Field effect semiconductor device having an unsaturated triode vacuum tube characteristic
BACKGROUND OF THE INVENTION 
     1. Field of the Invention: 
     This invention relates to a field effect transistor, and more particularly to a field effect transistor having a drain-current to drain-voltage characteristic similar to the anode-current to anode-voltage characteristic of the triode vacuum tube. 
     2. Description of the Prior Art: 
     There are two types in field effect transistors (FET&#39;s), i.e., a metal-oxide-semiconductor (MOS) type and a junction-gate (JUG) type. In both cases, the current of the carriers (unipolar) flowing from the source to the drain is effectively controlled by the gate voltage. The gate voltages applied with respect to the source voltage works to control the height of the depletion layer extending from the gate into the channel, which in turn controls the height of the region through which a current is allowed to flow. In a MOS FET, the current flowing through the channel formed beneath the gate electrode and insulated from the gate electrode by an oxide layer is controlled by the electric field established in the channel by the gate voltage. This is due to the variation in the height of the depletion layer extending from the oxide-semiconductor contact. In a JUG FET, a depletion layer formed around the PN junction is varied by the gate voltage and controls the current flowing through the channel. In conventional FET&#39;s of the both types, it is arranged that the current channel is open (conductive) when no gate voltage is applied externally and the conducting channel height is varied by the applied gate voltage. 
     The present inventors have found that various advantages can be obtained by forming an FET in such a fashion that the depletion layers (space charged layers) extending from the gates are substantially contiguous to each other even when no gate voltage is applied. This will be first described referring to a junction type FET proposed in Japanese Pat. application No. 28405/1971 by one of the present inventors, which has triode-like characteristics (unsaturated type) unlike the conventional current saturation type characteristics, and has a reduced series (source to drain) resistance so that the product of the series resistance r s  (this forms a factor for generating negative feedback) and the transconductance G m  is suppressed substantially less than unity. 
     A typical example of the characteristic curves is shown in FIG. 1, and a schematically illustrated structure which produces the characteristics of FIG. 1 is shown in FIG. 2. Namely, when the gate voltage is absent or small, the drain current I D  increases almost linearly with increasing the drain voltage V D , as is illustrated by curves 1, 2, and 3. This may be called resistance modulation, since the variation in the gate voltage results in a variation in the resistance between the source and the drain i.e., δV D  /δI D . When the negative gate voltage is increased in magnitude to suppress the drain current I D , the drain current I D  first does not begin to flow until the drain voltage V D  reaches a certain value, and then above said certain value rapidly increases more than linearly with increasing drain voltage V D  as is shown by curves 4, 5, and 6. The phenomenon .[.that.]. .Iadd.whereby .Iaddend.the drain current I D  increases linearly with increasing voltage V D  as is shown by curves 1, 2 and 3 mainly appears in the case where the depletion layers extending from the gate electrodes G and G&#39; .[.does.]. .Iadd.do .Iaddend.not .Iadd.yet .Iaddend.touch .[.yet.]. each other, whereas the phenomenon that the drain current I D  .[.do.]. .Iadd.does .Iaddend.not begin to flow until the drain voltage V D  reaches a certain positive value and increases rapidly with increasing drain voltage V D  above said certain value mainly appears when the depletion layers extending from the gates have grown large enough by the application of a gate voltage and touch (not touch, to say exactly, but become very close) each other. In the latter case, the applied drain voltage below the certain value is found to be used for decreasing the potential barrier of the pinch-off portion made in the current path by the depletion layers. 
     In the above example, linear characteristics as shown by curves 1, 2, and 3 appeared when the gate voltage was small in magnitude, and characteristics very closely resembling those of a triode vacuum tube as shown by curves 4, 5, and 6 appeared when the gate voltage exceeded a certain value. Further, .Iadd.it is desirable that .Iaddend.the value δV D  /δV G , which corresponds to the amplification factor μ of the triode vacuum tube, .[.is desired to.]. be large for obtaining a field effect transistor of a superior efficiency. Thus, it is desired to realize the characteristics corresponding to curves 4, 5, and 6 even in the region of small gate voltage, or in other words without the accompany of the characteristics corresponding to curves 1, 2, and 3, for providing elements of superior characteristics of a good efficiency and of little distortion. 
     It has been found by the present inventors that the above requirement can be satisfied by forming an FET in such a manner that the depletion layers extending from the gate electrodes are substantially contiguous (very close but not integrally connected) to each other even when no gate voltage is applied. 
     This can be achieved by using depletion layers due to carrier diffusion-recombination across a PN junction. Namely, the extent of a depletion .[.layers.]. .Iadd.layer .Iaddend.across the PN junction is determined by the barrier potential (or contact potential) and the impurity concentration (density) in the crystal. Practically, if the resistivity of the semiconductor crystal substrate is known, an FET having such depletion layers which are formed only by the carrier diffusion-recombination and are contiguous to each other even when no gate voltage is applied can be formed by appropriately selecting the distance between the gate electrodes G and G&#39;. In such a structure, since the depletion layers almost touch each other, the drain current I D  can easily show triode-like characteristics, not showing linear increase of the drain current with increasing drain voltage, even without the application of a large negative gate voltage V G . Namely, characteristics as shown in FIG. 3 are obtained with a reduction or absence of the linear region indicated by curves 1, 2, and 3 in FIG. 1. These transistors have such advantages that sufficient function can be obtained with a small gate voltage, that a large variation in the drain voltage V D  can be obtained by a small variation in the gate voltage V G , and that excellent action with less distortion can be performed. In addition to these advantages, capacitances between gate-and-source, and gate-and-drain are reduced and the frequency characteristics are improved. 
     The above description has been made on a transistor having a reduced series resistance, but it also holds for a conventional transistor having a large series resistance. A conventional FET having a large series resistance and showing pentode-like characteristics can be considered as the above-mentioned FET having a reduced series resistance and showing triode-like characteristics, itself, but now .[.provide wih.]. .Iadd.provided with .Iaddend.a negative feed back circuit, or in .[.another word,.]. .Iadd.other words, .Iaddend.the FET .[.operating.]. .Iadd.operates .Iaddend.in an emitter follower fashion. Therefore, the advantages of the present concept described above can be also applied to such kind of transistors. 
     Next, description will be made on the state in which the depletion layers respectively extending from the gates touch each other. As is described above, the height of the depletion layer is a function of the barrier potential at the junction or contact and the impurity concentration (density) in the crystal. Usually, the height of a depletion layer is calculated by assuming that no carriers exist in the depletion layer and that only space charges which are perfectly ionized exist in the depletion layer and solving the Poisson&#39;s equation. 
     For example, in a case where a plate shaped PN junction has a stepwise carrier concentration distribution, i.e. the carrier concentration on one side of the PN junction is far larger than that on the other side, so that a depletion layer grows only into the other side, the height of the depletion layer α is expressed by 
     
         α=R√ V/N.sub.b 
    
     where R is a factor dependent on the physical constants of the semiconductor, N b  the impurity concentration (density) in the semiconductor on that side in which the depletion layer grows, and V the applied voltage including the barrier potential. Strictly speaking, it is not that there are no carriers at all in the depletion layer, nor that a clear boundary exists at the edge of the depletion layer between the perfectly ionized region and the non-ionized region. Carriers are distributed according to the Fermi-Dirac distribution even into a depletion layer. The effective extent of a depletion layer is at least three times larger than the width of the depletion layer α calculated as above assuming that the depletion layer is perfectly ionized. Namely, the calculated height of the depletion layer based on the perfect ionization assumption is much lower than the actual effective height. Therefore, even if such semi-conductor materials in which the calculation with the perfect ionization assumption tells that the depletion layers touch each other only by the barrier potential with a gate-to-gate distance set at 20 micrometers is employed, the actual depletion layers can touch (become very close .Iadd.to.Iaddend.)  each other with the gate-to-gate distance set at about 60 micrometers. 
     SUMMARY OF THE INVENTION 
     An object of the invention is to provide a field effect transistor having triode vacuum-tube-like characteristics. 
     Another object of the invention is to provide a field effect transistor comprising a semiconductor substrate including a current channel, a source and a drain electrode, and gate electrodes sandwiching the current channel, the depletion layers extending into the channel from the gate electrodes being substantially contiguous to each other even in the absence of a gate voltage. 
     A further object of the invention is to provide a field effect transistor comprising a semiconductor substrate including a current channel of a low carrier concentration (density) and gate regions of a high carrier concentration, a source and a drain electrode formed on the semiconductor substrate at the both ends of the current channel, and gate electrodes formed on said gate regions. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a graphical chart showing the drain-current to drain-voltage characteristics of a field effect transistor of non-saturated current type; 
     FIG. 2 is a schematic cross sectional view of a field effect transistor having the characteristics as shown in FIG. 1; 
     FIG. 3 is a graphical chart showing the drain-current to drain-voltage characteristics of a field effect transistor according to the present invention; 
     FIG. 4 is a schematic cross sectional view of a junction type field effect transistor according to this invention; 
     FIGS. 5A and 5B are schematic perspective and schematic cross sectional views respectively of another embodiment of a junction type field effect transistor according to the invention; 
     FIGS. 6A and 6B are schematic perspective and partial cross sectional views, respectively, of a further embodiment of a junction type field effect transistor according to the invention; 
     FIGS. 7 and 8 illustrate further embodiments of junction type field effect transistors of high output power according to the invention; and 
     FIGS. 9 to 11 are cross sectional views of embodiments of MOS type field effect transistors according to the invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Now, this invention will be described on the preferred embodiments referring to the accompanying drawings. Throughout the figures illustrating the embodiments of the invention, the gate voltage is set at zero unless particularly specified. 
     A silicon FET is shown in FIG. 4 for illustrating the height of the depletion layer. In a semiconductor substrate, gate electrode regions indicated by .Iadd.a .Iaddend.hatched area are formed. Provided that the impurity concentration (density) in the gate regions is far larger than that in the channel region and that the impurity concentration in the channel region is uniformly distributed, the voltage V between the channel region and the gate region when the depletion layers extending from the gate regions touch each other is expressed by the equation 
     
         V=.sub.q N.sub.B /2ε · α.sup.2 
    
     on the basis of the assumption of perfect ionization, where q is the electron charge, N B  the impurity concentration in the channel region, ε the dielectric constant of the semi-conductor, and a the height of the depletion layer (in this case, equal to α half of the gate-to-gate distance). When no gate voltage is applied, the voltage V is entirely formed by the contact potential (i.e., the barrier potential). Assuming that this contact potential is 0.6 volt, the maximum half distance α between the gates becomes about 9, 3, and 0.9 micrometer(s) for the impurity concentrations N B  of 10 13  /cm 3 , 10 14  /cm 3 , and 10 15  /cm 3  respectively. Since these values are calculated on the assumption of perfect ionization, the actual maximum distances between the gates G and G&#39; (two times the height of a depletion layer) become approximately 18×3, 6×3, and 1.8×3 micrometers for the semiconductors having an impurity concentration of 10 13  /cm 3 , 10 14  /cm 3 , and 10 15  /cm 2  respectively. 
     FIGS. 5A and 5B show an embodiment of a junction-gate type FET having a circular transverse cross section. An annular gate is provided in the periphery of a cylindrical semiconductor body. In this case, the voltage V when the depletion layer touches itself and closes the current path is expressed by 
     
         V=.sub.q N.sub.B /4ε · r.sub.a.sup.2 
    
     on the assumption of perfect ionization, where r a  is the radius of the annular gate. Actually, since the width of a depletion layer is about three times as large as the calculated value, the depletion layer becomes contiguous when the radius r a  is about √2×9×3, √2×3×3, and √2×0.9×3 micrometers for the impurity concentration N B  of 10 13  /cm 3 , 10 14  /cm 3 , and 10 15  /cm 3 , respectively. 
     A further embodiment of a junction-gate type FET is shown in FIGS. 6A and 6B, in which a plurality of cylindrical gate regions are formed on a line with an interval of 2d. The pinch-off voltage in this case takes a little more complicated form and is expressed as 
     
         V=.sub.q N.sub.B /4εd.sup.2 (2 ln d/r.sub.3 +r.sub.j.sup.2 /d.sup.2 -l), 
    
     where r j  indicates the radius of one cylindrical gate region. At the interval about three times as large as the interval 2d calculated from the above equation, the depletion layer can be considered as contiguous. 
     For example in the embodiment of FIG. 5, the series resistance increases with increasing longitudinal length L of the gate electrode and decreases with decreasing length L. Thus, an FET of a large output power can be formed by connecting a large number of such channels. 
     FIG. 7 shows an embodiment of a large output FET along the above line. 
     Alternatively, a large output FET having a planar structure as shown in FIG. 8 may be formed. In this case, the distance 2a between the adjacent gates is also arranged considering the impurity concentration so that the current channel is interrupted by the contiguous depletion layers. The gates and the sources are respectively connected in parallel for a large power transistor. 
     Various alterations and modifications are possible within the spirit and scope of the present invention. 
     If the impurity concentration in the channel region is not uniform due to the employment of a diffusion process, etc., the calculation of the height of a depletion layer becomes complicated, but a value three times as large as the calculated value on the basis of the perfect ionization assumption also holds for the actual situation. 
     The present invention is not limited to junction-gate type FET&#39;s, but is also applicable to MOS FET&#39;s. The gist of the present invention lies in the depletion layers contiguous to each other. In a MOS FET, a space charge region is usually formed under an oxide film beneath the gate electrode. The dimension of the space charge region differs according to the properties of the oxide film but can be given by the Debye length which is dependent on the impurity concentration in the substrate. Thus, structures in which depletion layers touch each other even in the absence of a gate voltage can also be realized in MOS structure by utilizing the internal potential at an insulator-semi-conductor contact corresponding to the barrier potential at a junction. 
     FIGS. 9, 10, and 11 show embodiments of MOS FET&#39;s according to the invention. In FIG. 9 a source and a drain electrode is formed on the opposite surfaces and a gate electrode is formed around the source to effectively extend the depletion layer. The radius of the gate electrode is selected less than the Debye length so that the current channel from the source electrode is closed by the depletion layer even in the absence of a gate voltage. FIG. 10 shows an embodiment in which an electrically isolated region is formed in one surface of a semiconductor substrate, and a source, an annular gate and an annular drain electrode are formed on said region. 
     FIG. 11 shows another embodiment which is intended to provide a high output power by alternatively forming source and drain electrodes respectively connected in parallel. 
     In the above embodiments, the shape of the source and/or drain and/or gate electrode may be rectangular or comb form. The gate electrodes are insulated from the semi-conductor substrate by an insulator film such as an SiO 2  film. 
     The present invention is applied to silicon elements in the above embodiments but is also applicable to other semiconductor materials such as GaAs. Further, with the use of a hetero junction, a space charged region not only due to the carrier concentration but also due to the difference in the band structures can be utilized. 
     The present invention is described on various structures, but is most effective to those having a reduced series resistance to have a small output resistance. If such elements are assembled in an integrated circuit, there can be provided superior switching characteristics which are made more effective by the smallness of the accompanying capacitances. 
     When the gate-to-gate distance is further reduced, the standing-up point of the drain current shifts to higher drain voltage side and suitable circuit designs based on the thus obtained characteristics are possible. Therefore, this invention gives the upper limit for the gate-to-gate distance.