the size of minibacth, D is the size of x-vector, xj is the jth dimension of clean x-vector and yj is jth dimension of noisy x-vector. Both versions of the signal (i.e. clean and noisy) are given to the classifier. In this system a combination of cross-entropy and mean square error is used as the loss function (Eq. 3):

LMSE = B i=1 D j=1 (yj -xj) 2 (2)
LResNet-MSE = LCrossEntropy + LMSE (3)
During the training process, the speaker embedding converges toward an intermediate space between clean and noisy environments. Minimizing the MSE distance between noisy and clean x-vectors improves the performance in noisy environments while the performance in clean environments becomes a little worse because the clean samples move toward the noisy sample. This attribute is shown in Figure 3a. In the second proposed system, we resolve this problem.

ResNet-MSE2

In the second proposed system, the performance degradation in the clean environment is resolved. To do that, we used an as- sistance pretrained network which is the same as the baseline system. Firstly a speaker embedding network with a mixture of clean and noisy data is trained. We used both noisy and clean data to train this network because the previous research shows using more data and data argumentation improves the performance of speaker recognition systems for both clean and noisy environments [START_REF] Mohammad | Data augmentation versus noise compensation for x-vector speaker recognition systems in noisy environments[END_REF]. The pretrained network is used to extract xvectors for the clean version of the training dataset. We assume these vectors as the best version we can achieve. After that, another network is used to shift the noisy version of x-vectors towards the clean version extracted in the previous step. In this step, the system is trained from scratch with samples containing noisy and clean signals.

Experiments setup 4.1. Dataset

In this subsection, all the corpora used in our paper are described.

• Voxceleb. In our experiments we used Voxceleb 2 [START_REF] Nagrani | Voxceleb: Large-scale speaker verification in the wild[END_REF] for training x-vector extractors. There are 1.2m samples from 5,994 speakers. The clean version is augmented with Musan corpus. The final version of training data included 5.9m samples.

• Musan. Musan is music, speech, and noise corpus comprising 109 hours of speech data. This corpus is used for data augmentation to training x-vector extractors [START_REF] Sell | Musan: A music, speech, and noise corpus[END_REF].

• Freesound. This corpus included 3,000 RIR files and 4,275 noise files collected from Freesound noises. This corpus is used as artificial noise for evaluation protocols [START_REF] Font | Freesound technical demo[END_REF].

• BBC Noise. BBC Noise includes 16000 noise files, provided by BBC, these noises are used as artificial noise for an evaluation protocol1 .

• Fabiole. Fabiole 1 is a French corpus that contains 7,000 files from 130 speakers [START_REF] Ajili | FABIOLE, a speech database for forensic speaker comparison[END_REF]. We created two protocols from this dataset.

• Robovox. It is a French corpus collected from the Robovox project (A mobile robot). Each recording in this corpus has 5 channels. The fifth channel is a close microphone which we considered it as clean and the third channel is the farthest channel that we consider as noisy and reverberated2 .

• Voices. Voices are replayed speech recorded from Librispeech under different types of noises and in four different rooms. We created a protocol from Voices under the presence of noise in a room with high reverberation [START_REF] Armstrong | Voices obscured in complex environmental settings (voices)[END_REF].

x-vector extractors

All x-vector extractors are trained with Voxcleeb in 10,000 iterations. The learning rate at the beginning of the training is set to 0.2 and weight decay equals to 2 * 10 -4 . The momentum is set to 0.9. In all experiments, the stochastic gradient descent optimizer is used. The size of the feature maps is 32, 64, 128, and 256 for the 4 ResNet blocks.

• Baseline. In the baseline system, the training samples are chosen randomly from clean Voxceleb. The training data includes all clean files of Voxceleb and their augmented version with MUSAN Corpus and reverberated with a pool of RIR files 3 . Kaldi toolkit is used for data augmentation [START_REF] Boulianne | The kaldi speech recognition toolkit[END_REF]. The batch size is set to 128.

• ResNet-MSE1. In this system, a clean file from Vocxceleb was chosen randomly. After that its augmented version was chosen. Because we have two versions of each file at each minibatch, we reduced the size of each minibatch to 64.

• ResNet-MSE2. In this system at each minibatch, an xvector extracted from the baseline system was chosen. At the same time, the clean or noisy signals of the chosen files are selected. The modified system tries to reduce the distance between the clean x-vector and the x-vector extracted from the given signal.

Test protocols

• Fabiole1. In the first protocol, the Fabiole corpus is used. In this protocol 130 files (one file per speaker) are used as enrollment and 1,870 randomly chosen files are used for the test. In this protocol, the BBC noise files are added to the clean signal with different SNRs. In this protocol, the Kaldi toolkit is used to add noises to clean files.

• Fabiole2. The test and enrollment files in this protocol are the same as the previous one. But in this protocol, we used Freesound noises. We used Pyacoustics 4 for data simulation

• Robovox. In this protocol 26 files, one file per speaker, are used as the enrollment and 677 files are used as the test. The enrollment files are chosen from a close microphone with high quality but the test files are chosen from a far microphone between 1 and 3 meters.

• VoiCes. In this protocol 300 files, one file per speaker, are used as enrollment and 300 files are used as the test.

The enrollment files adopted from the Librispeech (the clean version of Voices) and the test files are the replayed files in VoiCes recorded in room 4 in the presence of severe music noise and reverberation. We used mic 5, which is the farthest microphone in Voices.

The details of all protocols are summarized in Table 2.

3 http://www.openslr.org/resources/28/rirs noises.zip 4 https://github.com/timmahrt/pyAcoustics

Results and discussion

In this section, the obtained results are discussed. Our results show that in all cases our proposed systems are more robust in noisy environments. However, the performance of the first proposed system reduces in clean environments in comparison to the baseline system, the performance of the second system for clean environments remains stable.

In Table 3 the results for Fabiole1 protocol are presented. As it is shown, the modified systems improve significantly in comparison to the baseline system. The first column shows the results for clean environments and the other columns include the results with different SNRs. For example, when SNR is between 0 and 5 the EER with the second proposed system (ResNet-MSE2) improves 15% compared to the baseline system. In the case of SNR between 10 and 15, the ResNet-MSE2 improves 20% in terms of EER. In the Fabiole2 protocol, we showed the generalizability of the proposed systems to other noises and RIR simulators. In this protocol, the same test and enrollment files as Fabiole1 protocol are used. But the Freesound noises dataset and Pyacoustics library are used for data simulation. The test and enrollment files are preserved as the previous protocol to show the robustness of the proposed systems against the impact of other noises and reverberations. Table 4 shows that in all cases the proposed systems reduce the impact of noise and reverberation. It deserved to be mentioned that in this protocol the results for the clean situation are worse in comparison to the Fabiole1 protocol because test files are truncated to 15 seconds for both clean and noisy situations. For the SNR between 0 and 5, the EER improves 14% with the RsNet-MSE2 system. In order to extend the capability of the proposed systems to real environments, the experiments are done on the Robovox dataset in Table 5. The first column shows the results with the best channel with a close microphone. As it is shown in Fabiole protocol the ResNet-MSE1 system is worse in the clean environment in comparison to the baseline system and the results for the ResNet-MSE2 system are the same as the baseline system. In the third column, the results are shown for the far microphone in the presence of noise and reverberation. Both adapted systems give better results in comparison to the baseline system. The last column shows the results with simulated noise in the Robovox protocol. In this experiment, the clean data from channel 3 is augmented with Freesound noises and Pyacosutics with SNR between 0 and 5. In this experiment the behavior of the proposed systems is the same. For real noise the relative improvement with the ResNet-MSE2 system is 16% and for simulated noise the gain is 10%. Finally, the systems are tested with a protocol created from the VoiCes dataset. The results are shown in Table 6. The experiments show that with the ResNet-MSE2 system there is 5% improvement of EER. The results obtained from ResNet-MSE1 in a clean environment show that reducing the distance between noisy and clean environments without fixing the clean point makes the system worse in clean environments because it converges to a space between the noisy and clean space. To solve this problem, we fixed the clean x-vector in the second proposed system. Also, the results show that the second system is superior in noisy environments because during the process of reducing the distance between noisy and clean x-vectors the noisy x-vector moves closer toward the clean point to minimize the MSE.

The MSE between noisy and clean x-vectors is shown in Table 7. The big distance between noisy and clean x-vectors of the same signal in the Baseline system shows that despite having high accuracy in speaker classification, a noisy x-vector of the same signal can be far from its clean version because the speaker classification's loss function doesn't impose on the system to have close or identical representations for the noisy and clean version of a specific signal. The presented results show that imposing on the speaker embedding system to extract close x-vectors for noisy and clean x-vectors makes the system more robust against noise and reverberation.

Conclusion

In this paper, we proposed two strategies to train ResNet-based speaker embeddings in order to make the speaker recognition systems more robust against additive noise and reverberation. In the first system, the network is updated to reduce the distance between pairs of noisy/clean x-vectors in the embedding layer. In the second system, an optimal clean point is fixed and at each iteration, the noisy and clean x-vectors given by the signal in the input are shifted toward the optimal point. Training x-vector extractors with the proposed strategies make the speaker embeddings more robust against additive noise and reverberation. The future potential work would be exploring other loss functions to reduce the difference between noisy and clean x-vectors and/or exploring different data augmentation techniques with proposed approaches to make the system more robust in a specific situation.

Figure 1 :

 1 Figure 1: Optimize the network in noisy and clean environment towards the same space.

Figure 2 :

 2 Figure 2: Train the network towards an ideal clean environment

Figure 3 :

 3 Figure 3: a) MSE reduction in ResNet-MSE1 (left) b) MSE reduction in ResNet-MSE2 (right)

  At the speaker embedding layer, the MSE between the fixed clean version and a given training sample (for both clean and noisy signals) is calculated. Both clean and noisy versions are given to the classifier and the weights are updated with all samples. This procedure is depicted in Figure 2. The steps of convergence towards the clean x-vector are shown in Figure 3b.

Table 1 :

 1 The baseline ResNet-34 architecture.

	Layer name	Structure		Output
	Input	-		60 × 400 × 1
	Conv2D-1	3 × 3, Stride 1	60 × 400 × 32
	ResNetBlock-1	3 × 3, 32 3 × 3, 32	× 3 , Stride 1 60 × 400 × 32
	ResNetBlock-2	3 × 3, 64 3 × 3, 64	× 4, Stride 2	30 × 200 × 64
	ResNetBlock-3	3 × 3, 128 3 × 3, 128	× 6, Stride 2 15×100×128
	ResNetBlock-4	3 × 3, 256 3 × 3, 256	× 3, Stride 2 8 × 50 × 256
	Pooling	-		8 × 256
	Flatten	-		2048
	Dense1	-		256
	Dense2 (Softmax) -		N
	Total	-		-

beddings consists of three modules: a set of ResNet Blocks, a statistics-level layer, and segment-level representation layers. • ResNet (Residual Network) uses stacks of many Residual Blocks. A Residual Block is made up of two 2dimensional convolutional Neural Networks (CNN) layers separated by a non-linearity (ReLU). The input of the Residual Block is added to its output in order to constitute the input of the next Residual Block.

Table 2 :

 2 Test protocols.

	Protocols	Test	Enroll Trials
	Fabiole1 1870	130	243k
	Fabiole2 1870	130	243k
	Robovox	677	26	17k
	Voices	300	300	90k

Table 3 :

 3 Fabiole 1 protocol(EER).

	System	Clean Noisy 0-5 Noisy 5-10 Noisy 10-15
	Baseline	5.20	7.96	7.43	7.00
	ResNet-MSE1	5.40	7.43	6.79	6.09
	ResNet-MSE2	5.19	6.79	5.98	5.66

Table 4 :

 4 Fabiole 2 protocol(EER).

	System	Clean Noisy 0-5
	Baseline	7.11	12.19
	ResNet-MSE1	7.30	11.18
	ResNet-MSE2	6.95	10.46

Table 5 :

 5 Robovox protocol (EER).

	System	Ch5 Ch3 Noisy 0-5
	Baseline	2.21 4.38	6.59
	ResNet-MSE1 2.36 4.10	6.05
	ResNet-MSE2 2.21 3.69	5.90

Table 6 :

 6 Voices protocol(EER).

	System	Clean Room 4 music
	Baseline	0.66	6.33
	ResNet-MSE1	0.66	6.33
	ResNet-MSE2	0.66	6.00

Table 7 :

 7 MSE distance between pairs of noisy-clean x-vectors.

	System	Fabiole1 Fabiole2 Robovox VoiCes
	Baseline	2.85	7.14	4.05	10.23
	ResNet-MSE1	0.06	0.015	0.09	0.02
	ResNet-MSE2	0.66	1.71	1.01	2.67

http://bbcsfx.acropolis.org.uk

https://robovox.univ-avignon.fr/

Acknowledgements

This work was supported by the Robovox ANR-18-CE33-0014 project.


G Sallen

A Tribu

T Aichele

R André

L Besombes

C Bougerol

S Tatarenko

K Kheng

J Ph

Poizat

Dark exciton optical spectroscopy of a semiconducting quantum dot embedded in a nanowire

Keywords: numbers: 78, 67, Lt, 78, 55, Et

Photoluminescence of a single CdSe quantum dot embedded in a ZnSe nanowire has been investigated. It has been found that the dark exciton has a strong influence on the optical properties. The most visible influence is the strongly reduced excitonic emission compared to the biexcitonic one. Temperature dependent lifetime measurements have allowed us to measure a large splitting of ∆E = 6 meV between the dark and the bright exciton as well as the spin flip rates between these two states.

Specific growth techniques developped about a decade ago have led to semiconducting nanowires (NW) that have attracted a great deal of interest since then. Their potential applications includes nanoelectronics [1,2,3], optoelectronics (light emitting diodes [4,5], nanolasers [6]), thermoelectrical energy conversion [7], and biological or chemical sensors [8].

By changing the material composition during the growth it is possible to change the chemical composition [9,10] along the longitudinal or radial directions. This enables the fabrication of well controlled 1D nanoscale heterostructures [10]. For example, as shown in this work, it is possible to insert a slice of a low band gap semiconductor within a high band gap NW and realize a light emitting quantum dot (QD) [11,12]. The absence of a wetting layer offers a better confinement compared to self-assembled QDs. This has allowed our group to produce single photon at high temperature (220 K) [12]. Furthermore, NW based heterostructures, being much less limited by lattice mismatches, greatly widen the possible materials combinations and enable well controlled stacking of several QDs in a single NW, offering interesting possibilities for quantum information processing [13].

In a QD, lowest energy excitons are the combination of an electron (spin ±1/2) and a heavy hole (spin ±3/2). This results in two different energy levels of spin ±1 and spin ±2. The spin ±1 states are optically connected to the zero spin empty dot state and called the bright exciton. The low energy spin ±2 states are called the dark exciton because they are not optically active. Indeed a photon is a spin 1 particle that can not carry away 2 quanta of angular momentum.

In a previous work we have performed a thorough spectroscopic analysis of a single CdSe QD embedded in a ZnSe NW by using photon correlation spectroscopy [17]. We have identified unambiguously the exciton, biexciton, and charged exciton lines using cross-correlations and obtained information on the charging dynamics of this QD. In order to fit the various correlation functions we had to include a dark exciton in the model. The most apparent manifestation of the dark exciton is the large predominance of the biexciton line with respect to the exciton line above saturation.

In this paper we have performed temperature dependent lifetime measurements on this CdSe/ZnSe NW. By fitting these data with a model involving an acoustic phonon bath [18] we are able to extract the value of the dark and bright exciton energy splitting ∆E and the spin flip rates between these two states.

ZnSe NWs are grown by Molecular Beam Epitaxy (MBE) in the Vapour-Liquid-Solid (VLS) growth mode catalysed with gold particles on a Si substrate. In order to fabricate QDs, a small region of CdSe is inserted in the ZnSe NW. This is done by interrupting the ZnSe growth, changing to CdSe for a short time and growing ZnSe again [12]. From the CdSe growth time, the height of the CdSe slice is estimated to be between 1.5 and 4 nm . The diameter (around 10 nm) is of the order of the bulk exciton Bohr diameter for CdSe (2a B = 11 nm). This means that the carriers in the CdSe QD are in the strong confinement regime. Details on the growth of the ZnSe NWs can be found in [19]. For the study of single NWs, the sample is sonicated in methanol, so that NWs broke off the substrate into the solution. Droplets of this solution are then deposited on a Si substrate, and a low density of individual NWs is obtained after evaporation.

The experimental set-up is a standard microphotoluminescence set-up. The samples are mounted on a XYZ piezo motor system in a He flow cryostat allowing experiments at a temperature of 4 K. Time resolved measurements are performed by illuminating the sample at a wavelength of λ = 440 nm with a frequency doubled Ti:sapphire laser operating at λ = 880 nm with pulse duration of 1 ps and a repetition rate of 80 MHz. Continuous wave excitation is provided by a 405 nm continuouswave (CW) diode laser. The ZnSe band gap (2.7 eV) corresponds to a wavelength of λ = 460 nm so that both excitation lasers create free carriers in the barrier.

The excitation light is illuminating the sample via a microscope objective of numerical aperture N A = 0.65 located in the cryostat. The NW emission is collected by the same objective and sent to a monochromator (1200 grooves/mm grating, 50 cm focal length). The monochromator has a switchable mirror inside that can direct the luminescence either onto a charge coupled device (CCD) camera for the measurement of the microphotoluminescence (µPL) spectra or through the exit slit towards a low jitter (40 ps) Avalanche Photodiode (APD).

The APD sends electrical pulses into a time-correlated single photon module that record the arrival time of the photon with respect to the the laser pulse. The overall temporal resolution of our set-up is essentially limited by the jitter of the APD and the dispersion of the monochromator grating. It was measured by sending the 1 ps laser pulses in the monochromator and a full width at half maximum of 70 ps was obtained. Typical spectra are shown in fig. 1. A comparison with relative energy positions of known emission lines in spectra of self-assembled CdSe/ZnSe QDs [14,15] suggests that these lines correspond to the exciton (X), the biexciton (XX) and the charged exciton (CX). The X-CX and X-XX energy splitting are found around 10 meV (20 meV) as compared to 15-22 meV (19-26 meV) for self-assembled QDs. The mean excitonic energy is also similar (2.25 ± 0.08 eV) as compared to 2.45 ± 0.2 eV for self-assembled CdSe/ZnSe QDs [16]. Unambiguous proof for the assignment of these lines has been given using photon correlation spectroscopy [17].

The ratio between charged and neutral QD luminescence is varying from dot to dot. We have also observed that increasing the temperature tends to neutralize the QD. The large linewidths have been attributed to spectral diffusion [20]. The most conspicuous feature is that the µPL intensity of the XX line at saturation is always a lot larger than that of the X line as it is shown in the power dependence of the different lines (Fig. 1 c)). This effect is the signature of a strong storage effect on the dark exciton (DX) state. The DX state reduces the luminescence of the X line owing to the leakage from the bright to the dark exciton but the DX state remains an efficient intermediate state for populating the XX state [21]. The QD photoluminescence properties are well described by a set of rate equations including the bright and dark exciton, and the biexciton as represented in fig.

2.

The population transfer between the bright and the dark exciton states is governed by the two temperature dependent rates γ d and γ u (see fig. 2). We assume that these transitions are assisted by acoustic phonons whose energy matches the X-DX energy splitting ∆E. At a temperature T the number N of acoustic phonons per quantum state of energy ∆E is given by the Bose-Einstein statistics and reads

N = 1 exp(∆E/k B T ) -1 . (1)
The downward transition rate γ d from the X to the DX state corresponds to the spontaneous and stimulated emission of a phonon, whereas the upward rate γ u corresponds to the absorption of a phonon [18]. They are given by

γ d = (N + 1)γ 0 , γ u = N γ 0 , (2)
where γ 0 is the zero temperature downward rate (N = 0). We have performed time resolved photoluminescence of the X state of QD1 at different temperatures. The results are presented in fig. 3. The decay time of the X level depends not only on the radiative decay rate γ X but also on the temperature dependent γ d and γ u rates between the bright and dark excitons. At low temperature (T = 4K), the luminescence exhibits a fast monoexponential decay with a time scale of the order of 1/(γ X + γ d ) corresponding to the radiative decay and the leakage towards the DX state. For intermediate temperatures (T = 20 K and T = 40 K), the fast decay is still present and there is the apparition of a slow time scale corresponding to the thermally activated reloading of the X state from the long lived DX state. For higher temperature (T = 80 K), the reloading from the dark to the bright exciton becomes even more efficient, and the decay appears as monoexponential with a time scale intermediate between the previous slow and fast time scales.

By fitting the lifetimes using the model of fig 2 we can extract the values for γ X , γ N R , γ d and γ u . Each of these parameters has a specific influence on the shape of the luminescence decay and can be evaluated with a good precision. The radiative decay rate of the exciton is found to be γ X = 1.4 ns -1 . The values for γ d and γ u are plotted in fig 4 as a function of temperature. This temperature dependence is well fitted using equations ( 1) and ( 2). This enables us to obtain the DX-X energy splitting ∆E = 6 meV and the zero temperature downward rate γ 0 = 1.4 ns -1 .

The rather large value for the DX-X energy splitting ∆E is an indication of the strong exciton confinement within the QD, owing to its relatively small size and the absence of a wetting layer [22]. The bulk DX-X energy splitting for CdSe is 0.12 meV. According to the calculation performed by Klingshirn et al [23], confinement induced enhancement of this splitting reaches a factor of 50 (that is ∆E = 6 meV for CdSe) for infinite barriers cylindrical dots of radius corresponding to the Bohr radius a B and of height corresponding to a B /4. These dimensions are compatible with the measured diameter (10 nm) of the NW and with the height expected from the CdSe growth duration. The DX-X energy splitting has been measured at 1.9 meV for self-assembled CdSe/ZnSe QD [22]. The larger value that we have observed is an indication of the larger confinement in NWs owing to the absence of a wetting layer. This ∆E = 6 meV splitting corresponds to the value for very small (about 2 nm diameter) colloidal spherical CdSe nanocrystal as reported in reference [24]. The value for zero temperature downward transition rate γ 0 = 1.4 ns -1 is comparable to what has been obtained for colloidal CdSe nanocrystals [18] or some self assembled InP/GaInP QDs [21]. Slower rates (γ 0 = 0.01 ns -1 ) have also been observed in In-GaAs/GaAs self assembled QDs [25].

A good fitting of the experimental data requires the inclusion of an effective non-radiative decay rate γ N R of the DX state. This rate slightly increases with temperature from γ N R = 0.2 ns -1 at 4K up to γ N R = 0.5 ns -1 at 80 K. These values are of similar order of magnitude that what was reported in InGaAs/GaAs self assembled QDs [25]. Non radiative phenomena in nanocrystals are generally slower ranging from hundreds of nanoseconds to a few microseconds in colloidal nanocrystals [18,26].

To summarize, we have performed temperature dependent lifetime measurements of a CdSe quantum dot embedded in a ZnSe nanowire. A careful quantitative analysis of these data has allowed us to confirm the strong influence of the dark exciton and to extract the darkbright exciton splitting together with the transition rates between these two levels. The rather large dark-bright exciton splitting that we have measured is a signature of the strong confinement of the exciton within the QD in this NW geometry. This value is three times larger than for self-assembled CdSe QDs although the excitonic energy and the X-XX and X-CX energy splittings are of same order of magnitude.

Figure 1 :Figure 2 :

 12 Figure 1: Above saturation microphotoluminescence spectra of two different QDs. a) QD1, b) QD2 (excitation power P =60 µW). c) QD2 line intensities as a function of excitation power

Figure 3 :

 3 Figure 3: Decay of the X line emission of QD1 for different temperatures. The pumping power is well below saturation (r ≪ γX ) so that the XX state is almost not populated.

Figure 4 :

 4 Figure 4: Downward and upward spin flip rates between X and DX as a function of temperature. The dotted lines are the fits using equations (1) and (2).

We thank M. Richard for many stimulating discussions and F. Donatini for very efficient technical support. T.A. acknowledges support by Deutscher Akademischer Austauschdienst (DAAD). Part of this work was supported by European project QAP (Contract No. 15848).