Patent Publication Number: US-11651894-B2

Title: Multilayer ceramic capacitor and semiconductor device

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority to Japanese Patent Application No. 2020-068180 filed on Apr. 6, 2020. The entire contents of this application are hereby incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a multilayer ceramic capacitor and a semiconductor device. 
     2. Description of the Related Art 
     A multilayer ceramic capacitor known in the art includes a multilayer body and a pair of outer electrodes. The multilayer body has a layered structure in which dielectric layers and inner electrodes are alternately stacked on one another. Each outer electrode of the pair of outer electrodes is disposed on a corresponding end surface of the multilayer body. 
     Such a multilayer ceramic capacitor is disclosed in U.S. Pat. No. 9,263,186. Referring to  FIG.  12   , multilayer ceramic capacitors  410  and solder balls  420  are disposed on a substrate  400 . The solder balls  420  in  FIG.  12    are arranged in a grid array on the substrate  400 , which has a rectangular shape. The multilayer ceramic capacitors  410  are disposed on the substrate  400  so as not to overlap the solder balls  420 . The solder balls  420  may, for example, be needed to dissipate heat from the substrate  400  and to provide signal paths. For this reason, it is not preferable to reduce the number of solder balls. 
     One of the multilayer ceramic capacitors  410  illustrated in  FIG.  12   , or more specifically, the multilayer ceramic capacitor  410  in the midsection is arranged obliquely to the edges of the substrate  400 . Some of the solder balls  420  may not be optimally positioned in relation to the multilayer ceramic capacitor  410  arranged obliquely to the edges of the substrate  400  and thus can come into contact with side surfaces of the multilayer ceramic capacitor  410 . 
     Referring to  FIG.  13   , a solder ball  420 A is in contact with a side surface of a multilayer ceramic capacitor  410 A, which is at the lower right of the substrate  400 . When the solder ball  420 A in the molten state flows along a side surface of the multilayer ceramic capacitor  410 A including a pair of outer electrodes  411 A, electrical continuity will be established between the outer electrodes  411 A, and consequently, a short circuit can occur. 
     As a workaround, the side surfaces of the multilayer ceramic capacitor  410  may be recessed inward, which may be a practical approach to eliminate or reduce the possibility that some of the solder balls  420  will come into contact with the side surfaces of the multilayer ceramic capacitor  410 . 
     Such a multilayer ceramic capacitor is disclosed in Japanese Unexamined Patent Application Publication No. 2000-195741. Referring to  FIG.  14   , a multilayer ceramic capacitor  140  has a pair of side surfaces  140   a , which each have a recess  150 . The dielectric layers and the inner electrodes are stacked on one another in a stacking direction T. When the multilayer ceramic capacitor  140  in  FIG.  14    is viewed in the stacking direction T, each recess  150  has a rectangular shape. The multilayer ceramic capacitor  140  includes a pair of outer electrodes  141 , which face each other in a length direction L. The side surfaces  140   a  face each other in a width direction W. The stacking direction T is orthogonal to the length direction L and the width direction W. 
     In the case that the multilayer ceramic capacitor  140  illustrated in  FIG.  14    is disposed so as to be arranged obliquely to the edges of the substrate  400  illustrated in  FIG.  12   , the recesses  150  in the side surfaces  140   a  eliminate or reduce the possibility that some of the solder balls  420  will come into contact with the side surfaces  140   a  of the multilayer ceramic capacitor  140 . 
     However, there is a downside to this. Forming the rectangular recesses  150  in the respective side surfaces  140   a  results in a reduction in the area of overlaps between the inner electrodes separated by the dielectric layers, and the capacitance of the multilayer ceramic capacitor  140  illustrated in  FIG.  14    is reduced correspondingly. 
     SUMMARY OF THE INVENTION 
     In order to reduce or prevent a reduction in capacitance, preferred embodiments of the present invention provide multilayer ceramic capacitors that each include side surfaces that are prevented from contacting solder balls on a substrate onto which the multilayer ceramic capacitor is mounted, and semiconductor devices each including such multilayer ceramic capacitors. 
     A multilayer ceramic capacitor according to a preferred embodiment of the present invention includes a multilayer body, a first outer electrode, and a second outer electrode. The multilayer body includes dielectric layers, first inner electrodes, and second inner electrodes. The dielectric layers and the first and second inner electrodes are stacked on one another. The multilayer body includes a first principal surface, a second principal surface, a first side surface, a second side surface, a first end surface, and a second end surface. The first principal surface is opposite the second principal surface in a stacking direction in which the dielectric layers, the first inner electrodes, the second inner electrodes are stacked on one another. The first side surface is opposite the second side surface in a width direction orthogonal or substantially orthogonal to the stacking direction. The first end surface is opposite the second end surface in a length direction orthogonal or substantially orthogonal to both the stacking direction and the width direction. The first outer electrode is electrically connected to the first inner electrodes and located on the first end surface of the multilayer body. The second outer electrode is electrically connected to the second inner electrodes and located on the second end surface of the multilayer body. The first side surface includes a first recess where a midsection of the first side surface in the length direction is recessed inward in the width direction. The second side surface includes a second recess where a midsection of the second side surface in the length direction is recessed inward in the width direction. When the multilayer ceramic capacitor is viewed in the stacking direction, a dimension of each of the first recess and the second recess in the length direction is smaller on an inner side than on an outer side in the width direction. 
     The above and other elements, features, steps, characteristics and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a perspective view of a multilayer ceramic capacitor according to a first preferred embodiment of the present invention. 
         FIG.  2    is a plan view of the multilayer ceramic capacitor in  FIG.  1   , illustrating the multilayer ceramic capacitor as seen in a stacking direction. 
         FIG.  3    is a sectional view of the multilayer ceramic capacitor taken along line in  FIG.  1   . 
         FIG.  4    is a sectional view of the multilayer ceramic capacitor taken along line IV-IV in  FIG.  1   . 
         FIG.  5    is a plan view of the multilayer ceramic capacitor in  FIG.  1   , illustrating the multilayer ceramic capacitor as seen in the stacking direction for the purpose of aiding in the explanation of a dimension of a first recess and a dimension of a second recess according to a preferred embodiment of the present invention. 
         FIG.  6    is a plan view of a semiconductor device, schematically illustrating a structure in which the multilayer ceramic capacitors according to the first preferred embodiment of the present invention are disposed on a substrate. 
         FIG.  7    is provided to explain a non-limiting example of a method for producing the multilayer ceramic capacitor according to the first preferred embodiment of the present invention, or more specifically, a method for punching holes corresponding to first recesses and second recesses of multilayer ceramic capacitors through a mother multilayer body. 
         FIGS.  8 A and  8 B  are provided to explain a non-limiting example of a method for producing multilayer chips by printing with a ceramic slurry and a conductive paste for forming inner electrodes. 
         FIG.  9    is a plan view of a multilayer ceramic capacitor according to a second preferred embodiment of the present invention, illustrating the multilayer ceramic capacitor as seen in the stacking direction. 
         FIG.  10    is a plan view of the multilayer ceramic capacitor in  FIG.  9   , illustrating the multilayer ceramic capacitor as seen in the stacking direction for the purpose of aiding in the explanation of dimension of a first recess and the dimension of a second recess according to a preferred embodiment of the present invention. 
         FIG.  11    is a plan view of a multilayer ceramic capacitor according to a third preferred embodiment of the present invention, illustrating the multilayer ceramic capacitor as seen in the stacking direction. 
         FIG.  12    is a plan view of the structure disclosed in U.S. Pat. No. 9,263,186, illustrating multilayer ceramic capacitors and solder balls disposed on a substrate. 
         FIG.  13    illustrates a state in which multilayer ceramic capacitors known in the art and solder balls are disposed on a substrate, with one of the solder balls being in contact with a side surface of one of the multilayer ceramic capacitors. 
         FIG.  14    is a perspective view of a multilayer ceramic capacitor disclosed in Japanese Unexamined Patent Application Publication No. 2000-195741, illustrating the multilayer ceramic capacitor whose side surfaces have their respective rectangular recesses. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, features of the present invention will be described with reference to preferred embodiments of the present invention and the drawings. 
     First Preferred Embodiment 
       FIG.  1    is a perspective view of a multilayer ceramic capacitor  10  according to a first preferred embodiment of the present invention.  FIG.  2    is a plan view of the multilayer ceramic capacitor  10  in  FIG.  1   , illustrating the multilayer ceramic capacitor  10  as seen in a stacking direction T.  FIG.  3    is a sectional view of the multilayer ceramic capacitor  10  taken along line III-III in  FIG.  1   .  FIG.  4    is a sectional view of the multilayer ceramic capacitor  10  taken along line IV-IV in  FIG.  1   . 
     The multilayer ceramic capacitor  10  includes a multilayer body  11 , a first outer electrode  20   a , and a second outer electrode  20   b . The first outer electrode  20   a  and the second outer electrode  20   b  face each other as illustrated in  FIG.  1   . 
     A direction in which the first outer electrode  20   a  and the second outer electrode  20   b  face each other is a length direction of the multilayer ceramic capacitor  10  and is herein denoted by L. A direction in which dielectric layers  12 , inner electrodes  13   a , and inner electrodes  13   b  are stacked on one another is herein referred to as a stacking direction and denoted by T. These layers and electrodes will be described later. A direction orthogonal or substantially orthogonal to both the length direction L and the stacking direction T is herein referred to as a width direction and denoted by W. Any two of these directions (i.e., the length direction L, the stacking direction T, and the width direction W) are orthogonal or substantially orthogonal to each other. 
     The multilayer body  11  includes a first end surface  15   a , a second end surface  15   b , a first principal surface  16   a , a second principal surface  16   b , a first side surface  17   a , and a second side surface  17   b . The first end surface  15   a  is opposite the second end surface  15   b  in the length direction L. The first principal surface  16   a  is opposite the second principal surface  16   b  in the stacking direction T. The first side surface  17   a  is opposite the second side surface  17   b  in the width direction W. 
     Corners and ridges of the multilayer body  11  are preferably rounded. Each corner is where three surfaces of the multilayer body  11  meet. Each ridge is where two surfaces of the multilayer body  11  meet. 
     Referring to  FIGS.  3  and  4   , the multilayer body  11  includes the dielectric layers  12 , first inner electrodes  13   a , and second inner electrodes  13   b , which are stacked on one another. More specifically, the multilayer body  11  has a layered structure in which the first inner electrodes  13   a  and the second inner electrodes  13   b  are alternately stacked and separated by the dielectric layers  12  in the stacking direction T. 
     As illustrated in  FIG.  4   , the dielectric layers  12  include outer dielectric layers  121 , inner dielectric layers  122 , and a margin  123 . In the stacking direction T, the outer dielectric layers  121  are each closer to outer surfaces of the multilayer body  11  than the outermost inner electrode (the inner electrode  13   a  or  13   b  closer than the other inner electrodes  13   a  and  13   b  to the outer surface in the stacking direction T). The inner dielectric layers  122  are each disposed between two inner electrodes (i.e., the inner electrodes  13   a  and  13   b ) adjacent to each other in the stacking direction T. When the multilayer body is viewed in the stacking direction T, none of the inner electrodes  13   a  and  13   b  is disposed in the margin  123 . 
     More specifically, one of the outer dielectric layers  121  is disposed between the outermost inner electrode  13   a  in the stacking direction T and the first principal surface  16   a  of the multilayer body  11 , and the other outer dielectric layer  121  is disposed between the outermost inner electrode  13   b  and the second principal surface  16   b  of the multilayer body  11 . Each of the inner dielectric layers  122  is disposed between the corresponding first inner electrode  13   a  and the corresponding second inner electrode  13   b  that are adjacent to each other in the stacking direction T. The margin  123  is closer than the outer dielectric layers  121  and the inner dielectric layers  122  to the outer surface in the width direction W. 
     The dielectric layers  12  are preferably made of a ceramic material including, for example, BaTiO 3 , CaTiO 3 , SrTiO 3 , SrZrO 3 , or CaZrO 3  as a principal component. The ceramic material may include, in addition to the principal component, minor amounts of an accessory component such as Mn compounds, Fe compounds, Cr compounds, Co compounds, or Ni compounds, for example. 
     The first inner electrodes  13   a  extend to the first end surface  15   a  of the multilayer body  11 . The second inner electrodes  13   b  extend to the second end surface  15   b  of the multilayer body  11 . 
     The multilayer body  11  may include, in addition to the first inner electrodes  13   a  and the second inner electrodes  13   b , inner electrodes that are not exposed at a surface of the multilayer body  11 . 
     The first side surface  17   a  of the multilayer body  11  includes a first recess  30   a , where the midsection of the first side surface  17   a  in the length direction L is recessed inward in the width direction W. The second side surface  17   b  of the multilayer body  11  includes a second recess  30   b , where the midsection of the second side surface  17   b  in the length direction L is recessed inward in the width direction W. These recesses will be described later. The first inner electrodes  13   a  and the second inner electrodes  13   b  are recessed inward in the width direction W and have a shape corresponding to the first recess  30   a  and the second recess  30   b.    
     The first inner electrodes  13   a  each include a facing electrode portion and an extended electrode portion. The facing electrode portion of each first inner electrode  13   a  faces the corresponding second inner electrode  13   b . The extended electrode portion extends between the facing electrode portion and the first end surface  15   a  of the multilayer body  11 . The second inner electrodes  13   b  each include a facing electrode portion and an extended electrode portion. The facing electrode portion of each second inner electrode  13   b  faces the corresponding first inner electrode  13   a . The extended electrode portion extends between the facing electrode portion and the second end surface  15   b  of the multilayer body  11 . 
     The facing electrode portion of the first inner electrode  13   a  and the facing electrode portion of the second inner electrode  13   b  face each other with the dielectric layer  12  therebetween such that a capacitance is generated, thus enabling the multilayer body to define and function as a capacitor. 
     The first inner electrodes  13   a  and the second inner electrodes  13   b  may preferably include a metal such as, for example, Ni, Cu, Ag, Pd, Pt, Fe, Ti, Cr, Sn, or Au or may include an alloy of these metals. The first inner electrodes  13   a  and the second inner electrodes  13   b  may include the same dielectric ceramic material as a dielectric ceramic material included in the dielectric layers  12 . In this case, the dielectric ceramic content in the first inner electrodes  13   a  and the second inner electrodes  13   b  may preferably be, for example, equal to or less than about 20 vol %. 
     It is not required that the inner electrodes  13   a  and  13   b  are made of the same material. Also, it is not required that each of the inner electrodes  13   a  and  13   b  is made of the same material. Different materials may be used for different portions of each inner electrode. 
     The first outer electrode  20   a  is disposed on the first end surface  15   a  of the multilayer body  11 . The first outer electrode  20   a  in the present preferred embodiment covers the entirety or substantially the entirety of the first end surface  15   a  of the multilayer body  11  and extends from the first end surface  15   a  onto the first principal surface  16   a , the second principal surface  16   b , the first side surface  17   a , and the second side surface  17   b.    
     The second outer electrode  20   b  is disposed on the second end surface  15   b  of the multilayer body  11 . The second outer electrode  20   b  in the present preferred embodiment covers the entirety or substantially the entirety of the second end surface  15   b  of the multilayer body  11  and extends from the second end surface  15   b  onto the first principal surface  16   a , the second principal surface  16   b , the first side surface  17   a , and the second side surface  17   b.    
     The first outer electrode  20   a  and the second outer electrode  20   b  may each include, for example, a base electrode layer and a plating layer on the base electrode layer. 
     The base electrode layer may include, for example, a baked electrode layer, a resin electrode layer, or a thin-film electrode layer, or varying combinations of these layers, each of which will be described later. The base electrode layer may be made of the same ceramic material as that of the dielectric layers  12  or a material similar to that of the dielectric layers  12  or may include glass, in which case the coefficient of linear expansion of the first outer electrode  20   a  and the second outer electrode  20   b  may be close to the coefficient of linear expansion of the dielectric layers  12 . In the case that the base electrode layer includes the ceramic material described above or glass, the ceramic material content or the glass content in the outer electrode is preferably, for example, equal to or more than about 30 vol % and equal to or less than about 70 vol %. 
     The base electrode layer may include one or more baked electrode layers, each of which includes glass and metal, for example. The baked electrode layer may include a metal such as, for example, Cu, Ni, Ag, Pd, Ti, Cr, or Au or may contain an alloy of these metals. 
     The baked electrode layer is obtained by baking a multilayer body coated with a conductive paste containing glass and metal. 
     The resin electrode layer may include conductive particles and a thermosetting resin, for example. The resin electrode layer may be provided directly on a ceramic raw material, in which case the baked electrode layer may be omitted. The base electrode layer may include one or more resin electrode layers, for example. 
     The thin-film electrode layer is a deposit of metallic particles and preferably has a thickness of, for example, not more than about 1 μm. The thin-film electrode layer may be formed by sputtering, vapor deposition, or any other known method for forming thin films. 
     The plating layer on the base electrode layer may include, for example, a metal such as Cu, Ni, Ag, Pd, Ti, Cr, or Au or may include an alloy made mainly of these metals. The base electrode layer may be overlaid with one or more plating layers. The plating layer preferably has a double-layer structure including a Ni plating layer and a Sn plating layer, for example. The Ni plating layer protects the base electrode layer from erosion by solder when the multilayer ceramic capacitor  10  is mounted. The Sn plating layer improves solder wettability needed for mounting of the multilayer ceramic capacitor  10 . 
     The first outer electrode  20   a  and the second outer electrode  20   b  may each be a plating layer disposed directly on the multilayer body  11 , in which case the base electrode layer may be omitted. 
     The first side surface  17   a  of the multilayer ceramic capacitor  10  according to the first preferred embodiment includes the first recess  30   a , where the midsection of the first side surface  17   a  in the length direction L is recessed inward in the width direction W. The second side surface  17   b  of the multilayer ceramic capacitor  10  includes the second recess  30   b , where the midsection of the second side surface  17   b  in the length direction L is recessed inward in the width direction W. 
     When the multilayer ceramic capacitor  10  is viewed in the stacking direction T, the dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is smaller on an inner side than on an outer side in the width direction W. The first recess  30   a  is defined by surfaces  31   a , and the second recess  30   b  is defined by surfaces  31   b . In the present preferred embodiment, the surfaces  31   a  and the surfaces  31   b  are flat. When the multilayer ceramic capacitor  10  is viewed in the stacking direction T, the surfaces  31   a  extend obliquely from the first side surface  17   a  toward the center of the multilayer body in the width direction W, and the surfaces  31   b  extend obliquely and from the second side surface  17   b  toward the center of the multilayer body in the width direction W. The dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is smaller on the inner side in the width direction W accordingly. With this structure, the first recess  30   a  and the second recess  30   b  as seen in the stacking direction T have a triangular or substantially triangular shape as illustrated in  FIG.  2   . 
     The multilayer ceramic capacitor  10  may preferably be, for example, about 0.6 mm long (in the length direction L), about 0.3 mm wide (in the width direction W), and about 0.3 mm high (in the stacking direction T). The dimension of each of the inner dielectric layers  122  (the dielectric layers  12  except for the outer dielectric layers and the margin) in the stacking direction T may preferably be, for example, equal to or more than about 0.3 μm and equal to or less than about 3.0 μm, and more preferably about 1.0 μm. The dimension of each of the first inner electrodes  13   a  and the second inner electrodes  13   b  in the stacking direction T may preferably be equal to or more than about 0.3 μm and equal to or less than about 3.0 μm, and more preferably about 0.7 μm. The dimension of the margin  123  in the width direction W, the dimension of each of the extended electrode portions of the first inner electrodes  13   a  in the length direction L, and the dimension of each of the extended electrode portions of the second inner electrodes  13   b  in the length direction L may each preferably be, for example, equal to or more than about 0.01 mm and equal to or less than about 0.1 mm, and more preferably about 0.03 mm. The thickness of each of the first outer electrode  20   a  and the second outer electrode  20   b  may preferably be, for example, equal to or more than about 3 μm and equal to or less than about 100 μm, and more preferably about 5 μm. 
     The dimension of the inner dielectric layers  122  in the stacking direction T may be determined by the following procedure. The multilayer ceramic capacitor  10  is ground such that the cross section passing through the midpoint of the multilayer ceramic capacitor  10  in the length direction L and extending in both the stacking direction T and the width direction W is exposed for observation under a scanning electron microscope. Then, the thickness of the inner dielectric layer  122  passing through the midpoint of the multilayer ceramic capacitor  10  in the stacking direction T is measured on five lines extending in the stacking direction T on the exposed cross section. The middle line among the five lines is the center line that passes through the midpoint in the width direction W. The five lines (the center line, two adjacent lines on one side in the width direction W, and two adjacent lines on the other side in the width direction W) are equally or substantially equally spaced in the width direction W. The average of the five measurement values obtained on the respective lines is taken as the dimension of each of the inner dielectric layers  122  in the stacking direction T. 
     For more precise measurements, the multilayer body  11  may be divided into an upper portion, a middle portion, and a lower portion that are aligned in the stacking direction T. The upper portion, the middle portion, and the lower portion are subjected to measurements to obtain five measurement values in each portion, and the average of the individual measurement values is taken as the dimension of each of the inner dielectric layers  122  in the stacking direction T. The dimension of each of the first inner electrodes  13   a  in the stacking direction T and the dimension of each of the second inner electrodes  13   b  in the stacking direction T may be determined in the same or similar manner. 
       FIG.  5    is a plan view of the multilayer ceramic capacitor  10  in  FIG.  1   , illustrating the multilayer ceramic capacitor  10  as seen in the stacking direction T for the purpose of aiding in the explanation of the dimension of the first recess  30   a  and the dimension of the second recess  30   b  according to the present preferred embodiment. Let L1 denote the dimension of the multilayer ceramic capacitor  10  in the length direction L, and let W1 denote the dimension of the multilayer ceramic capacitor  10  in the width direction W. The maximum dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is herein referred to as an indentation length and denoted by L2. The ratio of the indentation length L2 to the dimension L1 is preferably, for example, equal to or more than about 8.3% and equal to or less than about 83.4%, and more preferably about 16.7%. 
     The dimension of each of the first recess  30   a  and the second recess  30   b  in the width direction W is referred to as indentation depth and denoted by W2. The ratio of the indentation depth W2 to the dimension W1 is preferably, for example, equal to or more than about 3.3% and less than about 50.0%, and more preferably about 16.7%. 
     The bottom of the first recess  30   a  is denoted by  32   a , and the bottom of the second recess  30   b  is denoted by  32   b . Let L3 denote the dimension of a portion of the multilayer ceramic capacitor  10  between an end in the length direction L and the bottoms  32   a  and  32   b . The ratio of the dimension L3 to the dimension L1 may preferably be, for example, about 50%. 
     The dimension L1 of the multilayer ceramic capacitor  10  may preferably be, for example, about 0.6 mm. The dimension W1 may preferably be, for example, about 0.3 mm. The indentation length L2 is preferably, for example, equal to or more than about 0.05 mm and equal to or less than about 0.5 mm, and more preferably about 0.1 mm. The indentation depth W2 is preferably, for example, equal to or more than about 0.01 mm and less than about 0.15 mm, and more preferably about 0.05 mm. The dimension L3 may preferably be, for example, about 0.3 mm. 
     The size of the multilayer ceramic capacitor  10  may be changed as required. For example, dimensions of the multilayer ceramic capacitor  10  as expressed as “(the dimension in the length direction L, the dimension in the width direction W, the dimension in the stacking direction T)” may be (about 5.7 mm, about 5.0 mm, about 5.0 mm), (about 4.5 mm, about 3.2 mm, about 3.2 mm), (about 3.2 mm, about 1.6 mm, about 1.6 mm), (about 2.1 mm, about 1.2 mm, about 1.2 mm), (about 1.6 mm, about 0.8 mm, about 0.8 mm), (about 1.0 mm, about 0.5 mm, about 0.5 mm), or (about 0.4 mm, about 0.2 mm, about 0.2 mm). 
     When the multilayer ceramic capacitor  10  according to the present preferred embodiment is viewed in the stacking direction T, the dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is, as described above, smaller on the inner side than on the outer side in the width direction W. When the multilayer ceramic capacitor known in the art (i.e., the multilayer ceramic capacitor disclosed in Japanese Unexamined Patent Application Publication No. 2000-195741) is viewed in the stacking direction, its recesses have rectangular or substantially rectangular shapes and the dimension of each of the recesses in the length direction is constant on both the inner side and the outer side in the width direction. 
     When the depth of each of the first recess  30   a  and the second recess  30   b  (the dimension of each recess in the width direction) of the multilayer ceramic capacitor  10  according to the present preferred embodiment is equal to the depth of each recess of the multilayer ceramic capacitor known in the art, each recess of the multilayer ceramic capacitor  10  according to the present preferred embodiment is smaller than each recess of the multilayer ceramic capacitor known in the art. This means that the capacitance of the multilayer ceramic capacitor  10  according to the present preferred embodiment is greater than the capacitance of the multilayer ceramic capacitor disclosed in Japanese Unexamined Patent Application Publication No. 2000-195741. 
     The multilayer ceramic capacitor  10  according to the present preferred embodiment achieves the following advantage: the first recess  30   a  in the first side surface  17   a  and the second recess  30   b  in the second side surface  17   b  prevent the first side surface  17   a  and the second side surface  17   b  from contacting solder balls disposed on a substrate onto which the multilayer ceramic capacitor  10  is mounted. When the multilayer ceramic capacitor  10  is viewed in the stacking direction T, the dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is smaller on the inner side than on the outer side in the width direction W. This structure reduces or prevents the reduction in the capacitance of the capacitor. 
     The first inner electrodes  13   a  and the second inner electrodes  13   b  of the multilayer ceramic capacitor  10  according to the present preferred embodiment are recessed inward in the width direction W and have a shape corresponding to the first recess  30   a  and the second recess  30   b . In such a case, the area of each of the first inner electrodes  13   a  and the second inner electrodes  13   b  is greater than the area of each of the inner electrodes that have a rectangular or substantially rectangular shape, and the reduction in the capacitance of the capacitor will be reduced more effectively. 
     The multilayer ceramic capacitor known in the art includes rectangular or substantially rectangular recesses. When such multilayer ceramic capacitors are conveyed on a conveyor belt, a multilayer ceramic capacitor can partially get caught in a rectangular or substantially rectangular recess of another multilayer ceramic capacitor, such that cracks will be produced. Consequently, these multilayer ceramic capacitors will have poor yield rates. This is not the case with the multilayer ceramic capacitor  10  according to the present preferred embodiment. When the multilayer ceramic capacitor  10  is viewed in the stacking direction T, the dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is smaller on the inner side than on the outer side in the width direction W. This structure reduces or prevents the possibility that a multilayer ceramic capacitor conveyed on a conveyor belt will be partially caught in either of two recesses (i.e., the first recess  30   a  and the second recess  30   b ) of another multilayer ceramic capacitor. The reduction in yield will be reduced or prevented accordingly. 
     The rectangular recesses of the multilayer ceramic capacitor known in the art are each defined by three surfaces, which are formed by making three cuts in a multilayer ceramic capacitor in the process of production. The first recess  30   a  of the multilayer ceramic capacitor  10  according to the present preferred embodiment is defined by two surfaces, each of which is denoted by  31   a . The first recess  30   a  may thus be formed by making only two cuts in a multilayer ceramic capacitor in the process of production. 
       FIG.  6    is a plan view of a semiconductor device  100 , schematically illustrating a structure in which the multilayer ceramic capacitors  10  according to the first preferred embodiment are disposed on a substrate  40 . The semiconductor device  100  includes the substrate  40 , solder balls  50  on the substrate  40 , and the multilayer ceramic capacitors  10  on the substrate  40 . As illustrated in  FIG.  6   , the solder balls  50  are in a grid array on the substrate  40 . The multilayer ceramic capacitors  10  do not overlap the solder balls  50  on the substrate  40 . 
     Referring to  FIG.  6   , the substrate  40  has a rectangular or substantially rectangular shape, and a few of the multilayer ceramic capacitors  10  are oblique to the edges of the substrate  40 . Some of the solder balls  50  are immediately beside the multilayer ceramic capacitors  10  that are oblique to the edges of the substrate  40  and are not in contact with the multilayer ceramic capacitors  10 . 
     That is, the multilayer ceramic capacitors  10  according to the first preferred embodiment are disposed on the substrate  40  in such a manner as to avoid contact with the solder balls  50 . This layout offers an advantage that a larger number of solder balls may be disposed on the substrate. This layout thus enables the substrate  40  to achieve enhanced dissipation of heat and to provide a larger number of signal paths. 
     As an example of a practical application, the semiconductor device  100  described above may be incorporated in a music player, a video player, a navigation apparatus, a communication apparatus, a mobile phone, a smartphone, a mobile information terminal, a tablet terminal, or a notebook computer, for example. 
     Method for Producing Multilayer Ceramic Capacitors 
     The following describes a non-limiting example of method for producing the multilayer ceramic capacitors  10 . 
     In the first production step, ceramic green sheets, a conductive paste for forming inner electrodes, and a conductive paste for forming outer electrodes are prepared. The ceramic green sheets to be used may, for example, be well-known sheets and may each be obtained by coating a base material with a ceramic slurry including ceramic powder, resinous substances, and a solvent and by drying the ceramic slurry. 
     The ceramic slurry may include CaTi, ZrO 3 , SrZrO 3 , BaTiO 3 , BaTi, or CaO 3 , for example. The ceramic slurry may also, for example, resinous substances, each of which may be used as a dispersing agent or a binder. The concentration of solid matter in the ceramic slurry may preferably be, for example, equal to or more than about 10 vol % and equal to or less than about 27 vol %. The pigment volume concentration (PVC) of the ceramic powder, that is, the content of the ceramic powder in the total solid matter is preferably, for example, equal to or more than about 65% and equal to or less than about 95%. 
     The conductive paste for forming inner electrodes may include a metal, such as, for example, Ni, Cu, Ag, Pd, Pt, Fe, Ti, Cr, Sn, or Au, or a particle size precursor of the metal, and a solvent. The conductive paste for forming inner electrodes may also include, for example resinous substances, each of which may be used as a dispersing agent or a binder. 
     The viscosity of the paste for forming inner electrodes may preferably be, for example, equal to or more than about 5 mPa·s and equal to or less than about 50 Pa·s. The concentration of solid matter in the paste for forming inner electrodes may preferably be, for example, equal to or more than about 9 vol % and equal to or less than about 20.5 vol %. The PVC of the metal particles, that is, the content of metal particles in the total solid matter is preferably, for example, equal to or more than about 70% and equal to or less than about 95%. The diameter of metal particles may preferably be, for example, equal to or more than about 10 nm and equal to or less than about 500 nm. 
     The inner electrodes are formed in the subsequent production step, in which the ceramic green sheets are printed with the paste for forming inner electrodes. The paste for forming inner electrodes is applied to form a shape having an inwardly recessed outline so that the shape of the inner electrodes corresponds to the first recess  30   a  and the second recess  30   b.    
     Then, a mother multilayer body is produced by the following procedure. A predetermined number of ceramic green sheets including no inner electrode pattern formed thereon, ceramic green sheets including inner electrode patterns formed thereon, and a predetermined number of ceramic green sheets including no inner electrodes formed thereon are stacked on one another in this order. The mother multilayer body is formed such that a plurality of multilayer ceramic capacitors  10  are obtained at the same time from the multilayer body. 
     The mother multilayer body is then subjected to rigid pressing, isostatic pressing, or the like, for example. The mother multilayer body may be pressed at temperatures falling within the range of, for example, about 25° C. to about 200° C. The pressure applied to the mother multilayer body may be, for example, equal to or more than about 1 MPa and equal to or less than about 200 MPa. 
     Then, holes are punched through the mother multilayer body by using a push cutter, a mechanical punch, or the like, for example, such that the holes correspond to the first recesses  30   a  and the second recesses  30   b  of the multilayer ceramic capacitors  10 . The resultant state is illustrated in  FIG.  7   , in which the mother multilayer body is denoted by  70 , and the holes are denoted by  71 . Subsequently, multilayer chips are obtained by cutting the mother multilayer body  70  into a predetermined size with a dicing machine, laser beams, or the like, for example. Referring to  FIG.  7   , broken lines  72  denote lines along which the mother multilayer body  70  is cut. The cutting may be followed by barrel polishing or the like, for example, in which case corners and ridges of the multilayer chips are rounded. 
     Alternatively, the mother multilayer body  70  may be cut into a predetermined size when the holes corresponding to the first recesses  30   a  and the second recesses  30   b  are punched. The simultaneous cutting and punching may be accomplished by using, for example, a push cutter for cutting the mother multilayer body into pieces and punching the holes corresponding to the first recesses  30   a  and the second recesses  30   b.    
     As another alternative, a printing apparatus such as, for example, a 3D printer may be used to produce multilayer chips. That is, printing techniques may be used to produce multilayer chips, each of which is then fired to obtain the multilayer body including the first recess  30   a  and the second recess  30   b . Specifically, ceramic slurry  80  is applied to form layers each having the shape illustrated in  FIG.  8 A , and a conductive paste  81  for forming inner electrodes is then applied on the top layer to form a layer having the shape illustrated in  FIG.  8 B . Subsequently, the ceramic slurry  80  is applied thereon to form another layer having the shape illustrated in  FIG.  8 B , and the conductive paste  81  for forming inner electrodes is applied on the resultant layer to form still another layer having the shape illustrated in  FIG.  8 B . The ceramic slurry  80  is applied thereon to form a layer having the shape illustrated in  FIG.  8 A , and the conductive paste  81  for forming inner electrodes is applied on the resultant layer to form another layer having the shape illustrated in  FIG.  8 A . The ceramic slurry  80  and the conductive paste  81  for forming inner electrodes are alternately applied in the same manner. After this printing process is iterated, the ceramic slurry  80  is applied on the outer side in the stacking direction to form layers each having the shape illustrated in  FIG.  8 A . In this way, multilayer chips are produced. 
     A conductive paste for forming outer electrodes is then applied to the multilayer chips such that two end surfaces of each multilayer chip are coated with the paste and two principal surfaces and two side surfaces of each multilayer chip are partially coated with the paste. The conductive paste for forming outer electrodes may include, for example, a metal or a particle size precursor of the metal, and a solvent. The conductive paste for forming outer electrodes may also include, for example, resinous substances, each of which may be used as dispersing agent or a binder. The concentration of solid matter in the paste for forming outer electrodes may preferably be, for example, equal to or more than about 9 vol % and equal to or less than about 20.5 vol %. The PVC of the metal particles, that is, the content of metal particles in the total solid matter is preferably, for example, equal to or more than about 70% and equal to or less than about 95%. 
     In the subsequent step, the multilayer chips are fired. The multilayer chips may be fired at temperatures falling within the range of about 900° C. to about 1,300° C., for example. The firing temperature may be changed to better suit the ceramic material or the conductive paste that is used. In this way, a multilayer body and metal layers defining and functioning as outer electrodes are formed. 
     Alternatively, the multilayer chips may be fired before and after being coated with the paste for forming outer electrodes. 
     The metal layers may be finished by plating if appropriate. The metal layers may be plated with Ni and thereafter plated with Sn, for example. 
     These processes may be used in the production of the multilayer ceramic capacitors  10 . 
     Second Preferred Embodiment 
       FIG.  9    is a plan view of a multilayer ceramic capacitor  10 A according to a second preferred embodiment of the present invention, illustrating the multilayer ceramic capacitor  10 A as seen in the stacking direction T. The difference between the multilayer ceramic capacitor  10 A according to the second preferred embodiment and the multilayer ceramic capacitor  10  according to the first preferred embodiment is in the shape of the first recess  30   a  and the second recess  30   b.    
     There are some commonalities between the multilayer ceramic capacitor  10  according to the first preferred embodiment and the multilayer ceramic capacitor  10 A according to the second preferred embodiment. The first side surface  17   a  of the multilayer body  11  includes the first recess  30   a , where the midsection of the first side surface  17   a  in the length direction L is recessed inward in the width direction W, and the second side surface  17   b  of the multilayer body  11  includes the second recess  30   b , where the midsection of the second side surface  17   b  in the length direction L is recessed inward in the width direction W. When the multilayer ceramic capacitor  10 A is viewed in the stacking direction T, the dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is smaller on the inner side than on the outer side in the width direction W. As with the multilayer ceramic capacitor  10  according to the first preferred embodiment, the multilayer ceramic capacitor  10 A according to the second preferred embodiment thus offers the following advantage: the first recess  30   a  in the first side surface  17   a  and the second recess  30   b  in the second side surface  17   b  prevent the first side surface  17   a  and the second side surface  17   b  from contacting solder balls disposed on a substrate onto which the multilayer ceramic capacitor  10 A is mounted, and this structure reduces or prevents the reduction in capacitance. 
     In the present preferred embodiment, the first recess  30   a  and the second recess  30   b , respectively, are defined by a surface  31   a  and a surface  31   b , which are each substantially arc-shaped when the multilayer ceramic capacitor  10 A is viewed in the stacking direction T. The term arc herein refers to a circular arc, an elliptical arc, or any other suitable shape defined by a curve. 
       FIG.  10    is a plan view of the multilayer ceramic capacitor  10 A in  FIG.  9   , illustrating the multilayer ceramic capacitor  10 A as seen in the stacking direction T for the purpose of aiding in the explanation of the dimension of the first recess  30   a  and the dimension of the second recess  30   b  according to a preferred embodiment. Let L1 denote the dimension of the multilayer ceramic capacitor  10 A in the length direction L, and let W1 denote the dimension of the multilayer ceramic capacitor  10 A in the width direction W. The dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is herein referred to as indentation length and denoted by L2. The ratio of the indentation length L2 to the dimension L1 is preferably, for example, equal to or more than about 8.3% and equal to or less than about 83.4%, and more preferably about 38.3%. The dimension of each of the first recess  30   a  and the second recess  30   b  in the width direction W is herein referred to as indentation depth and denoted by W2. The ratio of the indentation depth W2 to the dimension W1 in the width direction is preferably, for example, equal to or more than about 3.3% and equal to or less than about 36.7%, and more preferably about 13.3%. The bottom of the first recess  30   a  is denoted by  32   a , and the bottom of the second recess  30   b  is denoted by  32   b . Let L3 denote the dimension of a portion of the multilayer ceramic capacitor  10 A between an end in the length direction L and the bottoms  32   a  and  32   b . The ratio of the dimension L3 to the dimension L1 may preferably be about 50%, for example. 
     The dimension L1 of the multilayer ceramic capacitor  10 A may preferably be, for example, about 0.6 mm. The dimension W1 may preferably be, for example, about 0.3 mm. The indentation length L2 is preferably, for example, equal to or more than about 0.05 mm and equal to or less than about 0.5 mm, and more preferably about 0.23 mm. The indentation depth W2 is preferably, for example, equal to or more than about 0.01 mm and equal to or less than about 0.11 mm, and more preferably about 0.04 mm. The dimension L3 may preferably be, for example, about 0.3 mm. 
     In the multilayer ceramic capacitor  10  according to the first preferred embodiment, the two flat surfaces  31   a  meet at the bottom  32   a  of the first recess  30   a , and the two flat surfaces  31   b  meet at the bottom  32   b  of the second recess  30   b . For this reason, cracks can be produced in the bottom  32   a  of the first recess  30   a  and the bottom  32   b  of the second recess  30   b . Alternatively, the bottoms  32   a  and  32   b  may be substantially arc-shaped to reduce or prevent the possibility of cracking. 
     In the multilayer ceramic capacitor  10 A according to the second preferred embodiment, the surface  31   a  defining the first recess  30   a  and the surface  31   b  defining the second recess  30   b  are substantially arc-shaped. That is, the surfaces  31   a  and  31   b  are curved. Accordingly, the possibility of cracking is further reduced or prevented. 
     Third Preferred Embodiment 
       FIG.  11    is a plan view of a multilayer ceramic capacitor  10 B according to a third preferred embodiment of the present invention, illustrating the multilayer ceramic capacitor  10 B as seen in the stacking direction T. The difference between the multilayer ceramic capacitor  10 B according to the third preferred embodiment and the multilayer ceramic capacitor  10  according to the first preferred embodiment is in the shape of the first recess  30   a  and the second recess  30   b.    
     There are some commonalities between the multilayer ceramic capacitor  10  according to the first preferred embodiment and the multilayer ceramic capacitor  10 B according to the third preferred embodiment. The first side surface  17   a  of the multilayer body  11  includes the first recess  30   a , where the midsection of the first side surface  17   a  in the length direction L is recessed inward in the width direction W, and the second side surface  17   b  of the multilayer body  11  includes the second recess  30   b , where the midsection of the second side surface  17   b  in the length direction L is recessed inward in the width direction W. When the multilayer ceramic capacitor  10 B is viewed in the stacking direction T, the dimension of each of the first recess  30   a  and the second recess  30   b  in the length direction L is smaller on the inner side than on the outer side in the width direction W. As with the multilayer ceramic capacitor  10  according to the first preferred embodiment, the multilayer ceramic capacitor  10 B according to the third preferred embodiment thus offers the following advantage: the first recess  30   a  in the first side surface  17   a  and the second recess  30   b  in the second side surface  17   b  prevent the first side surface  17   a  and the second side surface  17   b  from contacting solder balls disposed on a substrate onto which the multilayer ceramic capacitor  10 B is mounted, and this structure reduces or prevents the reduction in capacitance. 
     When the multilayer ceramic capacitor  10 B according to the present preferred embodiment is viewed in the stacking direction T, the first recess  30   a  and the second recess  30   b  have a trapezoidal or substantially trapezoidal shape. That is, the bottom  32   a  of the first recess  30   a  and the bottom  32   b  of the second recess  30   b  are flat. 
     The multilayer ceramic capacitor according to the present invention offers the following advantage: the first recess in the first side surface and the second recess in the second side surface prevent the first side surface and the second side surface from contacting solder balls disposed on a substrate onto which the multilayer ceramic capacitor is mounted. When the multilayer ceramic capacitor is viewed in the stacking direction, the dimension of each of the first recess and the second recess in the length direction is smaller on the inner side than on the outer side in the width direction. This structure is more effective in reducing or preventing the reduction in the capacitance of the capacitor than the structure in which the dimension of each recess in the length direction is constant on both the inner side and the outer side in the width direction. 
     It should be noted that the present invention is not limited to the preferred embodiments above and various applications and alterations are possible within the scope of the present invention. 
     While preferred embodiments of the present invention have been described above, it is to be understood that variations and modifications will be apparent to those skilled in the art without departing from the scope and spirit of the present invention. The scope of the present invention, therefore, is to be determined solely by the following claims.