J C Launay

V Mazoyer

M Tapiero

J P Zielinger

Z Guellil

Ph Delaye

G Roosen

Growth, Spectroscopic and Photorefractive investigation of vanadium-doped cadmium telluride

Keywords: 42.65, 42.70, 72.40. Growth, Spectroscopic and Photorefractive investigation of vanadium-doped cadmium telluride

We present new results on the growth of semi-insulating vanadium-doped cadmium telluride crystals and their characterizations by different optical techniques such as photoinduced current transient spectroscopy, absorption, photoconductivity spectra and photorefractive wave mixing. Our joint research program aims at developping optimized crystals for efficient optical processing in the near infrared through the photorefractive effect.

Introduction

The investigation of photorefractive semiconductors is strongly motivated by the compatibility of their operating wavelengths with semiconductor lasers and with fiber optics communications.

For a better understanding of the complex processes occuring in photorefractive materials, a variety of research area are now involved including not only nonlinear optical properties but also crystal growth, spectroscopy, etc.... In this context, the determination of deep trapping levels that directly affect the photorefractive properties is of prime importance.

For a long time, it was generally believed that only the dominant deepest levels were involved. However, since the advent of experiments conducted with pulsed high energy nanosecond and picosecond lasers, many new interesting phenomena have been discovered. Clearly, in the pulse regime, shallower levels play also an important role (1,2) . Any defect, provided that its concentration is of the order of 10 15 cm -3 , may be concerned. Therefore, a complete knowledge of the imperfection identity, thermal and photoionization energies, capture cross sections and concentration is desirable for optimum control of the material parameters to meet device requirements.

The introduction of transition metals (TM) into II-VI compounds usually causes considerable changes in the electrical, optical and photoelectrical properties due to charge compensation and additionnal extrinsic absorption and photoconductivity. Some years ago, vanadium (V) has been identified as a suitable dopant for producing appropriate deep levels in cadmium telluride, permitting the generation of the photorefractive effect (3) . The corresponding energy level is expected to act as a donor and to lie at E c -0.75 eV, i.e. in the middle of the band gap (4) . This is a location very favourable for the presence of the dopant in both unionized (0) and ionized (+) states, the unionized centers providing the photoinduced carriers.

Provided that the lattice relaxation of vanadium in CdTe is not too high, as can be expected from the pronounced covalent character of the compound, the onset of optical absorption and photorefractivity is expected at 1.7-1.5 eV. The relatively high thermal ionization energy prevents immediate reemission of the trapped charges.

Recently, photorefractive energy transfer at 1.5 µm has been reported in CdTe:V (5) showing that indeed this material is a good candidate for optical information processing using low power (mW) lasers.

Unfortunately, very little is known about vanadium in CdTe. Most of the informations were obtained in connection with the previously mentioned investigations of photorefractive properties.

Therefore, in France, we have recently started a joint research program with the aim of obtaining information on the influence of isocharge V impurities on the characteristics of doped CdTe crystals and then of optimizing them regarding the key photorefractive parameters.

We here present our first results. We have grown and vanadium doped good quality semi-insulating cadmium telluride crystals and have conducted spectroscopic and photorefractive characterizations on the same samples.

Crystal growth

Experimental conditions

The growth conditions were established to satisfy the following criteria:

-single crystallinity of the ingot, -low dislocation density and no tellurium precipitation.

V-doped CdTe crystals were grown using the modified Bridgman technique from CdTe (6-9's grade) in evacuated (10 -6 torr) graphitized quartz ampoules (to minimize nucleation sites). The purity and concentration of vanadium were respectively at least 5-9's grade and 10 19 -10 20 at.cm -3 . Crystals were grown with the dopant either added either compensated to the melt.

The ampoule took place in a vertical furnace under the following conditions: heating to 1125°C at a rate of 50°.h -1 and maintaining this temperature for 20h. Single crystals were grown at a rate of 6mm.day -1 in a typical gradient of 5°.cm -1 . Experimental conditions take into account the low thermal conductivity of CdTe. The single crystal volume is routinely greater than 80%.

Chemical composition

The distribution of Cd, Te and V, as observed from microprobe elementary mapping is homogeneous. The deviation of nominal composition inferred from the microprobe analysis is below the limit of detection sensitivity of this technique. No precipitate of Te was observed under IR microscopic examination. Substitutional V is paramagnetic in its neutral charge state V 2+ , corresponding to a 3d 3 configuration. At room temperature, the ESR signal of V 2+ is not observed due to short relaxation time or electronic delocalization. When cooled down to liquid helium temperature, delocalization might be stopped and we thus should observe the ESR signal (6) .

Lattice parameter

The lattice parameter (a) determined by X-ray diffraction is 0.6453 nm. This is smaller than the value (a = 0.6484 nm) reported for CdTe in ASTM data. The V atom (Z = 23) is smaller than the Cd atom (Z = 48). The screening effect of the electron shells is smaller in the V case than in the Cd one. This leads the V-Te bond length to be shorter than the Cd-Te one (0.2794 nm).

Microhardness

Microhardness tests were performed at room temperature using a Vickers microscope mounted indentor system SHIMADZU HMV-2000. Hardness data provide a good general impression of the mechanical properties of the materials and of their bounding strength. Many intents were made on each slice, with a rotation between them. This excludes any hardness variation due to cristallographic anisotropy of the average values that were obtained.

From H v = 1.854 F/ D 2 relation (F = test charge in Kg, D = length of the indent) the microhardness is the same along axis and radial ingot and similar to the CdTe one (47.5 +/-0.5 Kg.mm -2 ). No significant microhardness dependence appears with V dopant even at 10 20 at.cm -3 concentration.

Resistivity measurement

Electrical resistivity of the sample were measured by a conventional two point technic with silver contacts. The contact resistance was negligible. Actually, contact problems are less critical for high resistivity materials than for semiconductors. Measurements were carried out from room temperature to 400 K and then down to room temperature.

Resistivity is about 5x10 10 and 5x10 8 Ω.cm for CdTe:V with V concentrations of 10 20 (sample 6B) and 10 19 at.cm -3 (sample 1H). We notice that the results are reproducible after rising and cooling the temperature. These crystals thus present the required resistivity for the generation of optical nonlinearities through the photorefractive effect with low power lasers.

Spectroscopic characterization.

It must be pointed out that semi-insulating CdTe can also be grown by the travelling heater method (THM) using tellurium solvant with chlorine (7) . However, the electrical resistivity does not exceed 10 8 Ω.cm. In this type of material a large number of different trap species have been detected by using Thermally Stimulated Current (TSC)

and PhotoInduced Transient Spectroscopy (PICTS) techniques (7,8). The spectral resolution was not sufficient to allow a complete and precise determination of the trap parameters. Nevertheless, a few centers could be identified and characterized. Two levels may be efficient as traps in room temperature operation respectively at E C -0.58 eV (interstitial Cd or Te vacancy) and E C -0.7 eV (double negatively charged Cd vacancy V Cd --). On the other hand the single charged vacancy (V Cd -), state -located at E V + 0.4 eV in CdTe, is known to play an important role as a compensating acceptor and as a recombination center.

Introduction of TM may cause rather complex compensation phenomena between the various types of native defects. Actually only slight changes in the edge luminescence spectra were observed, as long as the V concentration was lower than 10 19 cm -3(9) .

However a further increase in V-concentration (10 20 cm -3 ) revealed new D-A transitions. The following interpretation was proposed: introduction of V at increasing concentrations first results in the filling of Cd vacancies and finally in the occupation of interstitial sites, giving rise to a new donor level.

As pointed out before, the determination of deep level spectra is one of the important problems. We report a set of first results obtained by an improved PICTS technique (10) .

3.1 Experimental method.

PICTS is a transient photoconductivity, computer based, measuring technique. The current transient, including both rise and decay, induced by a square light pulse in a biased sample, is recorded every 1 or 2 K, during a temperature scan (usually from 80 K up to 500 K, or vice versa). Sufficient time is provided for allowing the photocurrent to reach saturation and after that to decay to zero. A slow decay (typically 10 -3 s up to 10 s) indicates thermally stimulated emission from traps (Fig. 1).

The slow component has a complex thermal behaviour: both the amplitude, the shape and the decay time vary. Three types of numerical processing of the stored data allow us to extract the parameters of the traps: the apparent thermal ionization energy E t and capture cross section S t , the concentration N t for the dominant species and perhaps also the type n or p (10) .

In order to stress the difference between the three data treatments and hence the signification of the curves presented hereafter and also to emphasize the improvement of our procedure with respect to similar measurements bearing the same initials, we briefly recall the principles of the calculation.

For sake of simplicity we consider the single trap case. The analysis further assumes that the thermally released carriers are not retrapped, but are neutralized by carriers of opposite sign localized on deeper lying levels. The trapped charge n t (t) then decays exponentially according to:

n t (t) = N t exp(-t/τ t ) (1)
The relaxation time τ t is related to E t and S t :

τ t -1 = A S t T 2 exp(-E t /kT) (2)
where k is the Boltzmann constant and A a constant (7) .

Suppose a signal which directly reflects the decay of n t (equat.1) be recorded at various temperatures. As τ t stongly depends on T, the shape of the transient changes as shown in Fig. 2. If the signal is sampled at two fixed delay times t 1 and t 2 , the difference Δn = n t (t 1 ) -n t (t 2 ) obviously goes through a maximum at a temperature T m where τ t takes a defined value τ m which can be related mathematically to t 1 and t 2 using the condition for the maximum of the function

f(τ t )=exp(-t 1 /τ t ) -exp(-t 2 /τ t ).
The result is that τ m can be computed knowing t In practice, however n t (t) is not directly accessible. But the transient current, due to the thermal release of the trapped charge, can be measured. This current is proportionnal to dn t /dt = N t /τ t .exp(-t/τ t ). On the other hand, it depends on the mobility µ and on the recombination life time τ.

The current can be expressed as :

i(t) = {BµτN t / τ t }exp(-t/ τ t ) (3)
where B is a constant including the applied electrical field and a geometrical factor.

Usually the temperature dependence of µτ is neglected in (3) (10) . The relation expressing the condition for the maximum of g(τ t )= 1/τ t .[exp(-t 1 /τ t ) -exp(-t 2 /τ t )] is thus used for the determination of τ m . This simple but approximative conventional procedure does not yield very reliable values for the trap parameters.

A better alternative is to divide the double-gate signal by the photocurrent i(0) which is proportionnal to µτ (Fig. 1), a procedure which allows to eliminate, in a first approximation the µτ product in (3). This method is of special interest for the determination of the trap concentrations (10) . Actually it introduces another temperature dependant factor, i.e. the optical generation rate G of photocarriers. In general, however G can be kept fairly constant (see section 3.2) by properly adjusting the wavelength of the excitation.

The problem can be led back to the transient charge case (equation 1) simply by reading the current at four fixed delay times t 0 , t 1 , t 2 , t 3 and plotting the function :

Y(T)= [i(t 1 )-i(t 2 )]/[i(t 0 )-i(t 3 )] (4)
It must be pointed out that this "four-gate" treatment eliminates the pre-exponential factor in (3), including N t . Y(T) shows a maximum provided that t 0 <t 1 <t 2 <<t 3 (10) .

The four-gate data processing is a very sensitive method with high spectral resolution.

It represents a considerable improvement for the determination of the trap signatures (E t , S t ).

3.2 Results and discussion.

A. Electrical conductivity:

The electrical conductivity versus T has been measured on two samples 1H and 6B, the second one beeing stronger doped (~ 10 20 cm -3 ) than the first one (< 10 19 cm -3 ). In a temperature range extending from somewhat below 300 K up to 400 K, nearly the same activation energy was found with both samples : 0.76 eV for sample 1H and 0.72 eV for sample 6B. This result confirms that the dark Fermi level is pinned by a deep level lying close to the middle of the bandgap.

Figures 3 shows the normalized spectral responses of samples 1H and 6B respectively.

The peak at roughly 1.5 eV corresponds to band to band transitions.

In the case of sample 1H the extrinsic photoconductivity drops sharply for photon energies hν < 1.1 eV. This result fits well with the measured absorption spectrum We therefore conclude that, at low doping rate, V is not optically active.

The photoconductivity band for sample 6B on the contrary extends up to 1.7 µm. In this sample, photorefractivity should be observable at 1.3 -1.5 µm. As stated by P.I. Babii et al. (9) additionnal deep states can only be introduced by heavy doping.

C. Determination of trap parameters:

In order to obtain reliable results the PICTS technique requires optimal experimental conditions which depend on the material (10) . Concerning CdTe, we shall come back to this problem in a forthcoming paper when more complete results on a larger number of crystals will be available. We describe here only a few of the experimental conditions which are important for the understanding and discussion of the results. In this paper we present a list of the detected traps with a first estimation of their parameters.

Most of the presented results concern sample 1H. The transients were recorded while the temperature was scanned between 80 K and 330 K. A first experiment was performed the sample beeing excited with photons of energy close to the maximum of the photoconductivity spectrum.

The maximum photoconductivity near the absorption edge usually occurs for that wavelength λ = λ max corresponding to an absorption constant α max approximately equal to the reciprocal of the thickness d of the crystal, i.e. where (1-1/e) of the incident radiation is absorbed. For λ > λ max , the light is completely absorbed and the current should be constant. In fact it decreases due to the shorter recombination lifetime of photocarriers generated in the vicinity of the surface and the strongly increasing absorption.

During the temperature scan λ max was continiously adjusted to achieve maximum photoresponse. The optical generation rate G of photocarriers:

G = α max Φ o = Φ o /d (Φ o is the incident photons flux)
can thus be considered to be temperature independent. Under these conditions the plot of the photocurrent (i(0) on Fig. 1) versus temperature represents the temperature dependence of the µτ product. (Fig. 4, curve 1)

As an example, Fig. 4 also shows a double-gate (D.G) spectrum in the range 80 -300 K. Some poorly resolved structures are visible. They are clearly superimposed on a background which reflects the shape of the µτ = f(T) curve. The normalized doublegate (N.D.G) spectrum brings some improvement (Fig. 5). But the four-gate spectrum (F.G) undeniably provides the best spectral resolution. Six peaks appear in the considered temperature interval, but there is at least another one below 80 K and another one above 370 K.

Each of the F.G. peak has been analysed separately, according to the above defined procedure which yields an Arrhenius plot from which E t and S t are obtained (Fig. 6).

The results are listed in Table 1.

In order to explore the forbiden bandgap for deeper levels the temperature should be raised up to 500 K. The point is that above 350 K the dark current begins to increase more and more rapidly, making the differential measurements difficult. Nevertheless a first attempt has clearly revealed the presence of an additional peak at about 380 K corresponding to a trap depth E t = 0.7 eV.

It is out of scope of this paper to discuss in detail the results listed in table 1. However it is worthy making a few remarks :

-The values are reproducible when the excitation conditions are changed.

-Part of the detected traps are identical with those quoted in the introduction, but additional peaks are revealed which were not resolved in TSC or conventional PICTS (8) . In all probability, the same species are always simultaneously present in the material, whatever the growth technique used. However their concentration may differ from sample to sample, or at least depend on preparation, conductivity, doping, etc... Our method will allow to analyse this point (10) .

The investigation of trapping levels deeper than ~ 0.6 eV will be of particular interest for photorefractivity. Work will be continued in this direction.

Photorefractive analysis by two wave mixing

We here present the absorption, photoconductivity and energy transfer measurements we have conducted on sample 1H (CdTe:V with V concentrations of about 10 19 at.cm - 3 ). At wavelength λ = 1.06 µm, we determined a conductivity given by: σ = σ d + σ ph = (1.5 + 0.7 I 0 ). 10 -9 (Ω.cm) -1 where I 0 is the incident irradiance in mW.cm -2 . Taking the relative permittivity value ε r = 10.3 (12) , this corresponds to a dielectric relaxation time τ di = 14 µs for an incident illumination I 0 = 100 mW.cm -2 . From this value of σ ph , one derives an estimate of µτ, the mobility-life time product as:

σ ph = µτ Φ I a e/ hν
where I a is the absorbed intensity in the crystal, Φ the quantum efficiency, e the electron charge and hν the photon energy. The absorption coefficient of our sample being α = 2 cm -1 , assuming a quantum efficiency of 1, one gets:

µτ = 8. 10 -7 cm 2 V -1
As shown in ref.

2, this product is not by the presence of shallow traps that only change, in a reverse manner, µ and τ, i.e., reduce the mobility and increase the recombination time by factors that characterize these shallow traps.

At wavelength λ = 1.32 µm, we determined a conductivity expressed as:

σ = σ d + σ ph = (1.5 + 0.2 I 0 )
. 10 -9 (Ω.cm) -1 . Considering the absorbed energy, this correspond to nearly a 5 time drop in the photoconductivity compared to what we obtained at λ = 1.06 µm, as already seen on the photoconductivity spectra presented in section 3.

Effective trap density and diffusion length.

With the set-up we previously used for characterizing InP and GaAs (13) , we have investigated the photorefractive energy transfer between two waves interfering inside the crystal. At both λ = 1.06 and 1.32 µm, the light source was a diode pumped YAG laser. The beams were polarized +/-45° respective to the crystal (0,0,1) axis and were propagating along (1,-1,0). The grating wave vector was along the (1,1,0) direction.

Switching both beam polarizations from + 45° to -45° changes the sign of the photorefractive gain and thus permits to discriminate between different sources of energy transfer (14) . Our experiments show that we here get a genuine photorefractive effect.

We then rapidely studied the photorefractive gain as a function of the input intensity.

Its dependence has the form:

Γ(I 0 ) = Γ / (1+ I d / I 0 )
where Γ is the saturated gain coefficient and I d is the equivalent dark irradiance, i.e., the illumination at which photoconductivity equals dark conductivity. Figure 8 demonstrates that the gain saturates at illumination values as low as 20 mW.cm -2 ,

showing that this material is indeed a good candidate for optical information processing with low power lasers. At a grating spacing Λ = 0.9 µm, one gets a photorefractive gain Γ = 0. 7 cm -1 that exceeds typical gains in GaAs and InP by more than 50% (13) .

The analysis of the gain dependence with the grating period will provide us information about the effective density of traps involved in the photorefractive effect.

To always achieve the largest possible gain, we choose an input intensity that saturates the photorefractive gain. Considering a single deep level and two possible charge carriers, the gain expression is ( 16) :

! = 2" n 0 3 r 41 # cos$ k B T e k % 0 k 2 + b & c (k 2 + k 4 k 0 2 + b + c)
with:

k 0 2 = e 2 ! k B T N eff ! 0 = " n # " p ( ) " n + " p ( ) b = ! n " p 2
( )

! n + ! p ( ) c = ! p " n 2
( ) These results call on the following remarks. First, the ξ 0 value indicates an electronhole competition that is larger than previously seen in different samples (5) .

! n + ! p
Nevertheless, the photorefractive gain has an appreciable value. Second, coefficient b permits an estimation of the mobility-life time product of the minority carrier for the photorefractive effect. Assuming, as in ref. 17, that electrons are the majority photocarriers for the photorefractive effect, one gets κ n 2 << κ p 2 and derives for the minority carriers (holes in this case):

µτ = 9. 10 -8 cm 2 V -1 .
This value is about one order of magnitude smaller than what we determined by photoconductivity measurements that were giving the mobility-life time product for the majority carrier (assumed to be electrons).

From k 0 2 , we inferre the effective deep level density that contributes to the photorefractive effect, N eff = 4.3 x 10 15 cm -3 . As discussed in ref.

2, in the low illumination quasicontinuous regime as here considered, the presence of shallow traps does not change the steady state photorefractive effect. Thus, these CW photorefractive experiments do not feel the influence of the multiple shallow traps we saw in our spectroscopic studies. It is believed that the efficient deep level for the photorefractive effect might be the P7 level identified in table 1. Considering the results presented in section 3, it appears that this density might be determined by other defects than vanadium in the CdTe 1H crystal (7,8,12) .

We also conducted similar experiments at λ = 1.32 µm. First, as pointed out in section 3 and in 4.1, we observed a nearly five time drop of the photoconductivity. However, for the incident illuminations used, the dark conductivity is still overpassed. Second, the magnitude of the photorefractive gain was very small (Γ = 0.06 cm -1 at Λ = 1.5 µm), impeding any reliable measurement versus fringe spacing. One only estimates an electron-hole competition factor ξ 0 = 0.1 that corresponds to nearly balanced absorption coefficients, α n = α p .

It is clear that a contribution from multiple defects might produce such a reduction of the photorefractive gain. However, an important point we noticed, is that the photorefractive gain reverses its sign when changing the wavelength from 1.06 to 1.32 µm. This indicates a change in the nature of the photorefractive majority carrier. This result supports the approach we used for describing the photorefractive effect observed, i.e., a single deep level from which both electrons and holes are photoionized. Such a reverse in the sign of the photorefractive gain as the incident wavelength was varied, was not noticed for the crystals analyzed in ref. 17.

Conclusion.

We have here reported the first results of our joint research program for growth, caracterization and optimization of CdTe for photorefractive applications.

High resistivity samples have been synthetized and first characterizations including spectroscopic and photorefractive ones have been made. For sample 1H ( low vanadium concentration), 7 levels have been seen and their activation energy determined. The investigation of trapping levels deeper than 0.6 eV will be of particular interest for photorefractivity. This will be done after achieving a slight modification of the detection procedure of the current transients. This sample exhibits a fair photorefractive effect at λ = 1.06 µm with nevertheless a non negligible electronhole competition. At λ = 1.32 µm, the effect has a reverse sign and the competition is very strong leading to a nearly full compensation. The photoconductivity spectrum of sample 6B (more heavily vanadium doped) already shows that this crystal will better behave at longer wavelengths. Similar characterizations are now in progress with this crystal and samples with other specifications are currently prepared. During illumination the current rises up to a constant value i(0). The light is interrupted at time t = 0; t 0 , t 1 , t 2 , t 3 are delay times.

(

  section3) as well as with the photoconductivity curve of ref. 3 and their corresponding absorption spectrum. It also agrees with the absorption band of undoped CdTe (11) .

4. 1

 1 Absorption spectrum, photoconductivity and dielectric relaxation time. The absorption spectrum of sample 1H is shown in figure 7. The shape of this spectrum is very similar to the one measured in ref. 3. However our absorption values are smaller. We obtained: α = (2.16 +/-0.05) cm -1 at λ = 1.06 µm, α = (1.62 +/-0.05) cm -1 at λ = 1.32 µm, α = (1.55 +/-0.05) cm -1 at λ = 1.55 µm.

  α p are the absorption contributions that come from electron and hole generation respectively. κ n and κ p are the inverse of electron and hole diffusion lengths. k represents the grating wave number and N eff is the effective trap density (N eff = N + .N 0 /[N 0 +N + ] where N + and N 0 are the level concentrations in the ionized and neutral states respectively). Note that here we assume that electrons are the majority carrier for the photorefractive effect. In the opposite case, index n and p have to be exchanged. At present we do not know whether the dominant photorefractive carrier in this sample is electron or hole.As now routinely done, the photorefractive gain Γ is deduced from the measurement of the amplification (attenuation) of one of the interfering beam in presence of the other.Plotting our experimental data as k / Γ versus k 2 (fig.9) permits the determination of the characteristic photorefractive parameters (15) . For large values of k 2 , coefficients b and c are negligible and we get a straight line. Its slope and intercept at the origin give (r 41 ξ 0 k 0 2 -1 and (r 41 ξ 0 ) -1 . A departure from this straight line is visible at small values of k 2 . This indicates the influence of the carrier diffusion lengths. A full fit of the experimental data with the complete gain expression, i.e., without neglecting b and c, is now carried out using the previously determined quantities as starting parameters. the previously measured absorption: α = (2.16 +/-0.06) cm -1 .

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure2. Illustration of the principles of data processing (double-gate method). The left hand curve shows the transient at various temperatures; t 1 and t 2 are fixed delay times. The right hand curve shows the temperature dependance of the differential signal n t (t 1 ) -n t (t 2 ).

Figure 3 .

 3 Figure 3. Normalized photoconductivity spectrum; curve 1, weakly doped sample (1H); curve 2, strongly doped sample (6B).

Figure 4 .

 4 Figure 4. Curve 1: Photoconductivity versus temperature Curve 2: Typical double gate spectrum Figure 5. Typical normalized double gate (curve 1) and four gate (curve 2) spectra.

Figure 6 .Figure 7 .

 67 Figure 6. Typical Arrhenius plot for peak number 3 (E t = 0.24 eV and S t = 10 -17 cm 2 ) Figure 7. Absorption spectrum of sample 1H.

Figure 8 .

 8 Figure 8. Photorefractive gain of sample 1H versus incident illumination (Λ = 0.9 µm) showing a saturation of the gain for incident powers as low as 20 mW.cm -2 .

Figure 9 .

 9 Figure 9. Experimental Γ/k versus k 2 plot leading to the determination of the photorefractive parameters of crystal 1H. This plot was drawn with Γ in cm -1 and k in µm -1 .The dotted straight line is the fit obtained for large grating wave numbers while the full line curve represents the best fit with the whole gain expression.

Figure 1 Figure 2 Figure 3

 123 Figure 1

Figure 4 Figure 5

 45 Figure 4

Figure 6 Figure 7 Figure 8

 678 Figure 6

Figure 9

 9 Figure 9

 ------------------------------------------------------------------------------------------------P7 : ~0.7 :

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Ph Delaye

H J Von Bardeleben

G Roosen

BULK PHOTOREFRACTIVE SEMICONDUCTORS

The photorefractive effect (PRE) has been studied for more than twenty five years now 1,2 and many applications for optical signal processing such as correlation, real time holography, dynamic interconnections and optical memories have been developed. The materials, in which the PRE has been studied, were mainly oxides (ferroelectrics and sillenites), in which the useful spectral range lies in the visible. Applications for telecommunication systems and eye-safe devices have required an extension of the spectral range into the near infrared (1.0 to 1.5µm) and thus different materials have to be explored. It has been shown that the bulk semiinsulating III-V semiconductors GaAs and InP 3 and more recently the II-VI compound CdTe 4 were efficient materials for this spectral range. III-V materials offer the great advantage of being available as bulk semiinsulating materials of high crystalline perfection and homogeneity as regards to their electrical properties due to their importance as substrate materials in micro and optoelectronic technology. However these materials were not optimized for PRE applications and thus quantitative analyses of PRE experiments 5 related to the specific material defect properties are

necessary for further developments. It has equally been shown, that the PRE can be used as an efficient tool for the material characterization 6,7 .

THE PHOTOREFRACTIVE EFFECT IN BULK SEMICONDUCTORS

The PRE in a particular material depends on both its extrinsic, defect related and intrinsic properties : photoconductivity and carrier diffusion properties on one side and the electro-optic coefficients, dielectric constants and refractive index on the other. Photoconductivity is responsible for the creation of a space-charge field by a spatial redistribution of the trapped charges in the deep level due to a non uniform illumination by photons of below band gap energy. The free carriers, created by photoionization of deep levels in the bright region of the illumination pattern, take part in the redistribution of the charges through diffusion (no external applied field) or drift (under external applied field) towards dark region where they recombine. The electrooptic effect transforms the space-charge field in a spatially modulated index variation.

These basic mechanisms give hints of the key properties of the PRE :

1-The strength of the space-charge field depends on the quantity of charges redistributed and then is linked to the concentration of the deep level and to the defect occupancy.

2-The number of redistributed charges directly depends on the number of photons absorbed in the material, making the PRE strength governed by the optical beam energy (note that its speed is beam power dependent). Thus noticeable refractive index modulations are obtained with low power CW lasers.

3-The strength of the space-charge field can also be increased by applying an electric field leading to a charge redistribution effect controlled by the drift of free carriers, that is more efficient than their diffusion.

The expression of the photoinduced space-charge field is derived following the band transport model 8,9 with a single defect in a concentration N T which ionized part is in concentration N 0 and neutral part in concentration N T -N 0 (Fig. 1). We consider both thermal (ß) and optical (S) emission of electrons and holes from the defect. The illumination is given by a spatially modulated interference pattern along coordinate axis z,

I = I 0 1+ Re m e ikz ( ) (
) with a wave number k (k = 2! " , ! = " 2 n 0 sin# grating spacing with θ the half-angle between the two interfering beams inside the crystal, n 0 is the linear refractive index of the material, and λ the wavelength), a modulation m and a total incident illumination I 0 . In first approximation the space-charge field is spatially modulated with the same grating spacing than the illumination pattern and, when the stationary regime is reached, its amplitude is (for grating spacing smaller than the diffusion length of the carriers and no applied electric field) :

E 1 = ! i m k B T e k 1+ k 2 k 0 2 " 0 (1) ! 0 = S n N T " N 0 ( ) " S p N 0 A n S n N T " N 0 ( ) + A p S p N 0
is the electron-hole competition coefficient,

with A n = ! n + S n I 0 S n I 0 and A p = ! p + S p I 0 S p I 0 , k B T e ! 0.025eV .
! n = S n N T " N 0 ( ) (resp. ! p = S p N 0 ) corresponds to the part of absorption that generates electrons (resp. holes). Note that for generation of electrons only (or holes only) ! 0 is maximal (≈ ±1).

k 0 2 = e 2 ! k B T
N eff is the inverse squared of the Debye screening length with the effective trap density

N eff = N 0 N T ! N 0 ( ) N T (ε is the dielectric constant).
E 1 is purely imaginary , which means that the space-charge field grating is π/2-shifted from the illumination grating.

Through the linear electrooptic effect (Pockels effect), the spacecharge field grating gives rise to an index grating of amplitude 10 :

!n = n 0 3 r eff E 1 2 (2)
r eff is the effective electrooptic coefficient which depends on the orientation of the sample and on polarization of beams 11 . For example in the classical beam-coupling configuration, i.e. grating vector along [001], propagation along [ 1 10] and beam polarization along [110], for crystal of the 4 3m class of symmetry such as GaAs, InP or CdTe, we have r eff =r 41 .

The diffraction of the two beams on the index grating they create, gives an energy transfer from one beam to the other one 8 . This two wave mixing (TWM) process is characterized by a photorefractive gain Γ :

! = 2" n 0 3 r 4 1 # cos$ k B T e k 1+ k 2 k 0 2 % 0 (3)
Experimentally the energy transfer is measured as the ratio γ 0 of the intensity of a probe beam with and without the presence of a coherent pump beam (Fig. 2). In the condition of high pump-to-probe beam ratio (i.e. small modulation of the fringes), γ 0 is written :

! 0 = e " l (4)

TWO BEAM COUPLING IN SEMIINSULATING GaAs : A

QUANTITATIVE EXAMPLE

We now present, as an illustration, photorefractive experiments performed on a well characterized semiconductor : semiinsulating undoped GaAs. The PRE is analyzed through a TWM experiment in which we measure the energy transfer from a pump beam to a probe beam as a function of the grating wavenumber k. This is achieved at the two wavelengths 1.06µm and 1.32µm given by CW diode-pumped Nd-YAG lasers. From the measurement of the effective gain γ 0 (Fig. 2), we deduce photorefractive gain Γ (Fig. 3) according to expression (4). The results are analyzed using equation ( 3), in which the extrinsic material properties are contained in the electron-hole competition coefficient ! 0 and N eff the deep level effective trap density (i.e. k 0 2 ).

In LEC grown undoped GaAs the semiinsulating character of the material is due to the compensation of the residual shallow donors and acceptors, with concentrations N A >N D ≈10 15 cm -3 , by the intrinsic EL2 defect (N EL2 ≈ 1...2x10 16 cm -3 ) 12 , which gives rise to a deep 0/+ level at 0.75eV below the bottom of the conduction band 13 . EL2 defect is an arsenic-antisite related double donor defect. The electrical compensation and, related with this, the atomic structure of the EL2 defect have been the object of numerous studies and recent reviews are available 14 . Whereas the total EL2 concentration is relatively constant, around 2x10 16 cm -3 for high pressure LEC grown materials, the occupation ratio

EL2 + [ ] / EL2 0 [ ]
depends on the crystal growth conditions and on parameters such as the purity of the starting materials or the humidity of the encapsulation but equally on the position in the ingot. Occupation ratio between 1 and 0.1 can be found, but modern state of the art material optimized as substrate materials for microelectronics applications is characterized by a value of about 0.1. The EL2 defect, which is at the origin of the electrical compensation, is equally responsible for the photoconductivity in the 1-1.5µm spectral range 15 due to the optical cross sections S n and S p of EL2 0 and EL2 + respectively, which are both of importance at these excitation energies. The determination of the absolute values of these cross sections at room temperature has only been achieved recently 16 .

The quantitative analysis of the TWM experiment requires further the knowledge of the absolute concentrations of EL2 0 and EL2 + ; the values can either be obtained by an all optical absorption measurement at two different wavelengths 17 or by the application of the electron paramagnetic resonance (EPR) technique concerning EL2 + 18 . The application of this last technique is generally preferable due to its defect selective character, whereas the quality of an absorption measurement depends strongly on the absence of other deep levels. The EPR spectrum (Fig. 4) of the EL2 + defect is described by the Spin Hamiltonian :

H = gßBS + AIS (5)
with the Landé factor g=2.04 and the central hyperfine interaction constant A= 890x10 -4 cm -1 , both isotropic (with ß the Bohr magneton and B the magnetic field, S=1/2 is the electronic spin and I=3/2 is the nuclear spin) .

The spin concentration is obtained by a double integration of the experimental first derivative spectrum and a comparison with a spin standard sample.

With the help of the concentrations determined in the sample from absorption measurement for EL2 0 [ ] and from EPR measurements for

EL2 + [ ] ,
as well as the other parameters taken from the literature 16,19,20 we calculate the photorefractive gain (Fig. 3). We find a good agreement between calculated values and the experimental ones, thus confirming the model for the photorefractive effect. The change of the sign of photorefractive gain from λ=1.06µm to λ=1.32µm, indicates a change of the majority carrier for PRE. These curves have been obtained for a GaAs sample in which the compensation ratio

EL2 + [ ] / EL2 0 [ ] is close to one.
Thus the sign reversal for ! 0 follows the variation of the S n /S p ratio with wavelength (S n /S p >1 for λ=1.06µm ; S n /S p > for λ=1.32µm 16 ).

The importance of the electron-hole competition in PRE experiments is well illustrated by these results : in particular at the wavelength of 1.32µm the electron-hole competition is very sensitive to the compensation ratio due to the increasing importance of S p over S n . Thus a sample with a ratio EL2 + [ ] / EL2 0 [ ] close to 0.1 will not present a reverse of the sign of the gain between 1.06µm and 1.32µm contrary to this sample, this is what we indeed observed in our experiments. It becomes further clear that materials optimized for applications at 1.06µm are not necessarily suited for applications at 1.5µm. The optimization of the performances of GaAs at different wavelengths thus requires materials with different compensation ratios ; these can in principle be adapted by the growth conditions, but as currently semiinsulating GaAs is grown for microelectronics applications such material is not available on the market. A second approach would be to modify the compensation by post growth treatments such as electron irradiation or thermal treatments [START_REF] Ph | Digest of Topical Meeting on Photorefractive Materials, Effects and Devices IV[END_REF][START_REF] Cheng | [END_REF] .

A COMPARISON OF INFRARED ACTIVE MATERIALS

The evaluation of photorefractive performances of a material can be assessed through different criteria, such as the required irradiance, the electron-hole competition rate, the effective trap density or the refractive index change. We will now precise all these points.

In insulating materials, we usually consider that the steady-state value of the PRE does not depend on the incident illumination, which only affects the time constant at which the steady-state is reached. In semiconductors, this is a little more complex due to the semiinsulating nature of the material.

Carriers can be excited from the deep level either optically or thermally.

The thermal emission is not spatially modulated and its effect will be an isotropic redistribution of charges that will decrease the strength of the space charge field. This influence is expressed by the terms A n and A p in the ξ 0 expression (1). In a one carrier model (for example electrons), the photorefractive gain can be rewritten :

! = ! " 1+ # n S n I 0 (6)
Γ ∞ is the photorefractive gain obtained at an irradiance giving a number of photoexcited carriers larger than the thermally excited one : S n I 0 >> ß n , i.e.

A n =1. At low irradiance the gain is reduced due to the influence of ß n . We define the equivalent dark irradiance I d as the irradiance for which the gain is reduced by a factor 2. It corresponds, in a one defect model, to : S n I d = ß n .

In semiconductors with a monopolar conduction, the conductivity is defined as :

! = ! d + ! p h = e µ n " n N T # N 0 ( ) $ n N 0 + e µ n S n N T # N 0 ( ) $ n N 0 I 0 (7)
where µ n (µ p ) is the electron (hole) mobility, and γ n (γ p ) the recombination coefficient of electrons (holes). This means that I d can be defined as the irradiance for which photoconductivity σ ph equals dark conductivity σ d . In a bipolar model, I d can always be defined but its relation to conductivity is not as simple. Nevertheless, the comparison of photoconductivity and dark conductivity gives a good clue to the illumination dependence of photorefractive gain. We thus have a first criteria for the performance of a photorefractive crystal : the photoconductivity must overpass the dark conductivity. This condition gives the minimal irradiance at which a crystal can be effectively used (i.e. A n = A p =1).

The second important point is the electron-hole competition factor :

! 0 = S n N T " N 0 ( ) " S p N 0 S n N T " N 0 ( ) + S p N 0 ( 8
)
This coefficient varies between -1 and 1, the optimum condition being ! 0 = 1, i.e. monopolar case. The sign of ξ 0 gives the majority carrier for PRE : electrons correspond to ξ 0 >0, (holes to ξ 0 <0). In the case of an exact compensation (i.e. S n (N T -N 0 ) =S p N 0 ), the photorefractive gain equals zero.

A good photorefractive crystal should be the closest as possible to the monopolar case in order to exhibit high gains. This parameter is often hard to modify by post growth treatments as discussed above on the example of GaAs. For a fixed wavelength and a given defect only a modification in the compensation ratio (N T -N 0 )/N 0 can help to change the electron-hole competition. This implies a good control of the Fermi level in the as-grown crystals. As the optical cross sections S n and S p depend on the photon energy we have for each case an optimum wavelength ; however for practical reasons the wavelengths are fixed and this parameter can not be varied freely. Different doping can equally help to change the range utilization of a given material. In all cases it is necessary to characterize quantitatively the defect relevant for the PRE.

The third criteria deals with the effective trap density N eff . This quantity gives the maximum number of charges that can be redistributed and then the maximum space-charge field that can be induced. For a defect under two states of charge, N eff is given by the minority species, which means that even if a high defect concentration is obtainable, care as to be taken in the control of the compensation ratio of the material. Note that an increase of the concentration of the defect (by higher doping for example) also increases α the absorption of the crystal.

The last point to fully characterize the induced index change is given by the parameter n 0 3 r 4 1 . The higher n 0 3 r 4 1 , the higher the photorefractive gain. This gives for example an argument in favor of II-VI semiconductors for which n 0 3 r 4 1 is twice higher than for III-V materials.

Three materials are widely used for PRE in the infrared : undoped GaAs 3,5,23 , Iron doped InP 3,24,25 and more recently Vanadium doped CdTe 4,26,27 . Their characteristics are presented in Table1. Some other semiconductors are also studied (GaP 33 , ZnTe 34 , CdSe 35 ) but they are mainly developed for their properties in the visible even if some (ZnTe) have sensitivity which extends towards 1.32µm. Another possibility is the extension to alloys [START_REF] Ziari | Digest of Topical Meeting on Photorefractive Materials, Effects and Devices III[END_REF] , such as CdZnTe or CdMnTe which allow a choice of the band gap value and then a possible adjustment of some of their properties.

If we look at Table 1, keeping in mind the four important criteria for performances previously defined, we see that CdTe has the higher index change due to its higher electrooptic coefficient. Its sensitivity range extends beyond 1.5µm. GaAs is the crystal that possess the highest photoconductivity but, as discussed previously, the important point is the ratio between dark conductivity and photoconductivity. According to this criteria CdTe can be used with lower irradiance (of the order of 0.1mW.cm -2 ). Working with extrinsic semiconductors, the dark conductivity is related to the defect, giving rise to the Fermi level pinning.

This Fermi level pinning can lead to dark conductivity close to the intrinsic conductivity, determined by the energy band gap of the material. For example, undoped Bridgman CdTe is n-type conductive and then unsuitable for photorefractive applications; it is the vanadium doping which leads via a deep V 0/+ donor level and non identified acceptors to high resistive and photoconductive material [START_REF] Von Bardeleben | [END_REF] .

The highest photorefractive gain without applied electric field is obviously obtained in CdTe due to its higher electrooptic coefficient. When considering results currently obtained under applied DC field, the highest gains were obtained in InP:Fe. Indeed a resonant enhancement is achieved when photogeneration of holes and thermal emission of electrons equal each other 25 . This technique, only demonstrated for InP:Fe, requires an accurate control of both illumination and temperature. Classical techniques use either DC field and moving gratings 23 or AC field. This last techniques are currently developped in CdTe to obtain high photorefractive gains 27,32 .

Application of high electric fields raise equally the problem of suitable electrical contacts, homogeneity of the field distribution inside the crystal and the fact that defect properties can be sensitive to the electric field strength. This last point for example is of importance for the EL2 defect in GaAs 38 . The field dependent capture cross section of EL2 39 leads, for fields above 300V.cm -1 , to the formation of moving high field domains.

These problems may impede the use of GaAs in applications requiring external applied fields.

According to the values in Table 1, CdTe seems to be the most promising crystal for use in the 1.3-1.5µm spectral range with low power laser diodes. However the defect properties of CdTe:V are much less known than those of III-V semiconductors and more studies are required and are currently under way in various laboratories in order to optimize CdTe:V for PRE applications.

CONCLUSION

The main particularity of the photorefractive effect, that makes it attractive for beam processing, is an optical nonlinearity leading to efficient energy transfer and phase conjugation with low power lasers. The materials that are sensitive in the near infrared are the semiinsulating semiconductors.

Good correlation is obtained between the theoretical model describing the PRE and experimental results in that kind of crystals. This points out a possible use of the PRE as a characterization technique of deep levels in these materials which are of importance as substrates for microelectronics.

For optical processing applications in the near infrared, optimization has still to be continued in order to obtain an optimum effect for specified wavelengths. Nevertheless the magnitude of the effects already obtained has lead to the beginning of device realizations in different research groups.

An example of such a device is the Double Phase Conjugate Mirror (DPCM) 40

Fig. 1 :Fig. 2 :

 12 photorefractive gain in the spectral range 1.3-1.5µm with the low energies given by laser diodes

Fig. 3 :

 3 Fig.3 : Photorefractive gain Γ as a function of the grating wave vector k. The experimental curves show results for λ=1.06µm (+) and for λ=1.32µm (×). Straight and dashed lines represent theoretical curves.

Fig. 4 :

 4 Fig.4 : EPR spectrum of the EL2 defect.

Figure 1 Figure 2

 12 Figure 1

Figure 3

 3 Figure 3

Figure 4

 4 Figure 4


Jérôme Caudron
email: jerome.caudron@chu-rouen.fr

Jeannette Fares

Pierre-Hugues Vivier

Valentin Lefebvre

Caroline Petitjean

Jean-Nicolas Dacher

Pierre-Hugues Vivier

Jean-Nicolas Dacher

P.-H Vivier

J.-N Dacher

P.-H Vivier

J.-N Dacher

Diagnostic accuracy and variability of three semi-quantitative methods for assessing right ventricular systolic function from cardiac MRI in patients with acquired heart disease

Keywords: Cardiac MRI, Right ventricular function, Semiquantitative assessment, Diagnostic accuracy, Variability

Introduction

Evaluation of right ventricular (RV) structure and function is of importance in the management of most cardiac disorders. Indeed, previous studies have demonstrated the key role of RV function in predicting outcome in both congenital (CHD) [START_REF] Davlouros | The right ventricle in congenital heart disease[END_REF] and acquired heart disease (AHD), including heart failure [START_REF] Gavazzi | Value of right ventricular ejection fraction in predicting short-term prognosis of patients with severe chronic heart failure[END_REF][START_REF] Ghio | Independent and additive prognostic value of right ventricular systolic function and pulmonary artery pressure in patients with chronic heart failure[END_REF], ischaemic cardiopathies [START_REF] Mehta | Impact of right ventricular involvement on mortality and morbidity in patients with inferior myocardial infarction[END_REF], pulmonary hypertension [START_REF] Chin | The right ventricle in pulmonary hypertension[END_REF], arrhythmogenic right ventricular dysplasia (ARVD) [START_REF] Hulot | Natural history and risk stratification of arrhythmogenic right ventricular dysplasia/cardiomyopathy[END_REF], valvular heart disease [START_REF] Haddad | Right ventricular myocardial performance index predicts perioperative mortality or circulatory failure in high-risk valvular surgery[END_REF], myocarditis [START_REF] Mendes | Right ventricular dysfunction: an independent predictor of adverse outcome in patients with myocarditis[END_REF] and dilated cardiomyopathies [START_REF] Juillière | Additional predictive value of both left and right ventricular ejection fractions on long-term survival in idiopathic dilated cardiomyopathy[END_REF]. Yet, evaluation of RV function is often neglected in patients with AHD compared with CHD patients, in whom RV function and volumes are extensively evaluated. Noninvasive cardiac imaging plays a leading role in RV function assessment. However, RV imaging has always been considered challenging, mainly because of the complex motion and anatomy of the RV. Various imaging techniques can be used to evaluate RV function: transthoracic echocardiography (TTE) [START_REF] Lindqvist | Echocardiography in the assessment of right heart function[END_REF], cardiac MRI, radionuclide-based techniques [START_REF] Jain | Assessment of right ventricular function. Role of nuclear imaging techniques[END_REF] or multislice computed tomography [START_REF] Müller | Evaluation of right ventricular function with multidetector computed tomography: comparison with magnetic resonance imaging and analysis of inter-and intraobserver variability[END_REF]. Cardiac MRI, with the quantitative (Qt) 3D volumetric method, is considered the most reliable method for assessing RV volumes and ejection fraction (EF) and is routinely performed in a large spectrum of diseases [START_REF] Goetschalckx | Right ventricular function by MRI[END_REF]. However, cardiac MRI remains time consuming for RV function assessment, as reported in previously published studies [START_REF] Grothues | Interstudy reproducibility of right ventricular volumes, function, and mass with cardiovascular magnetic resonance[END_REF][START_REF] Beygui | Routine breath-hold gradient echo MRI-derived right ventricular mass, volumes and function: accuracy, reproducibility and coherence study[END_REF][START_REF] Mooij | Reproducibility of MRI measurements of right ventricular size and function in patients with normal and dilated ventricles[END_REF]. Indeed, postprocessing software solutions are less efficient for RV automatic segmentation than for LV, and RV segmentation remains mostly manual, even though improvement in postprocessing has recently been reported [START_REF] Grosgeorge | Automatic cardiac ventricle segmentation in MR images: a validation study[END_REF]. Therefore, the Qt method is rarely performed in daily practice, and RV functional assessment is mostly visually performed except in cases of specific indication, such as in patients with CHD, or in the context of research studies. Thus, for daily evaluation of patients with AHD, a quick and accurate method applicable as a first-line screening test would be useful, in order to determine those patients who would deserve exhaustive Qt evaluation. For that purpose, various semi-quantitative (SQt) methods have been described: tricuspid annular plane systolic excursion (TAPSE), RV fractional shortening (RVFS) and RV fractional area change (RVFAC). TAPSE and RVFAC were initially described in echocardiography with conflicting results according to various studies [START_REF] Kaul | Assessment of right ventricular function using two-dimensional echocardiography[END_REF][START_REF] Anavekar | Two-dimensional assessment of right ventricular function: an echocardiographic-MRI correlative study[END_REF][START_REF] Kjaergaard | Evaluation of right ventricular volume and function by 2D and 3D echocardiography compared to MRI[END_REF][START_REF] Schenk | Accuracy of echocardiographic right ventricular parameters in patients with different end-stage lung diseases prior to lung transplantation[END_REF][START_REF] Wang | Comparison of novel echocardiographic parameters of right ventricular function with ejection fraction by cardiac magnetic resonance[END_REF]. More recently, TAPSE and RVFS were also evaluated with cardiac MRI in a few studies [START_REF] Nijveldt | Semi-quantitative assessment of right ventricular function in comparison to a 3D volumetric approach: a cardiovascular magnetic resonance study[END_REF][START_REF] Morcos | Correlation of right ventricular ejection fraction and tricuspid annular plane systolic excursion in tetralogy of Fallot by magnetic resonance imaging[END_REF] but to date, no cardiac MRI study has evaluated the interest of RVFAC compared with TAPSE and RVFS. Moreover, the reproducibility of these SQt methods and particularly the effect of observers' experience were not clearly reported.

The aim of this study was to evaluate the diagnostic accuracy and variability of TAPSE, RVFS and RVFAC to assess RV systolic function from cardiac MRI in patients with acquired heart disease.

Materials and methods

This study was performed in accordance with the Standards for the Reporting of Diagnosis accuracy studies (STARD) statement recommendations [START_REF] Bossuyt | Towards complete and accurate reporting of studies of diagnosis accuracy: the STARD initiative[END_REF].

Cardiac MR protocol

Cardiac MRI examinations were performed at 1.5 T (Symphony Tim®, Siemens Medical Systems, Erlangen, Germany). A dedicated eight-element phased-array cardiac coil was used. A retrospective synchronisation with a balanced steady-state free precession (bSSFP) sequence was performed for cine analysis, with repeated breath-holds of 10-15 s. All conventional planes (2-, 3-and 4-chambers views) were acquired and a total of 8-12 contiguous cine short axis (SA) slices were performed from the base to the apex of the ventricles. Sequence parameters were as follows: TR = 50 ms; TE = 1.7 ms; flip angle = 55°; slice thickness = 7 mm; matrix size = 256×216; Field of view = 360-420 mm; 20 images per cardiac cycle. Other sequences (i.e. T2-weighted sequences, first-pass perfusion, phase contrast or late gadolinium enhancement) were performed according to clinical indication, but not considered in the present study.

Cardiac MR analysis

Observers

Three observers with various training-degree in cardiac MRI participated in the image analysis: observer 1 (Obs1) with 3 years' training, observer 2 (Obs2) with 1 year's training and observer 3 (Obs3) who had no cardiac MRI experience. Before the study, Obs3 received a 3-h basic cardiac MRI course including anatomy and the principles of cardiac segmentation with 5 examinations selected in our database.

Analyses were randomly performed and each measurement was performed blinded to the medical history. All analyses were retrospectively performed after completing inclusion of the 60 patients.

Quantitative analysis

All measurements were performed using commercially available software (Argus, Siemens Medical Solutions). In order to determine the RVEF (standard of reference of the study), the 2 most experienced observers (Obs1 and Obs2) independently assessed the Qt RV parameters (RVEF, enddiastolic and end-systolic RV volumes) from cine SA slices. Both observers manually delineated endocardial and epicardial borders on all SA slices, at end-diastole (ED) and end-systole (ES). Trabeculae and papillary muscles were included in the RV cavity. ED and ES were located on a mid-ventricular SA slice, and visually defined as the image with the largest and the smallest cavity respectively. The reference RVEF was then considered to be the mean value of Obs1 and Obs2 measurements.

Semi-quantitative analysis

Semi-quantitative RV parameters (TAPSE, RVFS and RVFAC) were determined using a 4-chamber view cine sequence (Fig. 1). TAPSE is the difference between ED and ES RV length. These lengths are measured from the lateral part of the tricuspid annulus to the RV apex. RVFS is the TAPSE indexed to the ED RV length. To determine RVFAC, ED and ES RV areas were measured on a 4chamber view; RVFAC was obtained by dividing the difference between the ED and ES areas by the ED area. As for Qt measurements, trabeculae and papillary muscles were included in the RV cavity for RVFAC measurement. For all SQt measurements, RV ED and ES were defined respectively as images with the largest and the smallest RV cavity area. To evaluate intra-and inter-observer variability and the effect of previous experience, each SQt analysis was performed twice at least 1 month apart. Obs1 and Obs2 performed Qt and SQt analyses blinded from each other with at least a 2-week interval.

Statistical analysis

Continuous variables are expressed as mean ± SD and qualitative variables as number and percentage. Considering that the second measurement of SQt parameter was performed to evaluate intra-observer variability, only the first measurement of each observer was taken into account to evaluate inter-observer variability, correlation between SQt and Qt methods, and ROC analyses. Pearson's correlation coefficient was used to evaluate the relation between the Qt and SQt methods. The Bland-Altman method [START_REF] Bland | Statistical methods for assessing agreement between two methods of clinical measurement[END_REF], the coefficient of variation (CV) and the intra-class correlation coefficient (ICC) were used to evaluate the intra-and inter-observer variability. In order to evaluate the diagnostic performance of each SQt method in predicting an RVEF <45%, we performed receiver operating characteristic (ROC) curve analysis and we calculated areas under the curve (AUC) for each observer's measurements. The statistical significance of the difference between AUC was evaluated using the method of DeLong et al. [START_REF] Delong | Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach[END_REF]. p<0.05 was considered significant.

Results

Correlation between semi-quantitative and quantitative methods

All SQt measurements correlated significantly with RVEF. RVFAC correlated better with RVEF for all observers and this was not related to cardiac MRI experience (R=0.741 for Obs1 and Obs2, = 0.716 for Obs3) (Table 2). In comparison, RVFS and TAPSE correlated less well with RVEF and differed among Obs1 (R=0.720 for RVFS, = 0.646 for TAPSE), Obs2 (R=0.583 for RVFS, = 0.499 for TAPSE) and Obs3 (R=0.534 for RVFS, = 0.482 for TAPSE). For the most experienced observer (Obs1) the correlation coefficient of TAPSE (R =0.646), RVFS (R=0.720) and RVFAC (R=0.741) were comparable. On the contrary, a marked difference between the correlation coefficient of TAPSE (R=0.482), RVFS (R=0.534) and RVFAC (R=0.716) was observed for the less experienced Obs3. Quantitative RV function assessment revealed that 10/60 (17%) patients had an RVEF <45%. In this patients' subgroup, correlation between RVFAC and RVEF was slightly decreased but remained comparable between observers (R=0.607 for Obs1, = 0.638 for Obs2, = 0.572 for Obs3). On the contrary, an effect of cardiac MRI experience was observed for TAPSE (R=0.691 for Obs1, = 0.341 for Obs2 and = 0.451 for Obs3) and for RVFS (R=0.762 for Obs1, = 0.453 for Obs2, = 0.616 for Obs3).

Reproducibility of semi-quantitative parameters

All observers had lower intra-observer variability for RVFAC compared with RVFS and TAPSE (Fig. 2, Table 3). Intra-observer variability of RVFAC was less subject to initial observer experience (CV and ICC ranging respectively from 6.7% and 0.955 for Obs1 to 13.8% and 0.825 for Obs3). Intra-observer variability was more experiencedependent for both RVFS (CV and ICC ranging respectively from 11.3% and 0.906 for Obs1 to 23.8% and 0.760 for Obs3) and TAPSE (CV and ICC ranging respectively from 11.6% and 0.912 for Obs1 to 26.0% and 0.756 for Obs3).

Inter-observer reproducibility (Fig. 3, Table 4) was good for RVFAC (CV and ICC ranging respectively from 7.7 to 10.5% and 0.825 to 0.937) and better than for RVFS (CV and ICC ranging respectively from 19.3 to 25.2% and 0.675 to 0.774) and TAPSE (CV and ICC ranging respectively from 21.0 to 25.3% and 0.709 to 0.784).

ROC analysis

Accuracy related to observer experience

All SQt parameters had a significant diagnostic value in predicting an RVEF <45% (p<0.0001 in all cases) (Fig. 4, Table 5). However, RVFAC was the most accurate parameter for all observers, without any effect of observer's experience on accuracy (AUC = 0.956 for Obs1, = 0.930 for Obs2, = 0.944 for Obs3, p = NS). On the contrary, TAPSE and RVFS were experience-dependent and their accuracy was significantly lower for Obs3 (AUC = 0.835 for TAPSE and 0.870 for RVFS) in comparison to Obs 1 (AUC = 0.929 for TAPSE and 0.944 for RVFS) (p<0.05 in both cases). Also, Obs3 had significantly lower AUC for TAPSE than for RVFAC (p=0.02), contrary to Obs1 and Obs2. No significant inter-observer difference was found among AUC of TAPSE, RVFS and RVFAC for the 2 most experienced observers, although a systematic trend for best accuracy was found for Obs1.

Optimal thresholds for detecting a RV dysfunction

Optimal thresholds of SQt parameter to predict RVEF <45% for each observer are listed in Table 5. For Obs1, who was both the most reproducible and best correlated with RVEF, an RVFAC <41% was able to predict an RVEF <45% with 90% sensitivity and 94% specificity. Similarly, an RVFS <20% and a TAPSE <16 mm predicted an RVEF <45% with respectively 90%/80% sensitivity and 88%/90% specificity.

Segmentation times

Mean time to completion of the Qt method was 13.4±3.9 min for Obs1 and 18.9±4 min for Obs2, i.e. the mean time of analysis was 16.2±4.8 min. On the contrary, post-processing of SQt parameters took less than 2 min for all observers, with mean time of analysis at 1.3±0.2 min for RVFAC, 0.5± 0.2 min for RVFS and 0.4±0.1 min for TAPSE.

Discussion

Correlation of RVFAC, TAPSE and RVFS with RVEF All SQt parameters correlated significantly with RVEF but we demonstrated that RVFAC performed better than TAPSE and RVFS. Contrary to TTE [START_REF] Kaul | Assessment of right ventricular function using two-dimensional echocardiography[END_REF][START_REF] Anavekar | Two-dimensional assessment of right ventricular function: an echocardiographic-MRI correlative study[END_REF][START_REF] Kjaergaard | Evaluation of right ventricular volume and function by 2D and 3D echocardiography compared to MRI[END_REF][START_REF] Schenk | Accuracy of echocardiographic right ventricular parameters in patients with different end-stage lung diseases prior to lung transplantation[END_REF][START_REF] Wang | Comparison of novel echocardiographic parameters of right ventricular function with ejection fraction by cardiac magnetic resonance[END_REF], few studies have investigated the accuracy of SQt methods in assessing RV function from cardiac MRI. Two previous cardiac MRI studies have evaluated the TAPSE: Morcos et al. [START_REF] Morcos | Correlation of right ventricular ejection fraction and tricuspid annular plane systolic excursion in tetralogy of Fallot by magnetic resonance imaging[END_REF] demonstrated that TAPSE correlated poorly with RVEF (R=0.50, p<0.05) in patients with tetralogy of Fallot, whereas Nijveldt et al. [START_REF] Nijveldt | Semi-quantitative assessment of right ventricular function in comparison to a 3D volumetric approach: a cardiovascular magnetic resonance study[END_REF] found a better correlation (R=0.62, p<0.01) in 60 subjects including controls and patients with pulmonary hypertension, acute myocardial infarction and Brugada syndrome. Our results are in line with those published by Nijvedlt et al., probably because we had no patients with CHD in our cohort. Also, we demonstrated that the relation between TAPSE and RVEF depended on the experience of the observer.

We found that RVFS correlated better with RVEF than did the TAPSE. This is in agreement with a previous study [START_REF] Nijveldt | Semi-quantitative assessment of right ventricular function in comparison to a 3D volumetric approach: a cardiovascular magnetic resonance study[END_REF] and can be explained by the indexation of the RVFS to the RV length. Indeed, TAPSE values are strongly influenced by the length of the RV, itself depending on the subject's constitutional cardiac anatomy.

To our knowledge, this is the first cardiac MRI study describing the usefulness of RVFAC for RV function assessment in clinical practice. Indeed, Kind et al. [START_REF] Kind | Right ventricular ejection fraction is better reflected by transverse rather than longitudinal wall motion in pulmonary hypertension[END_REF] recently reported a correlation coefficient of 0.76 between RVFAC and RVEF, but they did not compare this result with other longitudinal and transverse parameters evaluated in their study. Our results confirm previous reports based on TTE [START_REF] Anavekar | Two-dimensional assessment of right ventricular function: an echocardiographic-MRI correlative study[END_REF][START_REF] Kjaergaard | Evaluation of right ventricular volume and function by 2D and 3D echocardiography compared to MRI[END_REF][START_REF] Schenk | Accuracy of echocardiographic right ventricular parameters in patients with different end-stage lung diseases prior to lung transplantation[END_REF][START_REF] Wang | Comparison of novel echocardiographic parameters of right ventricular function with ejection fraction by cardiac magnetic resonance[END_REF], which demonstrated that RVFAC was more accurate than TAPSE. This better correlation is certainly due to the fact that RVFAC is varying accordingly with both the longitudinal and transverse motion of the RV. On Fig. 4 ROC curves for each semi-quantitative parameter and observer to predict RVEF <45% the contrary, TAPSE and RVFS only depend on the longitudinal shortening. In the subgroup of patients with RVEF <45% the correlation between RVFAC and RVEF was slightly decreased. This could be related to the small proportion of patients with a decreased RVEF (n=10/60, 17%). However, the correlation between RVFAC and RVEF remained comparable between observers, contrary to RVFS and TAPSE, for which correlation was clearly lower in less experienced observers.

Reproducibility of RVFAC, TAPSE and RVFS measurements

Contrary to echocardiographic studies [START_REF] Wang | Comparison of novel echocardiographic parameters of right ventricular function with ejection fraction by cardiac magnetic resonance[END_REF], RVFAC was the most reproducible semi-quantitative parameter in this study. This is probably due to the high-quality imaging provided by bSSFP sequences, facilitating the delineation of endocardial borders.

On the other hand, tricuspid annulus and RV apex are not always easy to define on cardiac MRI and subject to a wide range of variability. Importantly, RVFAC was less dependent on the observer's experience than TAPSE or RVFS, resulting in a significant reduction of variability. These findings could make RVFAC applicable in centres with limited experience in cardiac MRI.

Diagnostic accuracy of RVFAC, TAPSE and RVFS

Our report indicates that, regardless of the experience of the observer, all SQt parameters had diagnostic value regarding RV function. However, RVFAC was both the most accurate and the least experience-dependent method. We demonstrated that a TAPSE <16 mm and an RVFS <20% predicted an RVEF <45% with 80/90% and 90/88% sensitivity/specificity respectively. These cut-off values are in agreement with a previously published study [START_REF] Nijveldt | Semi-quantitative assessment of right ventricular function in comparison to a 3D volumetric approach: a cardiovascular magnetic resonance study[END_REF]. We also demonstrated that an RVFAC <41% predicted RV dysfunction with 90% sensitivity and 94% specificity. As far as we know there have been no previous cardiac MRI studies that have evaluated the diagnostic accuracy of RVFAC for assessing RV systolic function. Our results are in accordance with previous TTE studies that demonstrated an excellent correlation between TTE measurements of RVFAC and MRI-derived RVEF [START_REF] Anavekar | Two-dimensional assessment of right ventricular function: an echocardiographic-MRI correlative study[END_REF][START_REF] Kjaergaard | Evaluation of right ventricular volume and function by 2D and 3D echocardiography compared to MRI[END_REF][START_REF] Schenk | Accuracy of echocardiographic right ventricular parameters in patients with different end-stage lung diseases prior to lung transplantation[END_REF][START_REF] Wang | Comparison of novel echocardiographic parameters of right ventricular function with ejection fraction by cardiac magnetic resonance[END_REF].

Segmentation time

Despite automatic post-processing improvements [START_REF] Grosgeorge | Automatic cardiac ventricle segmentation in MR images: a validation study[END_REF], it remains difficult to assess RV function with a Qt 3D volumetric approach in a reasonable amount of time. Indeed, we found that even for an observer with 3 years' experience RV post-processing took about 13.4±3.9 min. On the contrary, all SQt methods are quick and can be routinely applied. Evaluation of RV function was demonstrated to be a prognostic factor in most ischaemic and non-ischaemic cardiomyopathies [START_REF] Davlouros | The right ventricle in congenital heart disease[END_REF][START_REF] Gavazzi | Value of right ventricular ejection fraction in predicting short-term prognosis of patients with severe chronic heart failure[END_REF][START_REF] Ghio | Independent and additive prognostic value of right ventricular systolic function and pulmonary artery pressure in patients with chronic heart failure[END_REF][START_REF] Mehta | Impact of right ventricular involvement on mortality and morbidity in patients with inferior myocardial infarction[END_REF][START_REF] Chin | The right ventricle in pulmonary hypertension[END_REF][START_REF] Hulot | Natural history and risk stratification of arrhythmogenic right ventricular dysplasia/cardiomyopathy[END_REF][START_REF] Haddad | Right ventricular myocardial performance index predicts perioperative mortality or circulatory failure in high-risk valvular surgery[END_REF][START_REF] Mendes | Right ventricular dysfunction: an independent predictor of adverse outcome in patients with myocarditis[END_REF][START_REF] Juillière | Additional predictive value of both left and right ventricular ejection fractions on long-term survival in idiopathic dilated cardiomyopathy[END_REF]. Thus, cardiac MRI reports should contain RV function estimation. In our study we demonstrated that RVFAC could be used as a quick screening test to evaluate RV function using a bSSFP fourchamber view.

Limitations

First, this study was monocentric and enrolled a limited number of patients. However, patients included in the study are representative of current routine cardiac MRI indications, with a panel of ischaemic and non-ischaemic AHD. Second, we did not investigate patients with CHD in this study. However, in cases of CHD, the Qt approach remains the standard and should be systematically performed because of the complex RV geometry and function. Third, we used in our study a threshold of 45% to define an abnormal RVEF.

Another study has considered a threshold as low as 35% [START_REF] Nijveldt | Semi-quantitative assessment of right ventricular function in comparison to a 3D volumetric approach: a cardiovascular magnetic resonance study[END_REF]. However, a threshold of 45% is in accordance with the lower range of normal RVEF used in clinical practice [START_REF] Haddad | Right ventricular function in cardiovascular disease, part I: anatomy, physiology, aging, and functional assessment of the right ventricle[END_REF]. Moreover, in a setting of screening RV dysfunction, a threshold as low as 35% or 40% could depress the test sensitivity and therefore decrease its accuracy. Fourth, MR examinations were performed with our routine protocols and therefore, due to variable field of view and fixed number of images per RR interval, neither the spatial nor temporal resolution were constant. This could have slightly influenced the results of quantitative measurements. Finally, a comprehensive evaluation of the RV function cannot be obtained from a simple RVEF estimate. In many clinical situations such as CHD or suspected ARVD [START_REF] Marcus | Diagnosis of arrhythmogenic right ventricular cardiomyopathy/dysplasia: proposed modification of the task force criteria[END_REF], RV volumes have to be precisely determined. MRI is the unquestionable reference examination for RV volume assessment, which cannot be inferred from SQt methods.

Conclusion

Despite its important prognostic value, RV function often remains disregarded in patients referred for cardiac MRI examination. We demonstrated that right ventricular fractional area change was a feasible, fast, accurate and reproducible semi-quantitative method for evaluating RVEF in daily practice, even in non-experienced observers. Thus, the timeconsuming quantitative method could be reserved for patients with abnormal right ventricular fractional area change.

Fig. 3

 3 Fig.3Bland-Altman plots: inter-observer variability of semi-quantitative parameters (x axis = average of the first measurements of the 2 observers; y axis = differences between the first measurements of the 2 observers)

Table 1

 1 Patients' baseline clinical characteristics

	Age (years)	53.5±17.5
	Gender (male/female)	42 (70%)/18 (30%)
	Height (cm)	172.4±9.1
	Weight (kg)	78.0±16.0
	Body surface area (m 2 )	1.90±0.22
	Heart rate during cardiac MRI (bpm)	68±11
	Cardiac MRI indication
	Myocarditis	10 (17%)
	Ischaemic cardiomyopathy	9 (15%)
	ARVD	8 (13%)
	Dilated cardiomyopathy	6 (10%)
	Hypertrophic cardiomyopathy	6 (10%)
	Aortic stenosis	6 (10%)
	Cardiac tumour	2 (3%)
	Haemochromatosis	2 (3%)
	Thoracic aorta aneurysm	2 (3%)
	LVEF assessment	2 (3%)
	Other	7 (13%)

Bpm beats per minute; ARVD arrhythmogenic right ventricular dysplasia; LVEF left ventricular ejection fraction Fig. 1 Measurement of semiquantitative parameters with 4chamber cine sequences in end-diastole and end-systole

Table 2

 2

	Correlation between
	semi-quantitative parameters and
	RVEF
	TAPSE tricuspid annular plane
	systolic excursion; RVFS right
	ventricular fractional shortening;
	RVFAC right ventricular frac-
	tional area change; RVEF right
	ventricular ejection fraction. In
	regression equations, y corre-
	sponds to the estimated RVEF
	and x to the measured semi-
	quantitative parameter

Fig.

2

Bland-Altman plots: intra-observer variability of semi-quantitative parameters (x axis = average of the 2 measurements of the observer; y axis = differences between the 2 measurements of the observer)

Table 3

 3 Intra-observer variability of semi-quantitative parameters

		Observer 1	Observer 2	Observer 3
	TAPSE (mm)
	Mean	22.3±6.2	20.8±6.0	22.6±7.9
	Mean difference	0.7±2.6	1.4±4.4	-0.5±5.9
	CV	11.6	21.3	26.0
	ICC	0.912	0.747	0.756
	RVFS (%)
	Mean	23.7±6.4	21.6±5.9	23.9±7.7
	Mean difference	1.0±2.7	1.0±4.8	-0.9±5.7
	CV	11.3	22.1	23.8
	ICC	0.906	0.715	0.760
	RVFAC (%)
	Mean	48.1±10.5	48.1±10.0	52.3±11.9
	Mean difference	-0.1±3.2	1.6±3.4	1.9±7.2
	CV	6.7	7.1	13.8
	ICC	0.955	0.933	0.825

Means and mean differences are expressed in mm for TAPSE and as percentages for RVFS and RFVAC. TAPSE tricuspid annular plane systolic excursion; RVFS right ventricular fractional shortening; RVFAC right ventricular fractional area change; CV coefficient of variation, expressed as a percentage; ICC intra-class correlation coefficient

Table 5

 5 Area

	under the receiver
	operating characteristics curve and
	cut-off values with sensitivity/
	specificity for each semi-
	quantitative parameter and
	observer to detect RVEF <45%
	TAPSE tricuspid annular plane
	systolic excursion; RVFS right
	ventricular fractional shortening;
	RVFAC right ventricular frac-
	tional area change; RVEF right
	ventricular ejection fraction; Se
	sensitivity; Spe specificity. Sen-
	sitivity and Specificity are given
	with 95% confidence intervals in
	brackets. * p<0.05 vs. RVFAC
	for intra-observer AUC compari-
	son; † p<0.05 vs. Obs1 for inter-
	observer AUC comparison

Acknowledgment The authors are grateful to Alexandre Klimoff and Agnes Malgouyres (Siemens France) who provided us with the Argus segmentation software used in this study.