Abstract:
Provided is a D/A converter circuit which copes with high-bit digital signals and has favorable linearity and small occupation area. In a capacitive divider type DAC, capacitances are simply provided in a one-to-one relationship correspondingly to lower order bit digital signals instead of providing capacitances one-to-one correspondingly to bits. In a reset period, voltages having a height corresponding to higher order bit digital signals are provided to one electrodes (first electrodes) of the capacitances thereby charging the capacitances. In a write period, voltages having a height corresponding to lower order bit digital signals are provided to the other electrodes (second electrodes) of the capacitances thereby charging the capacitances.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to a D/A converter (digital/analog converter) circuit (DAC) and, more particularly, to a DAC for use in a driver circuit of a semiconductor device. Further, the invention relates to a semiconductor device using such a DAC. 
     2. Description of the Related Art 
     Recently, researches and developments have been actively made on the thin film transistors (TFTs) using, in an active layer, a polysilicon film formed on a glass substrate. The TFT using a polysilicon film has a mobility higher by two orders of magnitude as compared to the TFT using an amorphous silicon film, and hence can sufficiently acquire a current value required for operating a circuit even where a TFT gate width is down scaled. Consequently, a system-on-panel is possible to realize having a pixel region of a matrix-formed flat display panel and a driver circuit thereof formed on the same substrate. 
     Realizing a system-on-panel makes it possible to reduce the cost owing to the reduction of display assembling and inspection processes. It also makes feasible the reduction in flat-panel display size and enhancement of definition. 
     In pursuing size reduction and definition enhancement furthermore of the flat display panel, it is problematic to realize a DAC capable of operating at high speed but less in occupation area on a substrate. 
     The DACs, although existing in various kinds, include representatively a capacitive divider type and a resistive divider type. The capacitive divider type DAC can operate at high speed with less area as compared to the resistive divider type. 
     FIG. 11 shows an example of a prior-art DAC of a capacitive divider type. The prior-art capacitive divider type DAC shown in FIG. 11 has switches SW[ 1 ]-SW[n] in the number of n to be controlled by the bits of n-bit digital signals D 1 -D n , capacitances C, 2C, . . . , 2 n−1 C in the number of n respectively connected to the switches, and a resetting switch SW R . The prior-art DAC is connected with a power source A (voltage V A ) and a power source B (voltage V B ). The power sources A and B are kept at different voltages. The voltage of an analog signal outputted from the DAC is supplied onto an output line. 
     Note that, in the present description, voltage corresponds to a potential difference from a ground potential. 
     The corresponding-bit digital signals are respectively inputted to the switches SW[ 1 ]-SW[n]. Whether the capacitance is to be connected to the power source A or to the power source B is selected depending upon the information of 0 or 1 possessed by the input digital signal. 
     The operation of the prior-art DAC is explained in due order. The operation of the prior-art DAC is explained by separation with a reset period T R  and a write period T A . 
     At first, in a reset period T R , the reset switch SW R  closes. The digital signal is also reset to connect all the switches SW[ 1 ]-SW[n] to the same power source. It is herein assumed that connections are to the power source B. FIG. 12A shows an equivalent circuit diagram of the prior-art DAC at immediately before terminating the reset period. Note that C T  means a resultant capacitance of all the capacitances. 
     After terminating the reset period T R , a write period T A  commences to open the reset switch SW R . Subsequently, the digital signal in each bit having an arbitrary piece of information of 0 or 1 controls the switch SW[ 1 ]-SW[n]. The capacitances are connected to the power source A or B depending upon the bit of information. Due to this, the capacitances in the number of n are charged and thereafter placed in a steady state. The equivalent circuit diagram at this time is shown in FIG.  12 B. Note that C A  means a resultant capacitance of the capacitance connected to the power source A while C B  a resultant capacitance of the capacitance connected to the power source B. 
     Due to a sequence of operations in the foregoing reset period T R  and write period T A , the digital signal can be converted into an analog signal. 
     The capacitive divider type DAC is expected in proceeding the size reduction of the flat panel display because its high-speed operation with comparatively less area as compared to the resistive divider type DAC as mentioned above. However, as the digital signal is increased in bits in order to enhance the definition of the flat panel display, it becomes difficult even for the capacitive divider type DAC to suppress an occupation area on the substrate. 
     Should a capacitive divider type DAC be designed with a reduced capacity in order to suppress its occupation area, reduced is the area and value of a capacitance corresponding to the lowermost order bit. In the capacitance, somewhat deviation occurs in capacitance value due to mask deviation or the like during manufacture. loosening of patterning, unexpected parasitic capacitance, etc. For this reason, the design with a reduced capacitance increases the deviation ratio of the capacitance corresponding to the lowermost bit to its capacitance value. This makes it difficult to form a capacitive divider DAC favored in linearity. 
     Meanwhile, the resistive divider type DAC, if the corresponding signal is increased in bits, causes increase in output resistance to make difficult high-speed operation besides making impossible the reduction of area. 
     In view of the foregoing problem, it is a problem to manufacture a DAC capable of reducing the area and operating at high speed even where the digital signals are increased in bits, in order to further reduce the size and enhance the definition of a flat panel display. 
     SUMMARY OF THE INVENTION 
     The present inventor has provided capacitances one-to-one correspondingly to the bits of the lower order bit digital signals instead of providing capacitances one-to-one correspondingly to the bits. It has been considered that, in a reset period, a voltage having a height corresponding to the higher order bit digital signal is provided to the one electrodes (first electrodes) of the capacitances to thereby charge the capacitances while, in a write period, a voltage having a height corresponding to the lower order bit digital signals is provided to the other electrodes (second electrodes) of the capacitances to thereby charge the capacitances. Hereinafter, a reset period is referred to as a precharge period. 
     Specifically, the capacitances are charged in a precharge period by controlling the operation of a resistive divider DAC or selector circuit due to a higher order bit digital signals. 
     In the case of a DAC corresponding, for example, to n-bit digital signals D 1 -D n  of the invention, there are provided a resistive divider type DAC (R-DAC) or selector circuit corresponding to the higher order (n−m)-bit (m&lt;n) digital signals D m+1 -D n  and capacitances in the number of m corresponding to the lower order m bits of D 1 -D m . Hereinafter, the capacitance in the number of m corresponding to the lower m bits are referred merely to as a capacitance (C U ). 
     The values of the capacitances in the number of m are represented as C U [ 1 ]=C, C U [ 2 ]=2C, C U [ 3 ]=2 2 C, . . . , C U [m−1]=2 m−2 C and C U [m]=2 m−1 C (C is a constant), in the order of the capacitance corresponding to the lower order bit digital signal. 
     The DAC of the invention is connected to a power source A (voltage V A ), a power source B (voltage V B ), a power source C (voltage V C ) and a power source D (voltage V D ). In a write period T A , voltage is supplied to the first electrode of the capacitances C U  in the number of m by the power source C and power source D. 
     Meanwhile, the resistive divider type DAC or selector circuit corresponding to the higher order n−m bits possessed by the DAC of the invention is connected to the power source A and power source B. In a precharge period T P , the higher order (n−m)-bit digital signals are converted into an analog signal. In the present description, the analog signal is referred to as a precharge analog signal (voltage V P ). The voltage of a precharge analog signal outputted from the resistive divider type DAC or selector circuit is supplied to the second electrodes of the capacitances C U  in the number of m to charge these capacitances. 
     The second electrodes of all the capacitances C U  are connected to one output line. Consequently, the voltage on the output line, in other words the voltage of an analog signal to be outputted from the DAC, is determined depending on the charge stored in the write period and precharge period. 
     The above configuration can form a DAC corresponding to high-bit digital signals without losing linearity while making use of the merit of the capacitive divider type that driving is possible at high speed and area can be comparatively suppressed. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a diagram showing a configuration of a DAC having a configuration of the present invention; 
     FIG. 2 is a chart for explaining switch operation possessed by the DAC of the invention; 
     FIGS. 3A and 3B are equivalent circuit diagrams to the DAC of the invention; 
     FIG. 4 is a diagram showing a relationship between the bits of a digital signal and a voltage of an output analog signal; 
     FIG. 5 is a diagram showing a configuration of a DAC having a configuration of the present invention; 
     FIG. 6 is a diagram showing a configuration of a DAC having a configuration of the present invention; 
     FIG. 7 is a diagram showing a configuration of a DAC having a configuration of the present invention; 
     FIG. 8 is a circuit diagram of a switch to be used in the DAC of the invention; 
     FIGS. 9A to  9 E are views showing a manufacturing process for TFTs: 
     FIGS. 10A to  10 H are views showing electronic appliance using the DAC of the invention; 
     FIG. 11 is a diagram showing a configuration of a prior-art capacitive divider type DAC; and 
     FIGS. 12A and 12B are equivalent circuit diagrams showing the prior-art capacitive divider type DAC. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     [Embodiment 1] 
     FIG. 1 shows a configuration of a DAC of the present invention. The DAC shown in FIG. 1 converts higher order (n−m) bit digital signals into a precharge analog signal in a resistive divider circuit (R-DAC)  101 . 
     Meanwhile, there are provided capacitances C U [ 1 ], C U [ 2 ], C U [ 3 ], . . . , C U [m−1] and C U [m] in the number of m corresponding to the lower order m bits. 
     The values of capacitances C U  are represented as C U [ 1 ]=C, C U [ 2 ]=2C, C U [ 3 ]=2 2 C, . . . , C U [m−1]=2 m−2 C and C U [m]=2 m−1 C (C is a constant), in the order of the capacitance corresponding to the lower order bit. 
     The resistive divider circuit (R-DAC)  101  is connected to supply an output to the second electrodes of the capacitances C U  in the number of m through a precharge switch SW P . Namely, when the precharge switch SW P  is off, the R-DAC  101  does not supply an output to the second electrodes of the capacitances C U  in the number of m. When the precharge switch SW P  is on, the R-DAC  101  supplies an output to the second electrodes of the capacitances C U  in the number of m. 
     The switching of the precharge switch SW P  is controlled according to a precharge signal (Pre). 
     The second electrodes of the capacitances CU in the number of m are all connected to an output line  102  (voltage V OUT ). 
     The R-DAC  101  has resistances R L [ 1 ], R L [ 2 ], R L [ 3 ], . . . , R L [2 n−m ] in the number of 2 n−m  and switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], . . . , SWa[2 n−m ] in the number of 2 n−m . 
     Note that, in the present description, the resistance has at least two terminals. The terminals include an input/output terminal to provide an input to or output from the resistance and, besides, a common terminal common to an input and an output. In the present invention, the two input/output terminals of a resistance are referred to as resistance terminals. 
     The resistances in the number of 2 n−m  all have the same resistance value represented as R L [ 1 ]=R L [ 2 ]=R L [ 3 ]= . . . =R L [2 n−m ]=R (R is a constant). The resistances R L [ 1 ], R L [ 2 ], R L [ 3 ], . . . , R L [2 n−m ] in the number of 2 n−m  are all connected in series wherein the resistances R L [ 1 ] and R L [2 n−m ] positioned at the both ends of connection are respectively connected to a power source B and a power source A. 
     Meanwhile, connection is made to output, from the R-DAC  101 , the voltages of between the resistances connected in series and the voltage of the power source A, respectively, through the switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], . . . , SWa[2 n−m ] in the number of 2 n−m . Namely, when the SWa[t] (t=1 to n−m−1) is on, the voltage between R L [t] and R L [t+1] is equal to the output voltage of the R-DAC  101 . Connection is made in such a way that, when the SWa[n−m] is on, the output of R-DAC  101  is equal to the voltage V A  of the power source A. 
     The output is supplied to the second electrodes of the capacitance C U  in the number of m through the precharge switch SW P . 
     Note that, differently from FIG. 1, connection may be made to output, from the R-DAC  101 , the voltages of between the resistances connected in series and the voltage of the power source B, respectively, through the switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], . . . , SWa[2 n−m ] in the number of 2 n−m . 
     The capacitances C U  respectively have first electrodes connected to a power source C or power source D through switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[m−1] and SWb[m] in the number of m in the order from the capacitance corresponding to the lower order bit. 
     The lower order m bits are inputted to the switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[m−1] and SWb[m] in the number of m. During a write period, the switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[m−1] and SWb[m] in the number of m are controlled in switching according to the information of 1 or 0 possessed by the lower order m bits. 
     The output line  102  has an interconnection capacitance (C W ). V G  means a ground voltage. Note that the interconnection capacitance is not necessarily formed between the ground and the output line  102  but may be formed between a power source other than the ground and the output line. 
     The operation of the DAC of the invention shown in FIG. 1 will be explained in due order. The operation of the DAC of the invention is explained by separation with a precharge period T P  and a write period T A . FIG. 2 shows the operation in a precharge period T P  and write period T A  of the switches possessed by the DAC of the invention. 
     At first, in a precharge period T P , the precharge switch SW P  is turned on (ON) by a precharge signal (Pre). 
     The switches SWa[ 1 ], SWa[ 2 ], . . . , SWa[2 n−m −1] and SWa[2 n−m ] in the number of 2 n−m  corresponding to the higher order (n−m) bits are controlled in operation by the higher order (n−m)-bit digital signals D m+1 , D m+2 , . . . D n−1  and D n . 
     Specifically, the higher order (n−m)-bit digital signals D m+1 -D n , respectively have pieces of information of 1 or 0. There are 2 n−m  combinations of the pieces of information of 1 and 0 possessed by the higher order (n−m)-bit digital signals. Any one of the switches SWa[ 1 ], SWa[ 2 ], . . . , SWa[2 n−m −1] and SWa[2 n−m ] in the number of 2 n−m  is selected and turned on according to the 2 n−m  combinations of the pieces of information. 
     For example, when the switch SWa[x] (1≦x≦2 n−m ) is selected and turned on, the voltage V L  of the precharge analog signal is expressed by the following two equations.                V   L     =           (         R   L          [   1   ]       +   …   +       R   L          [     x   -   1     ]         )       (         R   L          [   1   ]       +   …   +       R   L          [     2     n   -   m       ]         )            (       V   B     -     V   A       )       +     V   A               [Equation  2]                                
     Because the resistance values of the resistances R L [ 1 ], R L [ 2 ], R L [ 3 ], . . . , R L [2 n−m ] in the number of 2 n−m  all are the same, the following Equation 3 is derived from Equation 2.                V   L     =           x   -   1       2     n   -   m              (       V   B     -     V   A       )       +     V   A               [Equation  3]                                
     The voltage (V L ) having a value determined by x in Equation 3 is outputted as a precharge analog signal from R-DAC  101 . 
     The precharge analog signal voltage V L  is supplied to the second electrode of the capacitance C U  and to the output line  102  through the precharge switch SW P . 
     Furthermore, by the lower order m-bit digital signals, the switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[m−1] and SWb[m] in the number of m corresponding to the lower order m bits are all connected to the power source C. 
     The equivalent circuit diagram of the DAC of the invention immediately before terminating the precharge period T P  is shown in FIG.  3 A. The capacitance C T  corresponds to a resultant capacitance of all the capacitances C U [ 1 ], C U [ 2 ], C U [ 3 ], . . . , C U [m]. 
     The total charge Q WP  stored on the interconnection capacitance (C W ) and capacitance C T  in the precharge period T P  is expressed by the following Equation 4: 
     
       
           Q   WP   =C   W ·( V   L   −V   G )+ C   T ·( V   L   −V   C )  [Equation 4] 
       
     
     After terminating the precharge period T P , the precharge switch SW P  turns off. Then, a write period T A  commences. 
     The switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[m−1] and SWb[m] in the number of m corresponding to the lower order m bits correspond, one to one, to the lower order m-bit digital signals D 1 , D 2 , . . . D m−1  and D m . In the write period T A , the switch is controlled in operation according to the information of 0 or 1 possessed by each bit. 
     Specifically, connection is made between the first electrodes of the capacitances C U [ 1 ], C U [ 2 ], . . . C U [m] and the power source C or D through the switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[m−1] and SWb[m] in the number of m. Whether connected to the power source C or D is determined depending on the information 1 or 0 possessed by each bit of the lower order m bits of the digital signal. 
     Incidentally, in the write period, the switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], . . . , SWa[2 n−m ] in the number of 2 n−m  may be any of on and off. 
     FIG. 3B shows an equivalent circuit diagram of the DAC of the invention at immediately before terminating the write period T A . The capacitance C A  is a resultant capacitance of those connected to the power source C of among all the capacitances C U . Meanwhile, the capacitance C B  is a resultant capacitance of those connected to the power source D of among all the capacitances C U . Accordingly, it can be considered that the following relationship of Equation 5 is held. 
     
       
           C   T   =C   A   +C   B   [Equation 5] 
       
     
     Meanwhile, C A  and C B  are held in the relationship of the following Equation 6: 
     
       
           C   A   +C   B   =C ·(1+2+2 2 + . . . +2 m−1 ) =C· (2 m −1)  [Equation 6] 
       
     
     The charge Q WA  stored on the capacitances C W , C A  and C B  in the write period T A  is expressed by the following Equation 7: 
     
       
           Q   WA   =C   W ·( V   OUT   −V   G )+ CB ·( V   OUT   −V   D )+ C   A ·( V   OUT   −V   C )  [Equation 7] 
       
     
     Herein, the charge Q WP  and the charge Q WA  become equal due to the conservation of electric charge. Therefore, the following Equation 8 is derived from Equation 4 and Equation 6. 
     
       
           C   W ·( V   L   −V   G )+ C   T ·( V   L   −V   C )= C   W ·( V   OUT   −V   G )+ C   B ·( V   OUT   −V   D )+ C   A ·( V   OUT   −V   C )  [Equation 8] 
       
     
     From Equations 8 and 5, the following Equation 9 is derived.                V   OUT     =       V   L     +         C   B     ·     (       V   D     -     V   C       )           C   W     +     C   T                   [Equation  9]                                
     From Equations 3, 5, 6 and 9, the following Equation 10 is derived:                V   OUT     =           x   -   1       2     n   -   m              (       V   B     -     V   A       )       +     V   A     +         C   B     ·     (       V   D     -     V   C       )           C   W     +     C   ·     (       2   m     -   1     )                     [Equation  10]                                
     When the value of x is fixed, in order to change V OUT  by one tonal level, C B  varies by a unit capacitance C. Accordingly, from Equation 10, the difference Δ 1  of one tonal level of V OUT  when the value x is fixed is expressed by the following Equation 11.                Δ   1     =       C   ·     (       V   D     -     V   C       )           C   W     +     C   ·     (       2   m     -   1     )                   [Equation  11]                                
     Consideration is made on the case that the value of x is varied to vary V OUT  by one tonal level. Because the switch SWa[x] is controlled by the higher order bit, in a tonal level, e.g., immediately before x increases by one, the lower order bit has information that all the capacitances are connected to the power source D, thus resulting in C B =C T . In a tonal level that x has increased by one, the lower order bit has information that all the capacitances are connected to the power source C, thus resulting in C B =0. 
     Consequently, from Equation 10, a difference Δ 2  by one tonal level of V OUT , when the value of x is variable, is expressed by the following Equation 12.                Δ   2     =         1     2     n   -   m              (       V   B     -     V   A       )       -         C   T     ·     (       V   D     -     V   C       )           C   W     +     C   ·     (       2   m     -   1     )                     [Equation  12]                                
     The linearity of analog signal voltage V OUT  requires to make equal Δ 1  and Δ 2 . Accordingly, the following Equation 13 is derived from Equations 11 and 12.                (       V   D     -     V   C       )     =       1       2   n     ·   C            (       V   B     -     V   A       )          {       C   W     +     C   ·     (       2   m     -   1     )         }               [Equation  13]                                
     The analog signal voltage V OUT  against the n-bit digital signals shown in Equation 10, satisfying Equation 13, is shown in a graph of FIG.  4 . As shown in FIG. 4, the analog signal voltage V OUT  has linearity at between V A  and V M  against input n-bit digital signals. Incidentally, V M  is expressed by the following Equation 14.                V   M     =             2   n     -   1       2     n   -   m              (       V   B     -     V   A       )       +     V   A     +         C   ·     (       2   m     -   1     )            (       V   D     -     V   C       )           C   W     +     C   ·     (       2   m     -   1     )                     [Equation  14]                                
     The n-bit digital signals can be converted into an analog signal by the sequential operation of the foregoing precharge period T P  and write period T A . 
     The invention can form a DAC corresponding to high-bit digital signals without losing linearity while making use of the merit of the capacitive divider type that is capable of driving at high speed and suppressing area comparatively small. 
     [Embodiment 2] 
     This embodiment explains a configuration using a selector circuit in place of the R-DAC in the DAC of the invention. 
     FIG. 5 shows a configuration of a DAC of the invention using a selector circuit. In the DAC shown in FIG. 5, the higher order (n−m)-bit digital signals are converted into a precharge analog signal in a selector circuit  201 . 
     Also, there are provided capacitances C U [ 1 ], C U [ 2 ], C U [ 3 ], . . . , C U [m−1] and C U [m] in the number of m corresponding to the lower order m bits. 
     The values of the capacitances C U  are represented as C U [ 1 ]=C, C U [ 2 ]=2C, C U [ 3 ]=2 2 C, . . . , C U [m−1]=2 m−2 C and C U [m]=2 m−1 C, in the order of the capacitance corresponding to the lower order bit. 
     The selector circuit  201  has tone voltage line  204  in the number of 2 n−m  and switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], . . . , SWa[2 n−m ] in the number of 2 n−m . 
     The voltages on the tone voltage lines  204  are respectively expressed as V A , V B +(V A −V B )/2 n−m , V B +2(V A −V B )/2 n−m , V B +3(V A −V B )/2 n−m , . . . , V B +(2 n−m −1)(V A −V B )/2 n−m . 
     Connection is made respectively between the switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], . . . , SWa[2 n−m ] in the number of 2 n−m  and the tone voltage lines  204 , to output the voltages of the tone voltage lines  204  through the switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], . . . , SWa[2 n−m ] in the number of 2 n−m . 
     The voltage outputted from the selector circuit  201  is supplied to the second electrode of the capacitance C U  and to an output line  202  through a precharge switch SW P . 
     The capacitance C U  has first electrodes connected to the power source C or D respectively through switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[m−1] and SWb[m] in the number of m in the order from the capacitance corresponding to the lower order bit. 
     Whether the second electrode is connected to either the power source C or the power source D is determined depending on the information possessed by each bit of the lower order m bits inputted to the switch SWb[ 1 ], SWb[ 2 ], . . . , SWb[m−1] or SWb[m]. 
     The precharge switch SW P  is controlled in switching according to a precharge signal (Pre). 
     The output line  202  has an interconnection capacitance (C W ). V G  means a ground voltage. Note that the interconnection capacitance is not necessarily formed between the ground and the output line  202  but may be formed between a power source other than the ground and the output line. 
     Now, the operation of the DAC of the invention shown in FIG. 5 is explained by separation with a precharge period T P  and a write period T A . The operation of each switch is similar to the case shown in Embodiment 1 and the explanation thereof is omitted herein. By controlling the operation of each switch by the use of a digital signal, the voltage of an analog signal inputted to the output line has linearity with respect to the bit of the digital signal. 
     The invention can form a DAC corresponding to the high-bit digital signals without losing linearity while making use of the merit of the capacitive divider type that is capable of driving at high speed and suppressing area comparatively small. 
     EXAMPLES 
     Explanations will be made below on the example of the present invention. 
     Example 1 
     This example explains the case with m=n−2 in the DAC of the invention shown in FIG.  1 . 
     FIG. 6 shows a configuration of the DAC of this example. The DAC shown in FIG. 6 converts the higher order 2-bit digital signals into a precharge analog signal in the resistive divider circuit  301 . 
     Meanwhile, there are provided capacitances C U [ 1 ], C U [ 2 ], C U [ 3 ], . . . , C U [n−3] and C U [n−2] in the number of n−2 corresponding to the lower order n−2 bits. 
     The values of capacitances C U  are represented as C U [ 1 ]=C, C U [ 2 ]=2C, C U [ 3 ]=2 2 C, . . . , C U [n−3]=2 n−4 C and C U [n−2]=2 n−3 C, in the order of the capacitance corresponding to the lower order bit. 
     The output of a resistive divider circuit (R-DAC)  301  is connected to a second electrodes of the capacitances C U  and to an output line V OUT  through a precharge switch SW P . The precharge switch SW P  is controlled in switching according to a precharge signal (Pre). 
     The R-DAC  301  has four resistances R L [ 1 ], R L [ 2 ], R L [ 3 ], R L [ 4 ] and four switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], SWa[ 4 ]. 
     The four resistances all have the same resistance value represented as R L [ 1 ]=R L[2]=R   L [ 3 ]=R L [ 4 ]=R (R is a constant). 
     The four resistances R L [ 1 ], R L [ 2 ], R L [ 3 ], R L [ 4 ] are all connected in series wherein the resistances R L [ 1 ] and R L [ 4 ] positioned at the both ends of connection are respectively connected to a power source B and a power source A. 
     The four resistances R L [ 1 ], R L [ 2 ], R L [ 3 ], R L [ 4 ] and the four switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], SWa[ 4 ] are connected to output the voltages of between the resistances connected in series and the voltage of power source A from the R-DAC  301  respectively through the four switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], SWa [ 4 ]. 
     The capacitances C U  has first electrodes connected to a power source C or D respectively through the switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[n−3] and SWb[n−2] in the number of n−2 in the order from the capacitance corresponding to the lower order bit. 
     In a write period, whether one electrode of the capacitance is connected to either of the power source C or the power source D is determined depending on the information possessed by each bit of the lower n−2 bits inputted to the switch SWb[ 1 ], SWb[ 2 ], . . . SWb[n−3] or SWb[n−2]. 
     The output line  302  has an interconnection capacitance (C W ). V G  means a ground voltage. Note that the interconnection capacitance is not necessarily formed between the ground and the output line  302  but may be formed between a power source other than the ground and the output line. 
     Now, the operation of the DAC of the invention shown in FIG. 6 is explained by separation with a precharge period T P  and a write period T A . The operation of each switch is similar to that in Embodiment 1 and hence the explanation thereof is herein omitted. By controlling the operation of each switch by the use of a digital signal, the voltage of an analog signal inputted to the output line has linearity with respect to the bit of the digital signal. 
     The invention can form a DAC corresponding to the higher order bit digital signals without losing linearity while making use of the merit of the capacitive divider type that is capable of driving at high speed and suppressing area comparatively small. 
     Incidentally, although this example described on the case with m=n−2, the invention is not limited to this. It is possible for a designer to properly select a value of m. 
     Example 2 
     This example explains the case with m=n−2 in the DAC of the invention shown in FIG.  5 . 
     FIG. 7 shows a configuration of the DAC of this example. The DAC shown in FIG. 7 converts the higher order 2-bit digital signals into a precharge analog signal in the selector circuit  401 , thereby converting n-bit digital signals into an analog signal. 
     Meanwhile, there are provided capacitances C U [ 1 ], C U [ 2 ], C U [ 3 ], . . . , C U [n−3] and C U [n−2] in the number of n−2 corresponding to the lower order n−2 bits. 
     The values of capacitances C U  are represented as C U [ 1 ]=C, C U [ 2 ]=2C, C U [ 3 ]=2 2 C, . . . , C U [n−3]=2 n−4 C and C U [n−2]=2 n−3 C, in the order of the capacitance corresponding to the lower order bit. 
     The selector circuit  401  has four tone voltage lines  404  and four switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], SWa[ 4 ]. 
     The voltages on the tone voltage lines  404  are respectively expressed as V A , V A +(V B −V A )/4, V A +2(V B −V A )/4, V A +3(V B −V A )/4. 
     The tone voltage lines  404  and the switches SWa[ 1 ], SWa[ 2 ], SWa[ 3 ], SWa[ 4 ] are respectively connected to output the voltage of the tone voltage line  404  from the selector circuit  401  through the switch SWa[ 1 ], SWa[ 2 ], SWa[ 3 ] or SWa[ 4 ]. 
     The voltage outputted from the selector circuit  401  is supplied to the second electrodes of capacitances C U  and to an output line  202  through a precharge switch SW P . 
     The capacitances C U  have first electrodes connected to the power source C or D through respective switches SWb[ 1 ], SWb[ 2 ], . . . , SWb[n−1] and SWb[n−2] in the number of n−2 in the order from the capacitance corresponding to the lower order bit. 
     Whether the first electrode of the capacitance C U  is connected to either the power source C or the power source D is determined depending on the information possessed by each bit of the lower order n−2 bits inputted to the switch SWb[ 1 ], SWb[ 2 ], . . . , SWb[n−3] or SWb[n−2]. 
     The precharge switch SW P  is controlled in switching according to a precharge signal (Pre). 
     The output line  402  has an interconnection capacitance (C W ). V G  means a ground voltage. Note that the interconnection capacitance is not necessarily formed between the ground and the output line  402  but may be formed between a power source other than the ground and the output line. 
     Now, the operation of the DAC of the invention shown in FIG. 7 is explained by separation with a precharge period T P  and a write period T A . The operation of each switch is similar to the case shown in Embodiment 1 and the explanation thereof is omitted herein. By controlling the operation of each switch by the use of a digital signal, the voltage of an analog signal inputted to the output line has linearity with respect to the bit of the digital signal. 
     The invention can form a DAC corresponding to the higher order bit digital signals without losing linearity white making use of the merit of the capacitive divider type that is capable of driving at high speed and suppressing area comparatively small. 
     Example 3 
     This example shows one example of a switch corresponding to the higher order bits used in the DAC of the invention. 
     The switch of this example in FIG. 8 is a transmission gate having an n-channel transistor TFT and a p-channel transistor TFT. A digital signal and a signal of the digital signal inverted in polarity (inverted digital signal) are respectively inputted to IN and INb. 
     By the digital signal and inverted digital signal inputted to IN and INb, a voltage supplied to an input terminal is sampled and supplied to an output terminal. 
     Meanwhile, the switch corresponding to the lower order bit has two transmission gates shown in FIG.  8 . The two transmission gates have input signals to IN and INb alternately. 
     The switch used in the DAC of the invention is not limited to the configuration shown in FIG.  8 . 
     It is noted that the configuration of this example can be carried out by a free combination with Examples 1 and 2. 
     Example 4 
     An example of a process of manufacturing a TFT used in a DAC of the present invention is explained in Example 4. Note that although processes for manufacturing a p-channel TFT and an n-channel TFT are only shown in FIGS. 9A to  9 E, it is possible to produce all transistors used by the present invention based on the processes in FIGS. 9A to  9 E. 
     In addition to a glass substrate such as barium borosilicate glass or aluminum borosilicate glass, typically Corning Corp. #7059 or #1737, a plastic substrate having no optical anisotropy such as polyethelylene terephthalate (PET), polyethylene naphthalate (PEN), or polyethel sulfon (PES) can be used in a substrate  1001  in FIG.  9 A. Further, a quartz substrate may also be used. If heat treatment is performed in advance at a temperature on the order of 10 to 20° C. less than the distortion point of the glass when using a glass substrate, then changes in shape of the glass substrate in subsequent processes can be prevented. 
     A base film  1002  having a thickness of 10 to 200 nm is formed from an insulating film such as a silicon oxide film, a silicon nitride film, or a silicon nitride oxide film, on the surface of the substrate  1001  on which TFTs will be manufactured, in order to prevent impurity element diffusion. The base film may be formed by one layer of the insulating film, and may also be formed by a plurality of layers. 
     Island shape semiconductor layers  1003  and  1004  are formed from a crystalline semiconductor film in which a semiconductor film having an amorphous structure is crystallized by a method such as laser annealing, thermal annealing, or rapid thermal annealing (RTA). Further, a crystalline semiconductor film formed by a method such as sputtering, plasma CVD, or thermal CVD may also be used. Alternatively, the crystalline semiconductor layers  1003  and  1004  can also be formed by a crystallization method using a catalytic element, in accordance with a technique disclosed by Japanese Patent Application Laid-open No. Hei 7-130652. In this crystallization process, it is preferable to first remove hydrogen contained in the amorphous semiconductor layer. If crystallization is performed after the amount of contained hydrogen is made equal to or less than 5 atom % by performing heat treatment at 400 to 500° C. for approximately 1 hour, then roughness of the film surface can be prevented. Whichever method is used, the crystalline semiconductor film thus formed is selectively etched, forming the island shape semiconductor layers  1003  and  1004  in predetermined locations. 
     Alternatively, an SOI (silicon on insulator) substrate in which a single crystal silicon layer is formed on the substrate  1001  may also be used. There are many types known depending upon the structure and method of manufacture of the SOI substrate, and typically substrates such as SIMOX (separation by implanted oxygen), ELTRAN (epitaxial layer transfer, a trademark of Canon Corp.), or Smart-Cut (a trademark of SOITEC Corp.) can be used. Of course, it is also possible to use other SOI substrates. 
     A gate insulating film having a thickness of 40 to 150 nm is formed from an insulating film containing silicon by a method such as plasma CVD, sputtering, or reduced pressure CVD. For example, it may be formed from a film such as a silicon oxide film, a silicon nitride film, or a silicon nitride oxide film. This is taken as a gate insulating film  1005  having a first shape. A conductive layer  1006  is then formed on the first shape gate insulating film  1005  in order to form gate electrodes. It is preferable to form the conductive layer  1006  from a conductive material having resistance to heat. It may be formed from a single layer, and it may also have a lamination structure made from a plurality of layers, such as two layers or three layers, when necessary. For example, the conductive layer  1006  may be formed by an element selected from the group consisting of tungsten (W), tantalum (Ta), titanium (Ti), and molybdenum (Mo), or from an alloy with the above elements as constituents, or from an alloy film of a combination of the above elements. Further, the conducting layer may be formed into a lamination structure with a nitride compound of the above elements, such as tungsten nitride (WN), tantalum nitride (TaN), titanium nitride (TiN), or molybdenum nitride (MoN), or a silicide compound such as tungsten silicide, tantalum silicide, titanium silicide, or molybdenum silicide. A first shape mask  1007  is then formed. The first shape mask  1007  is formed by a photolithography technique using a resist material. 
     Etching of the conducting layer  1006  is performed next, as shown by FIG.  9 B. The etching process is performed using a dry etching method, preferably by using an ICP etching apparatus. A gas mixture of CF 4  and Cl 2  is used as an etching gas, and a bias voltage is applied to the substrate. At the very least, conducting layers  1008  and  1009  having a first tapered shape are formed on the island shape semiconductor layers  1003  and  1004 . The shape of the tapered portion can be changed in accordance with the etching gas mixture ratio, with the etching pressure, and with the bias voltage applied to the substrate. The bias voltage applied to the substrate is most suitable for controlling the tapered shape. 
     Dry etching is performed by elements such as fluorine (F) and chlorine (Cl), or by neutral particles or ionic particles of molecules containing fluorine or chlorine. Normally, etching proceeds in an isotropic manner if it is controlled by neutral seeds, and a tapered shape is difficult to form. Etching proceeds in an anisotropic manner by applying a positive or a negative bias voltage to the substrate. Etching for forming a tapered shape is performed by applying a bias voltage to the substrate, and by etching the resist at the same time, with the difference in etching rate between the film and the resist (also referred to as selective ratio, and expressed as the etching rate of the product to be processed/etching rate of resist) used as a value in a certain fixed range. By first making an appropriate resist shape, and then performing an etching gradually from an edge portion of the resist, a tapered shape can be formed in the film underneath. The shape of the first shape mask  1007  also changes, forming a second shape mask  1010 . Further, the surface of the gate insulating film  1005  under the conductive layer  1006  is exposed as etching proceeds, and the gate insulating film is also etched to a certain extent from its surface, forming a second shape gate insulating film  1011 . 
     The resist  1010  is then used as a mask, and a first doping process is performed. An impurity element is added to impart n-type conductivity to the island shape semiconductor layers  1003  and  1004 . An ion doping method or an ion injection method in which the impurity element is ionized, accelerated by an electric field, and then injected into the semiconductor layers, is used for the doping process. An impurity element imparting n-type conductivity passes through the gate insulating film and is added to the semiconductor layers  1003  and  1004  below. A portion of the n-type conductivity imparting impurity element passes through edge portions of the first shape gate electrodes  1008  and  1009 , and their vicinity, and can be added to the semiconductor layers below. 
     First impurity regions  1012  and  1013  contain the single conductivity type impurity element at a concentration of 1×10 20  to 1×10 21  atoms/cm 3 . Further, the concentration of the impurity element added to the semiconductor layer in second impurity regions  1014  and  1015  is low compared to that of the first impurity regions  1012  and  1013  by the amount in which the thickness of the second shape gate insulating film  1011  increases. A uniform concentration distribution is not always able to be obtained within the second impurity element regions  1014  and  1015 , but the impurity element is added so as to fall within a range of 1×10 17  to 1×10 20  atoms/cm 3 . 
     The second impurity regions  1014  and  1015  are formed under the gate insulating film  1011  and the tapered portions of the conductive layers  1008  and  1009 . The concentration distribution of the impurity element in the second impurity regions  1014  and  1015  decreases as distance from the first impurity regions  1012  and  1013  increases. The ratio of the decrease varies in accordance with conditions of the acceleration voltage and the dosage during ion doping, with the angle of the tapered portion, and with the thickness of the first shape gate electrodes  1008  and  1009 . 
     A second etching process is performed next, as shown in FIG.  9 C. In the second etching process, the first shape gate electrodes  1008  and  1009  are etched so as to make the width in a channel longitudinal direction shorter. The method of etching is the same as that of the first etching process, and an ICP etching apparatus is used. A gas mixture of CF 4  and Cl 2  is used as an etching gas, and a bias voltage is applied to the substrate, forming a second shape gate electrodes  1016  and  1017 . A portion of the base gate insulating film  1011  is etched from its surface in the second etching process, forming a second shape gate insulating film  1018 . Tapered portions are also formed in edge portions of the conductive layers  1016  and  1017  having the second tapered shape in FIG.  9 C. 
     A second doping process is then performed with the resist  1021  used as a mask, and the n-type conductivity imparting impurity element is added to the island shape semiconductor layers  1003  and  1004 . In this case, a portion of the impurity element can pass through the edge portions of the second shape gate electrodes  1016  and  1017 , and their vicinity, and can be added to the semiconductor layer below. 
     The second doping process is performed so that the single conductivity type impurity element is contained at a concentration of 1×10 16  to 5×10 18  atoms/cm 3 . The single conducting type impurity element is added in this process to the first impurity regions  1012  and  1013 , and to the second impurity regions  1014  and  1015  formed by the first doping process, but the amount added thereto is low, and therefore its influence can be ignored. Newly formed third impurity regions  1019  and  1020  are made to contain the single conducting type impurity element at a concentration of 1×10 16  to 5×10 18  atoms/cm 3 . In the third impurity regions  1019  and  1020  is reduced the concentration of the impurity element added to the semiconductor layer by the amount in which the thickness of the second tapered shape gate electrodes  1016  and  1017  increase. Although a uniform concentration distribution cannot necessarily be obtained within the third impurity regions  1019  and  1020 , the impurity element is made to be contained within the above concentration range. 
     The third impurity regions  1019  and  1020  are formed beneath the second shape gate insulating film  1018 , and beneath the tapered portions of the second shape gate electrodes  1016  and  1017 . Their concentration distributions decrease as distances from the first impurity regions  1012  and  1013  increase. The second shape gate electrodes  1016  and  1017  are used as gate electrodes. With the edge portions of the gate electrodes given a tapered shape, and by doping the impurity element through the tapered portions, impurity regions can thus be formed in the semiconductor layers existing under the tapered portion in which the concentration of the impurity element changes gradually. The present invention actively utilizes this impurity region. Forming this type of impurity region relieves a high electric field that develops in the vicinity of the drain region, and prevents the generation of hot carriers. Deterioration of the TFT can thus be prevented. 
     The island shape semiconductor layer  1003  is then covered with a resist mask  1022  as shown in FIG. 9D, and an impurity element which imparts p-type conductivity is added to the island shape semiconductor layer  1004 . The second shape gate electrode  1017  acts as a mask in this case as well, and the p-type conductivity imparting impurity element is added, forming an impurity region in a self-aligning manner. An impurity region  1023  formed here is formed by ion doping method using diborane (B 2 H 6 ). The concentration of the p-type conductivity imparting impurity element of the impurity region  1023  is set so as to be from 2×10 20  to 2×10 21  atoms/cm 3 . 
     However, the impurity region  1023  can be seen in detail to be divided into three regions containing the impurity element which impart n-type conductivity. A fourth impurity region  1023   a  contains the n-type conductivity imparting element at a concentration of 1×10 20  to 1×10 21  atoms/cm 3 , a fifth impurity region  1023   b  contains the n-type conductivity imparting element at a concentration of 1×10 17  to 1×10 20  atoms/cm 3 , and a sixth impurity region  1023   c  contains the n-type conductivity imparting element at a concentration of 1×10 16  to 5×10 18  atoms/cm 3 . However, the concentration of the p-type conductivity impurity element in the impurity regions  1023   b  and  1023   c  is made to be equal to or greater than 1×10 19  atoms/cm 3 , and the concentration of the p-type conductivity imparting impurity element in the fourth impurity region  1023   a  is made to be from 1.5 to 3 times the concentration of the impurity element which imparts n-type conductivity. As a result, there develops no problem in using the fourth impurity region  1023   b  as a source region or a drain region of a p-channel TFT. Further, a portion of the sixth impurity region  1023   c  is formed so as to overlap with of the second shape gate electrode  1017 . 
     Thus a first impurity region  1024 , which becomes a source region or a drain region, a second impurity region  1025 , which forms an LDD region not overlapping the gate electrode, a third impurity region  1026  which forms an LDD region a portion of which overlaps with the gate electrode, and a channel forming region  1027  are formed in the island shape semiconductor layer  1003 . Further, a first impurity region  1028 , which becomes a source region or a drain region, a second impurity region  1029 , which forms an LDD region not overlapping the gate electrode, a third impurity region  1030  which forms an LDD region a portion of which overlaps with the gate electrode, and a channel forming region  1031  are formed in the island shape semiconductor layer  1004 . 
     An interlayer insulating film  1032  and a wiring  1034  for forming contact with a source region or a drain region may also be formed next when necessary, as shown in FIG.  9 E. 
     It is possible to implement Example 4 by freely combining it with any of Examples 1 to 3. 
     Example 5 
     A semiconductor device having a DAC of the present invention can be used in various electronic devices. 
     Examples of electronic devices which use the DAC of the present invention include: video cameras; digital cameras, goggle type displays (head mounted displays); navigation systems; audio playback devices (such as car audio systems and audio component systems); notebook personal computers; game machines; portable information terminals (such as mobile computers, portable telephones, portable game machines, and electronic books); and image reproducing devices provided with a recording medium (specifically, devices provided with displays for displaying images when playing back a recording medium such as a digital versatile disk (DVD)). Specific examples of these electronic devices are shown in FIGS. 10A to  10 H. 
     FIG. 10A is a display device, and contains parts such as a frame  2001 , a support stand  2002 , a display portion  2003 , a speaker portion  2004 , and a video input terminal  2005 . The DAC of the present invention can be used in the display portion  2003  and in other control circuits. Note that display devices include all information display devices for, for example, personal computers, television broadcast transmitter-receivers, and advertisement displays. 
     FIG. 10B is a digital still camera, which contains parts such as a main body  2101 , a display portion  2102 , an image receiving portion  2103 , operation keys  2104 , external connection ports  2105 , and a shutter  2106 . The DAC of the present invention can be used in the display portion  2102  and in other control circuits. 
     FIG. 10C is a notebook personal computer, which contains parts such as a main body  2201 , a frame  2202 , a display portion  2203 , a keyboard  2204 , external connection ports  2205 , and a pointing mouse  2206 . The DAC of the present invention can be used in the display portion  2203  and in other control circuits. 
     FIG. 10D is a mobile computer, which contains parts such as a main body  2301 , a display portion  2302 , switches  2303 , operation keys  2304 , and an infrared port  2305 . The DAC of the present invention can be used in the display portion  2302  and in other control circuits. 
     FIG. 10E is a portable image reproducing device image reproducing device provided with a recording medium (specifically, a DVD playback device), which contains parts such as a main body  2401 , a frame  2402 , a display portion A  2403 , a display portion B  2404 , a recording medium (such as a DVD) read-in portion  2405 , operation keys  2406 , and a speaker portion  2407 . The display portion A  2403  mainly displays image information, and the display portion B  2404  mainly displays character information, and the DAC of the present invention can be used in the display portion A  2403  and in the display portion B  2404 , as well as in other control circuits. Note that family game machines and the like are included in the category of image reproducing devices provided with a recording medium. 
     FIG. 10F is a goggle type display (head mounted display), which contains a main body  2501 , a display portion  2502 , and arm portions  2503 . The DAC of the present invention can be used in the display portion  2502  and in other control circuits. 
     FIG. 10G is a video camera, which contains parts such as a main body  2601 , a display portion  2602 , a frame  2603 , external connection ports  2604 , a remote control signal receiving portion  2605 , an image receiving portion  2606 , a battery  2607 , an audio input portion  2608  and an operation keys  2609 . The DAC of the present invention can be used in the display portion  2602  and in other control circuits. 
     FIG. 10H is a portable telephone, which contains parts such as a main body  2701 , a frame  2702 , a display portion  2703 , an audio input portion  2704 , an audio output portion  2705 , operation keys  2706 , an external connection portion  2707 , and an antenna  2708 . The DAC of the present invention can be used in the display portion  2703  and in other control circuits. 
     Further, the aforementioned electronic devices often display information received through electronic communication lines such as the Internet and CATV (cable television), and opportunities for displaying moving pictures in particular have increased. The DAC of the present invention is capable of high speed operation, is capable of converting a high bit number of digital signal into an analog signal, and can ensure linearity of the output analog signal. The DAC of the present invention is therefore valuable. 
     The applicable range of the DAC of the present invention is thus extremely wide, and the DAC of the present invention can be used in electronic equipment in all fields. Further, the electronic devices of Example 5 may use DACs having any of the structures shown in Examples 1 to 4. 
     With the configuration of the invention, a DAC can be formed corresponding to the higher order bit digital signals without losing linearity while making use of the merit of the capacitive divider type that is capable of driving at high speed and suppressing area comparatively small.