Field effect transistors (hereinafter referred to as FET) are well known.  FIGS.  1A to 1D show a conventional manufacturing process for a conventional FET in a stepwise manner.  A silicon oxide film 2a is formed on a P type semiconductor substrate.  A layer 3a of silicon or a conductive material such as a metal having a high melting point is formed on the silicon oxide film. ( FIG.  1A).  The polysilicon layer 3a and the silicon oxide film 2 are simultaneously etched by a known etching method, and a gate electrode 3 and a gate insulating film 2 are formed (FIG.  1B).  A known etching method is disclosed in, for example, "Microfabrication Technique by Gas Plasma Etching Method," H Komiya et al.,  Proc.  of 7th Conference on Solid State Device 1975, Supplement to Japanese Journal of Applied Physics, Vol.  15, p.19 (1976).  N type impurities are implanted from above the semiconductor substrate 1 using the gate electrode 3 as a mask.  Thereafter, a heat treatment is performed.  Consequently, N.sup.+ impurity layers 4a and 4b are formed on a main surface of the semiconductor substrate 1 in self alignment.  The N.sup.+ impurity layers 4a and 4b constitute a source and a drain of a transistor ( FIG.  1C ).  An Al wiring layer is formed connected to the N.sup.+ impurity layers (FIG.  1D).  An enlarged view of the gate portion of the FET transistor structure as described above is shown in FIG.  2A. Since the N.sup.+ impurity layers 4a and 4b are formed by heat treatment, the impurities are also diffused in the transverse direction in accordance with the diffusion coefficient of the impurities.  Consequently, an overlap portion is generated between the gate electrode 3 and the source.multidot.drain diffusion layers 4.  The degree of overlap (the distance .DELTA.L) differs depending on the type of impurities and on the temperature of the heat treatment.  An equivalent circuit of the device of FIG.  2A is shown in FIG.  2B.
The overlapping portion (.DELTA.L) constitutes an additional capacitance between the gate and the source.multidot.drain as shown in the equivalent circuit of FIG.  2B. Therefore, if this MOS transistor is used in an integrated circuit or the like, the MOS transistor cannot operate at a high speed and the power consumption of the MOS transistor is relatively large.  If the dimension of the overlapping portion is relatively large, a so-called short channel effect will occur, thereby causing problems such as a change in the threshold voltage of the MOS transistor.  Therefore, the overlapping portion is also an obstruction in reducing the size of the MOS transistor. 
In addition to the above described problem, the conventional FET also exhibits a decrease in transconductance.  The transconductance is one of the characteristics of the transistor, which refers to the proportion of the drain current to the gate voltage.  FIG.  3 is a schematic diagram showing the electric field and the movement of electrons in a conventional FET.  The drain is maintained at a constant potential.  A plane of equal potential is formed in the vicinity of the drain as shown in the figure.  Therefore, an end portion of the drain has a high electric field.  If a prescribed potential is applied to the gate of the transistor, a channel region is formed on the main surface of the semiconductor substrate between the source 4a and the drain 4b, whereby electrons move from the source 4a to the drain 4b.  When the electrons reach the high electric field region near the drain, the electrons receive a large energy from the electric field, so that he electrons become hot electrons.  The hot electrons generated in this manner are trapped near the gate insulating film sandwiched between the gate electrode and the drain region.  Consequently, the surfaces of the drain and the channel region tend to invert to the P type.  Therefore, the concentration of the N type impurities becomes substantially low and the source resistance of the MOS transistor increases.  Normally, when a constant voltage.  is applied to the gate electrode of the FET, a constant current flows.  However, due to the above described reasons, a constant current does not flow even if a constant voltage is applied to the gate.