Multi-substrate hybrid integrated gallium nitride power module compatible with metal heat sink

Abstract

The invention relates to the technical field of power semiconductor devices and automotive electronics, in particular to a multi-substrate hybrid integrated gallium nitride power module compatible with a metal heat sink, which comprises a GaN chip comprising an upper tube GaN chip and a lower tube GaN chip; the DPC substrate is arranged between the upper tube GaN chip and the lower tube GaN chip, is used as a GaN chip carrier and can allow a large current to pass through; the FPC driving signal carrier is connected with the DPC substrate and the GaN chip and integrates a driving device and a passive device; the first-stage heat sink substrate is a double-sided metallized diamond substrate; the second-stage heat sink substrate is used for performing second-stage heat dissipation on the gallium nitride power module; and the cooling plate is used for carrying out heat exchange with the secondary heat sink substrate. The invention innovatively provides a hybrid 3D packaging structure. Due to the excellent structural characteristics, the power module meets the requirements of driving integration, negative pressure protection integration, full-size heat sink and metal pole plate compatibility while the thermal resistance of a material is minimized, and the heat dissipation performance is greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power semiconductor devices and automotive electronics, and particularly relates to a gallium nitride power module with multi-substrate hybrid integration and compatible metal heat sink. BACKGROUND

[0002] With the rapid development of new energy industry, power electronic conversion systems are widely used in various important scenarios such as rail transit, unmanned aerial vehicle electric drive, robot electric drive and electric vehicle. As an important component of core hardware such as inverter and electric drive system, the performance of power module directly affects the reliability and efficiency of the system. In recent years, the emergence of wide bandgap semiconductor gallium nitride (GaN) devices has brought revolutionary changes to power converters. Compared with other devices, gallium nitride high electron mobility transistor (GaNHEMT) has smaller gate charge and on-resistance, which can realize higher power density and efficiency. However, the fast switching speed of GaNHEMT makes it more sensitive to parasitic parameters. Parasitic inductance and capacitance not only increase switching loss, but also cause serious electromagnetic interference (EMI) problems.

[0003] At present, there are many researches on power modules integrated with gate drive. For example, one scheme integrates decoupling capacitor and drive on one side of printed circuit board (PCB), and places GaNHEMT on the other side, and forms a heat dissipation path by direct bonding copper substrate (DBC) or active metal brazing substrate (AMB) welding to GaNHEMT substrate. Another double-sided heat dissipation structure uses direct electroplated copper substrate (DPC) on the top of GaNHEMT and the substrate side for electrical connection and heat dissipation. In addition, there is also a scheme that integrates the driver device by using flexible printed circuit board (FPC), and increases the pad block on the substrate side to realize the complete heat sink area. These schemes improve the integration and heat dissipation performance of the power module to some extent, but there are still some problems.

[0004] In the prior art, the interconnection by bonding wire introduces a large amount of parasitic inductance, which reduces reliability and service life. For example, the single-sided heat dissipation scheme cannot fully reduce the junction-case thermal resistance; the double-sided heat dissipation structure is too thick and has poor thermal conductivity due to the increase in height of the sub-plate, resulting in large overall parasitic inductance of the power module and insufficient heat dissipation; the alloy pad welded on the GaN substrate introduces extremely high thermal resistance, which reduces the heat dissipation performance. In addition, the thermal conductivity of the DBC substrate is much smaller than that of the heat sink plate, which increases the thermal resistance and reduces the heat dissipation effect of the heat sink plate on the chip. SUMMARY

[0005] The purpose of the present application is to provide a gallium nitride power module with multi-substrate hybrid integration and compatible metal heat sink, which solves the problems of poor single-sided heat dissipation effect and large overall parasitic inductance of the power module caused by the double-sided heat dissipation structure in the prior art.

[0006] To achieve the above object, the application provides a GaN chip, including an upper GaN chip and a lower GaN chip, and the bottom of the GaN chip is a device substrate;

[0007] A DPC substrate is arranged between the upper GaN chip and the lower GaN chip, serving as a GaN chip carrier, passing through a large current and providing heat dissipation;

[0008] An FPC driving signal carrier is connected with the DPC substrate and the GaN chip, and is used for integrating a driving device and a passive device;

[0009] A copper bar is used for connecting the GaN chip substrate and a source;

[0010] A copper block is arranged at four corners of the FPC driving signal carrier, and is used for providing additional support; and the copper block is also arranged on the DPC substrate, and is used for providing additional support and an additional heat dissipation path;

[0011] A primary heat sink substrate is selected from a double-sided metallized diamond substrate, and is arranged outside the upper GaN chip, and is used for performing primary heat dissipation on the upper GaN chip, and insulating the substrate from the outside;

[0012] A secondary heat sink substrate is arranged outside the upper diamond substrate, and is used for performing secondary heat dissipation on the upper GaN chip, and is directly arranged outside the lower GaN chip, and is used for performing primary heat dissipation on the lower GaN chip;

[0013] A cooling plate is arranged outside the secondary heat sink substrates on the upper side and the lower side, and is used for performing heat exchange with the secondary heat sink substrates, and the cooling plate adopts a liquid cooling plate or an air cooling fin.

[0014] In some embodiments of the application, the gallium nitride power module adopts a vertical layout half-bridge structure, and the substrates of the upper GaN chip and the lower GaN chip are sequentially subjected to heat dissipation through the primary heat sink substrates on the upper side and the lower side and the secondary heat sink substrates.

[0015] In some embodiments of the application, the GaN chip adopts a bare chip design in a lateral structure, and can eliminate parasitic and thermal resistance introduced by a single chip package.

[0016] In some embodiments of the application, the copper column on the substrate of the upper GaN chip and the source pin side of the upper GaN chip is connected with the double-sided metallized double-sided metallized diamond substrate, so as to obtain a structure in which the substrate is connected with the source, and is used for reducing a dynamic on-resistance, and insulating the substrate of the upper GaN chip from the heat sink substrate; and the substrate of the lower GaN chip is directly connected with the secondary heat sink substrate.

[0017] In some embodiments of the application, the DPC substrate adopts a ceramic substrate, and is used for connecting the upper GaN chip and the lower GaN chip, providing support, heat dissipation and a matched thermal expansion coefficient.

[0018] In some embodiments of the present application, the FPC drive signal carrier is used to integrate the drive device, signal pin and four corner supports, and is connected to the DPC substrate through a solder pad interface.

[0019] In some embodiments of the present application, a copper block substrate is connected on the DPC substrate to form additional heat dissipation channels and supports.

[0020] In some embodiments of the present application, the area of the secondary heat sink substrate completely covers the gallium nitride power module, and the secondary heat sink substrate is one of a phase change vapor chamber, a copper plate, an aluminum plate or a metal graphene substrate.

[0021] The advantages and beneficial effects of the present application relative to the prior art are:

[0022] 1. The present application uses GaN bare chips and mixed multi-substrate packaging, uses GaN bare chips to eliminate the thermal resistance and parasitic inductance caused by single-chip packaging, and compares and studies the characteristics of various substrates to mix and match different substrates.

[0023] 2. The present application innovatively proposes a mixed 3D packaging structure. Its excellent structural characteristics enable the power module to minimize material thermal resistance while meeting the requirements of drive integration, negative pressure protection integration, full-size heat sink and metal plate compatibility.

[0024] 3. The present application completes the direct integration of the phase change vapor chamber on the high-voltage GaN bare chip, and has complete and good electrical performance. By using the integrated phase change vapor chamber, the serious local thermal concentration phenomenon of the GaN bare chip is greatly alleviated, and the heat dissipation performance of the power module is greatly improved.

[0025] The technical solutions of the present application will be further described in detail below through the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 FIG. 1 is a structural schematic diagram of a gallium nitride power module with mixed multi-substrate integration and compatible metal heat sink according to an embodiment of the present application;

[0027] Figure 2 FIG. 2 is a schematic diagram of a multi-substrate 3D mixed integration packaging structure according to an embodiment of the present application;

[0028] Figure 3 FIG. 3 is a schematic diagram of a conventional planar layout scheme according to an embodiment of the present application;

[0029] Figure 4 FIG. 4 is a schematic diagram of a vertical layout scheme according to an embodiment of the present application;

[0030] Figure 5 FIG. 5 is a schematic diagram of a heat transfer path according to an embodiment of the present application. DETAILED DESCRIPTION

[0031] In the description of the present application, it should be noted that the terms "upper", "lower", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the present application is usually placed, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In the description of the present application, it should be noted that, unless otherwise explicitly specified and limited, the terms "arrangement", "installation", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0032] The embodiments of the present application will be described in detail below with reference to the drawings.

[0033] As Figure 1 shown, the present application provides a gallium nitride power module with multi-substrate hybrid integration and compatible metal heat sink, comprising:

[0034] GaN chips, including upper tube GaN chips and lower tube GaN chips, the bottom of the GaN chips is a device substrate;

[0035] DPC substrate, arranged between the upper tube GaN chips and the lower tube GaN chips, as a GaN chip carrier, passing through a large current and providing heat dissipation;

[0036] FPC drive signal carrier, connected with the DPC substrate and the GaN chips, used for integrating the drive device and the passive device;

[0037] Copper bar, used for connecting the GaN chip substrate and the source;

[0038] Copper block, arranged at the four corners of the FPC drive signal carrier, used for providing additional support; also arranged on the DPC substrate, used for providing additional support and additional heat dissipation path;

[0039] Primary heat sink substrate, selected from a double-sided metallized diamond substrate, arranged outside the upper tube GaN chips, used for primary heat dissipation of the upper tube GaN chips, and insulating the substrate from the outside world;

[0040] Secondary heat sink substrate, arranged outside the upper diamond substrate, used for secondary heat dissipation of the upper tube GaN chips, and directly arranged outside the lower tube GaN chips, used for primary heat dissipation of the lower tube GaN chips;

[0041] Cooling plates are arranged outside the upper and lower two-stage heat sink substrates and used for heat exchange with the two-stage heat sink substrates, and the cooling plates adopt liquid cooling plates or air cooling fins.

[0042] In some embodiments of the present application, the gallium nitride power module adopts a vertical layout of a half-bridge structure, and the substrates of the upper and lower GaN chips are sequentially cooled by the upper and lower one-stage heat sink substrates and two-stage heat sink substrates.

[0043] In some embodiments of the present application, the GaN chip adopts a bare die design of a lateral structure, which can eliminate the parasitic and thermal resistance introduced by a single-chip package.

[0044] In some embodiments of the present application, the copper column on the source pin side of the upper GaN chip substrate is connected to the double-sided metallized diamond substrate with double-sided metallization, so as to obtain a structure of the substrate connected to the source, for reducing the dynamic on-resistance and insulating the upper GaN substrate from the heat sink substrate; and the lower GaN chip substrate is directly connected to the two-stage heat sink substrate.

[0045] In some embodiments of the present application, the DPC substrate adopts a ceramic substrate, which is used for connecting the upper and lower GaN chips, providing support, heat dissipation and matching thermal expansion coefficient.

[0046] In some embodiments of the present application, the FPC driving signal carrier is used for integrating the driving device, signal pin and four-corner support, and is connected to the DPC substrate through a pad interface.

[0047] In some embodiments of the present application, the copper block substrate is connected to the DPC substrate, for forming an additional heat dissipation channel and support.

[0048] In some embodiments of the present application, the area of the two-stage heat sink substrate completely covers the gallium nitride power module, and the two-stage heat sink substrate adopts one of a phase change uniform heating plate, a copper plate, an aluminum plate or a metal graphene substrate.

[0049] The present application has the following advantages and beneficial effects compared with the prior art:

[0050] 1. The present application uses GaN bare chips and mixed packaging of multiple substrates, adopts GaN bare chips to eliminate the thermal resistance and parasitic inductance caused by single-chip packaging, and compares and studies the characteristics of various substrates to mix and use different substrates.

[0051] 2. The present application innovatively proposes a mixed 3D packaging structure. The excellent structural characteristics of the present application enable the power module to minimize the material thermal resistance while meeting the requirements of driving integration, negative pressure protection integration, full-size heat sink and metal plate compatibility.

[0052] 3. The application completes the direct integration of the phase change vapor chamber on the high-voltage GaN bare chip, and has complete and good electrical performance. By using the integrated phase change vapor chamber, the serious local heat concentration phenomenon of the GaN bare chip is greatly alleviated, and the heat dissipation performance of the power module is greatly improved.

[0053] The system embodiment of the application will be described in detail below with specific examples.

[0054] First, the multi-substrate selection design is performed:

[0055] The FPC uses a polyimide (PI) film as an insulating layer, the thermal conductivity is 0.2 W / m·K, the breakdown field strength is 300 kV / mm, and the copper foil thickness is usually <1 oz. The total thickness of the four-layer FPC is <0.3 mm, and it can be bent, with the highest wiring density. The DPC substrate uses ceramic as an insulating medium, and when aluminum nitride (AlN) is used, the thermal conductivity of the DPC substrate can reach 170 W / m·K, which can be used as a heat sink substrate. However, due to process limitations, DPC can currently only produce two-layer boards, with a minimum board thickness of about 0.5 mm. Diamond is considered to have great application potential due to its breakdown voltage of >10 kV / mm and thermal conductivity of >1400 W / m·K. However, due to the limitations of the metallization process, the metal layer can usually only grow 0.5 um, and the cost is high, so it is used less. The phase change vapor chamber can be considered as a kind of metal substrate, and its main heat transfer mode is through the internal vapor cavity to complete the phase change heat transfer, and the theoretical thermal conductivity of the vapor cavity can be as high as 10000 W / m·K.

[0056] Based on the characteristics of each material, a multi-substrate hybrid packaging strategy is proposed, and the key points are as follows:

[0057] 1. DPC substrate as a power signal carrier: DPC substrate needs to be directly connected to GaN die and pass through large current, and the excellent thermal conductivity and matched CTE of AlN medium DPC substrate can improve the heat conduction and reliability of the power module.

[0058] 2. FPCB as a drive signal carrier: The drive substrate connects the driver and passive devices, and does not need to carry large power but requires high wiring density, and the low thermal conductivity of PI can effectively prevent the heat of the power substrate from being coupled to the gate driver to make it overheated.

[0059] 3. Double-sided metallized diamond substrate as a primary heat sink substrate: Diamond is used for preliminary heat dissipation of GaN die and insulation from the outside. At the same time, the thin layer of metal on its surface can be used for interconnection of GaN substrate and source. To avoid high cost, the diamond area is only slightly larger than the GaN die and is only used for the upper tube GaN in the half-bridge.

[0060] 4. Phase change vapor chamber as primary / secondary heat sink substrate: GaN die small area, large heat flux, phase change vapor chamber can quickly disperse hot spots, improve heat exchange efficiency.

[0061] Second step, mixed 3-D integrated structure design:

[0062] Using conventional 2D integration means that a height difference is formed between power devices and other devices, and the heat sink cannot cover other devices while being in close contact with power devices, which will greatly reduce the heat sink area and seriously reduce the heat dissipation performance. In order to solve the above problems, the present application proposes a multi-substrate 3D mixed integrated packaging structure, as shown in Figure 2 The present application has the following technical breakthroughs:

[0063] (1) Half-bridge vertical layout: thermal decoupling + compatible metal substrate:

[0064] Figure 3 (a) is a conventional planar layout scheme, which places the upper and lower tube power devices in parallel and side by side. This has the advantage of minimizing the vertical spacing of the power loop, but the disadvantage is that there will be serious thermal coupling between the upper and lower tube substrates. The power device substrate thermal resistance is less than the pin side thermal resistance, so in actual operation, most of the heat is transferred through the substrate side. Substrate side thermal coupling causes the device junction temperature to rise, and the device characteristics degrade and the reliability decreases. Figure 3 (b) shows that the conventional planar layout thermal decoupling requires the introduction of a large number of metal pads, which will introduce additional thermal resistance, which is not conducive to heat transfer. At the same time, the upper and lower tube substrate side heat sink needs to be connected to the same substrate, so it requires the substrate to have insulating properties and cannot use a metal substrate.

[0065] As shown in Figure 4 The present application uses a vertical layout scheme to separate the upper and lower tube substrates into two independent heat sinks for heat dissipation, and completely thermal decoupling. At the same time, the 0V substrate of the lower tube uses a separate metal heat sink substrate for heat dissipation, breaking through the physical limitation of low thermal conductivity of insulating substrate materials. The upper tube uses only a 0.3mm diamond substrate as an insulating primary heat sink, which eliminates the thermal electron effect while isolating the high voltage of the upper tube and minimizing thermal resistance. In addition, independent copper blocks with isolated potentials are added outside the half-bridge circuit, which can provide additional heat conduction paths for GaN devices to conduct heat from the pin side to the vapor chamber, further reducing thermal resistance. At the same time, these large-area copper blocks can act as auxiliary support to share the pressure of the GaN device from the shell, reinforcing the support to improve mechanical strength.

[0066] (2) 3D layer structure: drive integration + full-size heat sink:

[0067] The present application innovatively uses the thickness (1 mm) of the DPC substrate, and superimposes the upper pipe (0.28 mm) introduced in the vertical layout and the thickness of the diamond (0.3 mm), and the total thickness can exactly match the thickness (1.35 mm) of the highest isolation driver. This enables the present application to complete the complete drive and negative pressure protection integration while ensuring that the power device substrate is closest to the heat sink shell. The drive and negative pressure components are successfully integrated into the power module, and the maximum height of the substrate is slightly higher than the thickest isolation driver, ensuring that the heat sink can be fully covered. The rectangular blocks at the four corners of the FPC are used for mechanical support. Through this structure, the heat sink area can fully cover all components. The integration of negative pressure protection and drive can greatly improve the stability of the drive signal, and the full-size heat sink can improve the heat exchange efficiency between the external cold plate and the shell, and reduce the junction temperature.

[0068] Third step, phase change heat plate integration:

[0069] Through the 3-D integration scheme proposed by the present application, the area of the drive component is converted into the area of the heat sink, realizing full-size heat plate integration. As shown in Figure 5 the red arrow is the heat flow path, and the blue arrow is the phase change vapor propagation path. The phase change heat plate can rapidly conduct the heat source with an area of 12.54 mm2 to the heat plate shell with an area of 713 mm2, and the heat flow density is reduced by more than 50 times when exchanging heat with the external cold plate, reducing the heat treatment pressure of the external cold plate.

[0070] Meanwhile, the present application also uses the outer copper shell of the heat plate as an electrical function multiplexing to form an additional current path in addition to the FPC, solving the problem of FPC copper layer being too thin to flow through large current. Figure 5 The blue arrow is the additional same flow path formed by the multiplexing heat plate.

[0071] Fourth step, power module assembly:

[0072] In order to ensure the stable assembly of the multi-substrate structure, the present application formulates the following assembly scheme:

[0073] 1. First, use the solder paste with a melting point of 220℃ to weld the GaN bare chip, copper block and diamond to the DPC substrate.

[0074] 2. Use 138℃ solder paste to weld the logic driver on the FPCB, and use the four corner clamps to flatten the FPCB to prevent warping during the process.

[0075] 3. Connect the DPC and FPCB through the 138℃ solder paste at the interface.

[0076] 4. Weld the four corner copper columns, decoupling capacitors and interfaces on the FPCB.

[0077] 5. Using 138℃ solder paste, solder one side of the vapor chamber to the outer surface of the diamond and copper piece, using a fixture to hold during soldering.

[0078] 6. Using a fixture to hold, solder the other side of the vapor chamber to the back of the FPCB and the lower tube substrate.

[0079] In summary, the 3-D hybrid vapor chamber integrated GaN power module structure has the following obvious advantages:

[0080] 1. Compatible with metal surface heat sink substrates.

[0081] 2. Using GaN die design, eliminating parasitic and thermal resistance introduced by monolithic packaging.

[0082] 3. Double-sided heat sink covering the entire power module.

[0083] 4. Low profile height and fully utilized internal space, overall power module only slightly higher than the highest device in the module.

[0084] 5. Super-high uniform heating brought by phase change vapor chamber, heat spot handling capacity improved.

[0085] 6. Integration of drive components and negative pressure components.

[0086] 7. Internal loop magnetic cancellation design, parasitic inductance <0.8nH.

[0087] In the present application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. If there is an inconsistency between the commonly understood meaning of a term and the meaning of the term as set forth in the present specification or as implied by the context of the present specification, the meaning of the term as set forth in the present specification or as implied by the context of the present specification shall prevail. In addition, the terms used herein are merely for the purpose of describing the embodiments of the present application and are not intended to limit the present application.

[0088] Finally, it should be noted that the above examples are merely used to illustrate the technical solutions of the present application and are not intended to limit the present application. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or replacements should not make the modified or replaced technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A gallium nitride power module with multiple substrate hybrid integration and compatible metal heat sink, characterized in that, Comprise: GaN chip, including upper tube GaN chip and lower tube GaN chip, GaN chip bottom is device substrate; DPC substrate, set between upper tube GaN chip and lower tube GaN chip, as GaN chip carrier, pass through large current and provide heat dissipation; FPC drive signal carrier, connected with DPC substrate and GaN chip, for integrated drive device and passive device; Copper bar, for connecting GaN chip substrate and source; Copper pad, set in four corners of FPC drive signal carrier, for providing additional support; also set on DPC substrate, for providing additional support and additional heat dissipation path; Primary heat sink substrate, selected from double-sided metallized diamond substrate, set outside upper tube GaN chip, for primary heat dissipation of upper tube GaN chip, and insulating substrate from outside; Secondary heat sink substrate, set outside upper diamond substrate, for secondary heat dissipation of upper tube GaN chip, and directly set outside lower tube GaN chip, for primary heat dissipation of lower tube GaN chip; Cooling plate, set outside secondary heat sink substrate on both upper and lower sides, for heat exchange with secondary heat sink substrate, cooling plate adopts liquid cooling plate or air cooling fin.

2. The GaN power module with multiple substrates hybrid integration and compatible metal heat sink of claim 1, wherein, The gallium nitride power module adopts vertical layout half-bridge structure, and the substrates of upper tube and lower tube GaN chips are sequentially heat dissipated through upper and lower primary heat sink substrates and secondary heat sink substrates.

3. The GaN power module with multiple substrates hybrid integration and compatible metal heat sink of claim 1, wherein, The GaN chip adopts die design of horizontal structure, which can eliminate parasitic and thermal resistance introduced by single chip packaging.

4. The GaN power module with multiple substrates hybrid integration and compatible metal heat sink of claim 3, wherein, The copper column on the substrate of upper tube GaN chip and the source pin side of upper tube GaN chip is connected with double-sided metallized double-sided metallized diamond substrate, to obtain the structure of connected substrate and source, for reducing dynamic on-resistance, and insulating the substrate of upper tube GaN chip from heat sink substrate through diamond substrate; the substrate of lower tube GaN chip is directly connected with secondary heat sink substrate.

5. The GaN power module with multiple substrate hybrid integration and compatible metal heat sink of claim 4, wherein, The DPC substrate adopts ceramic substrate, for connecting upper tube and lower tube GaN chips, providing support, heat dissipation and matching thermal expansion coefficient.

6. The GaN power module with multiple substrate hybrid integration and compatible metal heat sink of claim 1, wherein, The FPC drive signal carrier is used for integrated drive device, signal pin and four corner support, connected to DPC substrate through solder pad interface.

7. The GaN power module with multiple substrate hybrid integration and compatible metal heat sink of claim 1, wherein, The copper block substrate is connected on the DPC substrate, for forming additional heat dissipation path and support.

8. The GaN power module with multiple substrate hybrid integration and compatible metal heat sink of claim 1, wherein, The area of secondary heat sink substrate completely covers gallium nitride power module, and the secondary heat sink substrate adopts one of phase change heat plate, copper plate, aluminum plate or metal graphene substrate.

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