The present invention relates to a structure of a semiconductor device including a thin film transistor. In particular, the present invention relates to a technique applicable to an active matrix liquid crystal display panel formed by using a thin film transistor (hereinafter abbreviated as TFT) for driving an image pixel. In the present specification, a semiconductor device represents an apparatus capable of functioning by utilizing semiconductor characteristics, and relates to an electro-optical device, a semiconductor circuit, and an electronic apparatus. Recently, techniques for using TFTs in a liquid crystal display device have actively been developed. This is because TFTs can provide a higher mobility than amorphous silicon TFTs. TFTs having the high mobility can be formed on a relatively large-sized substrate, and therefore, they are mainly used in the active matrix liquid crystal display device (hereinafter abbreviated as AM-LCD). There is a trend that needs for larger sizes and higher resolutions of AM-LCD are increasing. On the other hand, when a circuit is formed on a single crystal silicon substrate, the single crystal silicon substrate is required to have a size equal to a length (x-direction) of 5 inches or larger. In the case where a glass substrate is used for AM-LCD, it is difficult to produce a large-sized single crystal silicon substrate. Even though such a large-sized single crystal silicon substrate can be produced, it is small in the yield. Further, if a circuit is formed on such a single crystal silicon substrate, the cost of the substrate is increased to increase the cost of AM-LCD. Under the circumstances, a large-sized liquid crystal display device (including those having a size which is larger than that of AM-LCD) has been made by forming a TFT circuit on a glass substrate by using amorphous silicon (hereinafter abbreviated as a-Si). Even though, however, the circuit formation can be achieved by TFTs having the high mobility, the pixel pitch must be increased by the decreased number of the wirings. As a result, each of the pixels is increased in size. As an alternative, there is considered a technique for forming a pixel portion by using TFTs, and a peripheral circuit which operates in conjunction with the pixel portion by using a-Si. However, the following drawbacks are found in the AM-LCD of the peripheral circuit drive type. In a normally white mode AM-LCD, the ratio of a square of an effective pixel voltage to a square of a white peak voltage (hereinafter, square ratio) is a very important parameter. The white peak voltage means a voltage value when a liquid crystal is twisted to such a degree that light is transmitted and reaches a level of displaying white. When the square ratio is small, the obtained image is not clear. On the other hand, when the square ratio is large, power consumption is increased. The square ratio is determined by dividing an effective voltage applied to a liquid crystal when it is in a clear mode (no voltage is applied to the liquid crystal) by a voltage (hereinafter, white peak voltage) when the transmissivity is reversed to the maximum level (a level of displaying white). The larger the white peak voltage, the larger the value of the white peak voltage divided by the effective voltage, and the larger the square ratio. In other words, the white peak voltage and the effective voltage depend on the square ratio. A gate-source voltage (hereinafter, referred to as Vg) of a TFT is applied to a pixel electrode. In a TFT-type active matrix liquid crystal display device, a video signal is applied to a pixel electrode through a thin film transistor which is turned ON through a scanning signal from a gate wiring (gate signal wiring). In an ideal case, an ON-state drain current in the thin film transistor is in proportion to Vg-Vth, where Vg represents the gate-source voltage, and Vth represents a threshold voltage. In the above ideal case, a white peak voltage is increased as the square of a drain current is increased. That is, as the square of Vg-Vth is increased, the white peak voltage is increased. The threshold voltage Vth is determined by a channel length of a TFT and a carrier density of a channel. Thus, the threshold voltage Vth is substantially constant with respect to a large number of TFTs formed on a large-sized glass substrate. Accordingly, when the above-described method is applied to the above active matrix liquid crystal display device, the white peak voltage increases in association with the increase of the square ratio. A voltage applied to a pixel electrode can be increased to increase the white peak voltage. However, a driver circuit cannot be driven by the increased voltage because it is dependent on an output stage of the driver circuit. Further, even though a power source voltage for driving the liquid crystal panel can be increased in the active matrix liquid crystal display device, it is not preferable because it is not compatible with recent requirements for low power consumption. In order to achieve the compatibility of the power source voltage, the threshold voltage Vth must be lowered. However, in this case, when a gate voltage which is the same as or higher than the threshold voltage Vth is applied to the TFT, the drain current hardly flows, so that the video signal cannot be written in a pixel. In other words, when the drain current is compared with a gate voltage in the TFT, the threshold voltage Vth is compared with a drain voltage in the TFT, so that a relation between the drain current and the drain voltage is changed from the above ideal case. In consideration of the above, as the gate voltage in the TFT is increased to be higher than the threshold voltage Vth, the drain current increases in proportion to the gate voltage. However, when the drain current is compared with the drain voltage in the TFT, it is found that a relation between the drain current and the drain voltage is changed in a direction opposite to that of the above ideal case. That is, a drain current in the active matrix liquid crystal display device is generally compared with a gate voltage in the TFT in the following manner: a) when a value obtained by subtracting a value of the threshold voltage Vth from the gate voltage is smaller than 0 (V), a value obtained by dividing the drain current by the gate voltage is lower than 1 (I/V); b) when the value obtained by subtracting the value of the threshold voltage Vth from the gate voltage is not smaller than 0 (V), a value obtained by dividing the drain current by the gate voltage is not smaller than 1 (I/V); and c) the drain current is not proportional to the drain voltage when the value obtained by subtracting the value of the threshold voltage Vth from the gate voltage is not smaller than 0 (V), and a value obtained by dividing the drain current by the gate voltage is not smaller than 1 (I/V). Thus, when the voltage applied to the pixel electrode is large in the active matrix liquid crystal display device, the current which is the drain current of the TFT is greatly changed in accordance with the voltage when the TFT is turned ON. In addition, in the case where the peripheral circuit is formed of a TFT using a-Si, as described above, it is impossible to set the threshold voltage Vth to a sufficiently low level. As a result, it is difficult to achieve a large white peak voltage. As described above, when the voltage applied to the pixel electrode is large, the gate voltage of the TFT is determined by the drain voltage in the active matrix liquid crystal display device, so that the current which is the drain current of the TFT greatly changes in accordance with the voltage when the TFT is turned ON. In the peripheral circuit using a-Si, the gate voltage of the TFT cannot be greatly changed in accordance with the voltage applied to the drain, so that it is difficult to increase the white peak voltage in the peripheral circuit. FIG. 13 shows an example of an equivalent circuit of a TFT used for a pixel, and a parasitic capacity of the TFT, and a relation between the drain voltage and the drain current in the case where the gate voltage is large. In FIG. 13, there are shown a TFT 101 which is turned ON in response to a scanning signal .phi. supplied from a scanning signal line 102, a parasitic capacity 104 which is parasitic on the TFT 101, a liquid crystal which is driven by video signals supplied from a drain of the TFT 101, and a storage capacitor 103 which holds a voltage of the liquid crystal. Here, it is assumed that an amplitude of the video signal supplied to the drain of the TFT 101 is Vd, and a value of the parasitic capacity 104 is Cgd, and a capacitance value of the storage capacitor 103 is Cs. In FIG. 13, reference numerals 105 to 108 denote channel characteristics of the TFT 101