Abstract:
Many of the principles of an oxide semiconductor are still unclear and therefore there is no established method for evaluating an oxide semiconductor. Thus, an object is to provide a novel method for evaluating an oxide semiconductor. Carrier density is evaluated, and hydrogen concentration is also evaluated. Specifically, a MOS capacitor (a diode or a triode) is manufactured, and the C-V characteristics of the MOS capacitor are obtained. Then, the carrier density is estimated from the C-V characteristics obtained.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     A technical field of the present invention relates to an evaluation method, a method for manufacturing a semiconductor device, and the like. 
     2. Description of the Related Art 
     Reference 1 discloses a method for manufacturing a semiconductor device including an oxide semiconductor.
     [Reference 1] Japanese Published Patent Application No. 2007-123861   

     SUMMARY OF THE INVENTION 
     Many of the principles of a silicon semiconductor have already been understood, whereas many of the principles of an oxide semiconductor are still unclear and therefore there is no established method for evaluating an oxide semiconductor. 
     Thus, it is a first object to provide a novel method for evaluating an oxide semiconductor. 
     It is a second object to provide a method for feeding back a result of evaluation of an oxide semiconductor to a manufacturing process of a semiconductor device including an oxide semiconductor (a device including a semiconductor element such as a transistor or a diode). 
     It is a third object to provide a novel method for measuring the relative permittivity of an oxide semiconductor. 
     Note that the invention disclosed below solves at least one of the first to third objects. 
     In a silicon semiconductor, hydrogen is a favorable atom which compensates for dangling bonds. 
     On the other hand, as a result of research by the present inventors, it is found that hydrogen in an oxide semiconductor induces unwanted carriers and is therefore an unfavorable atom in the case where an oxide semiconductor is used for a channel formation region of a transistor. 
     Here, as the concentration of hydrogen in an oxide semiconductor decreases, the carrier density (carrier concentration) of the oxide semiconductor also decreases. 
     Then, if the carrier density can be evaluated, the concentration of impurities such as hydrogen can also be evaluated. 
     Thus, the evaluation of the carrier density makes it possible to make an evaluation as to what kind of process should be performed to decrease the hydrogen concentration. 
     For example, in the case of performing heat treatment, a plurality of samples are prepared under different heating conditions such as heating temperatures, heating time, or heating methods, and the carrier densities of the plurality of samples are compared with each other. Accordingly, it is possible to make an evaluation as to what is the optimum heating condition for removing hydrogen. 
     For example, in the case of forming an oxide semiconductor layer, a plurality of samples were prepared under different film formation conditions such as film formation temperatures, film formation atmospheres, or film formation chamber evacuating methods, and the carrier densities of the plurality of samples are compared with each other. Accordingly, it is possible to make an evaluation as to what is the optimum film formation condition for removing hydrogen. 
     Specifically, a MOS capacitor is manufactured, and the results of C-V measurement (C-V characteristics) of the MOS capacitor are evaluated. Accordingly, the carrier density can be measured. 
     In other words, an evaluation method includes the step of forming a MOS capacitor including an oxide semiconductor layer, the step of obtaining a C-V characteristic by plotting a relationship between a gate voltage V g  and a capacitance C of the MOS capacitor, the step of obtaining a graph by plotting a relationship between the gate voltage V g  and (1/C) 2  with the use of the C-V characteristic, and the step of calculating a carrier density N d  by obtaining a differential value of (1/C) 2  in a weak inversion region of the graph and substituting the differential value into the following mathematical formula (12). Note that in the mathematical formula (12), e is the electron charge, ε 0  is the vacuum permittivity, and ε is the relative permittivity of the oxide semiconductor layer. 
     
       
         
           
             
               
                 
                   
                     N 
                     d 
                   
                   = 
                   
                     
                       - 
                       
                         ( 
                         
                           2 
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ɛ 
                               0 
                             
                             ⁢ 
                             ɛ 
                           
                         
                         ) 
                       
                     
                     / 
                     
                       
                         ⅆ 
                         
                           
                             ( 
                             
                               1 
                               / 
                               C 
                             
                             ) 
                           
                           2 
                         
                       
                       
                         ⅆ 
                         V 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     In addition, an evaluation method includes the step of forming a first MOS capacitor by forming a first oxide semiconductor layer over a silicon wafer and forming a gate electrode over the first oxide semiconductor layer, the step of obtaining a first C-V characteristic of the first MOS capacitor, the step of obtaining a capacitance C a  in an accumulation region of the first C-V characteristic, the step of obtaining a relative permittivity ε of the first oxide semiconductor layer by substituting the capacitance C a  into the following mathematical formula (14), the step of forming a second MOS transistor by forming a second oxide semiconductor layer under a film formation condition which is identical to that of the first oxide semiconductor layer, the step of obtaining a second C-V characteristic by plotting a relationship between a gate voltage V g  and a capacitance C of the second MOS capacitor, the step of obtaining a graph by plotting a relationship between the gate voltage V g  and (1/C) 2  with the use of the second C-V characteristic, and the step of calculating a carrier density N d  by obtaining a differential value of (1/C) 2  in a weak inversion region in the graph and substituting the differential value and a relative permittivity ε of the first oxide semiconductor layer into the following mathematical formula (12). Note that in the mathematical formula (12), e is the electron charge and ε 0  is the vacuum permittivity, and in the mathematical formula (14), S is the area of the gate electrode and d is the thickness of the first oxide semiconductor layer. 
     
       
         
           
             
               
                 
                   ɛ 
                   = 
                   
                     
                       C 
                       a 
                     
                     ⁢ 
                     
                       1 
                       
                         ɛ 
                         0 
                       
                     
                     ⁢ 
                     
                       d 
                       S 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     N 
                     d 
                   
                   = 
                   
                     
                       - 
                       
                         ( 
                         
                           2 
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ɛ 
                               0 
                             
                             ⁢ 
                             ɛ 
                           
                         
                         ) 
                       
                     
                     / 
                     
                       
                         ⅆ 
                         
                           
                             ( 
                             
                               1 
                               / 
                               C 
                             
                             ) 
                           
                           2 
                         
                       
                       
                         ⅆ 
                         V 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     In addition, in an evaluation method, a MOS capacitor including an oxide semiconductor layer is formed, a C-V characteristic of the MOS capacitor is obtained, and a carrier density of the oxide semiconductor layer is determined with reference to a capacitance of the MOS capacitor when a gate voltage of the MOS capacitor is 0. 
     In addition, a method for manufacturing a semiconductor device includes the step of forming a MOS capacitor including an oxide semiconductor layer and a transistor including an oxide semiconductor layer at a time, the step of obtaining a C-V characteristic by plotting a relationship between a gate voltage V g  and a capacitance C of the MOS capacitor, the step of obtaining a graph by plotting a relationship between the gate voltage V g  and (1/C) 2  with the use of the C-V characteristic, the step of calculating a carrier density N d  by obtaining a differential value of (1/C) 2  in a weak inversion region in the graph and substituting the differential value into the following mathematical formula (12), and the step of performing heat treatment of the transistor when the carrier density is determined to be high. Note that in the mathematical formula (12), e is the electron charge, ε 0  is the vacuum permittivity, and ε is the relative permittivity of the oxide semiconductor layer. 
     
       
         
           
             
               
                 
                   
                     N 
                     d 
                   
                   = 
                   
                     
                       - 
                       
                         ( 
                         
                           2 
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ɛ 
                               0 
                             
                             ⁢ 
                             ɛ 
                           
                         
                         ) 
                       
                     
                     / 
                     
                       
                         ⅆ 
                         
                           
                             ( 
                             
                               1 
                               / 
                               C 
                             
                             ) 
                           
                           2 
                         
                       
                       
                         ⅆ 
                         V 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     In addition, a method for manufacturing a semiconductor device includes the step of forming a first MOS capacitor by forming a first oxide semiconductor layer over a silicon wafer and forming a gate electrode over the first oxide semiconductor layer, the step of obtaining a first C-V characteristic of the first MOS capacitor, the step of obtaining a capacitance C a  in an accumulation region of the first C-V characteristic, the step of obtaining a relative permittivity ε of the first oxide semiconductor layer by substituting the capacitance C a  into the following mathematical formula (14), the step of forming a second MOS capacitor and a transistor including a second oxide semiconductor layer formed under a film formation condition which is identical to that of the first oxide semiconductor layer, the step of obtaining a second C-V characteristic by plotting a relationship between a gate voltage V g  and a capacitance C of the second MOS capacitor, the step of obtaining a graph by plotting a relationship between the gate voltage V g  and (1/C) 2  with the use of the second C-V characteristic, the step of calculating a carrier density N d  by obtaining a differential value of (1/C) 2  in a weak inversion region in the graph and substituting the differential value and the relative permittivity ε of the first oxide semiconductor layer into the following mathematical formula (12), and the step of performing heat treatment of the transistor when the carrier density is determined to be high. Note that in the mathematical formula (12), e is the electron charge and ε 0  is the vacuum permittivity, and in the mathematical formula (14), S is the area of the gate electrode and d is the thickness of the first oxide semiconductor layer. 
     
       
         
           
             
               
                 
                   ɛ 
                   = 
                   
                     
                       C 
                       a 
                     
                     ⁢ 
                     
                       1 
                       
                         ɛ 
                         0 
                       
                     
                     ⁢ 
                     
                       d 
                       S 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     N 
                     d 
                   
                   = 
                   
                     
                       - 
                       
                         ( 
                         
                           2 
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ɛ 
                               0 
                             
                             ⁢ 
                             ɛ 
                           
                         
                         ) 
                       
                     
                     / 
                     
                       
                         ⅆ 
                         
                           
                             ( 
                             
                               1 
                               / 
                               C 
                             
                             ) 
                           
                           2 
                         
                       
                       
                         ⅆ 
                         V 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     As described above, a novel method for evaluating an oxide semiconductor can be provided. 
     In addition, by evaluating an oxide semiconductor and giving feedback, a high-performance semiconductor device can be provided. 
     Furthermore, a semiconductor element is manufactured and then evaluated, and when it is determined that hydrogen is not sufficiently removed, heat treatment is additionally performed. Accordingly, a so-called repair step can be performed. Note that repairing a semiconductor layer itself is a quite novel idea. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  each illustrate an example of a MOS capacitor. 
         FIGS. 2A and 2B  each show an example of C-V characteristics. 
         FIGS. 3A and 3B  show an example of C-V characteristics. 
         FIG. 4  illustrates an example of a MOS capacitor. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments will be described in detail with reference to the drawings. 
     Note that it is easily understood by those skilled in the art that the modes and details of the present invention can be modified in various ways without departing from the spirit and scope thereof. 
     Therefore, the scope of the present invention should not be interpreted as being limited to the description in the following embodiments. 
     Note that in structures described below, the same portions or portions having similar functions are denoted by the same reference numerals in different drawings, and explanation thereof will not be repeated. 
     The following embodiments can be implemented in combination as appropriate. 
     (Embodiment 1) 
       FIGS. 1A and 1B  each illustrate an example of a MOS capacitor. 
       FIG. 1A  is a diode and  FIG. 1B  is a triode. 
     In  FIG. 1A , a semiconductor layer  200  (Semiconductor) is provided over a metal layer  100  (Metal), and a gate insulating layer  300  (Gate Insulator) is provided over the semiconductor layer  200  (Semiconductor), and a gate electrode layer  400  (Gate Electrode) is provided over the gate insulating layer  300  (Gate Insulator). 
     In addition, in  FIG. 1A , the metal layer  100  (Metal) and the gate electrode layer  400  (Gate Electrode) are connected to each other through a power source. 
     In  FIG. 1B , a gate insulating layer  201  (Gate Insulator) is provided over a gate electrode layer  101  (Gate Electrode), and a semiconductor layer  301  (Semiconductor) is provided over the gate insulating layer  201  (Gate Insulator), and a source electrode layer  401  (Source) and a drain electrode layer  501  (Drain) are provided over the semiconductor layer  301  (Semiconductor). 
     In addition, in  FIG. 1B , the source electrode layer  401  (Source) and the drain electrode layer  501  (Drain) are connected to the gate electrode layer  101  (Gate Electrode) through a power source. 
     The diode of  FIG. 1A  has an advantage in that it can be easily manufactured without a photolithography step. 
     Thus, the diode is suitable for an experiment for examining the effectiveness of a specific step (for example, comparison of heating conditions, comparison of film formation conditions, and the like). 
     On the other hand, the triode of  FIG. 1B  has a structure obtained by electrically connecting a source and a drain of a transistor. 
     Thus, it is easy to form the triode at the same time as a transistor, and the triode is therefore suitable for evaluation in the case of forming a transistor. 
     Note that the semiconductor layer (Semiconductor) can be formed using, for example, an In—Ga—Zn—O-based oxide semiconductor, an In—Sn—Zn—O-based oxide semiconductor, an In—Al—Zn—O-based oxide semiconductor, a Sn—Ga—Zn—O-based oxide semiconductor, an Al—Ga—Zn—O-based oxide semiconductor, a Sn—Al—Zn—O-based oxide semiconductor, an In—Zn—O-based oxide semiconductor, a Sn—Zn—O-based oxide semiconductor, an Al—Zn—O-based oxide semiconductor, an In—O-based oxide semiconductor, a Sn—O-based oxide semiconductor, a Zn—O-based oxide semiconductor, or the like. 
     This embodiment can be implemented in combination with any of the other embodiments. 
     (Embodiment 2) 
     The evaluation of results of C-V measurement (C-V characteristics) of a MOS capacitor will be described. 
       FIGS. 2A and 2B  each show an example of results of C-V measurement (C-V characteristics) of an oxide semiconductor. 
     Here,  FIG. 2A  shows an example of results of C-V measurement (C-V characteristics) in the case where hydrogen is contained in an oxide semiconductor. 
     On the other hand,  FIG. 2B  shows an example of results of C-V measurement (C-V characteristics) in the case where hydrogen is not contained in an oxide semiconductor. 
     In an oxide semiconductor, hydrogen serves as a donor. 
     Therefore, an oxide semiconductor which contains hydrogen is an n-type semiconductor ( FIG. 2A ). 
     On the other hand, an oxide semiconductor which does not contain hydrogen is close to an i-type (intrinsic) semiconductor ( FIG. 2B ). 
     Thus, when hydrogen is contained in an oxide semiconductor, the graph of C-V characteristics is shifted to the left side (compare  FIG. 2A  to  FIG. 2B ). 
     In other words, it can be determined that the carrier density is increased if a capacitance C at V g  (gate voltage) of 0 is larger than that at V g  which is negative (in a strong inversion region). 
     In other words, it can be determined that the hydrogen concentration is increased if the capacitance C at V g  (gate voltage) of 0 is larger than that at V g  which is negative (in a strong inversion region). 
     This embodiment can be implemented in combination with any of the other embodiments. 
     (Embodiment 3) 
     In the case where only a small amount of hydrogen is contained, it may be difficult to make an evaluation according to the method described in Embodiment 2. 
     Thus, in this embodiment, an evaluation method which is different from that in Embodiment 2 will be described. 
     Specifically, a method for estimating the carrier density of an oxide semiconductor from a C-V curve will be described. 
     First, the mathematical formula (1) can be provided, where C is the capacitance per unit area of an oxide semiconductor which is measured by C-V measurement, C d  is the depletion layer capacitance per unit area of the oxide semiconductor, and C ox  is the capacitance of the gate insulating film. 
     
       
         
           
             
               
                 
                   
                     1 
                     C 
                   
                   = 
                   
                     
                       1 
                       
                         C 
                         d 
                       
                     
                     + 
                     
                       1 
                       
                         C 
                         ox 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     By transposing the mathematical formula (1), the mathematical formula (2) can be obtained. 
     
       
         
           
             
               
                 
                   
                     1 
                     
                       C 
                       d 
                     
                   
                   = 
                   
                     
                       1 
                       C 
                     
                     - 
                     
                       1 
                       
                         C 
                         ox 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Here, in the case of considering a weak inversion state, it is assumed that induced minority carriers are negligible. 
     Then, the charge Q per unit area which is generated in a depletion layer can be expressed by the mathematical formula (3), where N d  is the carrier density, W d  is the depletion layer width, and e is the electron charge.
 
Q=eN d W d   (3)
 
     Then, the capacitance C can be given by the mathematical formula (4), where V is the voltage applied to the gate electrode. 
     
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       ⅆ 
                       Q 
                     
                     
                       ⅆ 
                       V 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     On the other hand, the depletion layer capacitance C d  can be expressed by the mathematical formula (5) with the charge Q and the surface potential ψ. Note that ε 0  is the vacuum permittivity and ε is the relative permittivity of a semiconductor. 
     
       
         
           
             
               
                 
                   
                     C 
                     d 
                   
                   = 
                   
                     
                       
                         ⅆ 
                         Q 
                       
                       
                         ⅆ 
                         ψ 
                       
                     
                     = 
                     
                       
                         
                           ɛ 
                           0 
                         
                         ⁢ 
                         ɛ 
                       
                       
                         W 
                         d 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In addition, the surface potential ψ at a semiconductor interface can be given by the mathematical formula (6) by solving the Poisson equation. 
     
       
         
           
             
               
                 
                   ψ 
                   = 
                   
                     - 
                     
                       
                         
                           eN 
                           d 
                         
                         ⁢ 
                         
                           W 
                           d 
                           2 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ɛ 
                           0 
                         
                         ⁢ 
                         ɛ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     By substituting the mathematical formula (6) into the mathematical formula (5), the mathematical formula (7) can be derived. 
     
       
         
           
             
               
                 
                   ψ 
                   = 
                   
                     
                       - 
                       
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ɛ 
                             0 
                           
                           ⁢ 
                           ɛ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             N 
                             d 
                           
                         
                         2 
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           1 
                           
                             C 
                             d 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     From the mathematical formulae (3) to (7), the mathematical formula (8) can be derived. 
     
       
         
           
             
               
                 
                   
                     C 
                     d 
                   
                   = 
                   
                     
                       
                         ⅆ 
                         Q 
                       
                       
                         ⅆ 
                         ψ 
                       
                     
                     = 
                     
                       
                         
                           
                             ⅆ 
                             Q 
                           
                           
                             ⅆ 
                             V 
                           
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 ⅆ 
                                 ψ 
                               
                               
                                 ⅆ 
                                 V 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                       
                       = 
                       
                         
                           - 
                           
                             C 
                             ⁡ 
                             
                               ( 
                               
                                 2 
                                 
                                   
                                     eN 
                                     d 
                                   
                                   ⁢ 
                                   
                                     ɛ 
                                     0 
                                   
                                   ⁢ 
                                   ɛ 
                                 
                               
                               ) 
                             
                           
                         
                         / 
                         
                           ( 
                           
                             
                               ⅆ 
                               
                                 
                                   ( 
                                   
                                     1 
                                     / 
                                     
                                       C 
                                       d 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                             
                             
                               ⅆ 
                               
                                   
                               
                               ⁢ 
                               V 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     By taking reciprocals of both sides of the mathematical formula (8), the mathematical formula (9) can be given. 
     
       
         
           
             
               
                 
                   
                     1 
                     
                       C 
                       d 
                     
                   
                   = 
                   
                     
                       - 
                       
                         1 
                         C 
                       
                     
                     ⁢ 
                     
                       
                         
                           eN 
                           d 
                         
                         ⁢ 
                         
                           ɛ 
                           0 
                         
                         ⁢ 
                         ɛ 
                       
                       2 
                     
                     ⁢ 
                     
                       
                         ⅆ 
                         
                           
                             ( 
                             
                               1 
                               / 
                               
                                 C 
                                 d 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         ⅆ 
                         V 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     By substituting the mathematical formula (2) into the mathematical formula (9), the mathematical formula (10) can be obtained. 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       C 
                     
                     - 
                     
                       1 
                       
                         C 
                         ox 
                       
                     
                   
                   = 
                   
                     
                       - 
                       
                         1 
                         C 
                       
                     
                     ⁢ 
                     
                       
                         
                           eN 
                           d 
                         
                         ⁢ 
                         
                           ɛ 
                           0 
                         
                         ⁢ 
                         ɛ 
                       
                       2 
                     
                     ⁢ 
                     
                       
                         ⅆ 
                         
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   1 
                                   / 
                                   C 
                                 
                                 ) 
                               
                               - 
                               
                                 ( 
                                 
                                   1 
                                   / 
                                   
                                     C 
                                     ox 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         ⅆ 
                         V 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     N d  can be calculated from the mathematical formula (10) as expressed by the mathematical formula (11). 
     
       
         
           
             
               
                 
                   
                     N 
                     d 
                   
                   = 
                   
                     
                       - 
                       
                         
                           2 
                           ⁢ 
                           C 
                         
                         
                           e 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ɛ 
                             0 
                           
                           ⁢ 
                           ɛ 
                         
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             1 
                             C 
                           
                           - 
                           
                             1 
                             
                               C 
                               ox 
                             
                           
                         
                         ) 
                       
                       / 
                       
                         
                           ⅆ 
                           
                             
                               ( 
                               
                                 
                                   ( 
                                   
                                     1 
                                     / 
                                     C 
                                   
                                   ) 
                                 
                                 - 
                                 
                                   ( 
                                   
                                     1 
                                     / 
                                     
                                       C 
                                       ox 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         
                           ⅆ 
                           V 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Here, in a weak inversion state, it can be assumed that C&lt;&lt;C ox . Thus, 1/C ox  can be assumed to be 0, and therefore the mathematical formula (11) can be approximated. 
     Then, by approximating the mathematical formula (11), the mathematical formula (12) can be obtained. 
     
       
         
           
             
               
                 
                   
                     N 
                     d 
                   
                   = 
                   
                     
                       - 
                       
                         ( 
                         
                           2 
                           
                             e 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ɛ 
                               0 
                             
                             ⁢ 
                             ɛ 
                           
                         
                         ) 
                       
                     
                     / 
                     
                       
                         ⅆ 
                         
                           
                             ( 
                             
                               1 
                               / 
                               C 
                             
                             ) 
                           
                           2 
                         
                       
                       
                         ⅆ 
                         V 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     See  FIGS. 3A and 3B . 
       FIG. 3A  is a graph in which the relationship between gate voltage V g  and capacitance C is plotted, and  FIG. 3B  is a graph in which the relationship between gate voltage V g  and (1/C) 2  is plotted. 
     In  FIG. 3A , “A” corresponds to a strong inversion region; “B”, a weak inversion region adjacent to the strong inversion region; and “C”, an accumulation region. 
     Note that in order to calculate a differential value of (1/C) 2  in the mathematical formula (12), the weak inversion region is used, which is adjacent to the strong inversion region where it can be particularly assumed that C&lt;&lt;C ox . 
     Note that as the weak inversion region adjacent to the strong inversion region, a region where it can be assumed that C&lt;&lt;C ox  may be selected as appropriate. 
     Here, the slope of a straight line of a linear function which is indicated by a dotted line in  FIG. 3B  corresponds to the differential value of (1/C) 2  in the mathematical formula (12). 
     Therefore, the graph in which the relationship between gate voltage V g  and (1/C) 2  in the weak inversion region is plotted is obtained from results of C-V measurement (C-V characteristics), and the differential value of (1/C) 2  in the mathematical formula (12) is obtained from the graph as obtained above. 
     On the other hand, the carrier density N d  can be calculated by substituting the electron charge e, the vacuum permittivity ε 0 , the relative permittivity ε of a semiconductor, and the differential value of (1/C) 2  into the mathematical formula (12). 
     Note that the electron charge e (1.60217653×10 −19  coulomb) and the vacuum permittivity ε 0  (8.85418782×10 −12  m −3 kg −1 s 4 A 2 ) are constants; thus, these values may be used. 
     The relative permittivity ε of a semiconductor may be measured in advance by optical absorption spectrum measurement, electron energy loss spectroscopy, or the like. 
     An object of this embodiment is not to calculate an accurate carrier density but to evaluate whether hydrogen has been removed or not. Thus, the calculation may be performed using a region where C ox  is two or more times as large as C, as the region where it can be assumed that C&lt;&lt;C ox . 
     Note that it is more preferable that C ox  be five or more times, ten or more times, or a hundred or more times as large as C; however, there are cases where C ox  is less than five times, ten times, or a hundred times as large as a minimum of C. Thus, in this embodiment, the region where it can be assumed that C&lt;&lt;C ox  is a region where C ox  is two or more times as large as C. 
     This embodiment can be implemented in combination with any of the other embodiments. 
     (Embodiment 4) 
     The relative permittivity ε of an oxide semiconductor layer can also be obtained from C-V characteristics. 
     First, a diode as illustrated in  FIG. 4  is formed. 
     In  FIG. 4 , an oxide semiconductor layer  202  (Oxide Semiconductor) is provided over a p-type silicon wafer  102  (Silicon Wafer (P)), and a gate electrode layer  302  (Gate Electrode) is provided over the oxide semiconductor layer  202  (Oxide Semiconductor). Note that an n-type silicon wafer may be used. 
     The band gap of an oxide semiconductor layer is much wider than that of silicon. 
     Therefore, there is a potential barrier between the conduction band of the oxide semiconductor and the conduction band of silicon. Similarly, there is a potential barrier between the valence band of the oxide semiconductor and the valence band of silicon. 
     Due to the presence of these potential barriers, C-V characteristics can be obtained with the structure of  FIG. 4 . 
     Note that as the resistance of the oxide semiconductor layer increases, the leakage current decreases and the measurement accuracy thus increases. 
     Therefore, an oxide semiconductor layer having lower carrier density can be measured with higher accuracy. 
     Note that the methods described in Embodiments 1 to 3 are also suitable for evaluating the carrier density of an oxide semiconductor layer having low carrier density. 
     Here, in an inversion state (inversion region, where V g  is positive), the capacitance is the sum of the depletion layer capacitance of the p-type silicon wafer and the capacitance of the oxide semiconductor layer. 
     On the other hand, in an accumulation state (accumulation region, where V g  is negative), an inversion layer is not formed; thus, the capacitance is equal to the capacitance of the oxide semiconductor layer and is saturated. 
     Then, the saturation capacitance C a  in an accumulation state satisfies the relationship in the mathematical formula (13), where ε 0  is the vacuum permittivity, d is the thickness of the oxide semiconductor layer, and S is the area of the gate electrode. 
     
       
         
           
             
               
                 
                   
                     C 
                     a 
                   
                   = 
                   
                     
                       ɛ 
                       0 
                     
                     ⁢ 
                     ɛ 
                     ⁢ 
                     
                       S 
                       d 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     By modifying the mathematical formula (13), the mathematical formula (14) can be obtained. 
     
       
         
           
             
               
                 
                   ɛ 
                   = 
                   
                     
                       C 
                       a 
                     
                     ⁢ 
                     
                       1 
                       
                         ɛ 
                         0 
                       
                     
                     ⁢ 
                     
                       d 
                       S 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     The thickness d of the oxide semiconductor layer and the area S of the gate electrode are set at the time of manufacturing. 
     Note that the vacuum permittivity ε 0  (8.85418782×10 −12  m −3 kg −1 s 4 A 2 ) is a constant; thus, this value may be used. 
     By manufacturing a MOS capacitor having a special structure as illustrated in  FIG. 4  in the above manner, the relative permittivity can be calculated using the mathematical formula (14). 
     This embodiment can be implemented in combination with any of the other embodiments. Note that the MOS capacitor of this embodiment and MOS capacitors of other embodiments are formed separately. Thus, the oxide semiconductor layer of the MOS capacitor of this embodiment and oxide semiconductor layers of MOS capacitors of other embodiments are preferably formed under identical film formation conditions (the same film formation conditions). 
     (Embodiment 5) 
     An example of a method for utilizing evaluation results will be described. 
     A plurality of samples having the structure of  FIG. 1A  or  1 B is prepared. 
     In Example 1, the plurality of samples is a sample where the semiconductor layer is not heated, a sample where the semiconductor layer is heated at A° C., and a sample where the semiconductor layer is heated at B° C. 
     In Example 2, the plurality of samples is a sample where the semiconductor layer is not heated, a sample where the semiconductor layer is heated at A° C. in an oxygen atmosphere, and a sample where the semiconductor layer is heated at A° C. in a nitrogen atmosphere. 
     In Example 3, the plurality of samples is a sample where the semiconductor layer is formed at a first composition ratio, a sample where the semiconductor layer is formed at a second composition ratio, and a sample where the semiconductor layer is formed at a third composition ratio. 
     In Example 4, the plurality of samples is a sample where the semiconductor layer is formed at the first composition ratio by a sputtering method using only oxygen plasma, a sample where the semiconductor layer is formed at the first composition ratio by a sputtering method using only argon plasma, and a sample where the semiconductor layer is formed at the first composition ratio by a sputtering method using oxygen plasma and argon plasma. 
     Then, the carrier densities of the plurality of samples are compared by any of the evaluation methods in the other embodiments. 
     As a result of comparison of the carrier densities of the plurality of samples, the semiconductor layer formed under the conditions where the lowest carrier density is obtained can be determined to be the closest to an i-type (intrinsic) semiconductor layer. 
     In Example 1, it is possible to evaluate whether heating should be performed or not, whether the heating temperature is appropriate or not, and the like. 
     In Example 2, it is possible to evaluate whether heating should be performed or not, whether the heating atmosphere is appropriate or not, and the like. 
     In Example 3, it is possible to evaluate the tendency toward the optimum composition ratio. 
     In Example 4, it is possible to evaluate whether film formation atmosphere is appropriate or not. 
     By examining C-V characteristics with various different conditions as in Examples 1 to 4, the optimum process can be selected. 
     This embodiment can be implemented in combination with any of the other embodiments. 
     )Embodiment 6) 
     An example of a method for utilizing evaluation results will be described. 
     A triode having the structure of  FIG. 1B  and a bottom-gate TFT are formed over the same substrate. 
     Then, C-V characteristics of the triode are obtained by any of the evaluation methods in the other embodiments, and thus the carrier density is obtained. 
     When the carrier density is high, there is a possibility that heat treatment is not sufficient and hydrogen remains. 
     Thus, in the case where the carrier density is high, heat treatment is preferably performed again (at a temperature higher than or equal to 150° C. and lower than or equal to the upper temperature limit of the substrate, preferably at a temperature higher than or equal to 550° C. and lower than or equal to the upper temperature limit of the substrate). 
     Note that in the case where the carrier density is low, the process proceeds to the next step without heat treatment (in other words, no action is taken). 
     In addition, it is found from the experience of the present inventors that the off-state current of a transistor increases when the carrier density is 1×10 18  cm −3  or more. Therefore, the carrier density is preferably less than 1×10 18  cm −3 . 
     In other words, the carrier density is determined to be high when higher than or equal to 1×10 18  cm −3 . 
     However, the allowable range of characteristics required for a transistor changes depending on a device for which the transistor is used. Thus, a criterion for determining whether the carrier concentration is high or low may be set as appropriate. For example, the carrier concentration may be determined to be high when higher than or equal to 1×10 17  cm −3 , 1×10 16  cm −3 , 1×10 15  cm −3 , 1×10 14  cm −3 , or the like. 
     In this manner, in-process inspection and repair can be performed by using any of the evaluation methods in the other embodiments. 
     This embodiment can be implemented in combination with any of the other embodiments. 
     This application is based on Japanese Patent Application serial no. 2009-255230 filed with Japan Patent Office on Nov. 6, 2009, the entire contents of which are hereby incorporated by reference.