Patent Abstract:
A hermetic compressor includes a closed vessel for storing lubricating oil, an electric-driving element, and a compressing element driven by the electric-driving element. The compressing element includes a cylinder block forming a compression chamber, a piton that reciprocates inside the compression chamber, and an oiling device for supplying the lubricating oil to an outer circumference of the piston. A first oil groove is concavely formed on the outer circumference of the piston, and a second oil groove is concavely formed on a side opposite to the compression chamber relative to the first oil groove. The second oil groove has a spatial volume same or greater than that of the first oil groove. An expanded clearance portion is provided such that a clearance between the piston and the cylindrical hole portion broadens from a top dead point to a bottom dead point.

Full Description:
RELATED APPLICATIONS 
       [0001]    Pursuant to 35 U.S.C. §119(e), this application claims the benefit of the filing date of Provisional U.S. Patent Application Ser. No. 61/207,670 filed on Feb. 13, 2009. This application is a continuation application of PCT/JP2007/073935 filed on Dec. 12, 2007. The entire contents of these applications are hereby incorporated by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention relates to a semiconductor device, and more specifically to a semiconductor device having a surrounding gate transistor (SGT) which is a three-dimensional semiconductor. 
       BACKGROUND ART 
       [0003]    Through miniaturization of semiconductor devices using a planar transistor, the planar transistor is used in a wide range of fields, such as computers, communication devices, measurement devices, automatic control devices and domestic devices, as a low-power consumption, low-cost, high-throughput microprocessor, an ASIC, a microcomputer, and a low-cost, large-capacity memory. However, the planar transistor is two-dimensionally formed on a plane of a semiconductor substrate. Specifically, the planar transistor has a structure where a source, a gate and a drain thereof are arranged along a surface of a silicon substrate in a horizontal direction. In contrast, the SGT has a structure where a source, a gate and a drain thereof are arranged in a direction perpendicular to a surface of a silicon substrate while allowing the gate to surround a convex-shaped semiconductor layer (see, for example,  FIG. 20  in the following Non-Patent Document 1). Therefore, the SGT can largely reduce an occupancy area as compared with the planar transistor. However, in the SGT, along with miniaturization of ultra-large-scale integrated circuits (ULSI), a gate length becomes shorter to provide a lower channel resistance, whereas, as a silicon pillar becomes miniaturized, a diffusion-layer resistance and a contact resistance, i.e., a parasitic resistance, become larger to cause a reduction in drive current. Thus, in a miniaturized SGT device, it is essential to further reduce a parasitic resistance. 
         [0004]    There has been known a technique of reducing a contact resistance as a parasitic resistance of source and drain regions to achieve a higher-speed operation of the device, as disclosed, for example, in the following Patent Document 1.  FIG. 21  shows an SGT structure disclosed in the Patent Document 1, which is intended to reduce the contact resistance. In an SGT, along with scaling down of a silicon pillar, a contact area between the silicon pillar and a contact to be connected to a top of the silicon pillar becomes smaller to cause an increase in contact resistance. Consequently, a drive current of the SGT is reduced. As measures against this problem, the Patent Document 1 discloses a structure for increasing the contact area between the silicon pillar and the contact so as to reduce the contact resistance. Specifically, the structure is configured to allow the contact to come into contact with not only a top surface of the silicon pillar but also a part of a side surface of the silicon pillar, so that the contact area between the silicon pillar and the contact is increased to reduce the contact resistance. 
         [0005]    Non-Patent Document 1H. Takato et al., IEEE transaction on electron device, Vol. 38, No. 3, March 1991, pp 573-578 
         [0006]    Patent Document 1 JP 2007-123415A 
         [0007]    As an SGT structure for reducing the contact resistance, the Patent Document 1 proposes a structure where the contact area between the silicon pillar and the contact is set to become greater than an area of the top surface of the silicon pillar, to reduce the contact resistance. However, in order to actually achieve a higher-speed operation of an SGT constituting a ULSI, it is desirable that the contact resistance is less than a reference resistance of the SGT. 
         [0008]    In view of the above circumstances, it is an object of the present invention to provide a semiconductor device capable of reducing a contact resistance as a parasitic resistance to solve the problem of lowering in operation speed of an SGT. 
       SUMMARY OF THE INVENTION 
       [0009]    In order to achieve the above object, according to a first aspect of the present invention, there is provided a semiconductor device which comprises: a first silicon pillar formed on a semiconductor substrate; a second silicon pillar formed on the first silicon pillar; a first insulator surrounding a part of a surface of the second silicon pillar; a gate surrounding the first insulator; a third silicon pillar formed on the second silicon pillar; a first silicide surrounding a part of a surface of the first silicon pillar; and a second silicide surrounding a part of a surface of the third silicon pillar, wherein each of a contact resistance formed by the first silicide and the first silicon pillar, and a contact resistance formed by the second silicide and the third silicon pillar, is less than a reference resistance of the semiconductor device. 
         [0010]    According to a second aspect of the present invention, there is provided a semiconductor device which comprises: a second silicon pillar formed on a semiconductor substrate; a first insulator surrounding a part of a surface of the second silicon pillar; a gate surrounding the first insulator; a third silicon pillar formed on the second silicon pillar; and a second silicide surrounding a part of a surface of the third silicon pillar, wherein a contact resistance formed by the second silicide and the third silicon pillar is less than a reference resistance of the semiconductor device. 
         [0011]    According to a third aspect of the present invention, there is provided a semiconductor device which comprises: a first silicon pillar formed on a semiconductor substrate; a second silicon pillar formed on the first silicon pillar; a first insulator surrounding a part of a surface of the second silicon pillar; a gate surrounding the first insulator; and a first silicide surrounding a part of a surface of the first silicon pillar, wherein a contact resistance formed by the first silicide and the first silicon pillar is less than a reference resistance of the semiconductor device. 
         [0012]    As above, the present invention makes it possible to reduce a parasitic resistance of a semiconductor device element to provide a semiconductor device having a high-speed, low-power consumption ULSI. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]      FIG. 1  is a bird&#39;s-eye view showing a semiconductor device according to a first embodiment of the present invention. 
           [0014]      FIG. 2  is a sectional view of the semiconductor device, taken along the line A-A′ in  FIG. 1 . 
           [0015]      FIG. 3  is a top view of the semiconductor device in  FIG. 1 . 
           [0016]      FIG. 4  is a sectional view of the semiconductor device, taken along the line B-B′ in  FIG. 2 . 
           [0017]      FIG. 5  is a sectional view of the semiconductor device, taken along the line C-C′ in  FIG. 2 . 
           [0018]      FIG. 6  is a sectional view of the semiconductor device, taken along the line D-D′ in  FIG. 2 . 
           [0019]      FIG. 7  is a graph showing a relationship between a diameter W 1  and a length L 1  of a first silicon pillar  830  for satisfying a condition that a contact resistance formed by a silicide and the first silicon pillar  830  is less than a reference resistance in the semiconductor device in  FIG. 1 . 
           [0020]      FIG. 8  is a graph showing a relationship between a diameter W 2  and a length L 2  of a third silicon pillar  820  for satisfying a condition that a contact resistance formed by a silicide and the third silicon pillar  820  is less than a reference resistance in the semiconductor device in  FIG. 1 . 
           [0021]      FIG. 9  is a bird&#39;s-eye view showing a semiconductor device according to a second embodiment of the present invention. 
           [0022]      FIG. 10  is a sectional view of the semiconductor device, taken along the line A-A′ in  FIG. 9 . 
           [0023]      FIG. 11  is a top view of the semiconductor device in  FIG. 9 . 
           [0024]      FIG. 12  is a sectional view of the semiconductor device, taken along the line B-B′ in  FIG. 10 . 
           [0025]      FIG. 13  is a sectional view of the semiconductor device, taken along the line C-C′ in  FIG. 10 . 
           [0026]      FIG. 14  is a graph showing a relationship between a diameter W 2  and a length L 2  of a third silicon pillar  820  for satisfying a condition that a contact resistance formed by a silicide and the third silicon pillar  820  is less than a reference resistance in the semiconductor device in  FIG. 9 . 
           [0027]      FIG. 15  is a bird&#39;s-eye view showing a semiconductor device according to a third embodiment of the present invention. 
           [0028]      FIG. 16  is a sectional view of the semiconductor device, taken along the line A-A′ in  FIG. 15 . 
           [0029]      FIG. 17  is a top view of the semiconductor device in  FIG. 15 . 
           [0030]      FIG. 18  is a sectional view of the semiconductor device, taken along the line B-B′ in  FIG. 16 . 
           [0031]      FIG. 19  is a sectional view of the semiconductor device, taken along the line C-C′ in  FIG. 16 . 
           [0032]      FIG. 20  is a graph showing a relationship between a diameter W 1  and a length L 1  of a first silicon pillar  830  for satisfying a condition that a contact resistance formed by a silicide and the first silicon pillar  830  is less than a reference resistance in the semiconductor device in  FIG. 1 . 
           [0033]      FIG. 21  is a bird&#39;s-eye view showing one example of a conventional SGT. 
           [0034]      FIG. 22  is a top view of the conventional SGT. 
           [0035]      FIG. 23  is a sectional view of the conventional SGT, taken along the line I-I′ in  FIG. 22 . 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0036]    With reference to the drawings, a semiconductor device of the present invention will now be specifically described. 
       First Embodiment 
     Semiconductor Device 
       [0037]      FIG. 1  is a schematic bird&#39;s-eye view showing a transistor of a semiconductor device according to a first embodiment of the present invention.  FIG. 2  is a schematic sectional view taken along the line A-A′ in  FIG. 1 , and  FIG. 3  is a top view of the transistor in  FIG. 1 .  FIG. 4 ,  FIG. 5  and  FIG. 6  are a schematic sectional view taken along the line B-B′ in  FIG. 2 , a schematic sectional view taken along the line C-C′ in  FIG. 2 , and a schematic sectional view taken along the line D-D′ in  FIG. 2 , respectively. The semiconductor device according to the first embodiment comprises: a first silicon pillar  830  formed on a first conductive-type semiconductor substrate  100  to have a cross-sectionally circular shape; a second silicon pillar  810  formed on the first silicon pillar  830  to have a cross-sectionally circular shape; a first insulator  310  surrounding a part of a surface of the second silicon pillar  810 ; a gate  210  surrounding the first insulator  310 ; and a third silicon pillar  820  formed on the second silicon pillar  810  to have a cross-sectionally circular shape. 
         [0038]    The second silicon pillar  810  includes a second conductive-type high-concentration impurity region  520  formed as a part of the second silicon pillar  810 , and a second conductive-type high-concentration impurity region  530  formed as a part of the second silicon pillar  810 . 
         [0039]    The semiconductor substrate  100  includes a second conductive-type high-concentration impurity region  510  formed as a part of the semiconductor substrate  100 , and a silicide region (first silicide)  720  formed as a part of the high-concentration impurity region  510 . The semiconductor substrate  100  also has an element isolation region  910  formed therein. 
         [0040]    The third silicon pillar  820  includes a second conductive-type high-concentration impurity region  540  formed as a part of the third silicon pillar  820 , and a silicide region (second silicide)  710  is formed in the high-concentration impurity region  540 . 
         [0041]    The first silicon pillar  830  includes a second conductive-type high-concentration impurity region  550  formed as a part of the first silicon pillar  830 . 
         [0042]    The semiconductor device according to the first embodiment further comprises a contact  430  formed on the silicide region  720 , a contact  420  formed on the silicide region  710 , and a contact  410  formed on the gate  210 . 
         [0043]    Each of a contact resistance R 1  formed by the first silicon pillar  830  including the high-concentration impurity region  510  and the silicide region  720  formed in the first silicon pillar  830 , and a contact resistance R 2  formed by the third silicon pillar  820  including the high-concentration impurity region  540  and the silicide region  710  formed in the third silicon pillar  830 , is a parasitic resistance. In order to reduce the parasitic resistance, it is preferable that the contact resistances R 1 , R 2  satisfy the following relational formulas (1-1), (1-2) with respect to a reference resistance Rs: 
         [0000]      R1&lt;Rs  (1-1) 
         [0000]      R2&lt;Rs  (1-2) 
         [0044]    The reference resistance Rs is calculated according to the following formula (1-3) based on a current I (A) which flows between the contact  410  and the contact  430  in the above semiconductor device when 0 (V) is applied to one of the contacts  410 ,  430  and V (V) is applied to a remaining one of the contacts  410 ,  430 , while applying V (V) to the contact  420 , under a condition that the contact resistance R 1 =0 and the contact resistance R 2 =0: 
         [0000]        Rs=V/I   (1-3) 
         [0045]    Specifically, when a length of the gate  210 , a film thickness of the gate oxide layer, and a diameter of the second silicon pillar  810 , are, respectively, 20 nm, 1 nm, and 10 nm, the parasitic resistance R 1  of the first silicon pillar  830 , a contact resistivity ρ C , a sheet resistance ρ D  of a first conductive-type impurity region, a circumferential length K 1  of a cross-section of the first silicon pillar  830 , and a height dimension L 1  of the first silicon pillar  830 , satisfy the following formula (1-4), wherein α is expressed as the formula (1-5). Further, given that the circumferential length K 1  (cm) of the cross-section of the first silicon pillar  830  satisfies the following relational formula (1-6) with respect to a diameter W 1  (cm) of the first silicon pillar  830 . 
         [0000]    
       
         
           
             
               
                 
                   
                     R 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
                          
                         
                             
                         
                          
                         K 
                          
                         
                             
                         
                          
                         1 
                       
                     
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                         ( 
                         
                           
                             L 
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                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     1 
                      
                     
                       - 
                     
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                     4 
                   
                   ) 
                 
               
             
             
               
                 
                   α 
                   = 
                   
                     
                       ( 
                       
                         
                           ρ 
                           C 
                         
                         
                           ρ 
                           D 
                         
                       
                       ) 
                     
                     
                       1 
                       2 
                     
                   
                 
               
               
                 
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                   ( 
                   
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         [0046]    The parasitic resistance R 2  of the third silicon pillar  820 , a contact resistivity ρ C , a sheet resistance ρ D  of a first conductive-type impurity region, a circumferential length K 2  of a cross-section of the third silicon pillar  820 , and a height dimension L 2  of the third silicon pillar  820 , satisfy the following formula (1-7). Further, given that the circumferential length K 2  (cm) of the cross-section of the third silicon pillar  820  satisfies the following relational formula (1-8) with respect to a diameter W 2  (cm) of the third silicon pillar  820 . 
         [0000]    
       
         
           
             
               
                 
                   
                     R 
                      
                     
                         
                     
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                     2 
                   
                   = 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
                          
                         
                             
                         
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                         K 
                          
                         
                             
                         
                          
                         2 
                       
                     
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         [0047]    The formula (1-4) is assigned to the formula (1-1), and the formula (1-7) is assigned to the formula (1-2), to obtain the following conditional formulas (1-9), (1-10): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
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         [0048]    As one example, given that the contact resistivity ρ C  and the sheet resistance ρ D , are, respectively, 6.2e-8 (Ω-cm 2 ) and 6.4e-3/W 1  (Ω/sq.), and the current I (A) flowing between the contact  410  and the contact  430  in the above semiconductor device is 44 (μA) when 0 (V) is applied to one of the contacts  410 ,  430  and 1 (V) is applied to a remaining one of the contacts  410 ,  430 , while applying 1 (V) to the contact  420 , the reference resistance Rs is calculated as 2.3e-8 (Ω) according to the formula (1-3). These values are assigned to the formulas (1-9), (1-10) to obtain the following relational formula (1-11) between the height dimension L 1  of the first silicon pillar  830  and the circumferential length K 1  of the cross-section of the first silicon pillar  830 , and the following relational formula (1-12) between the height dimension L 2  (cm) of the third silicon pillar  820  and the circumferential length K 2  (cm) of the cross-section of the third silicon pillar  820 : 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0049]    If these conditional formulas (1-11), (1-12) are satisfied, the formulas (1-1) are satisfied. Thus, the following formulas (1-13), (1-14) are obtained (see  FIGS. 7 and 8 ): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         1 
                         
                           W 
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         [0050]    As another example, given that a circumferential length of the second silicon pillar  810 , each of the circumferential lengths of the third and first silicon pillars  820 ,  830  and the gate length are set, respectively, in the range of 8 nm to 100 μm, in the range of 8 nm to 100 μm and in the range of 6 nm to 10 μm. Further, given that the diameter of the second silicon pillar  810 , the contact resistivity ρ C  and the sheet resistance ρ D  are, respectively, 2.6 nm, 7e-9 (Ω-cm 2 ) and 6.4e-3/W 1  (Ω/sq.), and the current I (A) flowing between the contact  410  and the contact  430  in the above semiconductor device is 11.4 (μA) when 0 (V) is applied to one of the contacts  410 ,  430  and 1 (V) is applied to a remaining one of the contacts  410 ,  430 , while applying 1 (V) to the contact  420 , the reference resistance Rs is calculated as 9.0e-8 (Ω) according to the formula (1-3). These values are assigned to the formulas (1-8), (1-9) to obtain the following formulas (1-15), (1-16): 
         [0000]    
       
         
           
             
               
                 
                   
                     
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                             3 
                             / 
                             2 
                           
                         
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             2 
                           
                           
                             
                               W 
                                
                               
                                   
                               
                                
                               
                                 
                                   2 
                                   
                                     1 
                                     / 
                                     2 
                                   
                                 
                                 · 
                                 1.1 
                               
                                
                               
                                   
                               
                                
                               e 
                             
                             - 
                             3 
                           
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     4.3 
                      
                     
                         
                     
                      
                     e 
                      
                     
                         
                     
                      
                     10 
                   
                 
               
               
                 
                   ( 
                   
                     1 
                      
                     
                       - 
                     
                      
                     16 
                   
                   ) 
                 
               
             
           
         
       
     
         [0051]    If these conditional formulas (1-15), (1-16) are satisfied, the formulas (1-1), (1-2) are satisfied. Thus, the following formulas (1-17), (1-18) are obtained: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         1 
                         
                           W 
                            
                           
                               
                           
                            
                           
                             1 
                             
                               3 
                               / 
                               2 
                             
                           
                         
                       
                        
                       
                         coth 
                          
                         
                           ( 
                           
                             
                               L 
                                
                               
                                   
                               
                                
                               1 
                             
                             
                               
                                 W 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     1 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   · 
                                   1.1 
                                 
                                  
                                 
                                     
                                 
                                  
                                 e 
                               
                               - 
                               3 
                             
                           
                           ) 
                         
                       
                     
                     &lt; 
                     
                       4.3 
                        
                       
                           
                       
                        
                       e 
                        
                       
                           
                       
                        
                       10 
                     
                   
                   ⇒ 
                   
                     
                       R 
                        
                       
                           
                       
                        
                       1 
                     
                     &lt; 
                     Rs 
                   
                 
               
               
                 
                   ( 
                   
                     1 
                      
                     
                       - 
                     
                      
                     17 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         1 
                         
                           W 
                            
                           
                               
                           
                            
                           
                             2 
                             
                               3 
                               / 
                               2 
                             
                           
                         
                       
                        
                       
                         coth 
                          
                         
                           ( 
                           
                             
                               L 
                                
                               
                                   
                               
                                
                               2 
                             
                             
                               
                                 W 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     2 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   · 
                                   1.1 
                                 
                                  
                                 
                                     
                                 
                                  
                                 e 
                               
                               - 
                               3 
                             
                           
                           ) 
                         
                       
                     
                     &lt; 
                     
                       4.3 
                        
                       
                           
                       
                        
                       e 
                        
                       
                           
                       
                        
                       10 
                     
                   
                   ⇒ 
                   
                     
                       R 
                        
                       
                           
                       
                        
                       2 
                     
                     &lt; 
                     Rs 
                   
                 
               
               
                 
                   ( 
                   
                     1 
                      
                     
                       - 
                     
                      
                     18 
                   
                   ) 
                 
               
             
           
         
       
     
       Second Embodiment 
     Semiconductor Device 
       [0052]      FIG. 9  is a schematic bird&#39;s-eye view showing a transistor of a semiconductor device according to a second embodiment of the present invention.  FIG. 10  is a schematic sectional view taken along the line A-A′ in  FIG. 9 , and  FIG. 11  is a top view of the transistor in  FIG. 9 .  FIG. 12  is a schematic sectional view taken along the line B-B′ in  FIG. 10 , and  FIG. 13  is a schematic sectional view taken along the line C-C′ in  FIG. 10 . The semiconductor device according to the second embodiment comprises a second silicon pillar  810  formed on a first conductive-type semiconductor substrate  100  to have a cross-sectionally circular shape, and a third silicon pillar  820  formed on the second silicon pillar  810  to have a cross-sectionally circular shape. 
         [0053]    A part of a surface of the second silicon pillar  810  is surrounded by a first insulator  310 , and the first insulator  310  is surrounded by a gate  210 . The second silicon pillar  810  includes a second conductive-type high-concentration impurity region  520  formed as a part of the second silicon pillar  810 , and a second conductive-type high-concentration impurity region  530  formed as a part of the second silicon pillar  810 . 
         [0054]    The semiconductor substrate  100  includes a second conductive-type high-concentration impurity region  510  formed as a part of the semiconductor substrate  100 , and a silicide region (first silicide)  720  formed as a part of the high-concentration impurity region  510 . The semiconductor substrate  100  also has an element isolation region  910  formed therein. 
         [0055]    The third silicon pillar  820  includes a second conductive-type high-concentration impurity region  540  formed as a part of the third silicon pillar  820 , and a silicide region (second silicide)  710  is formed in the high-concentration impurity region  540 . 
         [0056]    The semiconductor device according to the second embodiment further comprises a contact  430  formed on the silicide region  720 , a contact  420  formed on the silicide region  710 , and a contact  410  formed on the gate  210 . 
         [0057]    Differently from the first embodiment, on an assumption that a contact resistance R 1  formed by the semiconductor substrate  100  including the high-concentration impurity region  510  and the silicide region  720  formed in the semiconductor substrate  100  is ignorable, the structure in the second embodiment is designed to satisfy the following formula (2-1): 
         [0000]      R1&lt;&lt;Rs, R 1 &lt;&lt;R2  (2-1) 
         [0058]    In this case, in order to reduce a contact resistance or parasitic resistance R 2  formed by the third silicon pillar  820  including the high-concentration impurity region  540  and the silicide region  710  formed in the third silicon pillar  830 , it is preferable that the contact resistance R 2  and a reference resistance Rs satisfy the following formula (2-2): 
         [0000]      R2&lt;Rs  (2-2) 
         [0059]    The reference resistance Rs is calculated according to the following formula (2-3) based on a current I (A) which flows between the contact  410  and the contact  430  in the above semiconductor device when 0 (V) is applied to one of the contacts  410 ,  430  and V (V) is applied to a remaining one of the contacts  410 ,  430 , while applying V (V) to the contact  420 , under a condition that the contact resistance R 1 =0 and the contact resistance R 2 =0: 
         [0000]        Rs=V/I   (2-3) 
         [0060]    Specifically, when a length of the gate  210 , a film thickness of the gate oxide layer, and a diameter of the second silicon pillar  810 , are, respectively, 20 nm, 1 nm, and 10 nm, the contact resistance R of the third silicon pillar  820 , a contact resistivity ρ C , a sheet resistance ρ D  of a first conductive-type impurity region, a circumferential length K 2  of a cross-section of the third silicon pillar  820 , and a height dimension L 2  of the third silicon pillar  820 , satisfy the following formula (2-4), wherein α is expressed as the formula (2-5). Further, given that the circumferential length K 2  (cm) of the cross-section of the third silicon pillar  820  satisfies the following relational formula (2-6) with respect to a diameter W 2  (cm) of the third silicon pillar  820 . 
         [0000]    
       
         
           
             
               
                 
                   
                     R 
                      
                     
                         
                     
                      
                     2 
                   
                   = 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
                          
                         
                             
                         
                          
                         K 
                          
                         
                             
                         
                          
                         2 
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             2 
                           
                           α 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     4 
                   
                   ) 
                 
               
             
             
               
                 
                   α 
                   = 
                   
                     
                       ( 
                       
                         
                           ρ 
                           C 
                         
                         
                           ρ 
                           D 
                         
                       
                       ) 
                     
                     
                       1 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     5 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     K 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     π 
                      
                     
                         
                     
                      
                     W 
                      
                     
                         
                     
                      
                     2 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
         [0061]    The formula (2-4) is assigned to the formula (2-1) to obtain the following conditional formulas (2-7): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
                          
                         
                             
                         
                          
                         K 
                          
                         
                             
                         
                          
                         2 
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             2 
                           
                           α 
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     R 
                     s 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     7 
                   
                   ) 
                 
               
             
           
         
       
     
         [0062]    As one example, given that the contact resistivity ρ C  and the sheet resistance ρ D  are, respectively, 6.2e-8 (Ω-cm 2 ) and 6.4e-3/W 1  (Ω/sq.), and the current I (A) flowing between the contact  410  and the contact  430  in the above semiconductor device is 44 (μA) when 0 (V) is applied to one of the contacts  410 ,  430  and 1 (V) is applied to a remaining one of the contacts  410 ,  430 , while applying 1 (V) to the contact  420 , the reference resistance Rs is calculated as 2.3e-8 (Ω) according to the formula (2-3). These values are assigned to the formula (2-7) to obtain the following relational formula (2-8) between the height dimension L 2  (cm) of the third silicon pillar  820  and the circumferential length K 2  (cm) of the cross-section of the third silicon pillar  820 : 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       1 
                       
                         W 
                          
                         
                             
                         
                          
                         
                           2 
                           
                             3 
                             / 
                             2 
                           
                         
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             2 
                           
                           
                             
                               W 
                                
                               
                                   
                               
                                
                               
                                 
                                   2 
                                   
                                     1 
                                     / 
                                     2 
                                   
                                 
                                 · 
                                 3.1 
                               
                                
                               
                                   
                               
                                
                               e 
                             
                             - 
                             3 
                           
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     3.6 
                      
                     
                         
                     
                      
                     e 
                      
                     
                         
                     
                      
                     9 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
         [0063]    If the conditional formula (2-8) is satisfied, the formula (2-1) is satisfied. Thus, the following formula (2-9) is obtained (see  FIG. 14 ): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         1 
                         
                           W 
                            
                           
                               
                           
                            
                           
                             2 
                             
                               3 
                               / 
                               2 
                             
                           
                         
                       
                        
                       
                         coth 
                          
                         
                           ( 
                           
                             
                               L 
                                
                               
                                   
                               
                                
                               2 
                             
                             
                               
                                 W 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     2 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   · 
                                   3.1 
                                 
                                  
                                 
                                     
                                 
                                  
                                 e 
                               
                               - 
                               3 
                             
                           
                           ) 
                         
                       
                     
                     &lt; 
                     
                       3.6 
                        
                       
                           
                       
                        
                       e 
                        
                       
                           
                       
                        
                       9 
                     
                   
                   ⇒ 
                   
                     
                       R 
                        
                       
                           
                       
                        
                       2 
                     
                     &lt; 
                     Rs 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
         [0064]    As another example, given that a circumferential length of each of the second and first silicon pillars  810 ,  830 , the circumferential length of the third silicon pillar  820  and the gate length are set, respectively, in the range of 8 nm to 100 μm, in the range of 8 nm to 100 μm and in the range of 6 nm to 10 μm. Further, given that the diameter of the second silicon pillar  810 , the contact resistivity ρ C  and the sheet resistance ρ D  are, respectively, 2.6 nm, 7e-9 (Ω-cm 2 ) and 6.4e-3/W 1  (Ω/sq.), and the current I (A) flowing between the contact  410  and the contact  430  in the above semiconductor device is 11.4 (μA) when 0 (V) is applied to one of the contacts  410 ,  430  and 1 (V) is applied to a remaining one of the contacts  410 ,  430 , while applying 1 (V) to the contact  420 , the reference resistance Rs is calculated as 9.0e-8 (Ω) according to the formula (2-3). Thus, the formula (2-7) is expressed as the following formula (2-10): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
                          
                         
                             
                         
                          
                         K 
                          
                         
                             
                         
                          
                         2 
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             2 
                           
                           α 
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     R 
                     s 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
         [0065]    The above values are assigned to the formula (2-10) to obtain the following formula (2-11): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       1 
                       
                         W 
                          
                         
                             
                         
                          
                         
                           2 
                           
                             3 
                             / 
                             2 
                           
                         
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             2 
                           
                           
                             
                               W 
                                
                               
                                   
                               
                                
                               
                                 
                                   2 
                                   
                                     1 
                                     / 
                                     2 
                                   
                                 
                                 · 
                                 1.1 
                               
                                
                               
                                   
                               
                                
                               e 
                             
                             - 
                             3 
                           
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     4.3 
                      
                     
                         
                     
                      
                     e 
                      
                     
                         
                     
                      
                     10 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     11 
                   
                   ) 
                 
               
             
           
         
       
     
         [0066]    If the conditional formula (2-11) is satisfied, the formula (2-1) is satisfied. Thus, the following formula (2-12) is obtained: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         1 
                         
                           W 
                            
                           
                               
                           
                            
                           
                             2 
                             
                               3 
                               / 
                               2 
                             
                           
                         
                       
                        
                       
                         coth 
                          
                         
                           ( 
                           
                             
                               L 
                                
                               
                                   
                               
                                
                               2 
                             
                             
                               
                                 W 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     2 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   · 
                                   1.1 
                                 
                                  
                                 
                                     
                                 
                                  
                                 e 
                               
                               - 
                               3 
                             
                           
                           ) 
                         
                       
                     
                     &lt; 
                     
                       4.3 
                        
                       
                           
                       
                        
                       e 
                        
                       
                           
                       
                        
                       10 
                     
                   
                   ⇒ 
                   
                     
                       R 
                        
                       
                           
                       
                        
                       2 
                     
                     &lt; 
                     Rs 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     
                       - 
                     
                      
                     12 
                   
                   ) 
                 
               
             
           
         
       
     
       Third Embodiment 
     Semiconductor Device 
       [0067]      FIG. 15  is a schematic bird&#39;s-eye view showing a transistor of a semiconductor device according to a third embodiment of the present invention.  FIG. 16  is a schematic sectional view taken along the line A-A′ in  FIG. 15 , and  FIG. 17  is a top view of the transistor in  FIG. 14   FIG. 18  is a schematic sectional view taken along the line B-B′ in  FIG. 15  and  FIG. 19  is a schematic sectional view taken along the line C-C′ in  FIG. 15 . The semiconductor device according to the third embodiment comprises: a first silicon pillar  830  formed on a first conductive-type semiconductor substrate  100  to have a cross-sectionally circular shape; a second silicon pillar  810  formed on the first silicon pillar  830  to have a cross-sectionally circular shape; a first insulator  310  surrounding a part of a surface of the second silicon pillar  810 ; a gate  210  surrounding the first insulator  310 ; and a third silicon pillar  820  formed on the second silicon pillar  810  to have a cross-sectionally circular shape. 
         [0068]    The second silicon pillar  810  includes a second conductive-type high-concentration impurity region  520  formed as a part of the second silicon pillar  810 , and a second conductive-type high-concentration impurity region  530  formed as a part of the second silicon pillar  810 . 
         [0069]    The semiconductor substrate  100  includes a second conductive-type high-concentration impurity region  510  formed as a part of the semiconductor substrate  100 , and a silicide region (first silicide)  720  formed as a part of the high-concentration impurity region  510 . The semiconductor substrate  100  also has an element isolation region  910  formed therein. 
         [0070]    The third silicon pillar  820  includes a second conductive-type high-concentration impurity region  540  formed as a part of the third silicon pillar  820 , and a silicide region (second silicide)  710  is formed in the high-concentration impurity region  540 . 
         [0071]    The first silicon pillar  830  includes a second conductive-type high-concentration impurity region  550  formed as a part of the first silicon pillar  830 . 
         [0072]    The semiconductor device according to the third embodiment further comprises a contact  430  formed on the silicide region  720 , a contact  420  formed on the silicide region  710 , and a contact  410  formed on the gate  210 . 
         [0073]    Differently from the first embodiment, on an assumption that a contact resistance R 2  formed by the third silicon pillar  820  including the high-concentration impurity region  540  and the silicide region  710  formed in the third silicon pillar  830  is ignorable, the structure in the third embodiment is designed to satisfy the following formula (3-1): 
         [0000]      R2&lt;&lt;Rs, R2&lt;&lt;Rs  (3-1) 
         [0074]    In this case, in order to reduce a contact resistance or parasitic resistance R 1  formed by the first silicon pillar  830  including the high-concentration impurity region  510  and the silicide region  720  formed in the first silicon pillar  830 , it is preferable that the contact resistance R 1  and a reference resistance Rs satisfy the following formula (3-2): 
         [0000]      R 1 &lt;Rs  (3-2) 
         [0075]    The reference resistance Rs is calculated according to the following formula (3-3) based on a current I (A) which flows between the contact  410  and the contact  430  in the above semiconductor device when 0 (V) is applied to one of the contacts  410 ,  430  and V (V) is applied to a remaining one of the contacts  410 ,  430 , while applying V (V) to the contact  420 , under a condition that the contact resistance R 1 =0 and the contact resistance R 2 =0: 
         [0000]        Rs=V/I   (3-3) 
         [0076]    Specifically, when a length of the gate  210 , a film thickness of the gate oxide layer, and a diameter of the second silicon pillar  810 , are, respectively, 20 nm, 1 nm, and 10 nm, the contact resistance R 1  of the first silicon pillar  830 , a contact resistivity ρ C , a sheet resistance ρ D  of a first conductive-type impurity region, a circumferential length K 1  of a cross-section of the first silicon pillar  830 , and a height dimension L 1  of the first silicon pillar  830 , satisfy the following formula (3-4), wherein α is expressed as the formula (3-5). Further, given that the circumferential length K 1  (cm) of the cross-section of the first silicon pillar  830  satisfies the following relational formula (3-6) with respect to a diameter W 1  (cm) of the first silicon pillar  830 . 
         [0000]    
       
         
           
             
               
                 
                   
                     R 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
                          
                         
                             
                         
                          
                         K 
                          
                         
                             
                         
                          
                         2 
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             1 
                           
                           α 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     3 
                      
                     
                       - 
                     
                      
                     4 
                   
                   ) 
                 
               
             
             
               
                 
                   α 
                   = 
                   
                     
                       ( 
                       
                         
                           ρ 
                           C 
                         
                         
                           ρ 
                           D 
                         
                       
                       ) 
                     
                     
                       1 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     3 
                      
                     
                       - 
                     
                      
                     5 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     K 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     π 
                      
                     
                         
                     
                      
                     W 
                      
                     
                         
                     
                      
                     1 
                   
                 
               
               
                 
                   ( 
                   
                     3 
                      
                     
                       - 
                     
                      
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
         [0077]    The formula (3-4) is assigned to the formula (3-1) to obtain the following conditional formula (3-7): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
                          
                         
                             
                         
                          
                         K 
                          
                         
                             
                         
                          
                         1 
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             1 
                           
                           α 
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     R 
                     s 
                   
                 
               
               
                 
                   ( 
                   
                     3 
                      
                     
                       - 
                     
                      
                     7 
                   
                   ) 
                 
               
             
           
         
       
     
         [0078]    As one example, given that the contact resistivity ρ C  and the sheet resistance ρ D  are, respectively, 6.2e-8 (Ω-cm 2 ) and 1.6e-3×4/W 1  (Ω/sq.), and the current I (A) flowing between the contact  410  and the contact  430  in the above semiconductor device is 44 (μA) when 0 (V) is applied to one of the contacts  410 ,  430  and 1 (V) is applied to a remaining one of the contacts  410 ,  430 , while applying 1 (V) to the contact  420 , the reference resistance Rs is calculated as 2.3e-8 (Ω) according to the formula (3-3). These values are assigned to the formula (3-7) to obtain the following relational formula (3-8) between the height dimension L 1  of the first silicon pillar  830  and the circumferential length K 1  of the cross-section of the first silicon pillar  830 : 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       1 
                       
                         W 
                          
                         
                             
                         
                          
                         
                           1 
                           
                             3 
                             / 
                             2 
                           
                         
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             1 
                           
                           
                             
                               W 
                                
                               
                                   
                               
                                
                               
                                 
                                   1 
                                   
                                     1 
                                     / 
                                     2 
                                   
                                 
                                 · 
                                 3.1 
                               
                                
                               
                                   
                               
                                
                               e 
                             
                             - 
                             3 
                           
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     3.6 
                      
                     
                         
                     
                      
                     e 
                      
                     
                         
                     
                      
                     9 
                   
                 
               
               
                 
                   ( 
                   
                     3 
                      
                     
                       - 
                     
                      
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
         [0079]    If the conditional formula (3-8) is satisfied, the formula (3-1) is satisfied. Thus, the following formula (3-9) is obtained (see  FIG. 20 ): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         1 
                         
                           W 
                            
                           
                               
                           
                            
                           
                             1 
                             
                               3 
                               / 
                               2 
                             
                           
                         
                       
                        
                       
                         coth 
                          
                         
                           ( 
                           
                             
                               L 
                                
                               
                                   
                               
                                
                               1 
                             
                             
                               
                                 W 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     1 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   · 
                                   3.1 
                                 
                                  
                                 
                                     
                                 
                                  
                                 e 
                               
                               - 
                               3 
                             
                           
                           ) 
                         
                       
                     
                     &lt; 
                     
                       3.6 
                        
                       
                           
                       
                        
                       e 
                        
                       
                           
                       
                        
                       9 
                     
                   
                   ⇒ 
                   
                     
                       R 
                        
                       
                           
                       
                        
                       1 
                     
                     &lt; 
                     Rs 
                   
                 
               
               
                 
                   ( 
                   
                     1 
                      
                     
                       - 
                     
                      
                     13 
                   
                   ) 
                 
               
             
           
         
       
     
         [0080]    As another example, given that a circumferential length of each of the second and third silicon pillars  810 ,  820 , the circumferential length of the first silicon pillar  830  and the gate length are set, respectively, in the range of 8 nm to 100 μm, in the range of 8 nm to 100 μm and in the range of 6 nm to 10 μm. Further, given that the diameter of the second silicon pillar  810 , the contact resistivity ρ C  and the sheet resistance ρ D  are, respectively, 2.6 nm, 7e-9 (Ω-cm 2 ) and 1.6e-3×4/W 1  (Ω/sq.), and the current I (A) flowing between the contact  410  and the contact  430  in the above semiconductor device is 11.4 (μA) when 0 (V) is applied to one of the contacts  410 ,  430  and 1 (V) is applied to a remaining one of the contacts  410 ,  430 , while applying 1 (V) to the contact  420 , the reference resistance Rs is calculated as 9e-8 (Ω) according to the formula (3-3). Further, given that L 1 =L 2  and K 1 =K 2 , the following formula (3-10) is obtained: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ρ 
                         C 
                       
                       
                         α 
                          
                         
                             
                         
                          
                         K 
                          
                         
                             
                         
                          
                         1 
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             1 
                           
                           α 
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     R 
                     s 
                   
                 
               
               
                 
                   ( 
                   
                     3 
                      
                     
                       - 
                     
                      
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
         [0081]    The above values are assigned to the formula (3-10) to obtain the following formula (3-11): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       1 
                       
                         W 
                          
                         
                             
                         
                          
                         
                           1 
                           
                             3 
                             / 
                             2 
                           
                         
                       
                     
                      
                     
                       coth 
                        
                       
                         ( 
                         
                           
                             L 
                              
                             
                                 
                             
                              
                             1 
                           
                           
                             
                               W 
                                
                               
                                   
                               
                                
                               
                                 
                                   1 
                                   
                                     1 
                                     / 
                                     2 
                                   
                                 
                                 · 
                                 1.1 
                               
                                
                               
                                   
                               
                                
                               e 
                             
                             - 
                             3 
                           
                         
                         ) 
                       
                     
                   
                   &lt; 
                   
                     4.3 
                      
                     
                         
                     
                      
                     e 
                      
                     
                         
                     
                      
                     10 
                   
                 
               
               
                 
                   ( 
                   
                     3 
                      
                     
                       - 
                     
                      
                     11 
                   
                   ) 
                 
               
             
           
         
       
     
         [0082]    If the conditional formula (3-11) is satisfied, the formula (3-1) is satisfied. Thus, the following formula (3-12) is obtained: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         1 
                         
                           W 
                            
                           
                               
                           
                            
                           
                             1 
                             
                               3 
                               / 
                               2 
                             
                           
                         
                       
                        
                       
                         coth 
                          
                         
                           ( 
                           
                             
                               L 
                                
                               
                                   
                               
                                
                               1 
                             
                             
                               
                                 W 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     1 
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   · 
                                   1.1 
                                 
                                  
                                 
                                     
                                 
                                  
                                 e 
                               
                               - 
                               3 
                             
                           
                           ) 
                         
                       
                     
                     &lt; 
                     
                       4.3 
                        
                       
                           
                       
                        
                       e 
                        
                       
                           
                       
                        
                       10 
                     
                   
                   ⇒ 
                   
                     
                       R 
                        
                       
                           
                       
                        
                       1 
                     
                     &lt; 
                     Rs 
                   
                 
               
               
                 
                   ( 
                   
                     3 
                      
                     
                       - 
                     
                      
                     12 
                   
                   ) 
                 
               
             
           
         
       
     
         [0083]    In the first to third embodiments, each of the first silicide region  710  and the second silicide region  720  may be made of one selected from the group consisting of nickel (Ni) silicide, platinum (Pt) silicide, erbium (Er) silicide, ytterbium (Yb) silicide and a combination of two or more thereof. 
         [0084]    As mentioned above, the present invention provides a semiconductor device which comprises: a first silicon pillar formed on a semiconductor substrate; a second silicon pillar formed on the first silicon pillar; a first insulator surrounding a part of a surface of the second silicon pillar; a gate surrounding the first insulator; a third silicon pillar formed on the second silicon pillar; a first silicide surrounding a part of a surface of the first silicon pillar; and a second silicide surrounding a part of a surface of the third silicon pillar, wherein each of a contact resistance formed by the first silicide and the first silicon pillar, and a contact resistance formed by the second silicide and the third silicon pillar, is less than a reference resistance of the semiconductor device. 
         [0085]    The present invention can provide a semiconductor device capable of solving problems of increase in power consumption and lowering in operation speed due to an increase in parasitic resistance of an SGT, to achieve high-speed SGT operation and low power consumption.

Technology Classification (CPC): 7