John David Grainger
email: john.grainger@cmft.nhs.uk

Paula H B Bolton-Maggs
email: paula.bolton-maggs@manchester.ac.uk

Bertrand Godeau
email: bertrand.godeau@hmn.aphp.fr

Jim Bussel
email: jbussel@med.cornell.edu

Hugo Donato
email: hugodonato@aol.com

Mohsen Elalfy
email: elalfym@hotmail.com

Ina Hainmann
email: ina.hainmann@uniklinik-freiburg.de

Axel Matzdorff
email: a.matzdorff@caritasklinik.de

Hannes Müller-Beissenhirtz
email: hannes.mueller-beissenhirtz@uk-essen.de

Alicia Rovó

John David Grainger

Andre Tichelli
email: tichelli@datacomm.ch

Diagnosis and management of chronic ITP: comments from an ICIS expert group

Keywords:

est destinée au dépôt

Introduction

Immune thrombocytopenia (ITP) is a common disorder in children and adults. In a patient with newly diagnosed ITP, the options and approaches to management are relatively well defined. Second-line treatments are more controversial, and management of chronic ITP (now defined as duration of more than 12 months) is even more so [START_REF] Rodeghiero | Standardization of terminology, definitions and outcome criteria in immune thrombocytopenic purpura of adults and children: report from an international working group[END_REF]. During the 3rd ICIS Expert Meeting on Consensus and Development of Strategies in ITP, held in Basel on September 3-5, 2009, a group of experts (see 'Acknowledgements') were tasked with reaching a consensus on some frequently asked questions relating to diagnosis and management of children and adults with chronic ITP. This article is designed to provide a practical support to trained haematologists in their care of patients with chronic ITP.

What is the role of the bone marrow examination in chronic ITP?

In patients with chronic ITP, bone marrow examination is usually unnecessary because of the past history including response to treatment if administered. However, refractoriness or poor response to first-line ITP therapy should always provoke review of the diagnosis, and therefore, bone marrow examination is highly recommended. In these situations, a bone marrow biopsy and cytogenetics should be routinely included with the smear in order to identify marrow failure syndromes or myelodysplasia [START_REF] George | Idiopathic thrombocytopenic purpura: a practice guideline developed by explicit methods of American Society of Hematology[END_REF][START_REF]British Committee for Standards in Haematology General Haematology Task Force (2003) Guidelines for the investigation and management of idiopathic thrombocytopenic purpura in adults, children and in pregnancy[END_REF].

Bone marrow investigations in chronic ITP patients are also recommended when the clinical or haematological pattern of the disease changes: for instance, the development of major bleeding in a patient with formerly mild 'ITP', occurrence of constitutional symptoms and appearance of unexplained anaemia, macrocytosis, neutropenia and/or dysplastic changes in the peripheral blood.

The side effects of thrombopoietin (TPO) mimetics include development of marrow reticulin fibrosis. Considering the restricted knowledge on long-term risk, a routine bone marrow biopsy before (if not recently obtained) and during therapy as surveillance is recommended [START_REF] Kuter | Evaluation of bone marrow reticulin formation in chronic immune thrombocytopenia (ITP) patients treated with romiplostim[END_REF][START_REF] Rice | Treatment of immune thrombocytopenic purpura: focus on eltrombopag[END_REF][START_REF] Jamali | Romiplostim for the treatment of chronic immune (idiopathic) thrombocytopenic purpura[END_REF].

Should we look for anti-platelet antibodies and how should we interpret them if obtained?

Increased levels of platelet-associated antibodies can be detected in most patients with ITP, but the results are neither sufficiently sensitive nor specific to justify use of these assays in patients with suspected ITP. The absence of anti-platelet antibodies does not eliminate the diagnosis and their presence does not affirm it.

The monoclonal antibody-specific immobilisation of platelet antigens assay [START_REF] Brighton | Prospective evaluation of the clinical usefulness of an antigen-specific assay (MAIPA) in idiopathic thrombocytopenic purpura and other immune thrombocytopenias[END_REF] and the modified antigen capture enzyme-linked immunosorbent assay test [START_REF] Fabris | Platelet-associated autoantibodies as detected by a solid-phase modified antigen capture ELISA test (MACE) are a useful prognostic factor in idiopathic thrombocytopenic purpura[END_REF] are able to detect antibodies against specific glycoproteins such as GPIIbIIIa and GPIbIX. These tests offer improved specificity but are less sensitive. Although they may possibly be useful in distinguishing between immune and non-immune thrombocytopenia in complex cases, their routine use in the diagnosis of ITP is not justified.

There is little published information regarding the impact of platelet auto-antibodies on the course of the disease or response to treatments. It has been suggested that chronic ITP accompanied by the presence of platelet antibodies could be more severe with higher risk of recurrence of the thrombocytopenia and more severe symptoms and bleeding. It has also been reported that the response to steroids could be better when platelet antibodies are present. However, conflicting results have been reported [START_REF] Sikorska | The effect of platelet autoantobodies on the course of the disease and clinical response of patients with idiopathic thrombocytopenic purpura[END_REF]. Finally, antibodies predomi-nantly directed against GPIIbIIIa are speculated to portend good response to intravenous immunoglobulin (IVIg) and poor response to GPIbIX. Overall reliable conclusions as to the diagnostic or prognostic usefulness of measurement of auto-antibodies in chronic ITP are not possible at this time.

Is it relevant to distinguish primary from secondary forms of chronic ITP?

Twenty percent of adults with chronic ITP are estimated to have it secondary to another underlying disorder [START_REF] Cines | The ITP syndrome: pathogenic and clinical diversity[END_REF]. The approach to secondary ITP differs in a number of cases.

All adult patients with ITP should be screened for HIV and hepatitis C. In HIV, the incidence of thrombocytopenia increases with progressive immunosuppression. Effective antiretroviral therapy (HAART) improves platelet counts in the great majority of patients [START_REF] Liebman | Viral-associated immune thrombocytopenic purpura[END_REF]. If counts do not increase with HAART, patients can be treated for short periods with corticosteroids but long-term use of steroids should be avoided because of the risk of secondary infections. IVIg, anti-D and splenectomy are safe and effective in refractory patients; anti-D is superior to IVIg in this patient group [START_REF] Scaradavou | Superior effect of intravenous anti-D compared with IV gammaglobulin in the treatment of HIV-thrombocytopenia: results of a small, randomized prospective comparison[END_REF]. Rituximab carries the risk of progressive multifocal leucoencephalopathy and infectious complications [START_REF] Carson | Progressive multifocal leukoencephalopathy after rituximab therapy in HIV-negative patients: a report of 57 cases from the Research on Adverse Drug Events and Reports project[END_REF]. TPO-R agonists have not yet been tried.

In hepatitis C patients, a platelet response to antiviral therapy is observed in approximately 50%, but initially, interferon treatment may create/worsen thrombocytopenia. Corticosteroids can be used if needed for short periods, but close monitoring of viral load and liver function is essential. IVIg and splenectomy may be effective. Possible co-infection with hepatitis B requires investigation and monitoring during therapy.

Up to 5-10% of chronic lymphocytic leukaemia or lymphoma (Hodgkin and non-Hodgkin) patients develop ITP. Occurrence and severity of ITP is not related to lymphoma stage. Therefore, treatment should primarily be directed to immune thrombocytopenia although with lymphoma, treatment of the lymphoma may often improve the ITP. Steroids and IVIg are preferred but thrombocytopenia usually recurs. Rituximab is also effective. Fludarabine and other purine analogues should be avoided. Consider splenectomy in refractory cases.

Autoimmune lymphoproliferative syndrome is an inherited disorder and usually seen in children. Genetic defects lead to impaired lymphocyte apoptosis, lymphoproliferation, immune cytopenia and malignancy. Thrombocytopenia is often persistent, and rituximab (which carries a special risk of hypogammaglobulinaemia) and mycophenalate mofetil appear to be effective.

Common variable immunodeficiency (CVID) patients develop ITP in 10% of cases. Their ITP respond to steroids but prolonged treatment may cause infections. The same applies to splenectomy although 4-weekly IVIg may lessen this risk. Most patients need to receive IVIg, but if this is insufficient, consider addition of rituximab.

ITP and autoimmune haemolytic anaemia (Evans syndrome) may develop spontaneously or secondary to SLE, CLL, lymphoma, CVID or other immunodeficiency and following stem cell or solid organ transplantation. Ideally, a direct antiglobulin test and especially reticulocyte count should be part of every ITP work-up. Steroids and IVIg are the usual first-line therapy of the ITP; anti-D is contraindicated. Rituximab, cyclosporine, mycophenolate mofetil, splenectomy (not recommended in children) and combination chemotherapy have been used in second-line treatment [START_REF] Norton | Management of Evans syndrome[END_REF].

Severe thrombocytopenia during periods of exacerbation of autoimmune disorders requires control of the underlying disease. In patients with no disease activity, treatment is similar to primary ITP.

Up to 10% of patients with ITP test positive for antiphospholipid antibodies and/or lupus anticoagulant. This does not change management of thrombocytopenia as long as these patients do not develop thrombosis [START_REF] Stasi | Prevalence and clinical significance of elevated antiphospholipid antibodies in patients with idiopathic thrombocytopenic purpura[END_REF]. Because of the risk of thrombosis associated with antiphospholipid antibodies/lupus anticoagulant, monitor patients closely for symptoms of thromboembolism when platelet counts rise during treatment and consider prophylaxis e.g. aspirin. Raise platelets only to levels, sufficient to prevent bleeding, not to the normal range.

Can we define a profile of patients with chronic ITP with a lower risk of bleeding complications?

ITP is a relatively benign disorder, and theoretically, many of the chronic ITP patients rarely require treatment. In clinical practice, certain patients may be over treated because the treatment decisions are based primarily on low platelet counts, independent of clinical manifestations. To predict the risk of bleeding in patients with chronic ITP, the recognition of an individualised adequate platelet levels can be helpful.

The course of ITP may be more serious in adults than in children. Major bleeding, including spontaneous intracerebral haemorrhage, occurs predominantly in patients with platelet counts <20×10 9 /L, generally <10×10 9 /L [START_REF] Psaila | Intracranial hemorrhage (ICH) in children with immune thrombocytopenia (ITP): study of 40 cases[END_REF][START_REF] Butros | Bussel JB Intracranial hemorrhage in immune thrombocytopenic purpura: a retrospective analysis[END_REF]. Haemorrhagic complications may be more common in patients older than 60 years of age and those with comorbidities. A number of bleeding assessment tools have been developed for adult ITP patients [START_REF] Page | The immune thrombocytopenic purpura (ITP) bleeding score: assessment of bleeding in patients with ITP[END_REF][START_REF] Khellaf | Assessment of a therapeutic strategy for adults with severe autoimmune thrombocytopenic purpura based on a bleeding score rather than platelet count[END_REF].

To define a low-risk patient, any physical activity in professional and social life that may be linked to an increased risk of traumatic injury should be taken into account. Cardiovascular aerobic exercises (fast walking, jogging, or swimming) or muscle strengthening has a lower risk for bleeding. Therefore, ITP patients can and should be encouraged to participate in this type of exercise. The practice of an activity with higher risk of trauma, such as contact sports, should not be considered low risk. In patients with unexpected bleeding, additional laboratory tests should be performed to identify platelet dysfunction [START_REF] Panzer | Platelet function to estimate the bleeding risk in autoimmune thrombocytopenia[END_REF] or an additional haemostatic abnormality e.g. underlying von Willebrand disease [START_REF] Michiels | Laboratory diagnosis and molecular basis of mild von Willebrand disease type 1[END_REF][START_REF] Sucker | Causes, etiology and diagnosis of acquired von Willebrand disease: a prospective diagnostic workup to establish the most effective therapeutic strategies[END_REF].

In conclusion, in chronic ITP, a low-risk profile for bleeding could be defined as: patients younger than 40 years, without co-morbidities, absence of any major bleedings during the course of ITP, no increased risk of injury in professional or social activity, previous brisk response to therapy and no requirement of anticoagulation or anti-aggregation therapy. In these cases, even when platelet counts are lower than 30×10 9 /L, a 'watch and wait' strategy is a reasonable option.

What to consider for decision making in treatment of childhood chronic ITP

The approach to chronic ITP in children is not well defined mainly because of the low incidence of chronic ITP in children. This section will provide pros and cons of newer treatments and includes a consideration of splenectomy (Table 1).

Despite the long experience of splenectomy for ITP, studies specific to children are limited. One large review of cases primarily in adults identified thousands of cases, but the children are generally not distinguished and the longterm effects, beyond sepsis, are not well delineated in any population [START_REF] Kojouri | Splenectomy for adult patients with idiopathic thrombocytopenic purpura: a systematic review to assess long-term platelet count responses, prediction of response, and surgical complications[END_REF]. Conversely, there are relatively few late relapses of splenectomy in children reported, but again there are little data.

Studies of patients with hereditary spherocytosis and splenectomy have raised concern that pulmonary hypertension may develop, and there is recognition of a long-lasting increased risk of arterial and venous thromboembolism [START_REF] Schilling | Delayed adverse vascular events after splenectomy in hereditary spherocytosis[END_REF].

Rituximab has been infused in approximately one million people including over 500 adults and 100 children with ITP. The obvious advantage of rituximab therapy is that it may provide a long-term 'remission', but the exact length of this remission and the frequency of it remain poorly defined. Serum sickness may be more common, 5-10%, in paediatric ITP [START_REF] Bennett | Prospective phase 1/2 study of rituximab in childhood and adolescent chronic immune thrombocytopenic purpura[END_REF]. Infections, including progressive multifocal leucoencephalopathy (PML), occurring after rituximab in children have not been reported [START_REF] Carson | Progressive multifocal leukoencephalopathy following rituximab therapy in HIV negative patients: a report of 57 cases from the Research on Adverse Drug Event and Reports (RADAR) project[END_REF] nor has there been hepatitis B activation in children with chronic ITP. Limited studies have suggested that upon their return, B-cell subpopulations may be changed by rituximab.

There are two ongoing TPO-R agonist studies which include children. Efficacy and dosing in the children may not be very different from that of adults. Safety assessment is precluded by the small numbers of children treated although no drug-related serious adverse events have been seen. In adults, the rate of efficacy with these agents is 70% or higher [START_REF] Bussel | Effect of eltrombopag on platelet counts and bleeding during treatment of chronic idiopathic thrombocytopenic purpura: a randomised, double-blind, placebo-controlled trial[END_REF][START_REF] Kuter | Efficacy of romiplostim in patients with chronic immune thrombocytopenic purpura: a double-blind randomised controlled trial[END_REF]. Toxicity issues include thrombosis and fibrotic changes in the marrow which remains of undetermined significance [START_REF] Kuter | Evaluation of bone marrow reticulin formation in chronic immune thrombocytopenia patients treated with romiplostim[END_REF]. A separate issue that remains to be defined is that once these agents are started, how long should treatment be continued and how should they be stopped?

With any therapy of chronic ITP, considerations of toxicity need to be weighed against perpetual low platelet counts in children. The 'watch and wait' approach for acute childhood ITP is based on the likelihood that children have a lower risk of severe bleeding and are likely to improve with time. However, children with chronic ITP have a far lower likelihood of immediate spontaneous improvement than adult patients. Restrictions in activity, concern of bleeding and diminished health-related quality of life become important and need to be factored into management decisions.

When should we use supportive therapy in chronic ITP?

Supportive therapy in ITP is an essential adjunct to therapy that increases the platelet count, whether in the setting of episodic severe bleeding or in mild persistent bleeding. It Concern regarding liver toxicity with one agent may be sufficient to promote haemostasis without additional systemic therapy or lessen the degree of systemic therapy required. The use of antifibrinolytic agents is established in dental treatment and mucosal bleeding [START_REF] Bruhn | Hämostaseologie für die Praxis[END_REF]. Antifibrinolytic drugs should be avoided in treating massive urogenital haemorrhages because of possible obstructive clot formation in the urinary tract but may be particularly effective in minor urinary bleeding by neutralising urokinase. Some patients may also benefit from desmopressin which has been shown to promote haemostasis in congenital or acquired platelet disorders [START_REF] Kobrinsky | Treatment of refractory thrombocytopenic bleeding with 1-desamino-8-D-arginine vasopressin (desmopressin)[END_REF]. The administration of desmopressin by intranasal spray has been shown to be effective in women with menorrhagia and platelet dysfunction disorders. Secondary iron deficiency is not unusual in patients with ITP and may contribute to further bleeding. Correction of co-existent iron deficiency is therefore recommended [START_REF] Valeri | Anemia-induced increase in the bleeding time: implications for treatment of nonsurgical blood loss[END_REF].

Recurrent epistaxis and gingival bleeding are some of the most common symptoms of patients with ITP. Many of these bleeding episodes can be treated conservatively using local application of adrenaline-soaked nosepads, collagencoated fleece and fibrin sealant. Nasal cautery may prove useful if an active bleeding vessel can be identified; however, the use of recurrent nasal cautery can promote mucosal damage and stimulate further bleeding.

Menorrhagia can be a major problem in female patients with chronic ITP. Progesterone-containing intrauterine contraceptive device and oral contraceptives can decrease the frequency and amount of menstrual bleeding [START_REF] Beatty | The levonorgestrel-releasing intrauterine system: safety, efficacy, and patient acceptability[END_REF]. Since progesterone can increase the platelet count in ITP, it is appropriate to use it orally or intramuscularly to control vaginal bleeding.

How to handle anticoagulation and/or anti-aggregation in patients with chronic ITP?

There are an increasing number of chronic ITP patients who require anticoagulation for cardiovascular co-morbidities. In ITP, thrombocytopenia of any degree does not appear to protect against thromboembolic events. At the same time, anticoagulant therapy may cause severe bleeding. Except for a small number of case reports [START_REF] Fruchter | Fatal acute myocardial infarction during severe thrombocytopenia in a patient with idiopathic thrombocytopenic purpura[END_REF][START_REF] Gracia | Invasive treatment performed for acute myocardial infarction in a patient with immune thrombocytopenic purpura[END_REF][START_REF] Theeler | A patient with idiopathic thrombocytopenic purpura presenting with an acute ischemic stroke[END_REF], there are minimal data to guide therapy in ITP patients who need anticoagulation.

For each individual patient, the risk of thromboembolic complications, e.g. stent thrombosis and stroke from atrial fibrillation, has to be weighed against the risk of bleeding based upon prior bleeding history, severity of thromboembolic risk, co-morbidities, age and access to emergency medical treatment.

In patients with ITP and coronary artery disease, the risk of myocardial infarction usually outweighs the risk of mild bleeding. Aspirin and thienopyridines (clopidogrel, prasugrel, etc.) should be given as in non-thrombocytopenic patients if the platelet count is above 30×10 9 /L. If severe bleeding develops, anticoagulant treatment has to be held or reduced. During the initial treatment period, the patient needs close monitoring. Coated coronary stents should not be used because they require more intensive anticoagulation.

In patients with ITP and atrial fibrillation, initial anticoagulation with low-molecular-weight heparins (LMWH) is preferred and subsequent continuation of anticoagulation only if no bleeding develops. Initial target international normalised ratio (INR) should be in the lower range (e.g. 1.5-2) and increased to the regular level (INR 2-2.5) only if this has been shown to be safe. Warfarin should be preferred to phenprocoumon because of the shorter half life.

Thromboprophylaxis in ITP patients with high-risk surgery (e.g. orthopaedic or cancer surgery) In these patients, platelet counts are usually raised to sufficient levels before intervention. As long as platelet counts stay above 30×10 9 / L, administer prophylactic dose LMWH as usual. If platelet counts drop below 30×10 9 /L, one may consider early mobilisation, compression stockings or pneumatic devices, or increasing the platelet count.

Treatment of thrombosis in ITP patients

With low platelet counts and thrombosis, start continuous unfractionated heparin (UFH) at half-therapeutic dose while increasing the platelet count. UFH has a short half life, and in the case of bleeding, the anticoagulant effect disappears quickly. If the patient tolerates half-therapeutic UFH for a few days, increase to therapeutic levels and later switch to LMWH or warfarin. With counts >30×10 9 /L, start with half-therapeutic dose LMWH, >50×10 9 /L with full dose LMWH. Consider giving LMWH for the duration instead of switching to vitamin K antagonists. There are no experiences with the new oral inhibitors (dabigatran, rivaroxaban) for prophylaxis or treatment of thromboembolism in ITP patients.

Summary

In summary, many of the questions raised above have at best partial answers derived from data and the answers are based on "expert opinion". Several of these questions would make good starting points for the design of ITP studies in the future.

Table 1

 1 Recognised treatment options for chronic ITP

		Pros	Cons
	Watch and wait	Spontaneous remissions or 'cure' in up to	May lead to restricted HRQoL
		10% of children per year
		The majority of children and adults remain	Ongoing risk of severe or life-threatening haemorrhage
		free of severe bleeding
		Inexpensive	Adverse effects of drugs used for break-through bleeds
	Splenectomy	'Cure' in 2/3-3/4 of patients	'Only' works in 2/3-3/4 of patients
		Side effects of procedure low	Risk that accessory splenectomy may be needed
		Apparent low rate of late complications of splenectomy	Undetermined optimal means of prophylaxis against sepsis
		especially following laparoscopic procedure
		Low rate of post-splenectomy sepsis	High cost
			Risk of peri-operative bleeding
			Potential removal of healing monocytes stored in spleen
			Anti-D ineffective after splenectomy
			Irreversible
			Potential long-term adverse outcomes: pulmonary hypertension,
			thrombotic events, sepsis and effects on immunity beyond
			decreasing filtration of organisms in blood
	Rituximab	Effective in at least 33% of cases with normalisation	Long-term toxicity not well defined in any population and
		of platelet count lasting at least 6-12 months	especially not in paediatrics
		Tolerable in that no overt major toxicity of infusions	Risk of long-lasting immunosuppression, development
		with slow initial rate and premedication	of PML and of activation of hepatitis B
		Dosing weekly for 4 weeks and then finished	High cost
		Effective both pre-and post-splenectomy	Rate of durable responses to rituximab does not exceed 40%
		Ability to retreat responders who relapse	No recognised predictive factor for response to rituximab
		No blocking effects on other ITP treatments	Serum sickness in an unclear percent of patients
			No randomised trials and unlicensed for ITP
	TPO-mimetic	Multiple placebo-controlled trials	Non-curative treatment
	agents	Greater percentage of response than other	Rebound of thrombocytopenia after cessation
		second-line treatments
		Effective both pre-and post-splenectomy	Long-term safety unknown including issues of marrow fibrosis
		Response almost always maintained while the	High cost
		drugs continue to be administered
		Evidence of improved quality of life	Potential for thrombosis
		Well tolerated	Potential rarely for malignancy
		Licensed for treatment of adults refractory to
		splenectomy (in the USA, Europe and Australia)

Ann Hematol (2010) 89 (Suppl 1):S11-S17

Acknowledgements We would like to thank all participants in the chronic ITP expert group who participated in the discussion at ICIS, namely: Bessho, Fumio-Moroyama, Japan; Diesch, Tamara-Basel, Switzerland; Erduran, Erol-Trabzon, Turkey; Fouda, Ashraf-Al-Mansoura, Egypt; Hainmann, Ina-Freiburg, Germany; Kaplinsky, Chaim-Tel Hashomer, Israel; Konja, Josip-Zagreb, Croatia; Kreuzbauer, Georg-Zug, Switzerland; Kroiss, Sabine-Zürich, Switzerland; Strauss, Gabriele-Berlin, Germany; Tamminga, Rienk-Groningen, Germany; and Veronese, Luisa-London, UK.


Z Habib

« Study of the hydration of CaO powder by gas-solid reaction »

Keywords: A kinetics, A hydration, B microstructure, D CaO, anti-Arrhenius

Hydration of CaO powders by reaction with water vapor has been studied in isothermal and isobaric conditions. Experimental tests were performed within the temperature range of 70°C -420°C and with a water vapor pressure from 5 to 160 hPa by means of a thermogravimetric device. Two powders, exhibiting slight differences in their physical properties, were studied. However, for one of the powders and under some temperature and pressure conditions, the reaction is not complete. The difference of behavior between both CaO powders was interpreted by considering the effect of the morphological properties on the mechanism of growth of Ca(OH) 2 .

INTRODUCTION

Hydration of calcium oxide (lime) by liquid water is a very well known reaction due to large domain of applications of hydrated calcium oxide in industry [1,2]. It is however surprising to see that only few papers have been published on the "dry" hydration of CaO or the interaction of water vapor with this oxide [3][4][5][START_REF] Wang | Effect of CaO[END_REF] in comparison with the recent growing interest of studies about CO 2 interactions on calcium oxides [7][8][9]. D.R.Glason [3] studied the interaction of water vapor with different kinds of lime with specific surface areas from 1 to 100m 2 .g -1 and he observed the agglomeration of particles during hydration at room temperature. A theoretical model for this reaction has been developed [4] with some experiments on CaO pellets at different water vapor pressure and temperature. They found that the two most important variables were the water vapor pressure and the calcination temperature. In some recent works [5][START_REF] Wang | Effect of CaO[END_REF] on CaO based sorbents, an anti-Arrhenius behavior was observed and the author linked this phenomenon to the initial content of CaO. They also studied the CaO hydration and Ca(OH) 2 decomposition over a multitude of cycles with as starting material crushed and sieved limestone (CaCO 3 ). The hydration rate decreased with increasing number of cycles.

The aim of this work is to reach a better knowledge of the mechanism of this reaction, studying the influence of the water pressure and temperature. Two distinct CaO powders were used under the same experimental conditions and the differences, observed on the curves giving the fractional extent of the reaction versus time, are discussed on the bases of the growth mechanism of the hydroxide and morphology of the two powders.

MATERIALS AND METHODS

Materials

The two types of powders used in this work were provided by Lhoist R&D SA. The first one was called "SBL" (Soft Burnt Lime) and the second one "HBL" (Hard Burnt Lime). The chemical analysis shows that SBL powder is composed of 94.7% in weight of CaO and HBL powder of 96.4% of CaO. The unburnt part is 2.8 % in SBL instead of 0.7 % in HBL. The other impurities are in the same proportions in both powders. Then the X-Ray patterns show the standard peaks for well crystallized CaO (Halite structure) for both the SBL and the HBL sample. For SBL the number of small particle seems to be greater than for HBL, as shown by the PSD curves. Indeed, it is clear from Figure 3 that the internal pores inside the SBL aggregates are larger than inside HBL ones. porosimeter (Micromeritics Autopore IV). Figure 4 shows the cumulative pore volume as a function of a pore diameter. We can notice both intra-granular and inter-granular voids. If we consider pores with diameters lower than 1 µm, it is clear that the pore volume inside the SBL aggregates (0.128 mL.g -1 ) is much higher than that inside the HBL aggregates (0.042 mL.g -1 ).

Methods

All experiments have been performed at fixed Temperature (T) and water vapor partial pressure (P) in a symmetrical thermobalance SETARAM TAG 24 associated with a water vapor generator Wetsys. The procedure was the same for all thermogravimetric (TG) experiments. All experiments were realized in isobaric and isothermal conditions. The sample temperature was raised up to the isothermal step and then the gases (helium and water vapor) were introduced. According to NIST data [START_REF] Jr | NIST-JANAF Themochemical Tables, Fourth Edition[END_REF] the equilibrium pressure of calcium oxide hydration is represented in Figure 5 by the plain curve.

With the Wetsys vapor generator, we could achieve water vapor pressures up to 160 hPa in helium flux. So our experimental field is included in the hatched area between the equilibrium curve and the dotted lines. All the experiments have been carried out far from equilibrium conditions -so much so that the corresponding term in the expression of the rate can be left out.

The TG software gave us mass variation versus time. We transformed this data into fractional extent α  of the reaction according to the chemical reaction [R1]:

CaO(s) + H 2 O(g) = Ca(OH) 2 (s) [R1]
The theoretical mass gain at α=1 should be of +32% of the initial mass of CaO. This initial mass is obtained after the experiment with a complete dehydration of Ca(OH) 2 . Thus, we can calculate the hydrated part of the initial product.

Derivation of the α(t) curves allows us to calculate the rate of reaction (dα/dt), which can be represented graphically versus α, to compare the results of experiments carried out in various temperature and water pressure conditions.

EXPERIMENTAL RESULTS

Influence of water vapor pressure

The influence of the water vapor pressure on the kinetic curves is illustrated in Figure 6. All experiments were realized with the SBL powder. The temperature was fixed at 150°C for all tests.

According to the experimental α(t) curves, the higher the pressure, the faster the reaction (Figure 6a). The maximal fractional extent observed for 80 and 160 hPa reaches mainly 1, which means that SBL powder can be totally transformed into Ca(OH) 2 . The rate versus α curve exhibits a maximum for the higher pressure experiment. It seems that all the curves present such a maximum close to the initial time.

Influence of temperature

Figure 7 shows α(t) curves obtained at various temperatures for SBL and HBL samples.

It can be seen that for both powders the higher the temperature, the slower the hydration. This can be observed from the dα/dt(α) curves shown in Figure 8 for SBL CaO powder. Such a behavior is quite unusual.

We could also note that the maximum of the curves moves from α=0.05 to nearly 0.4 when temperature increased.

Maximal extent of reaction: "blocking effect"

For HBL CaO powder and in some experimental conditions of dry hydration, the reaction was not complete and stopped at a fractional extent lower than 1. During the reaction something happen (for example a diffusion through the hydroxide layer became extremely slow) and the reaction rate is so slow that we can consider that the reaction is blocked. We will call this phenomenon the "blocking effect" in the following. Two curves of the fractional extent versus time are represented in figure 9 for two different temperatures with 5 hPa of water pressure.

HBL CaO powders

For HBL the blocking effect is clearly observed at 115°C and 5 hPa since a plateau is reached for α equal to 0.7. In the other experiment (150°C and 15 hPa), it can be foreseen that the fractional extent will not exceed 0.5. For SBL however, both reactions were not finished but the fractional conversion has reached values above 0.75 and does not seem to stop increasing well below 1.

DISCUSSION, MECHANISM OF THE REACTION

Kinetic laws

If we consider the hydration of SBL samples, the rate curves such as those in Figure 6b or Figure 8, exhibit a maximum, which suggests that the reaction involves simultaneous nucleation and growth processes of the new phase (Ca(OH) 2 in our case). In general [START_REF] Galwey | Thermal decomposition of ionic solids[END_REF], kinetic modeling of these reactions are done using a general expression of the reaction rate in the form dα/dt=Aexp(-Γ/RT).f(α) where A is a pre-exponential factor, Γ a temperature coefficient called apparent activation energy in the litterature, R the perfect gas constant, T the temperature and f(α) a function of the fractional conversion α (in the case of sigmoid α(t) curves, authors often use the Avrami laws A n or the Prout-Tompkins law B1). Nevertheless, Avrami laws and Prout-Tompkins law are not usable in the case of solid-gas reactions; and moreover the use of temperature dependence following an Arrhenius behavior should be done with care as explained in [START_REF] Pijolat | [END_REF]. We use a more general method based on surface nucleation followed by nuclei growth [START_REF] Soustelle | Handbook of heterogeneous kinetics[END_REF]. This means that nuclei of hydroxide are formed onto the surface of the initial oxide grains with a frequency γ, called the areic frequency of nucleation and expressed in number of nuclei.m - .s -1 . The nuclei thus formed then grow with a rate φ called the areic reactivity of growth and expressed in mol.m -2 .s -1 . The most common laws used for such a behavior are those of either Mampel's [START_REF] Mampel | [END_REF][15] (uniform surface nucleation, isotropic growth, inward development and internal rate-determinig step of growth) or of the different mechanisms with uniform nucleation and anisotropic growth as Jacobs and Tompkins' model for example [START_REF] Jacobs | Chemistry of the Solid State[END_REF][START_REF] Jacobs | [END_REF]. Such models are explained and detailed in reference [START_REF] Soustelle | Handbook of heterogeneous kinetics[END_REF].

In this text, we will only consider a general form, dα/dt=φ (P,T,…).f(t) [START_REF] Pijolat | Experimental tests to validate the rate-limiting step assumption used in the kinetic analysis of solid-state reactions[END_REF] if it is supposed that the growth rate is controlled by an elementary step. φ (T, P,…) will be expressed by the theoretical expression deduced from the mechanism of growth and this expression will help us to interpret experimental behavior (influence of temperature and partial pressure).

Proposal of a mechanism for growth and anti-Arrhenius behavior

For the growth of the calcium hydroxide layer, we refer to a traditional mechanism of solid-gas reaction taking into account both internal (between calcium hydroxide and calcium oxide) and external (between calcium hydroxide and water vapor) interfaces with diffusion of species through the hydroxide layer, with the specificity of the calcium hydroxide, which is insulating, and of water molecules which form easily hydrogen bonds while being likely to dissociate).

The various steps involved in the mechanism are detailed below:

At the external interface:

• The adsorption of water molecules with hydrogen bonds on two sites of adsorption (noted 's'):

s O H s 2s O H 2 2 - - ⇔ + [S.1]
• The formation of an hydroxide group from an hydroxide vacancy:

s + + - ⇔ + - - • • OH OH 2 OH H s V s O H s [S.2]
• The reaction between hydrogen and an oxygen ion in hydroxide position:

OH ' OH OH O H s + ⇔ + -• s [S.3]
In the hydroxide layer:

• The diffusion of the hydroxide vacancy and of the oxygen ion from the internal interface toward the external interface At the internal interface:

• The creation of the hydroxide vacancy and the oxygen ion in hydroxide position: The mechanism is solved by using the rate determining step method assuming that step [S.2] is the rate determining one [START_REF] Soustelle | Handbook of heterogeneous kinetics[END_REF]. We obtain for the areic reactivity of growth:

[ ] [ ] °⋅ - - = = OH 2 2 ] 2 [ V s O H s k φ φ (E1)
We write that all the steps i, apart from [S.2], are at equilibrium with the corresponding equilibrium constant K i and the electric neutrality:

[ ] [ ] [ ] ' OH OH O V H s = + - °° (E2)
Assuming a low coverage of adsorption sites, that is

: [ ] 1 H s 2 << - - s O and [ ] 1 H s << -+
, the areic reactivity of growth becomes :

3 4 1 2 1 2 K K K P K K k O H + = φ (E3)
According to this solution the areic reactivity of growth should not obey the Arrhenius law with temperature, which means that the temperature coefficient Γ does not have the meaning of an activation energy unless the condition

1 4 3 << K K
is fulfilled. In this last case, the solution becomes:

O H P K K K k 2 3 4 1 2 = φ (E4)
In this case, we can consider the temperature coefficient as an apparent activation energy connected to the activation energy E 2 of the rate determining step (formation of a hydroxide group from a hydroxide vacancy) and with the enthalpy ΔH i of the various steps i constantly at equilibrium:

4 3 1 2 2 H H H E E a Δ Δ Δ Γ + + + = = (E5)
One can note, that there is indeed every chance that the preceding linear combination of the enthalpies is strongly negative, knowing that only the enthalpy of the rate determining step does not appear in the sum and that the total enthalpy of the reaction is strongly negative. Thus negative apparent activation energy is only the translation of strongly exothermic steps preceding the rate determining one. This property is known as an anti-Arrhenius behavior.

The Blocking effect

In order to understand the origin of the blocking affect, the sample obtained at the end of the TG experiments were observed by SEM.

First, let's see the pictures of hydrated grains in an experiment with no blocking effect. Figure 11 shows hydrated SBL after experiment at 160°C and 160 hPa of water vapour pressure (no blocking effect). All the grains in the initial aggregate were transformed into Ca(OH) 2 leading to an arrangement of grains with a gypsum flower like shape. A lamellar structure can be noticed with thin flakes of less than 50 nm. This microstructure is in agreement with the hexagonal crystalline structure of calcium dihydroxide. From observations of different hydrated SBL samples, aggregates in Figure 11 as well as aggregates larger than 50 µm could be observed (cf Figure 12). They are all composed of assemblies of the same gypsum flower pattern. We can conclude from these observations that even if the transformation strongly modifies the microstructure of the initial particles, the global structure of the initial aggregates is not destroyed and they are still porous.

Figure 13 shows the morphology of the aggregates (13 b) and the surface of the aggregates (13 a)

in the case of a HBL sample hydrated at 115°C and 5hPa of water vapor pressure. For this sample, a blocking effect was observed with a value of 0.7 for the maximal fractional extent (cf Figure 10b). Aggregates look here very dense which is very different to the gypsum flower microstructure observed for the samples without blocking effect. It is not possible to distinguish individual grains like in the initial aggregates (cf Figure 3b). Furthermore, some faces of the aggregates look very smooth suggesting that a continuous layer of Ca(OH) 2 had spread out without pore formation, only few cracks were formed on these surfaces. On the other faces, however, the aggregates take more or less the lamellar microstructure previously observed with HBL, with some porosity.

Considering the results obtained in the cross experiment (cf Figure 10), the origin of the blocking effect may be attributed to the differences in the physical characteristics of both SBL and HBL CaO powders.

SEM observations reveal strong differences between SBL and HBL in the powder morphology after hydration: continuous superimposed layers for HBL with a global size slightly larger than the initial aggregates compared to individual grains transformed and gypsum flower pattern in the aggregates for SBL.

From these results we can imagine that the growth of Ca(OH) 2 may proceed according to two possible mechanisms. Indeed, calcium dihydroxide crystallizes in hexagonal structure (space group P3m1), which presents a strong anisotropy. So two directions of growth may be considered: either perpendicular or parallel to the hexagonal planes of the Ca(OH) 2 structure. The so-called perpendicular growth proceeds quite usual in gas-solid reactions: according to the mechanism described above and the inward advance of the internal interface. In the parallel mechanism, after the adsorption, the diffusion of calcium and oxygen ions may proceed from the internal interface by the side of the hexagonal planes of Ca(OH) 2 , thus leading to their possible extension by reacting with hydroxyls and proton ions present at the surface. This second way of Ca(OH)

2 growth better explains the gypsum flower microstructure observed by SEM in the hydrated samples. Thus the parallel mechanism seems to be predominant in both kinds of powders. However, the perpendicular one may occur too, at least in the firsts moments of the reaction, and as long as the thickness of Ca(OH) 2 layer reminds low. In such anisotropic crystals, the diffusion in the direction perpendicular to the layers is generally slow compared to surface diffusion, especially at the temperatures investigated in this study (lower than 420°C). In the case of SBL powder, where numerous open pores exist inside the aggregates, the reaction takes place in each particle separately, without interaction with the neighboring particles. Thus the water vapor may easily circulate inside the porosity, which is in favor of a total conversion of CaO into Ca(OH) 2 . On the other hand, since the HBL powder is composed of very compact aggregates, the parallel growth leads to much more continuous layers of Ca(OH) 2 , which tend to envelop very large areas of the aggregates. As a consequence, the access of the reacting gas inside the aggregates is strongly reduced, and it results in an incomplete transformation, the perpendicular growth being too sluggish in the temperature range investigated (up to 420°C).

CONCLUSIONS

CaO hydration by water vapor has been investigated using thermogravimetry at constant temperature and water partial pressure. The curves of the fractional extent versus time obtained for two distinct CaO powders revealed several interesting features:

-the influence of water vapor pressure enhanced the kinetics of reaction with a linear dependence of the pressure on the rate;

Figure 1 :Figure 2 :Figure 2

 122 Figure 1 : XRD patterns of both powders

Figure 3 :

 3 Figure 3: Microstructure of the SBL (a) and the HBL (b) CaO aggregates

Figure 4 :

 4 Figure 4 : Pore volume distribution as a function of pore diameter for SBL and HBL CaO

Figure 5 :

 5 Figure 5 : Equilibrium pressure of hydration of calcium oxide and experimental

Figure 6 :

 6 Figure 6 : influence of water vapor pressure on the hydration of SBL CaO powders at 150°C : α(t) (a) and dα/dt (b)

Figure 7 :Figure 8 :

 78 Figure 7: Influence of temperature on hydration of SBL and HBL CaO powders with a

Figure 9 :Figure 10 :

 910 Figure 9: blocking effect for HBL powder

[

  of steps [S.1], [S.2], [S.3] and [S.4] leads to the overall reaction: CaO (s) + H 2 O (g) = Ca(OH) 2 (s) [R1].

Figure 11 :

 11 Figure 11 : SEM picture of hydrated SBL 115°C, 5 hPa (No blocking effect)

Figure 12 :

 12 Figure 12 : SEM picture of hydrated SBL 160°C, 80 hPa (No blocking effect) : a) X 1500;

Figure 13 :

 13 Figure 13 : SEM picture of hydrated HBL 115°C, 5 hPa (blocking effect)

Figure 14

 14 Figure 14 illustrates schematically the differences in both possible mechanisms.

Figure 14 :

 14 Figure 14 : Schemes of perpendicular (a) and parallel (b) growth processes. Bold and

extremely exothermic reaction combined with a rate determining step leading to an expression of the rate including all the steps; -a "blocking effect" was also observed for only one of the powders (less inter aggregate porosity) with "in fine" packed aggregates attributed to the growth of Ca(OH) 2 continuous layers around the aggregates.


D Elvira

R Hostein

B Fain

L Monniello

A Michon

G Beaudoin

R Braive

I Robert-Philip

I Abram

I Sagnes

A Beveratos

Single InAsP/InP quantum dots as telecommunications-band photon sources

Keywords: numbers: 78.67.Hc Optical properties of Quantum dots, 78.47.jd Time resolved luminescence, 42.50.Ar Photon statistics and coherence theory

The optical properties of single InAsP/InP quantum dots are investigated by spectrally-resolved and time-resolved photoluminescence measurements as a function of excitation power. In the shortwavelength region (below 1.45 µm), the spectra display sharp distinct peaks resulting from the discrete electron-hole states in the dots, while in the long-wavelength range (above 1.45 µm), these sharp peaks lie on a broad spectral background. In both regions, cascade emission observed by time-resolved photoluminescence confirms that the quantum dots possess discrete exciton and multiexciton states. Single photon emission is reported for the dots emitting at 1.3 µm through antibunching measurements.

INTRODUCTION

The three-dimensional confinement of electrons and holes in semiconductor quantum dots gives rise to discrete electron-hole states and sharp absorption and emission lines, analogous to those in atomic systems [1]. These features have been exploited to produce quantum states of light, such as single photons [2,3], indistinguishable photons [4,5,40] and entangled photon pairs [7][8][9] that may be used in quantum communication protocols, such as quantum key distribution or quantum relays based on quantum teleportation [10][11][12][13]. At the same time, quantum dots have been used as gain media in photonic crystal nanolasers [14]. However, for highly-excited quantum dots placed inside photonic crystal nanocavities, it was found that the simple "artificial atom" model of the quantum dot, which successfully described the emission of one or two photons by the quantum dot in free space, could not adequately explain the emission of light by the dot into an apparently non-resonant nanocavity [15]. This cavity feeding required explicit consideration of multiply-excited states emitting into a broad quasicontinuum [16].

To date most such photon sources and nanolasers have been fabricated with quantum dots embedded in a GaAs matrix and thus emitting around 920 nm, while prospective applications require sources operating in the telecommunications wavelength range, particularly in the Oand C-bands, around 1.3 µm and 1.5 µm respectively. InAs/InP quantum dots can emit in these wavelength bands and are well suited as active media in semiconductor optical amplifiers or ridge laser systems useful for telecommunications applications [17]. However, attempts to grow such dots by Molecular Beam Epitaxy (MBE) did not give the desired results, as growth on (001)-InP substrate generally leads to the formation of quantum dashes or quantum wires [18,19], while growth on a (311)-InP oriented substrate [20] is not compatible with the standard processes used in the fabrication of photonic devices such as microcavities. Use of Metal-Organic Chemical Vapor Deposition (MOCVD), on the other hand, has made it possible to grow small InAsP/InP islands on a (100)-InP oriented substrate, as it allows for the spontaneous formation of a twodimensional wetting layer on which small islands can grow [21][22][23], while their spectral distribution [24] or density [25] can be adjusted during growth. Transmission Electron Microscopy (TEM) studies on MOCVD-grown samples have shown that the islands are truncated pyramids of diamond-shaped cross-section with diagonals of the order of 30 nm to 40 nm at the top [24].

Although these islands are small enough to have discrete electronic states, sharp spectral lines (identified as exciton and biexciton lines [25][26][27][28]) are observed only in the short wavelength side of the luminescence spectrum, from 1.3 µm up to 1.45 µm. By contrast, the emission spectrum around 1.55 µm generally exhibits a large number of low intensity peaks lying on a broad and intense background, a feature that may be interpreted as corresponding to a continuum of electron-hole states in the InAsP island. This spectral region has not been explored up to now, and the nature of the states that contibute to it, whether continuous or discrete, has not yet been clarified.

In this paper we investigate the light emission properties of InAsP/InP islands and show that they are indeed quantum dots whose discrete exciton states can provide individual photons, while their multi-exciton states give rise to cascaded emission that can feed a nanocavity and provide gain for nanolasers. The paper is organized as follows: We first describe the sample growth and the experimental setup. Then, we identify discrete exciton lines of two distinct quantum dots, emitting in each of the two spectral regions and study their saturation char-acteristics. Then, through time-resolved measurements, we show that both types of quantum dots have discrete multi-exciton states. Finally, we demonstrate single photon emission from a single quantum dot.

SAMPLE GROWTH AND EXPERIMENTAL SETUP

Samples were grown in a vertical-reactor lowpressure MOCVD system using hydrogen as the carrier gas and standard precursors (arsine, phosphine, and trimethylindium) [29]. The epitaxied InAsP islands were formed on a thick (∼200 nm) InP buffer layer deposited on a (001)-oriented semi-insulating InP:Fe substrate. The island growth was obtained at 510 • C by depositing 6.3 monolayers (ML) of InAsP at growth rate of 0.36 ML.s -1 and under a phosphine/arsine flow ratio of 30. Finally, a 63 nm thick InP capping layer was grown over the islands at a rate of 0.2 ML.s -1 . Such a growth sequence leads to the formation of InAsP islands with an average height of 3.8 nm and a density of 15x10 9 cm -2 , sitting on a 1.5 nm-thick wetting layer, measured by TEM experiments [24]. The average composition of the islands was measured to be InAs 0.8 P 0.2 , while the residual doping of the InP buffer layer was measured to be around 10 16 e -cm -3 , indicating that the islands may be charged, containing one or more electrons.

Small numbers of islands were isolated by etching mesas using the following technique. Layers of SiN and Polymethyl Methacrylate (PMMA) were deposited on top of the sample. 500 nm up to 2 µm diameter holes were formed in the PMMA layer by electron beam lithography. After deposition of a 40 nm thick layer of nickel followed by a lift-off, the SiN layer was etched by reactive ion etching (with gaz mixture of SF 6 and CHF 3 ), to form bilayer pillars of SiN and Ni on the semiconductor. These pillars acted as a mask in the subsequent semiconductor etching in an inductively coupled plasmareactive ion etching machine (with gaz mixture of HBr and O 2 ). This whole process led to the formation of 1.3 µm tall mesas in the semiconductor, with diameters ranging from 500 nm to 2 µm.

Time-resolved microphotoluminescence experiments were performed on the samples, placed in a liquid He flow cryostat, under pulsed excitation with 5 ps-long pulses at 80 MHz delivered by a Ti:Sa laser emitting at 840 nm. The excitation pulses were focused on the samples by a microscope objective (numerical aperture of 0.4) to a spot of a diameter of 5 µm. An incident power of 100 nW thus corresponds to a pulse energy of 125 nJ.cm -2 . The island luminescence was collected by the same microscope objective and separated from the pumping laser by means of a dichroic mirror and an antireflection coated Si filter. The spontaneous emission was spectrally dispersed by a 0.5 m spectrometer and detected either by a cooled InGaAs photodiode array (Roper Scientific) or time-resolved superconducting single photon counters (SCONTEL) with a time resolution of 50 ps, a measured quantum efficiency of 3% at 1.55 µm and dark count rates lower than 30 counts per second. Lifetime measurements were obtained by recording the histogram of the time interval between a photon detection and the subsequent laser pulse using a LeCroy 725Zi oscilloscope. The second order auto-correlation function was measured with a standard Hanbury-Brown and Twiss setup: The collected luminescence signal was split by a 50/50 fibered coupler and sent onto two single-photon detectors placed on each output of the beamsplitter. The auto-correlation function was deduced from the histogram of the time intervals between two single photon detection events. FIG. 1: Typical low-temperature photoluminescence spectra observed on a 1 µm diameter mesa under pulsed excitation at 840 nm with an incident power of Pin = 162 nW (cw equivalent power measured after the microscope objective, corresponding to 200 nJ/cm 2 per pulse).

SPECTRAL CHARACTERISTICS

The emission spectrum of the unprocessed sample (not shown here) consists of a broadband emission centered at 1.5 µm having full width at half-maximum of 0.13 µm and a long tail extending towards the shorter wavelengths, reflecting essentially the size statistics of the InAsP islands [31]. Figure 1 presents a typical emission spectrum obtained under pulsed excitation at 4 K on a 1 µm diameter mesa containing approximately 120 islands, of which probably 75 % are far enough from the mesa edge to luminesce properly. The spectrum, which consists of the superposition of the spectra of several islands, displays distinct and sharp intense peaks in the short wavelength part (below 1.45 µm). As wavelength increases, the peaks become denser, reflecting the size statistics of the quantum dots. At the same time, the peaks get less intense while a broad background becomes increasingly strong as wavelength increases. These spectral features have already been reported by several other groups [25][26][27][28] with similar, but not identical, systems, but their nature had not been investigated. In order to investigate in more detail the characteristics of the islands corresponding to different parts of the spectrum, we examined two emission lines, corresponding to the excitons of two different quantum dots, referred to as QD 1 (1298 nm) and QD 2 (1538 nm). As QD 2 lies in a relatively dense part of the spectrum, it was studied on a smaller mesa of diameter of 0.5 µm, containing less than 20 islands far enough from the edge so as to luminesce. A filter cutting-off wavelengths below 1500 nm was used. The photoluminescence spectra of the two mesas at 4 K at different incident powers under pulsed excitation, are shown on Figure 2. At low incident powers we observe sharp peaks that may be attributed to the emission from the exciton and the s-shells of the QD 1 and QD 2 quantum dots. These peaks lie on a broad background, whose intensity increases with increasing incident power. The intensity of the background is approximately twice as high around QD 2 as compared with QD 1 , because of the higher density of quantum dots at that wavelength. In order to confirm that the background signal arises from the islands themselves and not from the surrounding materials (wetting layer, impurities, defects...), a similar sample with just the wetting layer and no islands was grown and subsequently processed into mesas under the same conditions. No luminescence was observed on this sample at wavelengths longer than the spectral band edge of the wetting layer (around 1.15 µm i.e. 1.08 eV) at any incident power.

When the incident power is increased, we observe the emergence of additional lines attributable to p-shell emission. For QD 1 they are around 1250 nm to 1260 nm, giving a spacing between the s-and p-shells of ∼30 meV. The p-shell of QD 2 corresponds to a group of peaks around 1505 nm, giving a spacing between the s-and p-shells of at least ∼18 meV for QD 2 . It should be noted that at low incident intensities additional lines are present around 1510 nm, due to excitons from other quantum dots. Assuming that the islands correspond to rectangular potential wells for electron-hole pairs and that the p-shells involve only the two quantum numbers in the plane perpendicular to the growth direction, these values indicate that the bottom of the rectangular well (i.e. the effective bandgap of a layer confined in the growth direction to the height of the QDs) is at ∼935 meV for QD 1 and at ∼800 meV for QD 2 . Since the bandgap of InAs 0.8 P 0.2 is at 600 meV, if we assume that difference between QD 1 and QD 2 is due to confinement in the growth direction, the values of the effective bandgaps would indicate that QD 2 is 30 % taller than QD 1 .

While we conclude that the s-p shell spacing is of the order to 30 meV for QD1, this assertion would be strongly supported by a cross-correlation measurements. The latter was not possible due to the low intensity of these high-energy emission lines, requiring extremely long integration time. However the power dependence of their intensity give some insight on their nature. As expected for p-shell states, these emission lines only appear above the saturation of the exciton line and all associated sharp lines of the p-shell grow in a similar way. Their integrated emission does not saturate and follows closely the mean number of electron-hole pairs as function of the pump power from figure 6. Also the energy spacing is of the rigth order of magnitude when compared to theoretical predictions [30] The position of the wetting layer bandgap at approximately 1.08 eV indicates that QD 1 corresponds to a welldepth of about 150 meV accommodating some 8 electronhole levels (assuming a two-dimensional rectangular-well potential), while QD 2 has a well-depth of about 280 meV, with possibly at most 35 electron-hole levels. This approach is valid for quantum dots with relatively large lateral extension which is the case in the system under study. Recent STM measurements in cleaved InAsP/InP quantum dots [32,33] permitted the mapping of electron wavefunctions with as many as 5 nodes along the base of the dot in the exposed surface. Assuming a similar range of values for the quantum number in the perpendicular direction in an uncleaved dot, that would correspond to more than 25 electron levels, thus corroborating the possibility of having a few tens of electron-hole levels in the quantum dot. At low incident powers, only the lowest electron-hole level (exciton) is populated, giving rise to a single sharp line upon recombination. At higher incident powers, more than one electron-hole pair is injected in the quantum dot; emission from these multi-exciton states gives rise to the broad background [16]. The valence band offset for InAsP/InP quantum dots is higher than InAs/GaAs quantum dots [42], almost equally distributed between electron and holes. In conjunction with the STM images [32,33] a multi-level description of the quantum dot is consequently possible. The dependence of the intensity of the exciton emission lines for QD 1 and QD 2 on the incident power is presented on Figure 3, and is reasonably well described by a saturation formula of the form

I out = I 0 (1 -e -Pin/Psat ) (1)
which assumes Poisson statistics for the number of electron-hole pairs in the quantum dot, with P sat , the incident power at saturation, corresponding to the input power for which one electron-hole pair is injected on average in the quantum dot. Its value is 620 nW for QD 1 and 180 nW for QD 2 . At low incident powers, the intensity of these lines increases approximately linearly as it is proportional to the probability of trapping a single electron-hole pair in the quantum dot. Beyond P sat the intensity saturates to a constant level, as more than one electron-hole pair is trapped in the quantum dot during each excitation cycle: the multi-electron-hole pair state contributes to the broad background [16], as the pairs recombine successively, and only the last pair in the cascade contributes to the sharp emission line. Note that it is not simple to differentiate a neutral exciton from a charged exciton, and precise identification requires polarization resolved quasiresonant excitation [40]. Eventually, let's note the unexpected absence of biexciton lines, which is currently under investigation.

TIME RESOLVED MEASUREMENTS

The formation and recombination dynamics of the quantum dot excitons was investigated by monitoring the time dependence of the exciton emission line under pulsed excitation. When the laser pulse is absorbed, it generates a large number of electron-hole pairs in the InP buffer and the wetting layer, some of which are captured by the quantum dot, giving rise to its luminescence upon recombination. As the unexcited quantum dots may already contain one or two electrons due to the residual doping, the capture of carriers may proceed charge-bycharge, in the weak excitation regime [34]. The electrons generated by the absorption of the incident pulse remain in the buffer, as they are attracted to the ionized donors, while the holes are efficiently captured by the negatively-charged quantum dots, where they eventually recombine radiatively with the resident electrons to produce the quantum dot emission. Thus, at low incident powers, the time dependence of the QD 1 and QD 2 lines display a sharp rise limited by the temporal resolution of our setup of 70 ps, indicating that the exciton state is populated immediately through the capture of a hole (when the quantum dot already contains one electron) or the capture of an electron-hole pair (when the quantum dot is empty). This immediate response is followed by a rapid buildup of the exciton intensity (with an exponential characteristic time of about 400 ps), up to a maximum at ∆t = 500 ps later for QD 1 and ∆t = 200 ps for QD 2 (see Fig. 4). This delay indicates that the charge capture populates also a relay state which in turn feeds the exciton. As the relative weight of the relay state is of the same order as that of the exciton, even for incident intensities as low as 2% of saturation, it is quite likely that the relay state corresponds to the biexciton produced by the capture of two holes when the quantum dot already contains two electrons. Thus, at low incident intensities, the relative weights of the prompt and delayed components reflect essentially the doping statistics [35]. After reaching the maximum, the luminescence decays exponentially with a characteristic time of 2.2 ns for QD 1 and 1.4 ns for QD 2 (see Fig. 4), which correspond to the exciton lifetimes τ X in the two quantum dots.

When the incident power is increased, the decay curves change in two ways: First, the delay ∆t between the incident pulse and the maximum of the exciton intensity increases and, second, an additional fast decay emerges at short time delays, with a characteristic time of the order of 400 ps and 880 ps for QD 1 and QD 2 respectively. The increasing delay ∆t results from the injection of increasingly more electron-hole pairs in the island, which must decay before emission can occur from the one-exciton level that is being monitored. The fast component, on the other hand, is due to the emergence of the broad background whose contribution increases with incident power (see Fig. 2). This is confirmed by measuring the temporal traces of the background signal in the vicinity of QD 1 and QD 2 : the decay times are respectively 400 ps and 800 ps. Figure 5 (Top) shows the delay of the exciton line ∆t for both QD 1 and QD 2 as function of the normalized incident power. As this delay is directly related to the mean number of electron-hole pairs in the dot (µ), we can deduce µ from the time-resolved curves (see Appendix A). A plot of µ as a function of the normalized incident power is given in Fig. 5 (Bottom). These values were obtained by fitting the time-resolved curves using Eq. ( 7) for QD 1 with τ X = 2.2 ns and τ B = 0.72 ns and using Eq. ( 5) for QD 2 with τ X = 1.4 ns and τ B =0.9 ns. The exciton lifetime is directly measured from the curves, while τ B and µ are fitting parameters. The slight discrepancy between these values for τ B and those obtained directly (open red circles) as a function of incident power under pulsed excitation at 840 nm, in a log-log scale. The mean number of electron-hole pairs is obtained by fitting the exciton decay curves using Eq. ( 7) for QD 1 and Eq. ( 5) for QD 2 . The dotted line is a guide for the eye with unity slope.

from the decay of the background, is due to the fact that the former involve only those cascades that end up in the one-exciton line that is being monitored, while the latter involve all transitions at the corresponding wavelength. At low incident powers, the mean number of electronhole pairs present in the quantum dot is constant, corresponding to µ ≈1.1 for QD 1 and µ ≈0.5 for QD 2 , reflecting essentially the mean number of electrons resident in each dot due to the residual doping. This gives rise to the constant delay observed in the time resolved curves at low excitation power. Under these conditions, emission results from injecting in the dot a matching number of holes, charge-by-charge. At higher incident intensities, the number of captured charges exceeds the number of resident electrons and the average number of electronhole pairs increases with the incident power, initially linearly and then sublinearly. Deviation from linearity and saturation of µ are visible beyond 10 P sat . The reason is that under high incident power, a dense electron-hole gas is generated in the InP buffer layer so that bimolecular radiative recombination enters in competition with pair capture by the quantum dot: an increase of the electronhole population in the InP buffer gives rise to a quadratic increase radiative recombination rate inside the buffer layer and therefore a sub-linear increase in the pair capture by the quantum dot, as discussed in Appendix B.

As the statistics of injected pairs is masked by the doping statistics at low incident powers, we can compile a composite set of data for the mean number of injected pairs by using the intensity data of Fig. 3 at low incident powers (below P sat ) and the data of Fig. 5 (Bottom) at high incident powers (above P sat ). The resulting set of data is shown on Fig. 6 (Top), and is quite well fitted by Eq. ( 15), using VC/B = 4.7 for QD 1 and VC/B = 5.6 for QD 2 . This analysis indicates that only a small number of electron-hole pairs reaches the dot, even at very high incident intensities, because the excitation process involves the generation of an electron-hole gas in the buffer layer and a subsequent capture of electronhole pairs by the quantum dot: for incident intensities of the order of P in = 1000P sat the quantum dot contains only 20 to 25 pairs. Such a high number of levels is indeed expected from the STM experiments on equivalent quantum dots [32,33]. During the radiative cascade of a multiply-excited quantum dot, only the last electron-hole pair emits in the exciton line, while all others contribute to the broad background. This means that the background intensity should be proportional to the number of pairs present in the dot. Fig. 6 (Bottom) shows the background intensity as function of incident power in the vicinity of QD 1 and QD 2 . The curves are a fit using Eq. 15 with the same parameters as for the mean number of pairs above, plus an overall vertical scaling parameter to account for the arbitrary units of the intensity. The fit is quite good, considering that the background contains also contributions from other quantum dots, each with a different saturation power. Thus, this fit supports the assumption that the broad background emission arises directly from the electron-hole pairs captured by the quantum dot [16].

PHOTON CORRELATION MEASUREMENTS

Although cascade emission is a unique signature of confined 0D electronic states of single quantum dots, a direct proof of the unicity of the emitter is given by the observation of single-photon emission through antibunching. Photon correlation measurements were performed by measuring the normalized second-order corre- lation function g (2) (τ ) =<: I(t)I(t + τ ) :> / < I(t) > 2 where I(t) is the emission intensity at time t and <::> indicates the normal ordering of the creation and annihilation operators. Figure 7 shows a histogram of the delay times between detection events on the start and stop channels of the Hanbury-Brown and Twiss setup, obtained for QD 1 , at an incident power of 1.45 P sat .

Under pulsed excitation, the histogram of time delays consists of a series of peaks separated by the period of the pump cycle. When normalized by dividing by the count rates of the two detectors, by the experiment time, and by the period of the pump cycle, and after subtracting the accidental coincidences due to the dark counts, the area under each peak, except for the peak at τ = 0, is equal to 1 [36]. The value of the histogram in the region around τ = 0 measures the conditional probability of detecting a second photon during the excitation cycle given that a first photon has already been detected. It is expected to be below 0.5 for a single photon source. For QD 1 , the normalized intensity level of the central re- gion is 0.18. This value is essentially equal to the ratio between the sharp line and the contribution of the broad background at that wavelength and at an incident power of P = 1.45P sat , indicating that the QD 1 exciton is indeed a single photon emitter, and that the possibility of having a second photon is only due to the background emission. For QD 2 , it was not possible to obtain the second order autocorrelation function because of the lower count rate and the strong contribution of the broad background.

SUMMARY AND CONCLUSION

In this paper, we have examined the photoluminescence characterisics of InAsP/InP quantum dots emitting at telecommunications wavelengths. Timeresolved measurements have shown that these dots can be multiply excited and undergo a radiative cascade. All but the last step of the radiative cascade give rise to a broad spectrum, while the last step, which involves emission from the one-exciton state, gives rise to a sharp spectral line. The sharp line emission shows strong anti-bunching, indicating that InAsP/InP quantum dots are good single photon emitters, useful for quantum communications at telecommunications wavelengths. However, these quantum dots may not be suitable for some quantum information protocols, since the emission of the exciton and the biexciton lines will present a strong jitter due to the cascaded emission. The broad background resulting from the radiative cascade is important for the use of these quantum dots as gain material in photonic crystal nanolasers, as the broad spectrum permits efficient feeding of a nanocavity that would otherwise be out of resonance with the quantum dot exciton. However, as the number of electron-hole pairs in the dot grows sub-linearly as a function of pumping, it is possible that the lasing threshold may appear to be progressive rather than abrupt.

The number of excitons injected in a quantum dot follows, in principle, Poisson statistics. However, a fraction of these excitons is non-radiant (dark) and do not participate in the cascade that leads to the radiant (bright) exciton level being monitored. The resulting statistics of the fully radiant multiexciton states involves hyperbolic Bessel functions rather than exponentials. However, the limited precision of our experimental data does not permit us to distinguish between these statistics and those of the Poisson distribution which includes both radiant and non-radiant states. Thus, for the sake of simplicity, we consider here Poisson statistics.

For a Poisson distribution of the number of electronhole pairs N with mean µ, and for the case τ B /τ X ≈ 1, convolution of Eq. ( 3) with the exciton decay gives the exciton intensity as a function of time as: I X (t) = µe -t/τX e -µ exp[-t/τB ]

(5)

with a maximum at ∆t = τ B ln µ τ X τ B (6) while for the case τ B /τ X ≪ 1, the convolution of Eq. ( 4) gives the exciton intensity as:

I X (t) = e -t/τX e -µ exp[-t/τB ] (1 + µe -t/τB ) -e -µ (7) with a maximum at

∆t ≈ τ B ln µ τ X τ B . (8)

FIG. 2 :

 2 FIG.2: Low-temperature spectra of the emission lines associated with two different InAsP/InP quantum dots labeled QD 1 (Left) and QD 2 (Right) obtained under pulsed excitation at 840 nm, at different incident powers. Incident powers are normalized to Psat = 620 nW for QD 1 and Psat = 180 nW for QD2 . The vertical scales are in the same arbitrary units in all graphs. Note that the pics at 1290 nm and 1540 nm could arise from other quantum dots, since they display similar saturation behavior with increasing power.

FIG. 3 :

 3 FIG. 3: Intensity of the exciton peak of QD 1 (open black squares) and QD 2 (open red circles) as a function of incident power. Curves are fits to Eq. (1) with Psat = 620 nW for QD 1 and Psat =180 nW for QD 2 .

FIG. 4 :

 4 FIG. 4: Decay curves of the exciton emission lines associated to two different InAsP/InP quantum dots labeled QD 1 (Top) and QD 2 (Bottom) obtained under pulsed excitation at 840 nm for different incident powers. (Top) QD 1 : Pin = 0.8 Psat (black curve) and Pin = 23 Psat (blue curve) (Bottom) QD 2 : Pin = 0.07 Psat (black curve) and Pin = 7 Psat (blue curve). Note Psat = 620 nW for QD 1 and Psat =180 nW for QD 2

FIG. 5 :

 5 FIG. 5: (Top) Time delay between the incident excitation pulse and the intensity maximum of the exciton luminescence peak of QD 1 (open black squares) and QD 2 (open red circles) as a function of normalized incident power under pulsed excitation at 840 nm, in a log-linear scale. The normalization is with respect to Psat = 620 nW for QD 1 and Psat = 180 nW for QD 2 . (Bottom) Mean number of electron-hole pairs (µ) in QD 1 (open black squares) and QD2 (open red circles) as a function of incident power under pulsed excitation at 840 nm, in a log-log scale. The mean number of electron-hole pairs is obtained by fitting the exciton decay curves using Eq. (7) for QD 1 and Eq. (5) for QD 2 . The dotted line is a guide for the eye with unity slope.

FIG. 6 :

 6 FIG. 6: (Top) Mean number of electron-hole pairs (µ) injected in QD 1 (open black squares) and QD 2 (open red circles) as function of the normalized excitation power. (Bottom) Intensity of the background signal in the spectral vincinity of QD 1 (open black squares) and QD 2 (open red circles) as function of incident power under pulsed excitation at 840 nm, in log-log scale. All fits are obtained using Eq. (15).

FIG. 7 :

 7 FIG.7: Histograms of the time intervals between detection events on the start and stop detectors for the QD 1 line under pulsed excitation with an incident power of 1.45 Psat.

Acknowledgements: The authors are thankful to Dr. T. Debuisschert for lending critical experimental equipment. This work was partly supported by the C'Nano Ile-de-France project "CRYPHO" and the European project IST-249012 "Copernicus".

Appendix A: Radiative Cascades

In this Appendix, we examine the cascaded radiative decay of a multiply excited quantum dot. We consider a quantum dot initially containing N electron-hole pairs that recombine independently. During the successive recombination events, the quantum dot will emit a cascade of N -1 photons into the broad background until it reaches the one-exciton state whose emission is being monitored [37,38]. Assuming that the characteristic time for emission into the broad background τ B is independent of the number of excitons present, the probability of reaching the two-exciton state at time t is

Emission from this level feeds directly the exciton, whose luminescence corresponds to a sharp line and has a lifetime τ X . The time-evolution of the exciton emission is thus given by the convolution of the feeding mechanism of Eq. ( 2) with the exciton decay. The resulting summation of exponentials cannot be performed analytically for an arbitrary ratio τ B /τ X . Analytic approximations can nevertheless be obtained in two significant cases: (a) When τ B /τ X ≈ 1, we have:

and (b) when τ B /τ X ≪ 1, we have:

Appendix B: Carrier Capture

We consider the process whereby an incident light pulse is absorbed in a thick semiconductor layer, thus generating a density n of electron-hole pairs, which may either recombine radiatively or be captured by the quantum dots embedded in the semiconductor layer. The kinetics of the carriers in the semiconductor layer are described by:

where A, the monomolecular decay rate, includes capture of the electron-hole pairs by the quantum dots, radiative recombination involving the residual doping, as well as non-radiative recombination of the carriers. B is the familiar bimolecular radiative recombination coefficient. This differential equation has the well-known solution

where n 0 is the initial pair density produced by the absorption of the incident light pulse at t = 0. As carrier capture by the quantum dot is much faster than the radiative lifetime of the pairs in the dot (typically by 3 orders of magnitude) the kinetics of pair capture in the dot may be written as

where µ is the mean number of pairs in the dot, C is the capture rate per quantum dot and V is the volume of the quantum dot. Thus, the number of pairs captured by the dot may be written as:

In our experiments, we do not have direct access to n 0 , but we can assume that it is proportional to the incident pulse energy and thus to the mean incident power, P in .

The proportionality constant may be obtained by considering the number of captured pairs in the low-density limit of Eq. ( 12),

which, in Eq. ( 1) was assumed to be given by P in / P sat . Thus, the initial pair density in the excited semiconductor layer can be written as

so that the mean number of electron-hole pairs in the quantum dot as a function of the incident power reads

Thus, while at low incident powers Eq. ( 15) reduces to the familiar proportionality between the number of pairs captured by the quantum dot and those injected in the wetting layer, at high incident powers the competition between the capture process and the radiative bimolecular recombination causes the number of pairs in the quantum dot to increase very slowly as a function of incident power.

Eq. ( 15) can be used to fit our experimental data, with V C B as the only fitting parameter. An order of magnitude estimation of its value may be obtained by considering the orders of magnitude of the three parameters composing it: B ∼ 10 -10 cm 3 .s -1 , V ∼ 10 -18 cm 3 . The capture rate in multi-dot systems has been measured to be [39] A ∼ 10 11 s -1 , which would correspond to a capture rate of C ∼ 10 8 -10 9 s -1 per dot. Thus V C B ∼ 1 -10.

[1] M.A. Kastner, Physics Today 46, (1) 24 (1993).