L Omri

Fréchette

A Amnache

• M Omri

L G Fréchette

A silicon rectangular micro-orifice for gas flow measurement at moderate Reynolds numbers: design, fabrication and flow analyses

Keywords: Micro-orifice, Flowmeter, Discharge coefficient, Microfluidic, Flow rate

published or not. The documents may come

A silicon rectangular micro-orifice for gas flow measurement at moderate Reynolds numbers: design, fabrication and flow analyses

A. Amnache, M.

Introduction

Over the past decades, the range of microfluidic devices has continued to grow, including not only low Reynolds number bioMEMS, but also devices with higher Reynolds number gas flow such as microreactors [START_REF] Wiles | Recent advances in micro reaction technology[END_REF][START_REF] Jensen | Flow chemistry-microreaction technology comes of age[END_REF] and power MEMS [START_REF] Dunn-Rankin | Personal power systems[END_REF][START_REF] Fréchette | Micro energy conversion devices[END_REF]. This growth was accompanied by a significant development of adequate instrumentation. A key parameter is flow rate, which can be challenging to measure in microsystems. Microelectromechanical systems (MEMS) flow sensors have been implemented using thermal principles [START_REF] Cubukcu | A dynamic thermal flow sensor for simultaneous measurement of thermal conductivity and flow velocity of gases[END_REF][START_REF] Xue | A silicon-glass-based microfabricated wide range thermal distribution gas flow meter[END_REF][START_REF] Kuo | Micromachined thermal flow sensors-a review[END_REF] or non-thermal principles [START_REF] Berberig | The Prandtl micro flow sensor (PMFS): a novel silicon diaphragm capacitive sensor for flow-velocity measurement[END_REF][START_REF] Bouwstra | Resonating microbridge mass flow sensor[END_REF][START_REF] Nguyen | MEMS capacitive flow sensor for natural gas pipelines[END_REF]. Table 1 summarizes the major parameters of flow measurement obtained by various authors. One of the simplest non-thermal sensing principles is based on differential pressure drop across a calibrated flow obstruction inside a channel, where the generated pressure difference is proportional to the flow rate. Compared to the thermal flow sensors, the differential pressure sensors have many advantages: (1) thermal insulation is not critical [START_REF] Elwenspoek | Thermal flow micro sensors[END_REF], which is a big challenge in the miniature systems, (2) no electrical contact with the fluid, which indicates less corrosion and damage [START_REF] Wang | MEMS-based gas flow sensors[END_REF]). However, the disadvantage of the flow sensors based on differential pressure is that they have less measurement sensitivity at low-velocity flow regimes, since pressure difference, ΔP, is proportional to the square of velocity [START_REF] Svedin | A lift force sensor with integrated hot-chips for wide range flow measurements[END_REF], as illustrated in Fig. 1. On the other hand, thermal flow sensors such as calorimetric flow sensors have a high sensitivity in the low-velocity regime, but saturates at high velocities when the thermal boundary layer thickness became dominant [START_REF] Elwenspoek | Thermal flow micro sensors[END_REF]. Therefore, thermal flow sensors are more popular in microfluidic devices handling low velocity flow regimes and low Reynolds numbers, such as liquid flows in biochemical applications. However, with the appearance of microfluidic systems handling relatively high fluid pressure and flow rate such as micro-steam turbines, i.e., up 4.5 bars and 100 mg/s (100 < Re < 2000) [START_REF] Lee | A silicon microturbopump for a Rankine cycle power generation microsystem-part I: component and system design[END_REF][START_REF] Liamini | Design methodology for a rankine microturbine: thermomechanical analysis and material selection[END_REF], the differential pressure approach become of interest. Commercial flowmeters can measure the flow range of the micro-steam turbine. However, they cannot be integrated in situ, within a device. Also, the temperature of the steam flow (up to 250 °C) precludes the use of commercial flowmeters. Since the steam micro-turbine is essentially fabricated by deep etching and wafer bonding, the constriction differential pressure can be easily fabricated on the same chip and at the same time, without adding fabrication steps. In this paper, we focused on the gas flow measurement by differential pressure using an orifice micro-flowmeter. At macroscale, this flow measurement method is widely used. The discharge coefficient, Cd, defined as the ratio of the actual flow rate over the ideal flow rate, is an important design parameter for the orifice plate flowmeter. It has been exhaustively studied for circular geometries and high Reynolds numbers [START_REF] Miller | Flow measurement engineering handbook[END_REF][START_REF] White | Fluid mechanics[END_REF], which is characteristic for macroscale fluidic systems. However, few studies of the discharge coefficient have been performed at moderate Reynolds numbers [START_REF] Hollingshead | Discharge coefficient performance of Venturi, standard concentric orifice plate, V-cone and wedge flow meters at low Reynolds numbers[END_REF][START_REF] Johansen | Flow through pipe orifices at low Reynolds numbers[END_REF]. [START_REF] Jankovski | A series pressure drop representation for flow through orifice tubes[END_REF] developed a semiempirical correlation of Cd for an incompressible flow through a small circular orifice. They considered the effect of the orifice length on the Cd. The model was correlated and validated with numerical simulations and the experimental results from [START_REF] Hasegawa | Huge reduction in pressure drop of water, glycerol/water mixture, and aqueous solution of polyethylene oxide in high speed flows through micro-orifices[END_REF], [START_REF] Phares | Laminar flow resistance in short microtubes[END_REF] and [START_REF] Kiljanski | Discharge coefficient for free jets from orifices at low Reynolds number[END_REF] for orifice Reynolds numbers up to 3000. However, micro-orifices fabricated with microfabrication processes are usually non-circular in cross section and take two-dimensional extruded-like shapes. Unfortunately, the traditional Cd correlations for circular orifices are not valid for rectangular or planar shapes [START_REF] Amnache | An analytical and numerical study of rectangular orifice plate microflowmeters[END_REF]. It is therefore very desirable to study the discharge coefficient behavior in rectangular micro-orifices. [START_REF] Zivkovic | A pressure drop correlation for low Reynolds number Newtonian flows through a rectangular orifice in a similarly shaped micro-channel[END_REF] studied numerically the pressure drop of an incompressible flow across a rectangular micro-orifice. Their study developed a correlation between the loss coefficient as a function of orifice Reynolds number and geometry. However, the Reynolds number range was relatively low, from 0.005 to 0.1. [START_REF] Mishra | Incompressible and compressible flows through rectangular microorifices entrenched in silicon microchannels[END_REF] fabricated rectangular micro-orifice plates entrenched in silicon microchannels for orifice hydraulic diameters between 21 and 57 µm. They experimentally studied the compressible and incompressible single-phase flow behavior through these configurations. They developed a correlation of the discharge coefficient for the incompressible flow and they concluded that the Cd depends only on the area ratio (orifice width/channel width) for Reynolds numbers greater than its critical value, (200 ≤ Recrit ≤ 500). For compressible flow, the same authors determined the effect of the pressure ratio (upstream/downstream pressure) on the discharge coefficient. They observed that for pressure ratios greater than 2, which corresponds to choked flow, i.e., Mach number equal to unity, the discharge coefficient becomes a constant value. However, the evolution of the discharge coefficient below pressure ratios of 2 was not well characterized. In addition, for both compressible and incompressible flows, the effect of the aspect ratio on the discharge coefficient was not considered. [START_REF] Amnache | An analytical and numerical study of rectangular orifice plate microflowmeters[END_REF] numerically studied the gas flow through a rectangular micro-orifice and observed that the discharge coefficient strongly depends on the orifice aspect ratio.

In this paper, we design, fabricate and characterize rectangular orifice micro-flowmeters for measuring moderate gas flow. The design of this type of micro-flowmeter is based mainly on the knowledge of the discharge coefficient. However, the above brief literature survey shows that the discharge coefficient for compressible flow through micro-orifices with rectangular cross section has not been well studied. In this work, we endeavored to study numerically and experimentally the compressible gas flow through rectangular micro-orifices of various sizes, below the sonic limit. The discharge coefficient is characterized showing the effect of the Reynolds number, all the geometric parameters (orifice aspect ratio, area ratio, orifice length-to-hydraulic ratio) and compressibility.

This work provides a design methodology for microfabricated differential pressure flowmeters to allow their integration into embedded microfluidic devices that cannot use commercial flowmeters.

Rectangular orifice micro-flowmeter approach

Rectangular orifice micro-flowmeters are based on the Bernoulli obstruction theory. The orifice restriction as shown in Fig. 2 creates a Venturi effect, where the flow velocity increased to its maximum and the static pressure decreased to its minimum value at point 2, which corresponds to the vena contracta. The static pressure profile along the orifice microflowmeter is also illustrated in Fig. 2. It is a combination of the total pressure drop (Moody and head losses) and the dynamic pressure (Bernoulli effect). By measuring pressure difference, ΔP = P 1 -P 2 , between the pressure tap 1 and the pressure tap 2, the velocity of the flow can be determined, leading to the ideal mass flow rate, ṁid .

For an isentropic unidimensional compressible flow through a channel [START_REF] Shapiro | Dynamics and thermodynamics of compressible fluid flow[END_REF]):

(1)

T 0 T = 1 + k -1 2 M 2 ,
(2)

P 0 P = 1 + k -1 2 M 2 k k-1 ,
where P, T, and ρ are static pressure, static temperature and static density of the fluid. P 0 , T 0 and ρ 0 are, respectively, the total pressure, total temperature and total density. These relations are expressed as a function of Mach number, M, and depend on k, the specific heat ratio, which is equal to 1.4 for air.

The equation of state of an ideal gas is written as:

where R is the ideal gas constant, equal to 287 J/kg K for air. Assuming an ideal case with no losses between upstream (1) and downstream (2) of the orifice, the ideal static pressure ratio can be given by: Assuming that the cross-sectional area of the vena contracta, A v , is equal to the cross-sectional area of the orifice, A o , and from mass conservation, the ratio A o /A c can be expressed as:

Replacing the Mach number, M 1 , calculated from Eq. 5, in Eq. 6, the Mach number at the vena contracta, M 2 , can be determined by:

(3) 0 = 1 + k -1 2 M 2 1 k-1 , (4) P = RT,
(5)

P 1 P 2 = 1 + k-1 2 M 2 2 1 + k-1 2 M 2 1 k k-1 . (6) A o A c = 1 + k-1 2 M 2 2 1 + k-1 2 M 2 1 k+1 2(k-1)
. The ideal mass flow rate across the orifice can be obtained by [START_REF] Shapiro | Dynamics and thermodynamics of compressible fluid flow[END_REF]):

Pressure

P1 P2

Flow

To express the mass flow rate as a function of the pressure difference between upstream and downstream of the orifice, the Mach number, M 2 , is replaced by Eq. 7 and the density, ρ 2 , is replaced by: Then after rearrangement, the ideal mass flow rate can be expressed by: where β is the area ratio defined as the square root of the ratio of the orifice cross-sectional area, A o , to the channel cross-sectional area, A c , as: and Y is the expansion factor expressed for an adiabatic gas as:

The expansion factor, Y, describes the effect of compressibility. Indeed, if the pressure difference across the orifice is small, the expansion factor, Y, tends to unity. It results in no significant change in density of the gas and then the flow can be assumed incompressible.

In the actual case, there will be a total pressure drop across the orifice due to friction losses. Also, the section of the vena contracta at point 2 will not necessarily be equal to the orifice cross-sectional area. The ideal mass flow rate is therefore typically corrected by the discharge coefficient, (7)

M 2 2 = 1 - P 1 P 2 k k-1 k-1 2 P 1 P 2 k k-1 ⎛ ⎜ ⎜ ⎝ A o A c P 1 P 2 k k-1 ⎞ ⎟ ⎟ ⎠ 2 -k-1 2 . (8) ṁid = 2 A o M 2 √ kRT 2 . (9) 2 = 1 1 + k-1 2 M 2 2 1 k-1 . (10) ṁid = Y 1 √ 1 -4 A o √ 2 1 ΔP, (11) = √ A o A c (12) Y = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ P 2 P 1 2 k (1 -4 ) k k-1 1 - P 2 P 1 k k-1 1 - 4 P 2 P 1 2 k 1 - P 2 P 1 ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭ 0.5 .
Cd, which must be determined for a given geometry and flow conditions to account for these non-idealities. So, the actual mass flow rate, ṁ , can be written as:

Unlike the traditional circular orifice plate, the discharge coefficient is expected to depend on three geometric parameters: area ratio, β, orifice aspect ratio, δ, defined as the ratio of the orifice width, b o , over the channel depth, ω:

and orifice length-to-hydraulic diameter ratio, λ, defined as the ratio of the orifice length, l o , over its hydraulic diameter, dh o :

where dh o is defined as:

Design and microfabrication of rectangular orifice micro-flowmeters

A series of 13 rectangular orifice micro-flowmeters are designed with different geometries. To study the influence of the geometric parameters on the discharge coefficient, each micro-flowmeter geometry is defined by three dimensionless parameters: the area ratio, β, the orifice aspect ratio, δ, and the orifice length-to-hydraulic diameter ratio, λ. The dimensions and parameters of the micro-flowmeters are presented in Table 2. Localization of pressure taps for measuring average static pressure upstream, P 1 , and downstream, P 2 , of the orifice are designed to be in agreement with the American Society of Mechanical Engineers standardization at macroscale [START_REF] Miller | Flow measurement engineering handbook[END_REF]. Namely the upstream pressure and downstream pressure taps are located atb c , b c /2, respectively from the orifice. [START_REF] Amnache | An analytical and numerical study of rectangular orifice plate microflowmeters[END_REF] found these locations to be appropriate for rectangular orifice micro-flowmeters.

The fabrication process flow for rectangular orifice microflowmeters is schematically illustrated in Fig. 3. The microdevices are fabricated using silicon-on-insulator (SOI) wafer (100 mm, p-type, double side polished, 200 µm device layer, 300 µm handle layer and 200 nm silicon dioxide). After photolithography on the device layer using photoresist, channels, orifices and the pressure taps were formed by deep reactive ion etching (DRIE). DRIE gives re-entrant profiles when

(13) ṁ = Cd Y 1 √ 1 -4 A o √ 2 1 ΔP. (14) = b o (15) = l o dh o , (16)
dh o = 2b o b o + .
etching trenches are larger than 50 µm. However, verticality is important to have well-defined orifices and reproducible micro-flowmeters. To fabricate vertical channel walls, sacrificial structures were created near the wall, as represented in Fig. 3b, to create narrow trenches with vertical side walls. The width of the trench opening near the wall is 10 µm. These sacrificial structures fall when the silicon dioxide layer is reached due to under-etching on the side with a wider opening. The other requirement for reproducible results is control of the channel depth. Given the high selectivity with silicon dioxide, well controlled and uniform channel depth independent of the trench aspect ratio is achieved. Therefore, the depth of the all micro-flowmeters is defined by the SOI's device layer, measured here to be 207 µm, with an uncertainty of 2.5%.

The relative roughness of micro-channels (ratio of the average height of surface irregularities to the hydraulic diameter of the channel) is measured to be about 0.001 to 0.004.

Figure 4 shows a scanning electron microscopy image of the micro-orifice edge and the downstream pressure tap for device #10. The width of the pressure tap is 30 µm. The image shows good verticality of the wall after DRIE. Another photolithography and DRIE process was performed on the handle layer of the SOI wafer etching holes of 400 µm diameter through 300 µm of Si in order to create the fluid inlet/outlet and pressure tap connections (Fig. 3c). Prior to bonding, the silicon wafer was cleaned with SC1 solution (1:1:5 mixture of NH 4 OH:H 2 O 2 :H 2 O) for 15 min. The wafer was also immersed in a hydrofluoric acid solution (1:50 mixture of HF:H 2 O) for 30 s in order to remove the native oxide. To complete the micro-channels, the silicon wafer was anodically bonded to a Pyrex ® glass wafer (500 µm thickness), which is a good material choice for bond quality with silicon and to allow flow visualization in future studies (Fig. 3d). Finally, the wafer was diced into 5 × 1 cm rectangular chips with multiple flowmeters, as illustrated in Fig. 5. Distances between fluid inlet/outlet and the center of the orifice are 5.5 and 3.5 mm, respectively.

Experimental apparatus and procedure

A schematic of the experimental setup is represented in Fig. 6. In the current study, extra dry air (H 2 O < 10 ppm) is used as the working fluid. The chip of micro-flowmeters is by a pressure regulator. The air is filtered before passaging through the micro-flowmeters. The differential pressure between inlet and outlet of micro-orifices is measured by a differential pressure transducer (Scanivalve ® Zoc17IP/8PX-APC) capable of pressure up to 700 kPa with an uncertainty of 0.455 kPa. The upstream pressure P 1 is measured separately by a simple pressure transducer (Omega ® ) capable to measure pressure up to 1 MPa with an uncertainty of 2.5 kPa. The reason to measure P 1 is to calculate the density of the air at this location using Eq. assuming room temperature. In this experiment, we used mass flow controllers to control the mass flow rate with an uncertainty of 1% of full scale ® 1179A). Since we studied a large range of mass flow rates, we used three different mass flow controllers having different measurement ranges (0-200, 0-500 and 0-5000 sccm) to increase the precision of measurement. Finally, pressure and mass flow rate data were collected through a data acquisition and control (DAQ) system.

Results and discussion

The characteristics of the flow through the rectangular orifice plate micro-flowmeter have been evaluated experimentally for the 13 different sizes and over a range of operating conditions. The air at ambient temperature is used for these experiments. The results show the pressure difference across micro-flowmeter, and the effect of geometry, Reynolds number and compressibility on the discharge coefficient. Furthermore, the numerical simulations are validated by the experimental results.

Pressure difference across micro-orifices

The pressure difference, ΔP, across micro-orifices is measured by varying mass flow rate within the range of 1-106 mg/s. The upstream pressure, P 1 , is maintained at 0.8 MPa. Figure 8 shows the behavior of ΔP versus the mass flow rate for each micro-flowmeter. The ΔP increases quadratically as mass flow rate increases. As discussed previously, the results show that orifice micro-flowmeters have a sensitivity at high flow rate. Furthermore, the results revealed that a high orifice aspect ratio gives a high pressure difference when the area ratio is fixed. Indeed, the depth of channels is constant (207 µm), so when the aspect ratio increases, orifice cross-sectional area decreases and then the dynamic pressure becomes more important. Therefore, the static pressure at the vena contracta decreases resulting in a larger pressure difference.

The maximum mass flow rate range in these measurements was limited by (Fig. 8):

(a) The mass flow controller limit (106 mg/s at P 1 = 0.8 MPa) as shown for devices #7, #10 and #11. (b) The increase of the pressure losses inside the microchannel (upstream and downstream of the orifice) and the canalizations as shown for #3 and #4. (c) The critical flow where the Mach number reaches unity at the vena contracta as shown for #1, #2, #5, 6, #8, #9, #12 and #13. At this limit, the pressure differ-ence increased significantly due shock waves. It corresponds to the theoretical critical pressure ratio (P 2 /P 1 ) as shown in Fig. 8. The range of interest in this work will therefore stay below critical flow.

The Knudsen number, which evaluates the effect of rarefaction on flow properties, was estimated by Eq. 17 [START_REF] Morinin | The rarefaction effect on the friction factor of gas flow in microchannels[END_REF]) to be an order of 10 -5 , for the smallest device (#2). It is well below 10 -3 , so the flow can be considered as a continuum:

Re o is orifice Reynolds number defined as:

where ρ o , V o and µ are the fluid density, average velocity and viscosity at the orifice, respectively.

Discharge coefficient

Effect of geometric parameters

The discharge coefficient, Cd, of the flow through microorifices is plotted versus orifice aspect ratio and area ratio with varying orifice Reynolds number from 200 to 18,000.

uncertainty in the discharge coefficient comes from measurement error of the differential pressure transducer, flow controllers and dimensions of the micro-flowmeters.

As shown in Fig. 9, the general trend is a sharp increase in Cd from low o to reach a nearly constant value above Re o ≈ 3000. This behavior is expected since the viscous losses diminish as Re o increases, leading to a Cd closer to unity (ideal flow). At high Re o , we observe that Cd increases again in some cases (such as micro-flowmeters #5, #6, #9, #12 and #13). Here, the fluid velocity and pressure difference become more important, so compressibility effect appears. To better confirm the role of compressibility, the Mach number at the vena contracta, M 2 , is estimated by Eq. 19 [START_REF] Shapiro | Dynamics and thermodynamics of compressible fluid flow[END_REF]) and added to Fig. 9. We notice indeed that Cd begins to increase again when M 2 reaches the range of 0.25-0.4.

For micro-flowmeters #9, #12 and #13 the Cd behave differently at low Re o . Indeed, the Cd increases a maximum near Re o ≈ 2000, after which it decreases to reach a constant value (before increasing again due to compressibility, as Fig. 8 Measured pressure difference across the orifices for various micro-flowmeters. The upstream pressure P 1 is maintained at 0.8 MPa presented previously). The same behavior has been observed by [START_REF] Hollingshead | Discharge coefficient performance of Venturi, standard concentric orifice plate, V-cone and wedge flow meters at low Reynolds numbers[END_REF] for macroscale orifices with β = 0.5-0.7. They observed that the trend of Cd presents a local maximum at Re o ≈ 300. They explained this by the effect of the orifice plate thickness on the velocity profile at the vena contracta. In addition, the results from [START_REF] Jankovski | A series pressure drop representation for flow through orifice tubes[END_REF] for small circular orifices indicate that the Cd exhibits a maximum at low Re o when the length-to-hydraulic diameter ratio, λ, tends to zero. This is in agreement with the present results. Indeed, compared to other micro-flowmeters, the #9, #12 and #13 have the smallest λ, 0.4, 0.2 and 0.2, respectively. This suggests that all three geometric parameters, β, δ, and λ, should be considered in micro-flowmeters.

(17) Kn = √ k 2 M 2 Re o . ( 18
) Re o = o V o dh o = ṁ dh o A o , (19)
P 2 P 1 = k -1 2 M 2 2 + 1 -k k-
For a fixed area ratio, β, and orifice length-to-hydraulic diameter ratio, λ, the higher aspect ratios, δ, give higher discharge coefficients. This may be due to the velocity gradient that is becoming larger at the wall with smaller aspect ratios, which leads to high friction losses.

We compared the effect of the area ratio, β, on the Cd by fixing the aspect ratio, δ, to 1 as illustrated in Fig. 10. The data revealed that a higher β gives higher Cd. This is an unexpected result if we consider that an abrupt sudden contraction and sudden expansion tends to produce high friction losses. Furthermore, micro-flowmeter #4 has a higher λ, which increases the Moody losses. A plausible explanation is that the hypothesis taken in Eq. 6, mentioned that the area of the vena contracta is assumed equal to the area of the orifice, becomes invalid for rectangular orifice microflowmeters. Thus, the discharge coefficient determined in this study could be a combination of friction losses and vena contracta cross-sectional area deviation. To determine real friction losses through the orifice, the discharge coefficient should be divided by the contraction coefficient, Cc, defined as the ratio between the vena contracta and the orifice crosssectional areas. However, numerical simulations or experimental flow visualization would be required to know the actual vena contracta.

Compressibility effect

The above results show that the Cd is affected by both Reynolds number and compressibility. In order to uncouple these two effects, we used 3D numerical simulation of the microflowmeter #4. Thus, ANSYS Fluent 14.5 is used to solve the compressible and incompressible steady-state Navier-Stokes equations. As the flow is symmetric, we calculated only a quarter of micro-flowmeter #8. Non-uniform hexahedral grids were used to mesh the geometry. The mesh is finer near the wall and orifice where the velocity gradients are larger. The meshed geometry contained 707,500 hexahedral cells. Inlet and outlet flow are situated at 3 mm upstream and 4 mm downstream, respectively, from the orifice. We used Reynolds stress model, RSM, to predict the transitional and turbulent flow through the orifice micro-flowmeter. Eiamsaard et al. (2008) observed that the prediction of the flow through a circular orifice with RSM is in agreement with measurements. Pressure-based solver and simple scheme are used to solve the discretized equations. The convergence criterion is satisfied when the residual of overall conservation equations reached 10 -12 . The pressure drop across the orifice is evaluated by creating two surface planes at P 1 and P 2 taps location and calculating the average static pressure. A comparison of experimental results and numerical simulations of the discharge coefficient is shown in Fig. Two different series of numerical data as a function of Reynolds number are used. The first series has been performed using the same flow conditions as the experiment, i.e., compressible flow. The second series has been performed by simulating incompressible flow. The comparison revealed a good agreement of the experimental results with the numerical simulations taking into account the compressibility of the fluid. The deviation is less than 6%. On other hand, the numerical data for incompressible flow show concordance with the experimental results at low Re o ranging from 2000 to 6000. This range of Re o corresponds to 2 ranging from 0.07 to 0.2. However, the deviation starts to become significant at Re o = 6800. The related M 2 at this value is 0.25. Unlike the experimental measurement, the Cd remains constant with Re o from 2000 to 16,000. This result confirms that the Cd is not only dependant on Re o at high compressibility, but that the effect of Mach number should be considered.

Conclusion

In this work, a series of 13 non-traditional rectangular orimicro-flowmeters have been fabricated successfully by MEMS fabrication methods. The air mass flow rate measured by these micro-flowmeters ranged from 1 to 106 mg/s.

The paper presents results concerning the behavior of the discharge coefficient in micro-flowmeters for Reynolds number ranging from 200 to 18,000. It was found that it is affected by orifice Reynolds number, compressibility, orifice aspect ratio, area ratio and orifice length-to-hydraulic ratio. We also found that the hypothesis used for circular orifices at macroscale mentioning an equality of the vena contracta and orifice cross-sectional areas may be not valid for rectangular micro-orifices and that it may be affected significantly by the area ratio and length-to-hydraulic diameter ratio. Consequently, the calculated discharge coefficients in this study do not present only friction losses through the orifice, but rather a combination of friction losses and the contraction coefficient. Further research work on the exact vena contracta cross-sectional area is recommended. The results in this work provide results allowing the design of simple micro-flowmeters for moderate Reynolds numbers, and can also be a guideline for further investigation of the flow through rectangular micro-orifices. The agreement between the experimental and numerical results shows that numerical simulation using RSM model can serve as a good analysis tool for rectangular orifice micro-flowmeters, further opening the design options.

Fig. 1

 1 Fig. 1 Measurement sensitivity of the thermal-based calorimetric versus differential pressure-based flowmeters

Fig. 2

 2 Fig. 2 Schematic diagram of the orifice flowmeter measurement approach

Fig. 3

 3 Fig. 3 Microfabrication process flow of rectangular orifice microflowmeters

Fig. 4 Fig. 7

 47 Fig. 4 Scanning electron microscopy image showing orifice and pressure tap P 2 of the device #10. The air flows from right to left

Fig. 9 Fig. 10

 910 Fig. 9 Discharge coefficient plots with several area ratios. a β = 0.2, b β = 0.4, c β = 0.6 and d β = 0.8

Fig. 11

 11 Fig. 11 Comparison of experimental results of the discharge coefficient with numerical simulations for both incompressible and compressible flow (micro-flowmeter #8)

Table 1

 1 Major parameters of MEMS-based flow sensor for gas flow measurement

	References	Working principle	Gas	Flow range	Chip dimension
						Sensor size
	Xue and Yan (2012)	Thermal (calorimetric)	Air	0.016-57 mg/s	20 × 10 × 1.6 mm 3
						No data
	Cubukcu et al. (2014)	Thermal (calorimetric)	Air, He, Ne, Ar	0.04-2 m/s	No data
						1 mm diameter
	Svedin et al. (2003)	Hybrid: thermal/pressure force (drag	Air	Up to 1620 mg/s	No data
				force/hot wire)	Up to 4.3 m/s	3 × 3 mm 2
	Bouwstra et al. (1990)	Resonating (vibration)	Air	0-0.2 mg/s	No data
						0-3 m/s	600 × 200 × 21 µm 3
	Berberig et al. (1998)	Differential pressure (capacitive)	Air	0-22 m/s	5 × 8 × 1.4 mm 3
						No data
	Nguyen et al. (2015)	Pressure force (capacitive)	Air	0-19.2 m/s	No data
						5.5 × 5.5 mm 2
	This work		Differential pressure	Air	0-106 mg/s	5 × 1 cm 2 (10 dif-
						0-310 m/s	ferent sensors)
						207 × 125 µm 2 to
						3005 × 5102 µm 2
					Thermal-based (calorimetric)
	Pressure difference, ∆P (Pa)	∆T (K) Temperature diffrence,	Low sensitivity zone ∆T	Differential pressure-based High sensitivity zone
				∆P
				Flow velocity (m/s)

Table 2

 2

	Summary of fabricated micro-flowmeters dimensions	Devices	β	δ	λb c (µm)	b o (µm)	ω (µm)	l o (µm)	dh o (µm)
		1	0.2	1.7	3.9	3005	120	207	595	152
		2	0.2	2.6	3.4	205	80	207	395	115
		3	0.41	0.7	1.5	1890	310	207	370	248
		4	0.4	1	1.2	1260	205	207	245	206
		5	0.4	1.7	1	760	120	207	145	152
		6	0.4	2.6	0.8	510	80	207	95	115
		7	0.6	0.2	1.6	2787	1007	207	560	343
		8	0.6	1	0.5	565	205	207	105	206
		9	0.61	2.3	0.4	245	90	207	45	126
		10	0.8	0.15	1.3	2270	1455	207	470	362
		11	0.8	0.3	0.6	943	605	207	180	309
		12	0.8	1.3	0.2	253	160	207	45	181
		13	0.8	2.6	0.2	125	80	207	20	115
	(a) SOI wafer

(b) DRIE on the device layer to create channels. The sacrificial structures will fall at the end of etching (c) DRIE on the handle layer to create inlet/outlet and pressure tap holes (d) Anodic bonding with glass wafer (Pyrex ® )

  1 .

		800
				#1
				#2
				#3
	Pressure difference (kPa)	200 400 600	P 2 /P 1 =0.528	#4 #5 #6 #7 #8 #11 #12 #13 #9 #10
		0	02 04 06 08 01 00	120
			Mass flow rate (mg/s)

Acknowledgements

The authors would like to thank Dr. Gholamreza Mirshekari for his technical contribution in cleanroom fabrication and methods. This work was supported by the NSERC and Canada Research Programs. The authors gratefully acknowledge this support.


Julien Cattel
email: juliencattel@gmail.com

Julien Martinez

F Jiggins

L Mouton

P Gibert

Wolbachia -mediated protection against viruses in the invasive pest Drosophila suzukii

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Drosophila suzukii [START_REF] Matsumura | illustrated insects of Japan-empire[END_REF] (Diptera: Drosophilidae), the spotted-wing Drosophila, is an invasive species native to South East Asia [START_REF] Kanzawa | Studies on Drosophila suzukii mats[END_REF]. It was originally described in Japan in 1916 and, within the last decade, it has been observed for the first time in California [START_REF] Hauser | A historic account of the invasion of Drosophila suzukii (Matsumura) (Diptera:Drosophilidae) in the continental United States, with remarks on their identification[END_REF], in Spain and in Italy [START_REF] Calabria | First records of the potential pest species Drosophila suzukii (Diptera: Drosophilidae) in Europe[END_REF] in 2008, and then quickly spread throughout North America and Europe [START_REF] Cini | A review of the invasion of Drosophila suzukii in Europe and a draft research agenda for integrated pest management[END_REF] and more recently in Brazil [START_REF] Deprá | The first records of the invasive pest Drosophila suzukii in the South American continent[END_REF]. In contrast to the vast majority of Drosophila species, D. suzukii is an agricultural pest because its serrated ovipositor allows it to lay eggs on healthy ripening fruits still attached to the plant [START_REF] Mitsui | Spatial distributions and clutch sizes of Drosophila species ovipositing on cherry fruits of different stages[END_REF]. Damage is caused by larvae feeding on the pulp inside the fruits and berries. As a consequence D. suzukii can have a severe economic impact, such as in the Western United States where it causes losses of up to US$500 millions per year [START_REF] Goodhue | Spotted wing drosophila infestation of California strawberries and raspberries: economic analysis of potential revenue losses and control costs[END_REF]. Because of its remarkable invasive success and impact on agricultural production, D. suzukii is currently subjected to intense research from both fundamental and applied perspectives.

Until now little was known about the symbiotic community of D. suzukii, despite maternally-inherited symbionts being common and important components of arthropod biology and ecology [START_REF] Zchori-Fein | Manipulative tenants[END_REF]. Some studies revealed that D. suzukii naturally harbors Wolbachia [START_REF] Cordaux | Intense transpositional activity of insertion sequences in an ancient obligate endosymbiont[END_REF][START_REF] Siozios | Draft genome sequence of the Wolbachia endosymbiont of Drosophila suzukii[END_REF][START_REF] Hamm | Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella[END_REF][START_REF] Cattel | Wolbachia in european populations of the invasive pest Drosophila suzukii: regional variation in infection frequencies[END_REF], which is the most common endosymbiont in arthropods with an estimation of 52% of arthropod species infected [START_REF] Weinert | The incidence of bacterial endosymbionts in terrestrial arthropods[END_REF]. Only one strain of Wolbachia has been identified in field populations of D. suzukii based on MLST markers, at least in North America and in Europe, which is closely related to wRi [START_REF] Siozios | Draft genome sequence of the Wolbachia endosymbiont of Drosophila suzukii[END_REF][START_REF] Hamm | Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella[END_REF][START_REF] Cattel | Wolbachia in european populations of the invasive pest Drosophila suzukii: regional variation in infection frequencies[END_REF]. In many associations, the spread of Wolbachia in the host populations is achieved through their capacity to manipulate host reproduction either by biasing the host's sex ratio towards the production of females or, more commonly, by impeding the reproduction of uninfected females through a sterility phenomenon called Cytoplasmic Incompatibility (CI) [START_REF] Werren | Wolbachia: master manipulators of invertebrate biology[END_REF]. Theory predicts that the spread of CIinducing Wolbachia in a population is under positive frequency-dependence and that their maintenance depends on their transmission efficiency and on the intensity of CI [START_REF] Turelli | Cytoplasmic incompatibility in Drosophila simulans: dynamics and parameter estimates from natural populations[END_REF]. Wolbachia can also successfully invade host populations by bringing direct fitness benefits to infected individuals such as increasing fecundity [START_REF] Dobson | Mutualistic Wolbachia infection in Aedes albopictus: accelerating cytoplasmic drive[END_REF][START_REF] Dobson | Fitness advantage and cytoplasmic incompatibility in Wolbachia single-and superinfected Aedes albopictus[END_REF][START_REF] Fry | Variable fitness effects of Wolbachia infection in Drosophila melanogaster[END_REF][START_REF] Weeks | From parasite to mutualist: rapid evolution of Wolbachia in natural populations of Drosophila[END_REF][START_REF] Unckless | Maintenance of a male-killing Wolbachia in Drosophila innubila by male-killing dependent and male-killing independent mechanisms[END_REF], longevity [START_REF] Gavotte | Costs and benefits of Wolbachia infection in immature Aedes albopictus depend upon sex and competition level[END_REF][START_REF] Brelsfoard | Wolbachia effects on host fitness and the influence of male aging on cytoplasmic incompatibility in Aedes polynesiensis (Diptera: Culicidae)[END_REF][START_REF] Alexandrov | Removing endosymbiotic Wolbachia specifically decreases lifespan of females and competitiveness in a laboratory strain of Drosophila melanogaster[END_REF][START_REF] Toivonen | No influence of Indy on lifespan in Drosophila after correction for genetic and cytoplasmic background effects[END_REF] or provisioning nutrients [START_REF] Brownlie | Symbiont-mediated protection in insect hosts[END_REF][START_REF] Hosokawa | Wolbachia as a bacteriocyte-associated nutritional mutualist[END_REF][START_REF] Unckless | Maintenance of a male-killing Wolbachia in Drosophila innubila by male-killing dependent and male-killing independent mechanisms[END_REF]. In addition, Wolbachia can protect its host against viruses [START_REF] Hedges | Wolbachia and virus protection in insects[END_REF][START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF][START_REF] Osborne | Variation in antiviral protection mediated by different Wolbachia strains in Drosophila simulans[END_REF][START_REF] Bian | The endosymbiotic bacterium Wolbachia induces resistance to dengue virus in Aedes aegypti[END_REF][START_REF] Glaser | The native Wolbachia endosymbionts of Drosophila melanogaster and Culex quinquefasciatus increase host resistance to west nile virus infection[END_REF][START_REF] Blagrove | Wolbachia strain wMel induces cytoplasmic incompatibility and blocks dengue transmission in Aedes albopictus[END_REF]. Such benefits could explain the presence in natural populations of Wolbachia strains that do not appear to rely on the reproductive manipulation to spread. For example, the strain wMel, which induces a very low level of CI [START_REF] Hoffmann | Cytoplasmic incompatibility in Australian populations of Drosophila melanogaster[END_REF][START_REF] Hoffmann | Population dynamics of the Wolbachia infection causing cytoplasmic incompatibility in Drosophila melanogaster[END_REF], might be maintained in populations of D. melanogaster because of positive effects such as the protection it confers against several RNA viruses [START_REF] Hedges | Wolbachia and virus protection in insects[END_REF][START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF]. Similarly, wAu, which naturally infects D. simulans, does not induce CI but confers strong protection against viruses [START_REF] Osborne | Variation in antiviral protection mediated by different Wolbachia strains in Drosophila simulans[END_REF][START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF]. This antiviral protection, which has been observed only in Drosophila and mosquitoes, has been shown to be highly variable according to the host species and the Wolbachia strain [START_REF] Hedges | Wolbachia and virus protection in insects[END_REF][START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF][START_REF] Osborne | Variation in antiviral protection mediated by different Wolbachia strains in Drosophila simulans[END_REF][START_REF] Moreira | A Wolbachia symbiont in Aedes aegypti limits infection with Dengue, Chikungunya, and Plasmodium[END_REF][START_REF] Mousson | Wolbachia modulates Chikungunya replication in Aedes albopictus[END_REF][START_REF] Chrostek | Wolbachia variants induce differential protection to viruses in Drosophila melanogaster: a phenotypic and phylogenomic analysis[END_REF][START_REF] Chrostek | High antiviral protection without immune upregulation after interspecies Wolbachia transfer[END_REF][START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF].

Previous studies found that the prevalence of wSuz is highly variable in populations of D. suzukii from North America (7 to 58%) and Europe (0 to 100%) [START_REF] Hamm | Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella[END_REF][START_REF] Cattel | Wolbachia in european populations of the invasive pest Drosophila suzukii: regional variation in infection frequencies[END_REF] and, until now, there is no indication that this strain can induce strong reproductive manipulations in D. suzukii such as CI nor male killing [START_REF] Hamm | Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella[END_REF][START_REF] Cattel | Wolbachia in european populations of the invasive pest Drosophila suzukii: regional variation in infection frequencies[END_REF]. Moreover, in North American populations, it has been shown that wSuz is imperfectly vertically transmitted by wild-caught D. suzukii females, which would cause the bacterium to be lost from the population in the absence of any selection [START_REF] Hamm | Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella[END_REF]. All these results suggest that wSuz may bring a fitness advantage to D. suzukii but yet no effect has been found on fecundity, starvation tolerance or resistance to desiccation [START_REF] Hamm | Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella[END_REF].

wSuz belongs to the supergroup A [START_REF] Siozios | Draft genome sequence of the Wolbachia endosymbiont of Drosophila suzukii[END_REF], which contains several Wolbachia strains known to induce antiviral protection [START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF]. In the present study, we have thus tested whether wSuz can protect D. suzukii against viruses. Four host lines were compared, two from France, a country which was recently invaded by D. suzukii, and two from Japan, its native range [START_REF] Cini | A review of the invasion of Drosophila suzukii in Europe and a draft research agenda for integrated pest management[END_REF][START_REF] Asplen | Invasion of spotted wing Drosophila (Drosophila suzukii): a global perspective and future priorities[END_REF]. Two RNA viruses were tested, Drosophila C virus (DCV; highly pathogenic Drosophila virus) and the Flock House virus (FHV; isolated from a beetle) [START_REF] Scotti | Flock House Virus: a nodavirus isolated from Costelytra zealandica (White) (Coloeoptera: Scarabaeida)[END_REF][START_REF] Huszar | Drosophila viruses and the study of antiviral host-defense[END_REF].

We found that wSuz is able to protect D. suzukii against these two viruses but that the antiviral protection is very variable between the host lines. This beneficial effect could explain its maintenance in natural populations.

Results

Wolbachia protects D. suzukii against DCV infection

We measured the survival of Fr-CP (antibiotic-treated line) and Jp-OGH (introgressed line) flies uninfected or infected respectively with a French and Japanese Wolbachia isolate after inoculation with DCV (400 flies) or saline solution (Ringer, 400 flies) (Fig. 1A). In the mockinfected flies (Ringer's control treatment), the survival of Wolbachia-free and Wolbachiainfected individuals was not significantly different, indicating that there is no intrinsic effect of Wolbachia on the fly survival (Cox's mixed effect model; Main effect Wolbachia: χ 2 =0.92, d.f.=1, P=0.337; Host genotype x Wolbachia interaction: χ 2 =1.57, d.f.=1, P=0.210). However, the Fr-CP line had higher survival than the Jp-OGH line (Cox's mixed effect model; χ 2 =8.78, d.f.=1, P=0.003).

We found that Wolbachia increased the survival of flies infected with DCV (Cox's mixed effect model: χ 2 =21.74, d.f.=2, P<0.001; Fig. 1A) but the effect is significant for the Fr-CP line only (Cox's mixed effect model, Host genotype x Wolbachia interaction: χ 2 =4.1, d.f.=1, P=0.043; Tukey test, P<0.001 for Fr-CP and P=0.99 for Jp-OGH). As Fr-CP and Jp-OGH lines differ in both the host and bacterial genotypes, either of these may be causing the difference.

The DCV titer was lower in Wolbachia-infected flies than in uninfected ones (Twoway ANOVA, F=15.22, d.f.=1, P<0.001; Fig. 1B), and this effect of Wolbachia did not depend on the line (Two-way ANOVA, Wolbachia x host interaction: F=0.45, d.f.=1, P=0.509; Fig. 1B).

Wolbachia effect on FHV infection

Given the difference in the degree to which wSuz increases the survival of D. suzukii after DCV infection between lines we then investigated the effect of wSuz on FHV infection in four genetic backgrounds: the effect of the French Wolbachia isolate, wSuz-Fr, in two French backgrounds Fr-CP and Fr-BE, and the effect of the Japanese isolate, wSuz-Jp, in two Japanese backgrounds Jp-OGH and Jp-YSG. A total of 800 flies were stabbed with FHV and 800 others with Ringer's solution (Fig. 2A). In the absence of viral infection neither Wolbachia nor the host genetic background affected survival (Ringer control treatment, Cox's mixed effect model, Wolbachia effect: χ 2 =1.83, d.f.=1, P=0.180; host effect: χ 2 =1.43, d.f.=3, P=0.7; Wolbachia x host interaction: χ 2 =1.22, d.f.=3, P=0.750).

In FHV-infected flies, survival was significantly affected by the Wolbachia infection (χ 2 =31.88, d.f.=4, P<0.001), the host genetic background (χ 2 =39.55, d.f.=6, P<0,001) and we found a significant interaction between these two factors (χ 2 =14.99, d.f.=3, P=0.002). Because we cannot exclude the possibility that the French and the Japanese lines are infected by a different Wolbachia isolate (wSuz-Fr and wSuz-Jp respectively), we also tested the Wolbachia and the host genetic background effects on infected flies' survival for the French and Japanese lines separately. The French lines survival was significantly affected by the Wolbachia infection (χ 2 =17.75, d.f.=2, P<0.001), the host genetic background (χ 2 =34.14, d.f.=2, P<0,001) but there was no significant interaction between these two factors (χ 2 =3.73, d.f.=1, P=0.053). In the Japanese lines, the survival rate was affected by the Wolbachia infection (χ 2 =14.18, d.f.=2, P<0.001), the host genetic background (χ 2 =10.54, d.f.=2, P=0.005) and we detected a significant interaction between these two factors (χ 2 =8.41, d.f.=1, P=0.004). By comparison with the uninfected lines, the wSuz infection significantly increased the survival of the Fr-BE and the Jp-YSG backgrounds (Tukey HSD, P=0.012 and P<0.001 respectively) while it did not affect the survival of the Fr-CP and the Jp-OGH backgrounds (CP line, P=0.191; OGH line, P=0.849) (Fig. 2A).

As for DCV, we also measured FHV titers and we found a significant effect of both the Wolbachia infection status (Two-way ANOVA, F=5.04, d.f.=1, P=0.03) and the host genetic background (Two-way ANOVA, F=98.88, d.f.=1 P<0.001) on the RNA copy number (Fig. 2B), with a significant interaction between these two factors (Two-way ANOVA, F=11.54, d.f.=1, P<0.001). As for the survival data analysis, we tested the influence of the presence of Wolbachia and the host genetic background for the French and the Japanese lines separately. For the French lines the RNA copy number was affected by Wolbachia infection (Two-way ANOVA, F=4.32, d.f.=1, P=0.045), the host genetic background (Two-way ANOVA, F=189.82, d.f.=1, P<0.001) with a significant interaction between these two factors (Two-way ANOVA, F=21.01 , d.f.=1, P<0.001). For the Japanese lines, we also found a significant interaction between the Wolbachia infection and the host genetic background (Two-way ANOVA, F=13.18, d.f.=1 P<0.001), a significant effect of the host genetic background (Two-way ANOVA, F=88.80 , d.f.=1, P<0.001) but we did not detect a significant effect of the Wolbachia infection (Two-way ANOVA, F=1.05 , d.f.=1, P=0.311). More precisely, in the presence of wSuz, the RNA copy number significantly decreased (around 50% of reduction; Fig. 2B) in the Fr-BE and Jp-YSG backgrounds infected with wSuz-Fr and wSuz-Jp isolates respectively (Tukey HSD, P<0.001 and P=0.039 respectively), the two lines that exhibited a significant effect of Wolbachia on survival after FHV infection, and not in the two other lines (Tukey HSD test, Fr-CP line, P=0.665; Jp-OGH line, P=0.478).

Wolbachia density

Wolbachia density is known to be a major determinant of antiviral protection, with higher densities being associated to higher levels of protection [START_REF] Chrostek | High antiviral protection without immune upregulation after interspecies Wolbachia transfer[END_REF][START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF]. We therefore measured wSuz density in the four lines and found significant differences (One-way ANOVA, F=10.07, d.f.=3, P<0.001; Fig. 3): the two Japanese's backgrounds (Jp-OGH and Jp-YSG) showed a higher density than the two French backgrounds (Fr-CP and Fr-BE), but there was no significant differences between the two French lines (both infected by wSuz-Fr; Tukey HSD, P=0.991) and between the two Japanese lines (that both harbor the Japan Wolbachia isolate ; Tukey HSD, P=0.062).

Discussion

We have found that wSuz can protect its host against RNA viruses. In certain lines individuals infected with wSuz had higher survival and lower viral titers after infection with DCV and FHV. It is known since 2008 that Wolbachia can protect Drosophila against RNA viruses [START_REF] Hedges | Wolbachia and virus protection in insects[END_REF][START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF], but this is the first time that it is described in D.

suzukii. In a recent study another direct fitness benefit of Wolbachia has been observed in an Italian population of D. suzukii since infected females have a higher fecundity than uninfected ones [START_REF] Mazzetto | Wolbachia infection affects female fecundity in Drosophila suzukii[END_REF]. These phenotypes can potentially explain the maintenance of Wolbachia strains in natural populations without reproductive manipulation [START_REF] Fenton | Solving the Wolbachia paradox: modeling the tripartite interaction between host, Wolbachia, and a natural enemy[END_REF], as it has been found in American and European populations of D. suzukii [START_REF] Hamm | Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella[END_REF][START_REF] Cattel | Wolbachia in european populations of the invasive pest Drosophila suzukii: regional variation in infection frequencies[END_REF].

The variability of the wSuz prevalence could be the consequence of heterogeneity in virus-induced selection similarly to what was observed in the Pea Aphid Acyrthosiphon pisum. This species is protected against parasitoids by the symbiont Hamiltonella defensa, which has variable prevalence among populations and is thought to be maintained by negative-frequency dependent selection depending on the parasitism pressure in the field [START_REF] Oliver | Population dynamics of defensive symbionts in aphids[END_REF]. We found that Wolbachia mediated significant protection in D. suzukii (Fr-CP for DCV, Fr-BE and Jp-YSG for FHV) was associated with reduced viral titer.

However, for DCV, the presence of Wolbachia correlates with a lower viral titer even when no effect on the flies' survival was detected (Jp-OGH line). Several studies showed that antiviral protection is generally explained by a phenomenon of resistance that reduces the accumulation of virus but, in some cases, no differences in viral titers were observed despite the protective effect [START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF][START_REF] Osborne | Variation in antiviral protection mediated by different Wolbachia strains in Drosophila simulans[END_REF]. In the latter case, it is possible that Wolbachia does not affect the replication of the virus but rather makes the host more tolerant to viral infection.

Experimental studies have shown that Wolbachia-mediated antiviral protection is a common phenomenon in Drosophila and mosquitoes [START_REF] Bian | The endosymbiotic bacterium Wolbachia induces resistance to dengue virus in Aedes aegypti[END_REF][START_REF] Hedges | Wolbachia and virus protection in insects[END_REF][START_REF] Moreira | A Wolbachia symbiont in Aedes aegypti limits infection with Dengue, Chikungunya, and Plasmodium[END_REF][START_REF] Osborne | Variation in antiviral protection mediated by different Wolbachia strains in Drosophila simulans[END_REF][START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF][START_REF] Chrostek | Wolbachia variants induce differential protection to viruses in Drosophila melanogaster: a phenotypic and phylogenomic analysis[END_REF][START_REF] Chrostek | High antiviral protection without immune upregulation after interspecies Wolbachia transfer[END_REF][START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF] but is strongly dependent on the Wolbachia strain [START_REF] Hedges | Wolbachia and virus protection in insects[END_REF][START_REF] Osborne | Variation in antiviral protection mediated by different Wolbachia strains in Drosophila simulans[END_REF][START_REF] Chrostek | Wolbachia variants induce differential protection to viruses in Drosophila melanogaster: a phenotypic and phylogenomic analysis[END_REF][START_REF] Chrostek | High antiviral protection without immune upregulation after interspecies Wolbachia transfer[END_REF][START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF]. For instance, [START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF] showed that among 19 Wolbachia strains (originating from 16 Drosophila species) transferred into the same D. simulans genotype, only half of them induced protection against DCV and FHV. The effect of host genetics on protection is less well understood. However, the protective phenotype is affected by the host species. For example, the strain wInn protects its natural host D. innubila against FHV [START_REF] Unckless | Maintenance of a male-killing Wolbachia in Drosophila innubila by male-killing dependent and male-killing independent mechanisms[END_REF] but has no effect in D. simulans [START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF].

Here, we found that the level of antiviral protection varied among the lines we used. This difference was most dramatic in the DCV experiment, where we found large increases in the survival of the French line but not the Japanese line. This difference could be caused by genetic differences between the Wolbachia isolates, the flies or both. In the FHV experiment we were able to compare the same Wolbachia isolates in two host genetic backgrounds. We found a host background effect for both the Japanese and the French lines suggesting that host factors may affect the expression of the Wolbachia-mediated protection. However, we would caution that this needs further confirmation as we only have a single replicate line of each Wolbachia isolate in each genetic background, so we cannot rule out other possible differences (e.g. gut microbiota, or uncontrolled differences in the genetic background).

Wolbachia density is known to influence the level of protection [START_REF] Osborne | Variation in antiviral protection mediated by different Wolbachia strains in Drosophila simulans[END_REF][START_REF] Osborne | Antiviral protection and the importance of Wolbachia density and tissue tropism in Drosophila simulans[END_REF][START_REF] Chrostek | Wolbachia variants induce differential protection to viruses in Drosophila melanogaster: a phenotypic and phylogenomic analysis[END_REF][START_REF] Chrostek | High antiviral protection without immune upregulation after interspecies Wolbachia transfer[END_REF][START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF].

However, we didn't find any clear association between the level of protection and the density of Wolbachia. The variation in antiviral protection could also be influenced by tissue tropism of Wolbachia since [START_REF] Osborne | Antiviral protection and the importance of Wolbachia density and tissue tropism in Drosophila simulans[END_REF] highlighted that tissue tropism can partly explain variations in the level of protection. Therefore it is possible that, in the D. suzukii lines used in our study, the tissue tropism of Wolbachia was different despite showing very similar density at the whole fly level.

The importance of antiviral protection in natural populations of D. suzukii is unknown. It has been estimated that Wolbachia would need to generate a fitness benefit of 20% to be maintained in populations [START_REF] Hamm | Wolbachia do not live by reproductive manipulation alone: infection polymorphism in Drosophila suzukii and D. subpulchrella[END_REF]. To achieve this RNA viruses would need to be causing significant harm to the flies in nature and Wolbachia would need to be mitigating much of this harm. The effects of the presence of Wolbachia on viral titer and survival that we observed were mostly smaller than in many previous studies [START_REF] Hedges | Wolbachia and virus protection in insects[END_REF][START_REF] Teixeira | The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster[END_REF][START_REF] Chrostek | Wolbachia variants induce differential protection to viruses in Drosophila melanogaster: a phenotypic and phylogenomic analysis[END_REF][START_REF] Chrostek | High antiviral protection without immune upregulation after interspecies Wolbachia transfer[END_REF][START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF]. However, it is not possible to extrapolate this to effects in nature without further work.

Experimental procedures

D. suzukii lines and rearing

In this study, four lines of D. suzukii were used, two originating from France and two from Japan. The French lines were collected in Compiegne (named Fr-CP) and in Bellegarde (named Fr-BE) in 2011 and 2012 respectively and reared in large populations. The Japanese lines have been obtained from the Ehime-fly stock center in 2011: they were sampled in Yamagata (named Jp-YSG) (l#E-15016 YSG-11) and Tokyo (named Jp-OGH) (#E-15014OGH06-03) in 2006. These lines have been chosen because two are free of Wolbachia (Fr-BE and Jp-OGH) and the two others (Fr-CP and Jp-YSG) are 100% infected with Wolbachia (see below for diagnostic PCR test). The flies were reared on a cornmeal diet (agar: 1%, dextrose: 8.75%, maize: 8.75%, yeast: 2%, nipagin: 3%) and maintained in an incubator at constant temperature (22°C) and humidity (70%) with a 12-hours light/dark cycle. An MLST analysis performed on 6 genes (ftsZ, fbpA, hcpA, coxA, gatB and wsp) revealed the Wolbachia isolates from Fr-CP and Jp-YSG lines to be the same sequence type with 100% identity between the sequences. The sequences obtained in the present study are recorded in Genbank as KS308222-7.

Control of host genetic background and infection status

We used two different methods to obtain Wolbachia-infected and Wolbachia-free lines with similar genetic backgrounds: antibiotic treatments of the infected lines and introgression of Wolbachia into uninfected lines by back-crossing.

Antibiotic treatments were performed for 3 generations in Fr-CP and Jp-YSG lines.

At each generation larvae were fed on medium with 0.25 mg.mL -1 tetracycline. After 3 generations, 10 isofemale lines were established from treated females and the presence of assay, one viral aliquot was defrosted just before the infection and diluted in Ringer's solution [START_REF] Sullivan | Drosophila protocols[END_REF] to reach a viral concentration of 5x10 8 .mL -1 TCID50 for DCV and 3.6x10 10 .mL -1 TCID50 for FHV.

Survival assay

In order to test for a potential protective effect of wSuz, we measured the survival of flies after infection with DCV, FHV or mock infection with Ringer's solution. To infect flies, a 0.1 mm diameter anodized steel needle (26002-15, Fine Science Tools, CA, USA) was bent, 0.25 mm from the end, dipped in viral solution and the bent part of the needle pricked into the pleural suture on the thorax of flies [START_REF] Longdon | Previous exposure to an RNA virus does not protect against subsequent infection in Drosophila melanogaster[END_REF]. For DCV, we followed the survival of Wolbachia-free or Wolbachia-infected flies of the Fr-CP and Jp-OGH lines only.

Since, in that first experiment, we observed variation depending on the geographical origin of the flies, we performed the second experiment with FHV using the four genetic backgrounds (Fr-CP, Fr-BE, Jp-OGH and Jp-YSG). Survival of Ringer's controls was followed in parallel for these two experiments.

For each line 3 days-old females were collected. After being anaesthetized with CO 2 , they were inoculated with DCV, FHV or Ringer's solution by stabbing flies. Groups of 20 stabbed flies were immediately placed into a vial of fly cornmeal medium and stored at 22°C. Flies were transferred into fresh vials of food every 3 days and the number of dead flies was recorded every day. The survival assay was replicated 5 times on independent cohorts of flies across multiple days, corresponding to a total of 100 flies for each Wolbachia infection status and virus infection treatment.

Diagnostic polymerase chain reaction (PCR)

The Wolbachia infection status of individuals was verified by PCR for each line just before performing the experiments. DNA was extracted on pools of 10 individuals (one pool per line) homogenized in 200µL of 5% w/v Chelex resin in water (Biorad) with 4µL of proteinase K (20mg.mL -1 ) and kept at 56°C for 3h. After 15min at 95°C, samples were centrifuged at 16000g for 4min and stored at -20°C. Presence of Wolbachia was checked by amplifying the Wolbachia Surface Protein (wsp) gene using the primers wsp81F and wsp691R (Braig et al., 1998, Table S1). PCR reactions were performed in 25μL volumes containing 100μM dNTP, 200nM primers, 0.5IU DreamTaq® DNA polymerase (Eurobio) and 1μL of DNA template.

Cycling conditions were 94°C (2min), 94°C (30sec), 52°C (30sec), 72°C (45sec), 72°C (10min) for 35 cycles. PCR products were visualized in 1% agarose gels.

Real-time quantitative PCR (qPCR)

The Wolbachia density, DCV and FHV RNA copy number were measured by real-time quantitative PCR (qPCR) on the Light Cycler TM system using primers listed in Table S1. To estimate Wolbachia density, 10 pools of ten 3 days-old virus-free females for each line were prepared and the DNA extracted using the Gentra Pure gene Tissue Kit (Qiagen). The Wolbachia density was measured by quantifying the copy number of the Wolbachia gene ftsZ relative to the host gene Rpl32 using Sso Advanced Universal Probes Supermix (BioRad; 2min at 95°C followed by 40 cycles of 10sec at 95°C and 20sec at 60°C). The 10μL of multiplex reaction mix contained 400nM of Rpl32 primers and 200nM of ftsZ primers, 5μL of SsoADVUniver Probes Supermix, 200nM of each probe and 2μL of DNA sample. The Wolbachia density was estimated by dividing the copy number of the ftsZ gene by the copy number of the Rpl32 host gene. The antiviral protection was also examined by measuring the infection and the genetic background on survival for the control treatment (Ringer) without virus or after infection with a virus. The first model allowed testing whether wSuz infection modifies survival independently of viral infection and indirectly confirm that the survival of virus-infected flies cannot be explained by an inherent effect of Wolbachia on survival. The effects of Wolbachia, host genetic background and their interaction were considered as fixed effects and the replicate vials as a random effect. When a significant interaction was detected, differences between Wolbachia-free and Wolbachia-infected flies within each host genetic background were analyzed using pairwise comparisons (Tukey's Honest Significance test) (R package multcomp).

Viral titers and Wolbachia density were analyzed on log2-transformed data. For viral titers, a two-way ANOVA allowed testing for the effect of Wolbachia, the host genetic background and their interaction. A one-way ANOVA was done to test for the influence of the host genetic background on Wolbachia density. Pairwise comparisons (Tukey's Honest Significance test) were also done if a global effect of Wolbachia was detected.

Acknowledgements

This work was funded by CNRS (IFR41-UMR5558) and supported by ONEMA (APR Biodiversité-Ecophyto). J. Cattel is the recipient of a PhD studentship from the Rhône-Alpes region ("ARC Program" Grant).

Wolbachia was checked by PCR as described below in mothers and then for 3 generations more. Only one isofemale line was retained for each nuclear background (Fr-CP and Jp-YSG) and maintained for 12 generations before the experiments. The absence of Wolbachia in these lines was confirmed by real-time quantitative PCR (see below). Using this approach, we obtained infected and cured lines with the same genetic background, Fr-CP or Jp-YSG.

To obtain infected and uninfected individuals with the same Fr-BE or Jp-OGH genetic backgrounds, back-crosses were done for 8 generations. Two males from the uninfected line (Fr-BE or Jp-OGH) were mated with single virgin females from the infected lines from the same country, i.e. Fr-CP and Jp-YSG respectively. Backcrossing was performed for a total of 8 generations which lead to an introgression of around 99.6% of the nuclear background assuming no selection on the nuclear genome. However, compared with the use of antibiotics treatments, lines obtained with this method have different mitochondrial backgrounds. These two lines were maintained for 15 generations before the experiments. The Wolbachia infection status of each line was verified by PCR just before the viral infection experiment.

Viral isolates

Two viruses, Drosophila C virus (DCV) and Flock House virus (FHV), were used in this study. DCV is a highly pathogenic Drosophila virus, which belongs to the family Dicistroviridae [START_REF] Huszar | Drosophila viruses and the study of antiviral host-defense[END_REF]; FHV, which belongs to the Nodaviridae family, is not a natural pathogen of Drosophila species and was initially isolated from a beetle [START_REF] Scotti | Flock House Virus: a nodavirus isolated from Costelytra zealandica (White) (Coloeoptera: Scarabaeida)[END_REF]. Viruses were produced and titrated as described by [START_REF] Martinez | Symbionts commonly provide broad spectrum resistance to viruses in insects: a comparative analysis of Wolbachia strains[END_REF]. DCV was produced and titrated in Schneider's Line 2 cells (SL-2) and FHV was titrated in Schneider Drosophila Line 2 cells (DL2) (https://dgrc.bio.indiana.edu/cells/Catalog). For each infection RNA copy number after infection by both viruses. 3 days-old females were stabbed with DCV and FHV and frozen respectively 5 and 2 days after infection. After homogenization in TRIzol Reagent (Ambion), RNA was extracted from 10 pools of 10 flies for each experimental treatment using the RNA Easy Mini® kit following the manufacturer's instructions (Qiagen). Reverse-transcription was done using SuperScript® III First-Strand Synthesis System (Invitrogen) including a 30 min DNase digestion step at 37°C. The copy number of the viral RNA was compared to the control gene Rpl32. The qPCR reactions for DCV, FHV and Rpl32 were done separately with the same conditions (30sec at 95°C followed by 40 cycles of 10sec at 95°C and 20sec at 60°C). The 10μL reaction mix contained 200nM of each primer, 5μL of SsoADV Univer SYBR Green Supermix, and 1μL of DNA sample. The RNA copy number and the Wolbachia density were estimated by calculating the ratio:

with Ct=Ct flygene -Ct virus/Wolbachia where E corresponds to the efficiency of the PCR reaction calculated from a dilution series for each set of primers and Ct to the cycle threshold [START_REF] Pfaffl | A new mathematical model for relative quantification in real-time RT-PCR[END_REF].

Statistical analysis

Survival data were analyzed with a Cox's proportional hazards mixed-effect model using the coxme package in R (R Core team, 2013). The Cox's model estimates hazard ratios with the probability of a Wolbachia-infected fly dying at a given time-point divided by the probability of a Wolbachia-free fly dying. Flies that were alive at the end of the experiment were treated as censored data.

Survival data for DCV, FHV and their respective controls (Ringer) were analyzed separately. For each virus, two models were fitted to test a potential effect of the Wolbachia


Mark C A York
email: mark.york@usherbrooke.ca

Antoine Mailhot

Abderraouf Boucherif

Richard Arès

Vincent Aimez

Simon Fafard
email: simon.fafard@usherbrooke.ca

Monochromatic conversion efficiencies in excess of 60% have been achieved with Vertical Epitaxial HeteroStructure Architechture laser power converters (with anywhere from 5 to 20+ n/p junctions stacked vertically). We are presently investigating the applicability of this design to solar cells, whereby the individual junctions of a multi-junction cell are replaced with a current matched stack of subcells. If viable, such a design offers the potential for efficiency gains via reduced I R 2 losses and elevated V oc . Moreover, splitting the short- circuit current over additional junctions opens up the possibility of operation under concentration ratios otherwise considered impractical for conventional cells.

Introduction

III-V photovoltaic cells are fundamental to both laser power converters (LPCs) and concentrated photovoltaics (CPVs), and in turn, both of these technologies stand to benefit from the ability to produce higher efficiency cells. There is a growing interest in LPCs, as these can be useful to any system which requires galvanic shielding, e.g. sensory equipment [START_REF] Worms | Lightning-safe monitoring of wind turbine rotor blades using optically powered sensors[END_REF][START_REF] De Nazare | [END_REF], medical implants [3,4], telecommunications [5], etc. High conversion efficiencies for GaAs LPCs have been reported in the literature . However, the Vertical Epitaxial HeteroStructure Architechture (VEHSA) technology [30][31][32][33][START_REF] York | Enhanced photocarrier extraction mechanisms in ultra-thin photovoltaic gaas n/p junctions[END_REF][35][START_REF] Fafard | Advances with vertical epitaxial heterostructure architecture (vehsa) phototransducers for optical to electrical power conversion efficiencies exceeding 50 percent[END_REF][START_REF] Fafard | Ultra-efficient n-junction photovoltaic cells with voc > 14v at high optical input powers Photovoltaic Specialists Conference[END_REF][38] has presented a major breakthrough in the field, with reported conversion efficiencies just under 70% (c.f. a previous reporting of 53.4% in Ref. [START_REF] Bett | III-V solar cells under monochromatic illumination Photovoltaic Specialists Conference[END_REF] in 2008), exceeding the approximately 65% limit stipulated in Ref. [START_REF] Bett | III-V solar cells under monochromatic illumination Photovoltaic Specialists Conference[END_REF] for these kinds of cells.

A common goal within the CPV community is the manufacture of a solar cell with a conversion efficiency exceeding 50% [39,40], seen by many as the next major milestone. Research has focused on dilute nitrides [START_REF] Wiemer | 43.5% efficient lattice matched solar cells[END_REF], increasing the number of junctions via wafer bonding [START_REF] Chiu | [END_REF], perovskites [43] as well as alternative strategies oriented towards module design [44]. We would like to bridge the gap between research in LPCs and CPVs by proposing that we apply the very technology that makes VEHSA devices so efficient to CPV cells themselves, namely, stacked thin junctions. The working principle here is that splitting the photocurrent over many junctions reduces I R 2 losses and loads on the tunnel junction, allowing for the possibility of operation under high solar concentration (with the goal being in excess of 1000 suns [45]). There is an added benefit of using a vertical arrangement of thin junctions since thin layers achieve a greater Fermi level splitting [46], which on a per-junction level offers a marginal boost in V oc when compared to a planar arrangement of bulk cells (potentially 92 mV per junction [38]).

The outline of this text is as follows: we will begin with an overview of VEHSA LPC devices (those used for power-over-fibre applications). Section 3 contains a presentation of how the VEHSA design would be applied to solar cells, focusing on an "enhanced" tandem cell as a specific case. Sections 4 and 5 close with a discussion and our conclusions.

Overview of VEHSA monochromatic cells

A schematic representation of a typical VEHSA device is shown in Fig. 1 (not to scale, and omitting certain window / buffer layers). These devices consist of alternating stacked GaAs n/p (n-on-p) junctions separated by AlGaAs tunnel junctions and GaInP buffer / window layers. Illumination is via a monochromatic source within the range of wavelengths where the GaAs junctions are opaque while all other layers (generally AlGaAs and GaInP) are transparent (in effect, the upper frequency limit is set by the band gap of the AlGaAs tunnel junctions, for an allowable range of approximately 750 nm-875 nm, depending on the Al molar fraction). Since the topmost window layer is transparent to the source wavelength, we are able to employ a characteristically larger window than would be otherwise typical of multi-junction solar cells. Gridline density is assumed to be sufficient to allow for efficient carrier extraction even at high source intensities, with minimal shadowing.

VEHSA LPCs are grown via MOCVD with an Aixtron 2600 multiwafer reactor. AlGaAs n++/p++ tunnel junctions are employed with Al fraction in the range 10%-30% and dopant densities exceeding -1E19 cm 3 . GaAs junctions are typically doped over the range 3 , with thinner junctions doped more heavily. Prior to a growth, the thicknesses of each junction are determined by initially targeting a specific wavelength (and hence uniform value of the absorption coefficient α in GaAs) and setting the layers such that each junction produces an equal amount of photocurrent. For a typical design wavelength of 850 nm, total GaAs thickness may reach 3.6 µm when summed over all junctions (so that the sum of the junctions is nearly fully absorbent). Due to variations in growth, the wavelength at which peak conversion efficiency is observed can generally deviate slightly from design, of the order 10nm.

- 5E17 cm 3 - - 1.5E18 cm
Actual devices are known experimentally to achieve a very high degree of current matching, supplemented by photon-recycling [35] which has made it possible to consistently observe efficiencies of 60-70% for a range of devices and experimental conditions, as captured by the IV ( ) curves in Fig. 2. Broadcom (www.broadcom.com) now offers such devices commercially, with products for various applications. With regards to the labeling PTN , N represents the number of junctions, i.e. PT20 contains 20 stacked junctions. Devices with over 20 junctions have also been fabricated.

Though the text focuses on solar, it is worth mentioning that we are also actively seeking to develop phototransducers with ⪢ N 20 (e.g. PT60), discussed in Ref. [38]. A tentative PT100 device would contain individual subcells as thin as 10nm (noting that this value is sensitive to the wavelength chosen, and in turn should be treated as an estimate) considered to be pushing the limits of viability, though such a device is interesting in its own right due to individual junctions effectively becoming quantum wells. When individual subcells reach this size, we are additionally able to consider altering their molar composition and strain, opening up the possibility of even further enhancements of V oc , as well as fine tuning of the absorption per subcell.

Models

PTN devices are simulated using Atlas, employing standard values for carrier mobilities in GaAs and GaInP, radiative recombination rates of the order ∼ - 10 cm /s 10 3

and SRH lifetimes of the order 10nsfor both species at -1E18 cm 3 doping (lifetimes are adjusting for doping). Parameters are tabulated in detail in Ref. [38], and these are generally consistent with other authors. Carrier lifetimes are sensitive to the quality of the crystal growth, and values obtained from the literature will not necessarily be well matched to a specific device, requiring some degree of calibration of the actual models.

In our case, all of our wafers have been grown using the same equipment, and therefore, we expect little variation of crystal quality between growths. Our models have been calibrated and exhibit very close agreement with the PV characteristics of single junction cells. The same set-up when used to model a PT12 device shows agreement with experiment at the level depicted in Fig. 3, which is still arguably a very close fit considering the random variation in layer thicknesses etc.

VEHSA solar cells

Using a tandem or triple junction cell as a starting point, two possible enhancements are shown in Figs. 4 and5.I nFig. 4 what we have done is taken a standard GaInP / GaAs tandem cell, and "duplicated" each individual junction [START_REF] Boucherif | P1467US0 Duplic[END_REF]. Layers are not drawn to scale, but relative variations in thickness are illustrated, with current matching enforcing a specific ratio between upper and lower subcell thicknesses. Whereas the cell on the left of Fig. 4 comprises two subcells, the cell on the right comprises two substacks -we refer to cell on the right (and similar) as a VEHSA solar cell (noting the distinction from the VEHSA phototransducers in Section 2). A substack need not contain only 2 subcells; rather, as with the VEHSA phototransducers, the number of subcells is arbitrary, provided that subcells and substacks are current matched.

Due to the relative difference between the GaInP -GaAs bandgaps, a VEHSA tandem is current matched when (roughly) both substacks are quasi-fully-absorbing (for frequencies above each bandgap). For an actual device with 2-junction substacks 4 n/p junctions total), this would necessitate a topmost GaInP junction thickness ≲ 100 nm (see Table A1).

Fig. 5 depicts an alternative configuration involving a Ge VEHSA substack in lieu of the usual monolithic Ge substrate (other junctions are merely shown as duplicated) for an initially triple junction cell (with the Ge as such to permit excess current recovery and better overall current matching [START_REF] Aiken | Ingap/gaas/ge multi-junction solar cell efficiency improvements using epitaxial germanium Photovoltaic Specialists Conference[END_REF]). The Ge substack as shown is somewhat speculative, as the relative thickness of these layers (compared to the III-Vs) would present challenges for growth (however, see Ref. [START_REF] Bosi | [END_REF]). Also, SiGe alloys [51] can be of interest, in particular for the tunnel junctions of the lower substack.

For clarity, it should be stated that this approach is not a means to achieve revolutionary efficiency with a small number of bandgaps. Specifically, a VEHSA solar cell with a large number of junctions is not equivalent to a hypothetical multi-junction cell containing a large number of distinct bandgaps, and hence, the design presented does not approach the Shockley-Queisser with an increasing number of (single alloy) junctions. However, the VEHSA solar cell design does offer the possibility of modest increases in efficiency due to a reduction in resistive losses, as well as the potential for applications under extreme concentrations.

Models

Models of these devices are used primarily to assess the impact of layer thicknesses on current matching, as well as gauging the relative performance gains for VEHSA enhanced cells. Prior simulations of 2 and 4 junction monochromatic cells have been adapted to the schematic in Fig. 4, noting that in lieu of a monochromatic source, we employ an AM1.5 spectrum at concentrations 1 -1000 suns. 1 Aside from differences in the alloy compositions of each layer, VEHSA solar devices also possess a significantly thinner topmost window layer when compared to PTN s. For simplicity, we assume that all window and back surface field (BSF) layers are AlInP, which reduces the number of model parameters at the expense of deviating from an actual device which would more suitably employ AlGaInP quaternaries. For the purpose of assessing trends in performance, this approximation is justifiedhowever, any model used to infer layer thicknesses necessary for current matching necessarily requires that actual values for the refractive index of each layer be used (discussed further in the next section).

Current matching

As a starting point, for a given heterostructure and source spectrum (in our case AM1.5 G), short-circuit current is calculated using the Beer-Lambert law,

= - Tλ e () i αλt () ii ( 1
)
where Tλ () i is the transmittance through layer i, α λ ()

i
is the wavelength and material dependent absorption coefficient (which we have obtained from Cyrium Technologies data sets), and t i is the thickness of layer i. Integrating over the spectrum, the optimal set of junction thicknesses are obtained by adjusting the t i such that each junction produce the same amount of photocurrent (solved for e.g. using a Matlab based algorithm). We initially assume no loss from the AR coating.

Following this, quantum efficiency (QE) and the reflectance are taken into account by adjusting the absorbed photocurrent in each layer as follows:

∫ =- - I dI dλ λT λ R λ d λ • Q E () • ( 1 () () )
abs avail [START_REF] De Nazare | [END_REF] where I abs and I avail are absorbed and available photocurrent respec- tively, suppressing the index i denoting the layer. The reflectance R is obtained from Fresnel equations, and transmittance T is as above. λ QE( ) is estimated from Ref. [52]. The advantage of this method is that non-radiative (SRH and Auger) recombination processes are represented by the albeit ad hoc QE term. However, these can be validated self-consistently following growth. One limitation is that Eq. ( 2) omits photon recycling from emitted photons which are reabsorbed in neighboring junctions. 4. A schematic of a 2 junction tandem on the left, augmented by doubling the number of junctions (while holding the total GaInP / GaAs thickness approximately fixed). For the GaInP region on the left, we refer to the corresponding 2 junction GaInP region on the right as a substack, likewise for GaAs. Dashed lines represent all of the layers that would otherwise be required between each cell, specifically back surface field, tunnel junction, and window layers. The optimal set of layer thicknesses for a VEHSA tandem resulting from this procedure are stated in Table A1 (which includes losses from an AR coating). Note that in constructing this table, not all layers are allowed to vary: windows, BSF and tunnel junctions are fixed in advance (which we have set at 80 nm), and only the thicknesses of the actual n/p junctions are varied. Due to the thinness of the topmost subcell, current from the window and BSF layers are including in the "total" attributed to that junction [52]. This is done for other subcells as well; however, in these cases, the contributions not arising from the actual n/p junction layers are much smaller. Tunnel junction absorption is simulated as current loss.

To assess the impact of the QE and reflectance corrections in Eq. ( 2), Tables A2 to A5 compare between a simplified model of the standard and VEHSA tandem cell. Specifically, we assume no absorption from the buffer or window layers, and hence omit these entirely. For these abridged heterostructures we have calculated J sc and optimal layer thicknesses with and without the QE adjustment in Eq. ( 2): factoring in the QE represents about a 14% loss of J sc , and a 26 nm adjustment to the thickness of the topmost subcell.

Lastly, the absorption spectra of both the standard and VEHSA tandems are shown in Figs. 6 and7 for reference.

Discussion

Our benchmarks and model / experimental results for VEHSA devices have all been previously reported under monochromatic illumination, for which PV efficiencies are well beyond those presently attainable for multi-junction PV devices. The main reasons for this are as follows:

(i) under these conditions, thermalization losses can be minimal, since the target wavelength can be set adjacent to the band edge, (ii) photon recycling compensates for variations in layer thicknesses (due to growth) and source detuning, which serves to redistribute photo-current between junctions.

In switching to an AM1.5 source, we would be faced with thermalization losses on par with multi-junction cells. However, we believe that the potential for enhancement due to photon recycling persists in the VEHSA solar cells, noting that:

(i) not all junctions will necessarily possess the same band-gap, therefore this opens up the possibility of additional losses from reemitted photons which are unable to excite photocurrent in the higher gap layers, in particular the thinnest topmost layers, (ii) as such, an underperforming GaInP junction would not be compensated for by a neighboring GaAs junction, though the converse is true.

Layer thicknesses stated in Appendix A are estimated by either assuming ideal conditions (no reflections, no recombinations) or by assuming a quantum efficiency <100% for each layer, as well as internal reflections, etc. as per the previous section. An idealized model (the former) is of interest, as it is a best case scenario, effectively an upper bound on performance. However, a realistic model (the latter) is essential to correctly specify the layer thicknesses for a growth, which unfortunately requires ad hoc input. In Section 3.2, the parameters inferred from the study in Ref. [52] are an educated guess, as the QE will in general vary between layers, depending on factors related to growth as well as doping, and can only be known precisely following growth. This raises the possibility of reduced performance from detuning: grown devices exhibiting current mismatch. Nominal layer thicknesses are computed using a nominal QEif in fact the realized QE differs from the nominal value, then the resulting heterostructure will no longer be optimal per se. And, if in fact the performance depends strongly on the realized QE, this would necessitate an impractical finetuning of junction thicknesses.

To assess the degree of fine tuning required, we have simulated the performance of a VEHSA tandem while varying the thicknesses of individual junctions (while holding other layers fixed), for which there are two extreme outcomes: a) efficiency deteriorates rapidly with variation in layer thickness or b) efficiency is insensitive to variations in layer thickness. From inspecting Fig. 8, what we observer is that the modeled VEHSA tandem more closely falls into regime b) rather than a). Foremost, the plateau in the upper panel suggests that there is a lot of free-play in the (thinnest) topmost cell thickness, provided that it is not so thin as to reduce the fill factor. In particular, the width of the plateau exceeds the 26 nm difference in topmost subcell thickness when computed using lossless and lossy models of the heterostructure. In the lower panel, the peak is more pronounced, however, the dependence of efficiency on junction thickness is still fairly weak, given that a window of 1% variation in efficiency spans a thickness variation of approxi- mately 70 nm, well over 10% of the junction width. Therefore, it is ap- parent that these devices are in fact tolerant of detuning, much like what has been observed for the monochromatic PTN s.

Concerning the reproducibility of the growth process, in practice the energy gap for any binary alloys (e.g. GaAs) is very close to nominal, for example within a few meV. For the ternary InGaP, the main deviation is typically from the ordering present in this alloy. These devices are implemented on commercial reactors with demonstrated calibration and uniformities. The ordering and the alloy calibrations are controlled by the growth processes, and parameters such as growth temperature, III-V over-pressure, gas flux calibrations, etc. The resulting reproducible accuracy for the InGaP alloys is typically of the order of 10meV.

Alloy variations in the window/back surface field/tunnel junction alloys have little impact because these layers are relatively thin and mostly transparent (higher bandgaps), but nevertheless can be controlled to a similar level of precision as InGaP. The layer thickness variations with state-of-the-art MOCVD reactors are typically less than 5% over the useful wafer area. The ability to achieve the nominal thickness values depends on the quality of the calibration procedure, but reproducibility at the level of 5% or better is achievable. It should also be noted that in epitaxy the most common deviation from the nominal thickness is a systematic error in the growth rate calibration, which would result in all layers being a few % thicker or thinner than expected. Finally, deviations from nominal doping concentration in the range of 20% typically have every little impact on the overall performance of the devices, and are within the range of reproducibility of standard MOCVD operations.

The most pressing question is how much of an efficiency upgrade could the VEHSA solar methodology actually afford? A heuristic estimate would be a potential maximum increase of 3 -4%, assuming a V oc scaling on par with the observed ∼ 92 mV per junction for PT6 devices when compared with an equivalent 6 cell planar configuration [38]. This would require multiple splittings per subcell. In simulating the VEHSA tandem, the model indicates an increase of approximately 1% under 1000 sun conditions (a jump from 36.5% to 37.6% for the modeled cell). In addition, as mentioned above, the resulting cell operation at lower currents and higher voltages can allow performance gains for solar CPV working at higher concentrations (for instance, higher V oc cells would be used in strings containing fewer cells, there- fore reducing the losses in performance from current matching within a string, and reduced current would result in less heating of a cell through resistive losses in its window layer.)

Summary and conclusions

We have presented an overview of a preliminary analysis of the practicality of applying the VEHSA design to concentrated photovoltaic cells, including the detailed layer thicknesses and composition of a tentative VEHSA tandem cell. The impact of detuning and layer thickness errors on performance has been investigated using simulated devices, and we have observed that these devices show relatively mild sensitivity to the individual layer thicknesses of each subcell, which bodes well for the viability of this technology.

The advantage of this approach is that VEHSA solar cells possess increased V oc and reduced J sc , in turn able to operate at concentrations otherwise considered high or extreme for standard cells. Heuristic estimates based on the observed performance of VEHSA phototransducers, as well as the enhanced Fermi level splitting in thin junctions suggest the possibility of efficiency gains of the order several per cent when comparing between VEHSA and stand multi-junction solar cells. Moreover, these estimates are consistent with the modeled performance of a simulated VEHSA tandem cell, for which an efficiency of 1.1% above that of the simulated standard GaInP / GaAs tandem was determined.

Table A3

Same structure as Table A2, except with J sc calculated under realistic conditions including recombination and reflectance.

Fig. 1 .

 1 Fig. 1. A schematic of a typical VEHSA LPC (shown above for a 20 junction device). GaAs n/p junctions are labeled s1 through s20, and tunnel junctions are c1 through c19. The topmost n-type emitter is explicitly shown, though omitted for the other subcells. Reproduced from Refs. [47,38].

Fig. 2 .Fig. 3 .

 23 Fig. 2. IV () curves for = N 5 up to 20 junction devices, with an illuminated cell shown in the lower right corner. Reproduced from Refs. [32,38].

Fig.

  Fig.4. A schematic of a 2 junction tandem on the left, augmented by doubling the number of junctions (while holding the total GaInP / GaAs thickness approximately fixed). For the GaInP region on the left, we refer to the corresponding 2 junction GaInP region on the right as a substack, likewise for GaAs. Dashed lines represent all of the layers that would otherwise be required between each cell, specifically back surface field, tunnel junction, and window layers.

Fig. 5 .

 5 Fig. 5. Similar to Fig. 4, except illustrating a speculative enhancement of a triple junction cell.

Fig. 6 .Fig. 7 .

 67 Fig.6. AM1.5 G and simulated absorption spectra for a standard GaInP/GaAs solar cell[52].

Table A1

 A1 Computed short-circuit current for a tentative VEHSA tandem, with detailed information about each layer, factoring in losses from reflectance and recombination. The rightmost column indicates the total current extracted (or lost) from each junction.

	Material	Type	Doping	Thickness	J sc (mA/	Total junction
				(nm)	cm 2 )	J sc (mA/cm 2 )
	SiO 2	ARC Window	-	100 000	--
	Al 2 O 3	ARC 1	-	90	--
	TiO 2	ARC 2	-	50	--
	Al 40 Ga 60 InP	Window	n+	40	1.46	6.51
	GaInP	Junction	n	26	3.43
	GaInP	Junction	p	27
	Al 20 Ga 80 InP	BSF	p+	80	1.63
	Al 70 Ga 30 As	TJ	p++	40	0.03	0.03 (loss)
	Al 70 Ga 30 As	TJ	n++	40
	Al 20 Ga 80 InP	Window	n+	80	0.99	6.50
	GaInP	Junction	n	100	5.50
	GaInP	Junction	p	900
	Al 20 Ga 80 InP	BSF	p+	80	0.01
	Al 35 Ga 65 As	TJ	p++	40	0.03	0.03 (loss)
	Al 35 Ga 65 As	TJ	n++	40
	GaInp	Window	n+	80	0.03	6.56
	GaAs	Junction	n	100	6.51
	GaAs	Junction	p	264
	GaInp	BSF	p+	80	0.02
	Al 35 Ga 65 As	TJ	p++	40	0.0005	0.0005 (loss)
	Al 35 Ga 65 As	TJ	n++	40
	GaInp	Window	n+	80	0.01	6.51
	GaAs	Junction	n	100	6.50
	GaAs	Junction	p	2900

Table A2

 A2 Maximum (best case) short-circuit current for a GaInP / GaAs tandem cell, assuming no absorption in window or buffer layers (hence these are not stated).

	Material	Type	Doping	Thickness	J sc (mA/	Total junction J sc
				(nm)	cm 2 )	(mA/cm 2 )
	GaInP	Junction	n	100	15.97	15.97
	GaInP	Junction	p	440
	GaAs	Junction	n	100	15.99	15.99
	GaAs	Junction	p	2900

For reference, diode ideality factors have been extracted from the simulations via concentration -V oc dependence. We obtain a characteristic value of 1.12 for the 4 junction cell at 1000 suns (vs. unity at 1 sun). In general model values are observed to be of the order ≳ 1, increasing as a function of concentration.

Acknowledgments

The authors would like to acknowledge our collaborators including the authors of Refs. [31,30,32,53,33,34,36,37,54,55], as well as all of the sources of funding in those papers, including support by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Appendix A. Detailed layer thickness and absorption Fig. 8. Efficiency and J sc vs. subcell thickness, when varying the topmost GaInP and GaAs subcells (upper and lower panels respectively, modeled at 100 suns). The reduction in efficiency not matched by a reduced J sc in the top panel results from diminished fill factor.

Material