Patent Publication Number: US-6982456-B2

Title: Nonvolatile semiconductor memory device and method for fabricating the same

Description:
This application is a DIV of Ser. No. 10/366,420, filed on Feb. 14, 2003, now U.S. Pat. No. 6,770,931 which is a DIV of Ser. No. 09/902,942, filed on Jul. 12, 2001, now U.S. Pat. No. 6,538,275. 

   BACKGROUND OF THE INVENTION 
   The present invention relates to a nonvolatile semiconductor memory device and to a method for fabricating the same. At present, flash EEPROM (Electrically Erasable Programmable ROM) devices are used widely in electronic equipment as nonvolatile semiconductor memory devices which allow for electrical write and erase operations. The structures of memory cells in the nonvolatile semiconductor memory devices can be divided broadly into two types. The first one is a stacked-gate type having a multilayer electrode structure-composed of a floating gate electrode and a control gate electrode which are stacked successively on a semiconductor substrate. The second one is a split-gate type having an electrode structure composed of a floating gate electrode and a control gate electrode which are disposed adjacent to each other in opposing relation to a channel region in a semiconductor substrate. 
   Referring to the drawings, a description will be given herein below to a conventional split-gate nonvolatile semiconductor memory device. 
     FIG. 42  shows a cross-sectional structure of a split-gate nonvolatile semiconductor memory device disclosed in U.S. Pat. No. 5,780,341, which has a stepped portion formed in a portion of a semiconductor substrate underlying a floating gate electrode. As shown in  FIG. 42 , a main surface of a semiconductor substrate  201  composed of, e.g., p-type silicon is formed with a stepped portion  205  composed of a first surface region  202  serving as an upper stage, a second surface region  204  serving as a lower stage, and a step side region  204  connecting the upper and lower stages. 
   A control gate electrode  210  is formed on the first surface region  202  of the stepped portion  205  with a gate insulating film  211  interposed therebetween. A floating gate electrode  212  formed to cover up the stepped portion  205  is capacitively coupled to the side surface of the control gate electrode  210  closer to the stepped portion and opposed to the second surface region  203  with a silicon dioxide film  213  serving as a tunnel film interposed therebetween. 
   A heavily doped n-type source region  221  is formed in the first surface region  202  of the semiconductor substrate  201 , while a lightly doped n-type drain region  222   a  is formed in an area of the second surface region  203  underlying the floating gate electrode  212  and a heavily doped drain region  222   b  is formed externally of the lightly doped drain region  222   a.    
   In an area of the first surface region  202  underlying the floating gate electrode  212 , a p-type impurity region  223  containing a p-type impurity at a concentration higher than in the semiconductor substrate  201  is formed. In such a structure, the floating gate electrode  212  is positioned in the direction in which electrons that have been injected into the heavily source region  221  flow so that the efficiency with which channel electrons are injected is improved. 
   As a result of conducting various studies including simulation and the like, the present inventors have concluded that the conventional split-gate nonvolatile semiconductor memory device is unsatisfactory in terms of the effect of increasing the efficiency of electron injection which is exerted by the stepped portion  205  formed in the semiconductor substrate  201 . 
   When an electric field is applied during a write operation, a high electric field is hard to propagate upwardly from the lower corner of the stepped portion  205  in the source-side end portion of the lightly doped drain region  222   a  so that the localization of the electric field is likely to occur only in the vicinity of the lower corner of the stepped portion  205 . As a result, a region where the electric field is intensest deviates to a lower portion from the step side region  204  into which the channel electrons from the floating gate electrode  212  are intended to be actually injected. The channel electrons flow directly to the lightly doped drain region  222   a  through a region at a distance from the step side region  204 . This prevents the channel electrons from being injected into the floating gate electrode  212  with a sufficiently high efficiency. 
   During an erase operation, the electrons accumulated in the floating gate electrode  212  are extracted as a FN tunnel current to the heavily doped drain region  222   b  through a tunnel film composed of the portion of the silicon dioxide film  213  opposed to the floating gate electrode  212 . With the increasing miniaturization of the element, however, the area of the portion of the tunnel film which permits the passage of the electrons is reduced so that the erase operation becomes difficult. 
   For an easier erase operation, there is a method of enhancing the electric field applied to the tunnel film by increasing the drain voltage. In accordance with the method, however, holes having high energy (hot holes) generated in the heavily doped drain region  222   b  are generated simultaneously. The hot holes causes the problem that the reliability of the tunnel film is lowered or that the hot holes are captured in the tunnel film to degrade the characteristics of the element. 
   As the element is reduced in size, especially the gate length of the control gate electrode  210  is reduced, a short-channel effect, which is obscure in the conventional split-gate flash EEPROM device, is observed distinctly disadvantageously. 
   SUMMARY OF THE INVENTION 
   It is therefore a first object of the present invention to ensure, by solving the foregoing conventional problems, an improved efficiency with which electrons are injected into a nonvolatile semiconductor memory device having a stepped portion and allow a low-voltage and high-speed write operation. 
   A second object of the present invention is to increase an erase speed, while suppressing the occurrence of hot holes during an erase operation. A third object of the present invention is to allow miniaturization of an element by suppressing a short-channel effect. 
   To attain the first object, the present invention provides a nonvolatile semiconductor memory device having a stepped portion on the drain side, wherein a heavily doped impurity region of the conductivity type opposite to that of the drain region is formed at a position at a distance from and opposed to the upper corner of the stepped portion so as not to reach a first surface region and a step side region or adopts a method in which a proper substrate voltage is applied during a write operation. 
   To attain the second object, the present invention forms a drain region in which an impurity concentration is progressively higher with distance from a source region. To attain the third object, the present invention provides an impurity region of the conductivity type opposite to that of the source region such that the source region is covered with the impurity region. 
   Specifically, a first nonvolatile semiconductor memory device according to the present invention attains the first object and comprises: a stepped portion formed in a semiconductor substrate, the stepped portion being composed of a first surface region serving as an upper stage, a second surface region serving as a lower stage, and a step side region connecting the upper and lower stages; a first insulating film formed on the first surface region; a control gate electrode formed on an area of the first surface region located in the vicinity of the stepped portion with the first insulating film interposed therebetween; a floating gate electrode formed on the semiconductor substrate so as to cover up the stepped portion, the floating gate electrode being capacitively coupled to a side surface of the control gate electrode closer to the stepped portion with a second insulating film interposed therebetween and opposed to the second surface region with a third insulating film interposed therebetween; a source region formed in an area of the first surface region opposite to the floating gate electrode relative to the control gate electrode; a drain region formed in an area of the second surface region underlying the floating gate electrode; and a depletion control layer formed in the semiconductor substrate to extend from a position located under the first surface region and at a distance from an upper corner of the stepped portion toward a lower corner of the stepped portion and adjoin the drain region without reaching the step side region, the depletion control layer being composed of a heavily doped impurity region of a conductivity type opposite to a conductivity type of the drain region. 
   The first nonvolatile semiconductor memory device is of a split-gate type comprising the depletion control layer which is formed within the semiconductor substrate and has the conductivity type opposite to that of the drain region. The arrangement prevents the depletion layer from extending to a region at a distance from the stepped portion during a write operation even when the drain region is provided in the second surface region serving as the lower stage of the stepped portion. In addition, a high electric field caused by the drain region is brought into a reverse-biased state due to the pn junction between the drain region and the depletion control layer and the potential difference across the pn junction is increased, so that a path of carriers flowing toward a high electron temperature region generated in the vicinity of the lower corner of the stepped portion is formed. This ensures an improved efficiency with which the electrons which have become hot electrons in the vicinity of the step side region are injected from the step side region into the floating gate electrode. 
   Preferably, the first nonvolatile semiconductor memory device further comprises a high-electric-field forming layer formed between the upper corner of the stepped portion and the depletion control layer, the high-electric-field forming layer being composed of an impurity region of the same conductivity type as the conductivity type of the depletion control layer. In the arrangement, an energy level in the step side region has a sharper gradient due to the pn junction portion composed of the interface between the high-electric-field forming layer and the drain region. As a result, a high electric field is generated at the interface between the high-electric-field forming layer and the drain region to overlap each of a high electric field caused by the stepped structure and a high electric field generated at the interface between the depletion control layer and the drain region, so that an electron temperature in the vicinity of the lower corner of the step side region is further increased. This increases the number of electrons in the channel that have become hot electrons and remarkably improves the efficiency with which the electrons are injected into the floating gate electrode. 
   In the first nonvolatile semiconductor memory device, an impurity concentration of the high-electric-field forming layer is preferably lower than an impurity concentration of the depletion control layer and higher than an impurity concentration of the semiconductor substrate. In the arrangement, the high-electric-field forming layer formed between the depletion control layer at a distance from the stepped portion and the stepped portion is depleted during a write operation so that the channel region is generated reliably in the vicinity of the step side region. 
   A second nonvolatile semiconductor memory device according to the present invention comprises: a stepped portion formed in a semiconductor substrate, the stepped portion being composed of a first surface region serving as an upper stage, a second surface region serving as a lower stage, and a step side region connecting the upper and lower stages; a first insulating film formed on the semiconductor substrate so as to cover up the stepped portion; a floating gate electrode formed on the first insulating film so as to cover up the stepped portion; a control gate electrode formed on the floating gate electrode with the second insulating film interposed therebetween, the control gate electrode being capacitively coupled to the floating gate electrode; a source region formed in an area of the first surface region opposite to the stepped portion relative to the floating gate electrode; a drain region formed in an area of the second surface region underlying the floating gate electrode; and a depletion control layer formed in the semiconductor substrate to extend from a position located under the first surface region and at a distance from an upper corner of the stepped portion toward a lower corner of the stepped portion and adjoin the drain region without reaching the step side region, the depletion control layer being composed of a heavily doped impurity region of a conductivity type opposite to a conductivity type of the drain region. 
   The second nonvolatile semiconductor memory device is of a stacked-gate type comprising the depletion control layer which is formed within the semiconductor substrate and has the conductivity type opposite to that of the drain region. The arrangement prevents the depletion layer from extending to a region at a distance from the stepped portion during a write operation even when the drain region is provided in the second surface region serving as the lower stage of the stepped portion. In addition, a high electric field is caused by the drain region at the pn junction between the drain region and the depletion control layer so that a path of carriers flowing toward a high electron temperature region generated in the vicinity of the lower corner of the stepped portion is formed. This ensures an improved efficiency with which the electrons which have become hot electrons in the vicinity of the step side region are injected from the step side region into the floating gate electrode. 
   Preferably, the second nonvolatile semiconductor memory device further comprises a high-electric-field forming layer formed between the upper corner of the stepped portion and the depletion control layer, the high-electric-field forming layer being composed of an impurity region of the same conductivity type as the conductivity type of the depletion control layer. 
   In this case, an impurity concentration of the high-electric-field forming layer is preferably lower than an impurity concentration of the depletion control layer and higher than an impurity concentration of the semiconductor substrate. 
   In the first or second nonvolatile semiconductor memory device, an end portion of the drain region closer to the source region is preferably located in the step side region without reaching the first surface region. In the arrangement, an area of the conductivity type opposite to that of the drain region is formed in the step side region so that the channel region is formed reliably by using the area as a depletion layer and an inversion layer. 
   In the first or second nonvolatile semiconductor memory device, the drain region preferably has at least three impurity regions formed to have respective impurity concentrations which are progressively higher with distance from the source region along a surface of the second surface region. In the arrangement, the area of the drain region opposite to the channel region is high in impurity concentration so that the intensity of an electric field in the area closer to the channel region is reduced relatively and the occurrence of hot holes in the peripheral region of the drain region during an erase operation is suppressed. This prevents the lowering of the reliability of a tunnel film and suppresses a short-channel effect as well, thereby attaining the second and third objects. 
   Preferably, the first or second nonvolatile semiconductor memory device further comprises an impurity region formed in the first surface region so as to cover a junction interface of the source region, the impurity region having a conductivity type opposite to a conductivity type of the source region to suppress a short-channel effect. The arrangement suppresses the expansion of the depletion layer in the channel region and suppresses the short-channel effect and a punch-through effect as well, thereby attaining the third object. 
   A third nonvolatile semiconductor memory device according to the present invention comprises: a stepped portion formed in a semiconductor substrate, the stepped portion being composed of a first surface region serving as an upper stage, a second surface region serving as a lower stage, and a step side region connecting the upper and lower stages; a first insulating film formed on the first surface region; a control gate electrode formed on an area of the first surface region located in the vicinity of the stepped portion with the first insulating film interposed therebetween; a floating gate electrode formed on the semiconductor substrate so as to cover up the stepped portion, the floating gate electrode being capacitively coupled to a side surface of the control gate electrode closer to the stepped portion with a second insulating film interposed therebetween and opposed to the second surface region with a third insulating film interposed therebetween; a source region formed in an area of the first surface region opposite to the floating gate electrode relative to the control gate electrode; a drain region formed in an area of the second surface region underlying the floating gate electrode; and an impurity region formed in the semiconductor substrate to be located in the vicinity of an corner between the first surface region and the step side region, the impurity region having an impurity concentration higher than an impurity concentration of the semiconductor substrate and a conductivity type opposite to a conductivity type of the drain region, the drain region having at least three impurity diffusion regions formed to have respective impurity concentrations which are progressively higher with distance from the source region along a surface of the second surface region. 
   The third nonvolatile semiconductor memory device is of a split-gate type comprising an impurity region which is formed within the semiconductor substrate to be located in the vicinity of the corner between the first surface region and the step side region and has the conductivity type opposite to that of the drain region. As a result, a high electric field is generated at the pn junction interface between the impurity region and the drain region and the number of electrons in the channel that have become hot electrons is increased, which improves the efficiency with which the electrons are injected into the floating gate electrode. The third nonvolatile semiconductor memory device also has at least three impurity diffusion regions formed to have respective impurity concentrations which are progressively higher with distance from the source region along the surface of the second surface region. This relatively reduces the intensity of an electric field in the area of the drain region closer to the channel region and suppresses the occurrence of hot holes in the area of the drain region located around the channel during an erase operation and suppresses the short-channel effect as well. 
   A fourth nonvolatile semiconductor memory device according to the present invention comprises: a stepped portion formed in a semiconductor substrate, the stepped portion being composed of a first surface region serving as an upper stage, a second surface region serving as a lower stage, and a step side region connecting the upper and lower stages; a first insulating film formed on the first surface region; a control gate electrode formed on an area of the first surface region located in the vicinity of the stepped portion with the first insulating film interposed therebetween; a floating gate electrode formed on the semiconductor substrate so as to cover up the stepped portion, the floating gate electrode being capacitively coupled to a side surface of the control gate electrode closer to the stepped portion with a second insulating film interposed therebetween and opposed to the second surface region with a third insulating film interposed therebetween; a source region formed in an area of the first surface region opposite to the floating gate electrode relative to the control gate electrode; a drain region formed in an area of the second surface region underlying the floating gate electrode; a first impurity region formed in the semiconductor substrate to be located in the vicinity of an corner between the first surface region and the step side region, the impurity region having an impurity concentration higher than an impurity concentration of the semiconductor substrate and a conductivity type opposite to a conductivity type of the drain region; and a second impurity region formed in the first surface region so as to cover a junction interface of the source region, the second impurity region having a conductivity type opposite to a conductivity type of the source region to suppress a short-channel effect. 
   The fourth nonvolatile semiconductor memory device is of a split-gate type comprising the first impurity region which is formed within the semiconductor substrate to be located in the vicinity of the corner between the first surface region and the step side region and has a conductivity type opposite to that of the drain region. As a result, a high electric field is generated at the pn junction interface between the first impurity region and the drain region and the number of electrons in the channel that have become hot electrons is increased, which improves the efficiency with which the electrons are injected into the floating gate electrode. The fourth nonvolatile semiconductor memory device also has the second impurity region formed to cover the junction interface of the source region and having a conductivity type opposite to that of the source region. This suppresses the expansion of the depletion layer in the channel region and suppresses the short-channel effect and the punch-through effect as well. 
   A fifth nonvolatile semiconductor memory device according to the present invention comprises: a stepped portion formed in a semiconductor substrate, the stepped portion being composed of a first surface region serving as an upper stage, a second surface region serving as a lower stage, and a step side region connecting the upper and lower stages; a first insulating film formed on the semiconductor substrate so as to cover up the stepped portion; a floating gate electrode formed on the first insulating film so as to cover up the stepped portion; a control gate electrode formed on the floating gate electrode with the second insulating film interposed therebetween, the control gate electrode being capacitively coupled to the floating gate electrode; a source region formed in an area of the first surface region opposite to the stepped portion relative to the floating gate electrode; a drain region formed in an area of the second surface region underlying the floating gate electrode; and an impurity region formed in the semiconductor substrate to be located in the vicinity of an corner between the first surface region and the step side region, the impurity region having an impurity concentration higher than an impurity concentration of the semiconductor substrate and a conductivity type opposite to a conductivity type of the drain region, the drain region having at least three impurity diffusion regions formed to have respective impurity concentrations which are progressively higher with distance from the source region along a surface of the second surface region. 
   The fifth nonvolatile semiconductor memory device is of a stacked-gate type comprising an impurity region which is formed within the semiconductor substrate to be located in the vicinity of the corner between the first surface region and the step side region and has the conductivity type opposite to that of the drain region. As a result, a high electric field is generated at the pn junction interface between the impurity region and the drain region and the number of electrons in the channel that have become hot electrons is increased, which improves the efficiency with which the electrons are injected into the floating gate electrode. The third nonvolatile semiconductor memory device also has at least three impurity diffusion regions formed to have respective impurity concentrations which are progressively higher with distance from the source region along the surface of the second surface region. This relatively reduces the intensity of an electric field in the area of the drain region closer to the channel region and suppresses the occurrence of hot holes in the area of the drain region located around the channel during an erase operation and suppresses the short-channel effect as well. 
   A sixth nonvolatile semiconductor memory device according to the present invention comprises: a stepped portion formed in a semiconductor substrate, the stepped portion being composed of a first surface region serving as an upper stage, a second surface region serving as a lower stage, and a step side region connecting the upper and lower stages; a first insulating film formed on the semiconductor substrate so as to cover up the stepped portion; a floating gate electrode formed on the first insulating film so as to cover up the stepped portion; a control gate electrode formed on the floating gate electrode with the second insulating film interposed therebetween, the control gate electrode being capacitively coupled to the floating gate electrode; a source region formed in an area of the first surface region opposite to the stepped portion relative to the floating gate electrode; a drain region formed in an area of the second surface region underlying the floating gate electrode; a first impurity region formed in the semiconductor substrate to be located in the vicinity of an corner between the first surface region and the step side region, the impurity region having an impurity concentration higher than an impurity concentration of the semiconductor substrate and a conductivity type opposite to a conductivity type of the drain region; and a second impurity region formed in the first surface region so as to cover a junction interface of the source region, the second impurity region having a conductivity type opposite to a conductivity type of the source region to suppress a short-channel effect. 
   The sixth nonvolatile semiconductor memory device is of a stacked-gate type comprising the first impurity region which is formed within the semiconductor substrate to be located in the vicinity of the corner between the first surface region and the step side region and has a conductivity type opposite to that of the drain region. As a result, a high electric field is generated at the pn junction interface between the first impurity region and the drain region and the number of electrons in the channel that have become hot electrons is increased, which improves the efficiency with which the electrons are injected into the floating gate electrode. The sixth nonvolatile semiconductor memory device also has the second impurity region formed to cover the junction interface of the source region and having a conductivity type opposite to that of the source region. This suppresses the expansion of the depletion layer in the channel region and suppresses the short-channel effect and the punch-through effect as well. 
   In any one of the first to sixth nonvolatile semiconductor memory devices, a substrate voltage is preferably applied to the semiconductor substrate such that a channel region in which carriers flow from a portion of the first surface region underlying the floating gate electrode toward the step side region is formed. In the arrangement, a potential at the floating gate is relatively increased in the portion of the semiconductor substrate enclosed with the first surface region and the step side region so that the carriers are strongly attracted to the surface of the semiconductor substrate. In addition, the current density is increased only during the application of the substrate voltage so that power consumption while a write operation is not performed is reduced significantly. 
   In any one of the first to sixth nonvolatile semiconductor memory devices, a specified drain voltage and a specified control gate voltage are preferably applied to the drain region and to the control gate electrode, respectively, such that a channel region in which carriers flow from a portion of the first surface region underlying the floating gate electrode toward the step side region is formed. 
   A seventh nonvolatile semiconductor memory device according to the present invention comprises: a stepped portion formed in a semiconductor substrate, the stepped portion being composed of a first surface region serving as an upper stage, a second surface region serving as a lower stage, and a step side region connecting the upper and lower stages; a first insulating film formed on the first surface region; a control gate electrode formed on an area of the first surface region located in the vicinity of the stepped portion with the first insulating film interposed therebetween; a floating gate electrode formed on the semiconductor substrate so as to cover up the stepped portion, the floating gate electrode being capacitively coupled to a side surface of the control gate electrode closer to the stepped portion with a second insulating film interposed therebetween and opposed to the second surface region with a third insulating film interposed therebetween; a source region formed in an area of the first surface region opposite to the floating gate electrode relative to the control gate electrode; a drain region formed in an area of the second surface region underlying the floating gate electrode; and an impurity region formed in the first surface region and step side region of the semiconductor substrate to have an impurity concentration higher than an impurity concentration of the semiconductor substrate and a conductivity type opposite to a conductivity type of the drain region, wherein a substrate voltage is applied to the semiconductor substrate such that a channel region in which carriers flow from a portion of the first surface region underlying the floating gate electrode toward the step side region is formed. 
   The seventh nonvolatile semiconductor memory device is of a split-gate type in which, even if a depletion control layer is not provided in a portion of the semiconductor substrate at a distance from the step side region of the stepped portion, a potential at the floating gate electrode over the portion of the semiconductor substrate enclosed with the first surface region and the step side region is increased relatively by applying, e.g., a substrate voltage of a polarity opposite to that of the drain voltage during a write operation, i.e., by applying a negative substrate voltage in the case of an n-type channel and applying a positive substrate voltage in the case of a p-type channel. As a result, the carriers are strongly attracted to the surface of the semiconductor substrate so that the efficiency with which the carriers are injected into the floating gate electrode is improved. 
   An eighth nonvolatile semiconductor memory device according to the present invention comprises: a stepped portion formed in a semiconductor substrate, the stepped portion being composed of a first surface region serving as an upper stage, a second surface region serving as a lower stage, and a step side region connecting the upper and lower stages; a first insulating film formed on the semiconductor substrate so as to cover up the stepped portion; a floating gate electrode formed on the first insulating film so as to cover up the stepped portion; a control gate electrode formed on the floating gate electrode with the second insulating film interposed therebetween, the control gate electrode being capacitively coupled to the floating gate electrode; a source region formed in an area of the first surface region opposite to the stepped portion relative to the floating gate electrode; a drain region formed in an area of the second surface region underlying the floating gate electrode; and an impurity region formed in the first surface region and step side region of the semiconductor substrate to have an impurity concentration higher than an impurity concentration of the semiconductor substrate and a conductivity type opposite to a conductivity type of the drain region, wherein a substrate voltage is applied to the semiconductor substrate such that a channel region in which carriers flow from a portion of the first surface region underlying the floating gate electrode toward the step side region is formed. 
   The eighth nonvolatile semiconductor memory device is of a stacked-gate type in which, even if a depletion control layer is not provided in a portion of the semiconductor substrate at a distance from the step side region of the stepped portion, a potential at the floating gate electrode over the portion of the semiconductor substrate enclosed with the first surface region and the step side region is increased relatively by applying a negative substrate voltage in the case of an n-type channel and applying a positive substrate voltage in the case of a p-type channel. As a result, the carriers are strongly attracted to the surface of the semiconductor substrate so that the efficiency with which the carriers are injected into the floating gate electrode is improved. 
   A first method for fabricating a nonvolatile semiconductor memory device according to the present invention comprises: a first step of forming a control gate electrode on a semiconductor substrate with a first insulating film interposed therebetween; a second step of masking a region of the semiconductor substrate to be formed with a source, ion-implanting a high-concentration impurity of a first conductivity type into the semiconductor substrate by using the control gate electrode as a mask, and thereby forming a heavily doped impurity region; a third step for forming a sidewall composed of an insulating film on a side surface of the gate electrode, etching the semiconductor substrate by using the formed sidewall and the control gate electrode as a mask and masking the source formation region, and thereby forming a recessed portion in the semiconductor substrate, while forming, in the semiconductor substrate, a stepped portion composed of a first surface region in which a portion of the semiconductor substrate underlying the sidewall serves as an upper stage, a second surface region in which a bottom surface of the recessed portion serves as a lower stage, and a step side region connecting the upper and lower stages; a fourth step of selectively ion-implanting a low-concentration impurity of a second conductivity type into the second surface region of the semiconductor substrate and thereby forming a lightly doped drain region of the second conductivity type in the second surface region, while inverting a conductivity type of each of portions of the heavily doped impurity region located in the vicinity of the first surface region, an upper corner of the stepped portion, and the step side region of the stepped portion and thereby forming a depletion control layer composed of the heavily doped impurity region and located discretely at a distance from the first surface region and the step side region to adjoin the lightly doped drain region; a fifth step of removing the sidewall and forming a second insulating film over the side surface of the control gate electrode closer to the stepped portion, the first surface region, the step side region, and the second surface region; a sixth step of depositing a conductor film over the entire surface of the second insulating film, etching the deposited conductor film, and thereby forming by self alignment a floating gate electrode covering up the stepped portion, capacitively coupled to the side surface of the control gate electrode closer to the stepped portion with the second insulating film interposed therebetween, and opposed to the second surface region with the second insulating film interposed therebetween; and a seventh step of ion-implanting an impurity of the second conductivity type into the semiconductor substrate by using the control gate electrode and the floating gate electrode as a mask and thereby forming a source region of the second conductivity type in the first surface region, while forming a drain region of the second conductivity type in the second surface region. 
   The first method for fabricating a nonvolatile semiconductor memory device comprises the step of selectively ion-implanting the low-concentration impurity of the second conductivity type into the second surface region composed of the bottom surface of the recessed portion in the semiconductor substrate and thereby forming the lightly doped drain region of the second conductivity type in the second surface region, while inverting the conductivity type of each of the portions of the heavily doped impurity region located in the vicinity of the first surface region, the upper corner of the stepped portion, and the step side region of the stepped portion and thereby forming the depletion control layer composed of the heavily doped impurity region of the first conductivity type and located distinctly at a distance from the first surface region and the step side region to adjoin the lightly doped drain region. This ensures the fabrication of the first nonvolatile semiconductor memory device according to the present invention. 
   In the first method for fabricating a nonvolatile semiconductor memory device, the second step preferably includes the step of: ion-implanting again an impurity of the first conductivity type into the heavily doped impurity region that has been formed and thereby forming another impurity region of the first conductivity type which is shallower in diffusion depth than the heavily doped impurity region and the fourth step includes the step of: forming a high-electric-field forming layer composed of the other impurity region between an upper corner of the stepped portion and the depletion control layer. 
   Preferably, the first method for fabricating a nonvolatile semiconductor memory device further comprises, after the seventh step: an eighth step of depositing a third insulating film on the floating gate electrode, ion-implanting an impurity of the second conductivity type into the semiconductor substrate by using the deposited third insulating film and the floating gate electrode as a mask, and thereby forming, in the second surface region, a heavily doped drain region of the second conductivity type which is higher in impurity concentration than the drain region. This ensures the fabrication of the third nonvolatile semiconductor memory device according to the present invention. 
   Preferably, the first method for fabricating a nonvolatile semiconductor memory device further comprises, after the fourth step, the step of: masking a region extending from the control gate electrode to the second surface region and forming, in the source formation region, an impurity region of the first conductivity type which is deeper in diffusion depth than the source region. This ensures the fabrication of the fourth nonvolatile semiconductor memory device according to the present invention. 
   A second method for fabricating a nonvolatile semiconductor memory device according to the present invention comprises: a first step of selectively ion-implanting a high-concentration impurity of a first conductivity type into a region of a semiconductor substrate to be formed with a drain and thereby forming a heavily doped impurity region of the first conductivity type; a second step of selectively etching the heavily doped impurity region except for an end portion thereof closer to a region of the semiconductor substrate to be formed with a source and thereby forming a recessed portion in the semiconductor substrate, while forming, in the semiconductor substrate, a stepped portion composed of a first surface region in which the end portion of the heavily doped impurity region serves as an upper stage, a second surface region in which a bottom surface of the recessed portion serves as a lower stage, and a step side region connecting the upper and lower stages; a third step of selectively ion-implanting a low-concentration impurity of a second conductivity type into the second surface region of the semiconductor substrate and thereby forming a lightly doped drain region of the second conductivity type in the second surface region, while inverting a conductivity type of each of portions of the heavily doped impurity region located in the vicinity of the first surface region, an upper corner of the stepped portion, and the step side region of the stepped portion and thereby forming a depletion control layer composed of the heavily doped impurity region and located discretely at a distance from the first surface region and the step side region to adjoin the lightly doped drain region; a fourth step of successively forming a first insulating film, a floating gate electrode, a second insulating film, and a control gate electrode on the semiconductor substrate such that the stepped portion is covered up therewith; and a fifth step of ion-implanting an impurity of the second conductivity type into the semiconductor substrate by using the control gate electrode as a mask and thereby forming a source region of the second conductivity type in the source formation region, while forming a drain region of the second conductivity type in the drain formation region. 
   The second method for fabricating a nonvolatile semiconductor memory device comprises the step of selectively ion-implanting the low-concentration impurity of the second conductivity type into the second surface region of the semiconductor substrate and thereby forming the lightly doped drain region of the second conductivity type in the second surface region, while inverting the conductivity type of each of the portions of the heavily doped impurity region of the first conductivity type located in the vicinity of the first surface region, the upper corner of the stepped portion, and the step side region of the stepped portion and thereby forming the depletion control layer composed of the heavily doped impurity region and located distinctly at a distance from the first surface region and the step side region to adjoin the lightly doped drain region. This ensures the fabrication of the second nonvolatile semiconductor memory device according to the present invention. 
   In the second method for fabricating a nonvolatile semiconductor memory device, the first step preferably includes the step of: ion-implanting again an impurity of the first conductivity type into the heavily doped impurity region that has been formed and thereby forming another impurity region of the first conductivity type which is shallower in diffusion depth than the heavily doped impurity region and the third step includes the step of: forming a high-electric-field forming layer composed of the other impurity region between an upper corner of the stepped portion and the depletion control layer. 
   Preferably, the second method for fabricating a nonvolatile semiconductor memory device further comprises, after the fifth step: a sixth step of depositing a third insulating film on the control gate electrode, etching the deposited third insulating film, and thereby forming sidewalls on respective side surfaces of the floating gate electrode and the control gate electrode; and a seventh step of ion-implanting an impurity of the second conductivity type into the semiconductor substrate by using the control gate electrode and the sidewalls as a mask and thereby forming, in the second surface region, a heavily doped drain region of the second conductivity type which is higher in impurity concentration than the drain region. This ensures the fabrication of the fifth nonvolatile semiconductor memory device according to the present invention. 
   Preferably, the second method for fabricating a nonvolatile semiconductor memory device further comprises, after the third step, the step of: masking a region extending from the control gate electrode to the second surface region and forming, in the source formation region, an impurity region of the first conductivity type which is deeper in diffusion depth than the source region. This ensures the fabrication of the sixth nonvolatile semiconductor memory device according to the present invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a structural cross-sectional view showing a memory element in a split-gate nonvolatile semiconductor memory device according to a first embodiment of the present invention; 
       FIG. 2  is an enlarged cross-sectional view of a stepped portion and its vicinity in the split-gate nonvolatile semiconductor memory device according to the first embodiment, which shows electrons flowing toward a high electron temperature region generated in the vicinity of the lower corner of the stepped portion; 
       FIG. 3A  is an enlarged cross-sectional view of the stepped portion and its vicinity in the split-gate nonvolatile semiconductor memory device according to the first embodiment, which shows the result of simulation using a calculator for a current density during a write operation; 
       FIG. 3B  is an enlarged cross-sectional view of a stepped portion and its vicinity in a conventional split-gate nonvolatile semiconductor memory device, which shows the result of simulation using a calculator for a current density during a write operation; 
       FIGS. 4A to 4D  are cross-sectional views illustrating the individual process steps of a method for fabricating the split-gate nonvolatile semiconductor memory device according to the first embodiment; 
       FIGS. 5A to 5D  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the first embodiment; 
       FIGS. 6A and 6B  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the first embodiment; 
       FIG. 7  is a structural cross-sectional view of a memory element in a split-gate nonvolatile semiconductor memory device according to a second embodiment of the present invention; 
       FIGS. 8A to 8D  are cross-sectional views illustrating the individual process steps of a method for fabricating the split-gate nonvolatile semiconductor memory device according to the second embodiment; 
       FIGS. 9A to 9D  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the second embodiment; 
       FIGS. 10A and 10B  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the second embodiment; 
       FIG. 11  is a structural cross-sectional view of a memory element in a stacked-gate nonvolatile semiconductor memory device according to a third embodiment of the present invention; 
       FIGS. 12A to 12D  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the third embodiment; 
       FIGS. 13A to 13D  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the third embodiment; 
       FIG. 14  is a cross-sectional view illustrating the process step of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the third embodiment; 
       FIG. 15  is a structural cross-sectional view of a memory element in a stacked-gate nonvolatile semiconductor memory device according to a fourth embodiment of the present invention; 
       FIGS. 16A to 16D  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the fourth embodiment; 
       FIGS. 17A to 17D  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the fourth embodiment; 
       FIG. 18  is a cross-sectional view illustrating the process step of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the fourth embodiment; 
       FIG. 19A  is a structural cross-sectional view of a memory element in a split-gate nonvolatile semiconductor memory device according to a fifth embodiment of the present invention; 
       FIG. 19B  is a structural cross-sectional view of a memory element in a stacked-gate nonvolatile semiconductor memory device according to the fifth embodiment; 
       FIG. 20  is a structural cross-sectional view of a memory element in a split-gate nonvolatile semiconductor memory device according to a sixth embodiment of the present invention; 
       FIGS. 21A and 21B  are enlarged cross-sectional views of a stepped portion and its vicinity in the split-gate nonvolatile semiconductor memory device according to the sixth embodiment, of which  FIG. 21A  shows a flow of electrons during a write operation and  FIG. 21B  shows a flow of electrons during an erase operation; 
       FIGS. 22A to 22D  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the sixth embodiment; 
       FIGS. 23A to 23D  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the sixth embodiment; 
       FIGS. 24A and 24B  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the sixth embodiment; 
       FIG. 25  is a structural cross-sectional view of a memory element in a split-gate nonvolatile semiconductor memory device according to a variation of the sixth embodiment; 
       FIG. 26  is a structural cross-sectional view of a memory element in a split-gate nonvolatile semiconductor memory device according to a seventh embodiment of the present invention; 
       FIGS. 27A to 27D  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the seventh embodiment; 
       FIGS. 28A to 28D  are cross-sectional views illustrating the individual process steps of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the seventh embodiment; 
       FIG. 29  is a cross-sectional view illustrating the process step of the method for fabricating the split-gate nonvolatile semiconductor memory device according to the seventh embodiment; 
       FIG. 30  is a structural cross-sectional view of a memory element in a split-gate nonvolatile semiconductor memory device according to a variation of the seventh embodiment; 
       FIG. 31  is a structural cross-sectional view of a memory element in a stacked-gate nonvolatile semiconductor memory device according to an eighth embodiment of the present invention; 
       FIGS. 32A to 32D  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the eighth embodiment; 
       FIGS. 33A to 33D  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the eighth embodiment; 
       FIGS. 34A and 34B  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the eighth embodiment; 
       FIG. 35  is a structural cross-sectional view of a memory element in a stacked-gate nonvolatile semiconductor memory device according to a variation of the eighth embodiment; 
       FIG. 36  is a structural cross-sectional view of a memory element in a stacked-gate nonvolatile semiconductor memory device according to a ninth embodiment of the present invention; 
       FIGS. 37A to 37D  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the ninth embodiment; 
       FIGS. 38A to 38D  are cross-sectional views illustrating the individual process steps of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the ninth embodiment; 
       FIG. 39  is a cross-sectional view illustrating the process step of the method for fabricating the stacked-gate nonvolatile semiconductor memory device according to the ninth embodiment; 
       FIG. 40  is a structural cross-sectional view of a memory element in a stacked-gate nonvolatile semiconductor memory device according to a variation of the ninth embodiment; 
       FIGS. 41A and 41B  show flows of hot holes in the vicinity of a stepped portion during an erase operation in a split-gate nonvolatile semiconductor memory device, of which  FIG. 41A  is a cross-sectional view when a comparative method for bias application is used and  FIG. 41B  is a cross-sectional view when a method for bias application according to a tenth embodiment of the present invention is used; and 
       FIG. 42  is a structural cross-sectional view of a memory element in a conventional split-gate nonvolatile semiconductor memory device. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Embodiment 1 
   A first embodiment of the present invention will be described with reference to the drawings. 
     FIG. 1  shows a cross-sectional structure of a memory element in a split-gate nonvolatile semiconductor memory device according to the first embodiment. As shown in  FIG. 1 , a semiconductor substrate  11  composed of p-type silicon has an active region surrounded by an isolation layer  12  composed of LOCOS or trench isolation. The principal surface of the active region is formed with a stepped portion composed of a first surface region  13  serving as an upper stage, a second surface region  14  serving as a lower stage, and a step side region  15  connecting the upper and lower stages. 
   A control gate electrode  21  is formed on the first surface region  13  with a first insulating film  22  interposed therebetween. A floating gate electrode  23  formed to cover up the stepped portion  16  is capacitively coupled to the side surface of the control gate electrode  21  closer to the stepped portion  16  with a second insulating film  24  interposed therebetween, while it is opposed to the second surface region  14  with a third insulating film  25  serving as a tunneling film interposed therebetween. The first and third insulating films  22  and  25  may be composed of a single film and the second and third insulating films  24  and  25  may be composed of a single film. 
   An n-type source region  31  is formed in the first surface region  13  of the semiconductor substrate  11 , while an n-type drain region  32  is formed in a region under the floating gate electrode  23 . 
   The nonvolatile semiconductor memory device according to the first embodiment features a depletion control layer  33  which is composed of a heavily doped p-type impurity region and formed within the semiconductor substrate  11  to be located in the vicinity of the stepped portion  16 . The depletion control layer  33  extends from a position at a distance from the upper corner of the stepped portion  16  and under the floating gate electrode  23  toward the lower corner of the stepped portion  16  and adjoin the end portion of the drain region  32  without reaching the step side region  15 . 
   A description will be given to exemplary data write, erase, and read operations in the nonvolatile semiconductor memory device according to the present embodiment. 
   During the data write operation, a gate voltage of about 4.0 V to 7.0 V is applied to the control gate electrode  21 , the source region  31  is grounded, and a drain voltage of about 4.0 V to 6.0 V is applied to the drain region  32 . The application of the voltages generates hot electrons in the vicinity of the lower corner of the stepped portion  16 , which pass through the third insulating film  25  to be injected into the floating gate electrode  23 . 
   During the data erase operation, a gate voltage of about −5.0 V to −7.0 V is applied to the control gate electrode  21 , a drain voltage of about 4.0 to 6.0 V is applied to the drain region  23 , and the source region  31  is grounded. As a result, electrons accumulated in the floating gate electrode  23  are extracted to the drain region  32  through the third insulating film  25  due to a FN (Fowler-Nordheim) tunneling phenomenon. 
   During the data read operation, a source voltage of about 1.0 V to 3.0 V is applied to the source region  31 , the drain region  32  is grounded, and a gate voltage of about 2.0 V to 4.0 V is applied to the control gate electrode  32  or, alternatively, a drain voltage of about 1.0 V to 3.0 V is applied to the drain region  32 , the source region  31  is grounded, and a gate voltage of about 2.0 V to 4.0 V is applied to the control gate electrode  21 . At this time, the threshold voltage of the control gate electrode  21  have different values depending on the presence or absence of the electrons accumulated in the floating gate electrode  23  to produce a difference in the amount of current flowing between the source and the drain, so that the presence or absence of data is determined by detecting the amount of the current. 
   In the nonvolatile semiconductor memory according to the present embodiment, the depletion control layer  33  composed of the heavily doped p-type impurity region is formed at a position not reaching the first surface region  13  and step side region  15  of the stepped portion  16  to have the end portion thereof closer to the drain region  32  adjoining the drain region  32 . During the write operation, therefore, electrons as carriers flowing toward a high electron temperature region  1  and a maximum electron temperature region  2  each generated in the vicinity of the lower corner of the stepped portion  16  to form a path (which is a channel), as shown in the diagram of  FIG. 2 . As a result, the channel electrons which have become hot electrons in the vicinity of the step side region  15  are injected efficiently into the floating gate electrode  23 . 
     FIG. 3A  shows the result of calculating a current density during the write operation in the vicinity of the stepped portion  16  in the nonvolatile semiconductor memory device according to the present embodiment by simulation using a calculator.  FIG. 3B  is for comparison, which shows the result of simulation in a conventional nonvolatile semiconductor memory device unformed with the depletion control layer  33 . 
   As shown in  FIG. 3A , the depletion control layer  33  in the semiconductor memory device according to the present embodiment is not depleted because of a p-type impurity contained therein at a high concentration. Instead, the portion of the semiconductor substrate  11  enclosed with the first surface region  13 , the step side region  15 , and the depletion control layer  33  is depleted to function as a channel region. As a result, electrons in the channel flow expansively toward the step side region  15 . 
   Since a path of carriers is blocked by the depletion control layer  33 , charges are accumulated in the floating gate electrode  23  to lower a potential at the floating gate electrode  23 . Even if the electrons are strongly attracted to the drain region  32 , the electrons passing through the portion of the channel region underlying the control gate electrode  21  are prevented from flowing directly into the drain region  32  so that the path of carriers flowing toward the lower corner of the stepped portion is retained. This provides a steady carrier path irrespective of the potential at the floating gate electrode  23  and improves the efficiency with which carriers are injected into the floating gate electrode  23 . 
   In the conventional nonvolatile semiconductor memory device shown in  FIG. 3B , by contrast, a region at a distance from the first surface region  13  and side surface region  15  of the stepped portion  16  is depleted disadvantageously during a write operation because of a p-type impurity contained therein at a low concentration so that the region functions as a channel. As a result, electrons in the channel flow directly into the drain region  32  without passing through the maximum electron temperature region generated in the vicinity of the lower corner of the stepped portion  16 . This reduces the probability that the electrons are injected into the floating gate electrode  23 . 
   The depletion control layer  33  also has the following effects. Since the depletion control layer  33  composed of the heavily doped p-type impurity region is formed to adjoin the end portion of the drain region  32 , a pn junction with a sharp concentration gradient is formed at the interface between the depletion control layer  33  and the drain region  32  so that a high electric field is generated at the interface. By providing the depletion control layer  33  such that the high electric field generated at the interface therebetween is located in the vicinity of the lower corner of the stepped portion  16 , the electron temperature in the high electron temperature region generated in the vicinity of the lower corner of the stepped portion  16  increases drastically, which greatly increases a write speed. 
   If the drain region  32  thoroughly covers the lower corner of the stepped portion  16 , the potential at the corner is held high during the write operation due to the drain potential so that the potential across the step side region  15  presents a sharp gradient. As a result, the high electron temperature region generated in the vicinity of the lower corner of the stepped portion  16  expands to the step side region  15  and the write speed is increased. 
   Although the present embodiment has formed the step side region  15  of the stepped portion  16  which is nearly perpendicular to the second surface region  14 , the angle formed between the step side region  15  and the second surface region  14  may be obtuse. 
   A description will be given herein below to a method for fabricating the nonvolatile semiconductor memory device thus constituted with reference to the drawings. 
     FIGS. 4A to 6B  show the cross-sectional structures of the nonvolatile semiconductor memory device according to the first embodiment in the individual process steps of the fabrication method therefor. 
   First, as shown in  FIG. 4A , an isolation layer  52  having, e.g., a trench isolation structure, is formed in a semiconductor substrate  51  composed of p-type silicon. Then, a protective oxide film  53  with a thickness of about 20 nm is formed by thermal oxidation or CVD on an active region  10  surrounded by the isolation layer  52 . Thereafter, a first resist pattern  91  having a pattern for forming a p-type well region in the active region  10  is formed on the semiconductor substrate  51 . Subsequently, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the protective oxide film  53  with an implant energy of about 300 keV by using the first resist pattern  91  as a mask, whereby the p-type well region having a near-surface impurity concentration of about 5×10 13  cm −3  to 1×10 14  cm −3  is formed in the active region  10 . Then, boron (B) ions for threshold voltage control at an implant dose of about 0.5×10 13  cm −2  to 1×10 13  cm −2  are further implanted into the entire surface of the active region  10  with an implant energy of about 30 keV through the protective oxide film  53 . 
   Next, as shown in  FIG. 4B , the first resist pattern  91  and the protective oxide film  53  are removed and then a gate oxide film  54  serving as a first insulating film is formed again on the active region  10  by CVD or thermal oxidation. Thereafter, a first polysilicon film is deposited by, e.g., CVD over the entire surface of the semiconductor substrate  51 . The deposited first polysilicon film is patterned by photolithography to form a control gate electrode  55  composed of polysilicon. Subsequently, a second resist pattern  92  having an opening over the region of the active region  10  to be formed with a drain is formed on the semiconductor substrate  51 . By using the formed second resist pattern  92  and the control gate electrode  55  as a mask, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the gate oxide film  54  with an implant energy of about 15 keV, whereby a heavily doped p-type impurity layer  56  is formed in the drain formation region. 
   Then, as shown in  FIG. 4C , the second resist pattern  92  is removed. Thereafter, a BPSG film is deposited by CVD over the entire surface of the semiconductor substrate  51 . Subsequently, anisotropic etching is performed with respect to the deposited BPSG film to form sidewalls  57  composed of the BPSG film on the side surfaces of the control gate electrode  55 . By adjusting the thickness of the deposited BPSG film, the distance between the side surface of the control gate electrode  55  and a stepped portion, which will be formed in the semiconductor substrate  51  in the subsequent step, can be determined by self alignment. 
   Next, as shown in  FIG. 4D , a third resist pattern  93  having an opening over the drain formation region is formed on the semiconductor substrate  51 . By using the formed third resist pattern  93 , the gate electrode  55 , and the sidewalls  57  as a mask, dry etching is performed with respect to the semiconductor substrate  51 , thereby forming a recessed portion  51   a  in the drain formation region of the semiconductor substrate  51 . 
   Next, as shown in  FIG. 5A , arsenic (As) ions at an implant dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 10 keV by using the third resist pattern  93 , the gate electrode  55 , and the sidewalls  57  as a mask, whereby a lightly doped n-type drain region  58  is formed in the drain formation region. 
   At this time, the concentration of the p-type impurity in the portion of the heavily doped p-type impurity layer  56  underlying the sidewall  57  is lowered by a compensating effect exerted by the n-type impurity implanted during the formation of the lightly doped drain region  58 . What results is a depletion control layer  56   a  composed of the heavily doped p-type impurity layer  56  and formed in the stepped portion  51   b  of the recessed portion  51   a  in the semiconductor substrate  51  closer to the control gate electrode  55  to extend from a position located under the control gate electrode  55  and at a distance from the upper corner of the stepped portion  51   b  toward the lower corner of the stepped portion  51   b  and adjoin the lightly doped drain region  58  without reaching the step side region. 
   Next, as shown in  FIG. 5B , the third resist pattern  93  is removed and then the sidewalls  57  and the exposed portion of the gate oxide film  54  are removed by wet etching, whereby the stepped portion  51   b  composed of a first surface region  59  serving as an upper stage, a second surface region  60  serving as a lower stage, and a step side region  61  connecting the upper and lower stages and the side surface of the control gate electrode  55  are exposed. 
   Next, as shown in  FIG. 5C , a thermal oxide film  62  serving as second and third insulating films is formed by thermal oxidation on the exposed surface of the semiconductor substrate  51  including the stepped portion  51   b  and on the surface of the control gate electrode  55 . The thermal oxide film  62  may also be a silicon dioxide film formed by CVD or the like. 
   Next, as shown in  FIG. 5D , a second polysilicon film is deposited by, e.g., CVD over the entire surface of the semiconductor substrate  51  including the control gate electrode  55 . By performing anisotropic etching with respect to the deposited second polysilicon film, a floating gate electrode  63  composed of polysilicon, capacitively coupled to the side surface of the control gate electrode  55  closer to the stepped portion  51   b  with the thermal oxide film  62  interposed therebetween, and opposed to the second surface region  60  with the thermal oxide film  62  interposed therebetween is formed by self alignment so as to cover up the stepped portion  51   b . The region of the thermal oxide film  62  sandwiched between the floating gate electrode  63  and the semiconductor substrate  51  functions as a tunnel film. 
   Next, as shown in  FIG. 6A , an insulating film  64  composed of a silicon dioxide or the like is formed over the entire surface of the semiconductor substrate  51 . By subsequently etching the formed insulating film  64 , the semiconductor substrate  51  is exposed. 
   Next, as shown in  FIG. 6B , arsenic (As) ions are implanted into the semiconductor substrate  51  by using the control gate electrode  55 , the floating gate electrode  63 , and the insulating film  64  as a mask so that a heavily doped source region  65  is formed in the region of the semiconductor substrate  51  opposite to the floating gate electrode  63  relative to the control gate electrode  55  and a heavily doped drain region  66  is formed in the region of the semiconductor substrate  51  closer to the floating gate electrode  63  than to the control gate electrode  55  and connecting to the lightly doped drain region  58 , whereby the memory element in the nonvolatile semiconductor memory device is completed. 
   Thus, in accordance with the method for fabricating the nonvolatile semiconductor memory device of the first embodiment, the heavily doped p-type impurity layer  56  is formed in the drain formation region of the semiconductor substrate  51 . Then, the recessed portion  51   a  is formed in the semiconductor substrate  51  by using the sidewalls  57  on the control gate electrode  55  as a mask, whereby the stepped portion  51   b  using the portion of the semiconductor substrate  51  underlying the sidewall  57  as the first surface region  59  (upper stage) and using the bottom surface of the recessed portion  51   a  as the second surface region  60  (lower stage) is formed. In subsequently forming the lightly doped n-type drain region  58  by implantation in the second surface region  60 , the depletion control layer  56   a  having a desired impurity profile and located discretely in spaced apart and opposing relation to the upper corner of the stepped portion  51   b  to adjoin the lightly doped drain region  58  can be formed reliably by the compensating effect exerted on the heavily doped impurity layer  56 . 
   Embodiment 2 
   A second embodiment of the present invention will be described with reference to the drawings. 
     FIG. 7  shows a cross-sectional structure of a memory element in a split-gate nonvolatile semiconductor memory device according to the second embodiment. In  FIG. 7 , the description of the same components as used in the first embodiment and shown in  FIG. 1  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 7 , the nonvolatile semiconductor memory device according to the second embodiment features a high-electric-field forming layer  34  formed between the upper corner of the stepped portion  16  and the depletion control layer  33  and composed of a p-type impurity region having the same conductivity type as the depletion control layer  33 . The concentration of a p-type impurity in the high-electric-field forming layer  34  has been adjusted to be lower than the concentration of a p-type impurity in the depletion control layer  33  and higher than the concentration of a p-type impurity in the semiconductor substrate  11 . 
   Since the second embodiment has provided the p-type high-electric-field forming layer  34  between the upper corner of the stepped portion  16  and the depletion control layer  33 , an energy level in the step side region  15  has a sharper gradient due to a pn junction portion composed of the interface between the high-electric-field forming layer  34  and the drain region  32 . As a result, a high electric field is generated at the interface between the high-electric-field forming layer  34  and the drain region  32  to overlap each of the high electric field generated by the lower corner of the stepped portion  16  and a high electric field generated at the interface between the depletion control layer  33  and the drain region  32 , so that an electron temperature in the vicinity of the lower corner of the stepped portion  16  is further increased. This increases the number of electrons in the channel that have become hot electrons and remarkably improves the efficiency with which the electrons are injected into the floating gate electrode  23 . 
   In addition, the high-electric-field forming layer  34  formed independently of the depletion control layer  33  achieves the effect of enhancing the controllability of the threshold voltage of the memory element. 
   As described in the first embodiment, for the portion of the semiconductor substrate  11  enclosed with the depletion control layer  33 , the first surface region  13 , and the step side region  15  to function as the channel and for the channel electrons to retain a path of carriers flowing expansively toward the step side region  15 , the high-electric-field forming layer  34  preferably has an impurity concentration sufficient to be depleted during a write operation. 
   In the present embodiment also, the angle formed between the step side region  15  and the second surface region  14  may be obtuse. 
   A description will be given herein below to a method for fabricating the nonvolatile semiconductor memory device thus constituted with reference to the drawings. 
     FIGS. 8A to 10B  show the cross-sectional structures of the nonvolatile semiconductor memory device according to the second embodiment in the individual process steps of the fabrication method therefor. 
   First, as shown in  FIG. 8A , the isolation layer  52  having, e.g., a trench isolation structure, is formed in the semiconductor substrate  51  composed of p-type silicon. Then, the protective oxide film  53  with a thickness of about 20 nm is formed by thermal oxidation or CVD on the active-region  10  surrounded by the isolation layer  52 . Thereafter, the first resist pattern  91  having a pattern for forming a p-type well region in the active region  10  is formed on the semiconductor substrate  51 . Subsequently, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the protective oxide film  53  with an implant energy of about 300 keV by using the first resist pattern  91  as a mask, whereby the p-type well region having a near-surface impurity concentration of about 5×10 13  cm −3  to 1×10 14  cm −3  is formed in the active region  10 . Then, boron (B) ions for threshold voltage control at an implant dose of about 0.5×10 13  cm −2  to 1×10 13  cm −2  are further implanted into the entire surface of the active region  10  with an implant energy of about 30 keV through the protective oxide film  53 . 
   Next, as shown in  FIG. 8B , the first resist pattern  91  and the protective oxide film  53  are removed and then the gate oxide film  54  serving as the first insulating film is formed again on the active region  10  by CVD or thermal oxidation. Thereafter, the first polysilicon film is deposited by, e.g., CVD over the entire surface of the semiconductor substrate  51 . The deposited first polysilicon film is patterned by photolithography to form the control gate electrode  55  composed of polysilicon. Subsequently, the second resist pattern  92  having an opening over the region of the active region  10  to be formed with the drain is formed on the semiconductor substrate  51 . By using the formed second resist pattern  92  and the control gate electrode  55  as a mask, boron (B) ions are implanted in two steps with different acceleration voltages. In the first step, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the gate oxide film  54  with an implant energy of about 30 keV, whereby a first heavily doped p-type impurity layer  56  is formed in the drain formation region. In the second step, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the gate oxide film  54  with an implant energy of about 15 keV, whereby a second heavily doped p-type impurity layer  71  having a junction depth shallower than that of the first heavily doped impurity layer  56  is formed in the drain formation region. 
   Then, as shown in  FIG. 8C , the second resist pattern  92  is removed. Thereafter, the BPSG film is deposited by CVD over the entire surface of the semiconductor substrate  51 . Subsequently, anisotropic etching is performed with respect to the deposited BPSG film to form the sidewalls  57  composed of the BPSG film on the side surfaces of the control gate electrode  55 . By adjusting the thickness of the deposited BPSG film, the distance between the side surface of the control gate electrode  55  and the stepped portion, which will be formed in the semiconductor substrate  51  in the subsequent step, can be determined by self alignment. 
   Next, as shown in  FIG. 8D , the resist pattern  93  having an opening over the drain formation region is formed on the semiconductor substrate  51 . By using the formed third resist pattern  93 , the gate electrode  55 , and the sidewalls  57  as a mask, dry etching is performed with respect to the semiconductor substrate  51 , thereby forming the recessed portion  51   a  in the drain formation region of the semiconductor substrate  51 . 
   Next, as shown in  FIG. 9A , arsenic (As) ions at an implant dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 10 keV by using the third resist pattern  93 , the gate electrode  55 , and the sidewalls  57  as a mask, whereby the lightly doped n-type drain region  58  is formed in the drain formation region. 
   At this time, the concentration of the p-type impurity in the portion of the heavily doped p-type impurity layer  56  underlying the sidewall  57  is lowered by the compensating effect exerted by the n-type impurity implanted during the formation of the lightly doped drain region  58 . What results is the depletion control layer  56   a  composed of the first heavily doped p-type impurity layer  56  and formed in the stepped portion  51   b  of the recessed portion  51   a  in the semiconductor substrate  51  closer to the control gate electrode  55  to extend from a position located under the control gate electrode  55   c  and at a distance from the upper corner of the stepped portion  51   b  toward the lower corner of the stepped portion  51   b  and adjoin the lightly doped drain region  58  without reaching the step side region. 
   At the same time, a high-electric-field forming layer  71   a  which is lower in concentration than the first heavily doped impurity layer  56  due to the compensating effect during the formation of the lightly doped drain region  58  can be formed from the second heavily doped p-type impurity layer  71  to be located between the upper corner of the stepped portion  51   b  and the depletion control layer  56   a.    
   Next, as shown in  FIG. 9B , the third resist pattern  93  is removed and then the sidewalls  57  and the exposed portion of the gate oxide film  54  are removed by wet etching, whereby the stepped portion  51   b  composed of the first surface region  59  serving as the upper stage, the second surface region  60  serving as the lower stage, and the step side region  61  connecting the upper and lower stages and the side surface of the control gate electrode  55  are exposed. 
   Next, as shown in  FIG. 9C , the thermal oxide film  62  serving as the second and third insulating films is formed by thermal oxidation on the exposed surface of the semiconductor substrate  51  including the stepped portion  51   b  and on the surface of the control gate electrode  55 . The thermal oxide film  62  may also be a silicon dioxide film formed by CVD or the like. 
   Next, as shown in  FIG. 9D , the second polysilicon film is deposited by, e.g., CVD over the entire surface of the semiconductor substrate  51  including the control gate electrode  55 . By performing anisotropic etching with respect to the deposited second polysilicon film, the floating gate electrode  63  composed of polysilicon, capacitively coupled to the side surface of the control gate electrode  55  closer to the stepped portion  51   b  with the thermal oxide film  62  interposed therebetween, and opposed to the second surface region  60  with the thermal oxide film  62  interposed therebetween is formed by self alignment to cover up the stepped portion  51   b . The region of the thermal oxide film  62  sandwiched between the floating gate electrode  63  and the semiconductor substrate  51  functions as the tunnel film. 
   Next, as shown in  FIG. 10A , the insulating film  64  composed of a silicon dioxide or the like is formed over the entire surface of the semiconductor substrate  51 . By subsequently etching the formed insulating film  64 , the semiconductor substrate  51  is exposed. 
   Next, as shown in  FIG. 10B , arsenic (As) ions are implanted into the semiconductor substrate  51  by using the control gate electrode  55 , the floating gate electrode  63 , and the insulating film  64  as a mask so that the heavily doped source region  65  is formed in the region of the semiconductor substrate  51  opposite to the floating gate electrode  63  relative to the control gate electrode  55  and a heavily doped drain region  66  is formed in the region of the semiconductor substrate  51  closer to the floating gate electrode  63  than to the control gate electrode  55  and connecting to the lightly doped drain region  58 , whereby the memory element in the nonvolatile semiconductor memory device is completed. 
   Thus, in accordance with the method for fabricating the nonvolatile semiconductor memory device of the second embodiment, the first heavily doped p-type impurity layer  56  and the second heavily doped impurity layer  71  having a junction shallower than that of the first heavily doped impurity layer  56  are formed in the drain formation region of the semiconductor substrate  51 . Then, the recessed portion  51   a  is formed in the semiconductor substrate  51  by using the sidewalls  57  on the control gate electrode  55  as a mask, whereby the stepped portion  51   b  using the portion of the semiconductor substrate  51  underlying the sidewall  57  as the first surface region (upper stage) and using the bottom surface of the recessed portion  51   a  as the second surface region  60  (lower stage) is formed. In subsequently forming the lightly doped n-type drain region  58  by implantation in the second surface region  60 , the depletion control layer  56   a  having a desired impurity profile and located discretely in spaced apart and opposing relation to the upper corner of the stepped portion  51   b  to adjoin the lightly doped drain region  58  can be formed reliably by the compensating effect exerted on the first heavily doped impurity layer  56 . In addition, the high-electric-field forming layer  71   a  composed of the second heavily doped impurity layer  71  and having a desired impurity profile can be formed between the upper corner of the stepped portion  51   b  and the depletion control layer  56   a.    
   Although the second embodiment has formed the first and second heavily doped impurity layers  56  and  71  by performing the two consecutive steps of ion implantation using the same third resist pattern  93  and thereby formed different impurity profiles desired in the respective heavily doped impurity layers, it will easily be appreciated that the desired impurity profiles can also be achieved in the first and second heavily doped impurity layers  56  and  71  even if the first and second steps of ion implantation are performed by using different mask patterns. 
   Embodiment 3 
   A third embodiment of the present invention will be described with reference to the drawings. 
     FIG. 11  shows a cross-sectional structure of a memory element in a stacked-gate nonvolatile semiconductor memory device according to the third embodiment. In  FIG. 11 , the description of the same components as shown in  FIG. 1  will be omitted by retaining the same reference numerals. 
   The nonvolatile semiconductor memory device according to the third embodiment comprises a floating gate electrode  23 A formed to cover up the stepped portion  16  formed in the active region of the semiconductor substrate  11  with the first insulating film  22  serving as a tunnel insulating film interposed therebetween and a control gate electrode  21 A formed on the floating gate electrode with the second insulating film  24  interposed therebetween to be capacitively coupled to the floating gate electrode  23 A. 
   Thus, the nonvolatile semiconductor memory device according to the third embodiment is of a stacked gate type having the drain region  32  in the second surface region  14  serving as the lower stage of the stepped portion  16 , while having the floating gate electrode  23 A and the control gate electrode  21 A stacked successively on the substrate to cover up the stepped portion. The nonvolatile semiconductor memory device according to the present embodiment has the depletion control layer  33  composed of a heavily doped impurity region of the conductivity type opposite to that of the drain region  32  and formed within the semiconductor substrate  11  to extend from a position located under the first surface region  13  and at a distance from the upper corner of the stepped portion  16  toward the lower corner of the stepped portion  16  and adjoin the drain region  32  without reaching the step side region  15 . 
   Since the depletion control layer  33  of the conductivity type opposite to that of the drain region is provided at the position at a distance from the upper corner of the stepped portion  16  to adjoin the drain region  32 , similarly to the first embodiment, the depletion control layer  33  containing a p-type impurity at a high concentration is not depleted during a write operation. Instead, the portion of the semiconductor substrate  11  enclosed with the first surface region  13 , the step side region  15 , and the depletion control layer  33  is depleted to function as a channel. This causes electrons in the channel to flow expansively toward the step side region  15  and improves the efficiency with which carriers are injected into the floating gate electrode  23 A. 
   Moreover, since the depletion control layer  33  composed of the heavily doped p-type impurity region is formed to adjoin the end portion of the n-type drain region  32 , a pn junction with a sharp concentration gradient is formed at the interface between the depletion control layer  33  and the drain region  32  so that a high electric field is generated at the interface. By providing the depletion control layer  33  such that the high electric field generated at the interface therebetween is located in the vicinity of the lower corner of the stepped portion  16 , the electron temperature in the high electron temperature region generated in the vicinity of the lower corner of the stepped portion  16  increases drastically, which greatly increases a write speed. 
   If the drain region  32  thoroughly covers the lower corner of the stepped portion  16 , the potential at the corner is held high during the write operation due to the drain potential so that the potential in the step side region  15  presents a sharp gradient. As a result, the high electron temperature region generated in the vicinity of the lower corner of the stepped portion  16  expands to the step side region  15  and the write speed is increased. 
   In the present embodiment also, the angle formed between the step side region  15  and the second surface region  14  may be obtuse. 
   A description will be given herein below to a method for fabricating the nonvolatile semiconductor memory device thus constituted with reference to the drawings. 
     FIGS. 12A to 14  show the cross sectional structures of the nonvolatile semiconductor memory device according to the third embodiment in the individual process steps of the fabrication method therefor. 
   First, as shown in  FIG. 12A , the isolation layer  52  having, e.g., a trench isolation structure, is formed on the semiconductor substrate  51  composed of p-type silicon. Then, the protective oxide film  53  with a thickness of about 20 nm is formed by thermal oxidation or CVD on the active region  10  surrounded by the isolation layer  52 . Thereafter, the first resist pattern  91  including a pattern for forming a p-type well region in the active region  10  is formed on the semiconductor substrate  51 . Subsequently, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −1  are implanted into the semiconductor substrate  51  through the protective oxide film  53  with an implant energy of about 300 keV by using the first resist pattern  91  as a mask, whereby the p-type well region having a near-surface impurity concentration of about 5×10 13  cm −3  to 1×10 14  cm −3  is formed in the active region  10 . Then, boron (B) ions for threshold voltage control at an implant dose of about 0.5×10 13  cm −2  to 1×10 13  cm −2  are further implanted into the entire surface of the active region  10  with an implant energy of about 30 keV through the protective oxide film  53 . 
   Next, as shown in  FIG. 12B , the first resist pattern  91  is removed and then the second resist pattern  92  having an opening over the drain formation region of the active region  10  is formed on the semiconductor substrate  51 . By using the formed second resist pattern  92  as a mask, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −1  are implanted into the semiconductor substrate  51  through the gate oxide film  54  with an implant energy of about 15 keV, whereby the heavily doped p-type impurity layer  56  is formed in the drain formation region. 
   Then, as shown in  FIG. 12C , the second resist pattern  92  is removed and the third resist pattern  93  for masking a region to be formed with a source and the end portion of the heavily doped impurity layer  56  closer to the source formation region is formed on the semiconductor substrate  51 . By using the formed third resist pattern  93  as a mask, dry etching is performed with respect to the semiconductor substrate  51 , thereby forming the recessed portion  51   a  in the drain formation region of the semiconductor substrate  5   i . At this time, the dimension of the depletion control layer  56   a  in the direction of the gate length, which will be formed from the heavily doped impurity layer  56  in the subsequent step, can be optimized by adjusting the amount of masking (overlapping) the end portion of the heavily doped impurity layer  56  closer to the source formation region. 
   Next, as shown in  FIG. 12D , arsenic (As) ions at an implant dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 10 keV by using the third resist pattern  93  as a mask, whereby the lightly doped n-type drain region  58  is formed in the drain formation region. 
   At this time, the concentration of the p-type impurity in the portion of the heavily doped p-type impurity layer  56  underlying the sidewall  57  is lowered by the compensating effect exerted by the n-type impurity implanted during the formation of the lightly doped drain region  58 . What results is the depletion control layer  56   a  composed of the heavily doped p-type impurity layer  56  and formed in the stepped portion  51   b  of the recessed portion  51   a  in the semiconductor substrate  51  closer to the control gate electrode  55  to extend from a position located under the control gate electrode  55  and at a distance from the upper corner of the stepped portion  51   b  toward the lower corner of the stepped portion  51   b  and adjoin the lightly doped drain region  58  without reaching the step side region. 
   Next, as shown in  FIG. 13A , the third resist pattern  93  and the protective oxide film  53  are removed, whereby the stepped portion  51   b  composed of the upper surface of the semiconductor substrate  51 , i.e., the first surface region  59  serving as the upper stage, the second surface region  60  serving as the lower stage, and the step side region  61  connecting the upper and lower stages is exposed. 
   Next, as shown in  FIG. 13B , the gate oxide film  54  serving as the first insulating film is formed on the exposed surface of the semiconductor substrate  51  including the stepped portion  51   b . Then, a first polysilicon film  63 A, a silicon dioxide film  67 A serving as the second insulating film, and a second polysilicon film  55 A are deposited by, e.g., CVD over the entire surface of the gate oxide film  54 . The silicon dioxide film  67 A may also be formed as a thermal oxide film. 
   Next, as shown in  FIG. 13C , a fourth resist pattern  94  including a pattern for a gate electrode which covers up the stepped portion  51   b  is formed on the second polysilicon film.  55 A. By using the formed fourth resist pattern  94  as a mask, anisotropic etching is performed with respect to the second polysilicon film  55 A, the silicon dioxide film  67 A, and the first polysilicon film  63 A, thereby forming a floating gate electrode  63 B composed of the first polysilicon film  63 A, a capacitance insulating film  67 B composed of the silicon dioxide film  67 A, and a floating gate electrode  55 B composed of the second polysilicon film  55 A. The gate oxide film  54  between the semiconductor substrate  51  and the floating gate electrode  63 B functions as the tunnel film. 
   Next, as shown in  FIG. 13D , the fourth resist pattern  94  is removed. Then, as shown in  FIG. 14 , a fifth resist pattern  95  having an opening over the source formation region and the drain formation region is formed. By using the formed fifth resist pattern  95  and the control gate electrode  55 B as a mask, arsenic (As) ions are implanted into the semiconductor substrate  51  so that the heavily doped source region  65  is formed in the first surface region  59  of the semiconductor substrate  51  and the heavily doped drain region  66  is formed in the area of the second surface region  60  of the semiconductor substrate  51  connecting to the lightly doped drain region  58 , whereby the memory element in the stacked-gate nonvolatile semiconductor memory device is completed. 
   Thus, in accordance with the method for fabricating the nonvolatile semiconductor memory device of the third embodiment, the heavily doped p-type impurity layer  56  is formed in the drain formation region of the semiconductor substrate  51 . Then, the recessed portion  51   a  is formed in the semiconductor substrate  51  by masking the end portion of the heavily doped impurity layer  56  closer to the source region, whereby the stepped portion  51   b  using the portion of the semiconductor substrate  51  underlying the sidewall  57  as the first surface region  59  (upper stage) and using the bottom surface of the recessed portion  51   a  as the second surface region  60  (lower stage) is formed. In subsequently forming the lightly doped n-type drain region  58  by implantation in the second surface region  60 , the depletion control layer  56   a  having a desired impurity profile and located discretely in spaced apart and opposing relation to the upper corner of the stepped portion  51   b  to adjoin the lightly doped drain region  58  can be formed reliably by the compensating effect exerted on the heavily doped impurity layer  56 . 
   Embodiment 4 
   A fourth embodiment of the present invention will be described with reference to the drawings. 
     FIG. 15  shows a cross-sectional structure of a memory element in a stacked-gate nonvolatile semiconductor memory device according to the fourth embodiment. In  FIG. 15 , the description of the same components as used in the third embodiment and shown in  FIG. 11  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 15 , the nonvolatile semiconductor memory device according to the fourth embodiment features the high-electric-field forming layer  34  composed of a p-type impurity region having the same conductivity type as the depletion control layer and formed between the upper corner of the stepped portion  16  and the depletion control layer  33 . The concentration of a p-type impurity in the high-electric-field forming layer  34  has been adjusted to be lower than the concentration of a p-type impurity in the depletion control layer  33  and higher than the concentration of a p-type impurity in the semiconductor substrate  11 . 
   Since the fourth embodiment has provided the p-type high-electric-field forming layer  34  between the upper corner of the stepped portion  16  and the depletion control layer  33 , an energy level in the step side region  15  has a sharper gradient due to a pn junction portion composed of the interface between the high-electric-field forming layer  34  and the drain region  32 . As a result, a high electric field is generated at the interface between the high-electric-field forming layer  34  and the drain region  32  to overlap each of the high electric field generated by the lower corner of the stepped portion  16  and the high electric field generated at the interface between the depletion control layer  33  and the drain region  32 , so that the electron temperature in the vicinity of the lower corner of the stepped portion  16  is further increased. This increases the number of electrons in the channel that have become hot electrons and remarkably improves the efficiency with which the electrons are injected into the floating gate electrode  23 . 
   In addition, the high-electric-field forming layer  34  formed independently of the depletion control layer  33  achieves the effect of enhancing the controllability of the threshold voltage of the memory element. 
   As described in the first embodiment, for the portion of the semiconductor substrate  11  enclosed with the depletion control layer  33 , the first surface region  13 , and the step side region  15  to function as the channel and for the channel electrons to retain a path of carriers flowing expansively toward the step side region  15 , the high-electric-field forming layer  34  preferably has an impurity concentration sufficient to be depleted during a write operation. 
   In the present embodiment also, the angle formed between the step side region  15  and the second surface region  14  may be obtuse. 
   A description will be given herein below to a method for fabricating the nonvolatile semiconductor memory device thus constituted with reference to the drawings. 
     FIGS. 16A to 18  show the cross-sectional structures of the nonvolatile semiconductor memory device according to the fourth embodiment in the individual process steps of the fabrication method therefor. 
   First, as shown in  FIG. 16A , the isolation layer  52  having, e.g., a trench isolation structure, is formed in the semiconductor substrate  51  composed of p-type silicon. Then, the protective oxide film  53  with a thickness of about 20 nm is formed by thermal oxidation or CVD on the active region  10  surrounded by the isolation layer  52 . Thereafter, the first resist pattern  91  having a pattern for forming a p-type well region in the active region  10  is formed on the semiconductor substrate  51 . Subsequently, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the protective insulating film  53  with an implant energy of about 300 keV by using the first resist pattern  91  as a mask, whereby the p-type well region having a near-surface impurity concentration of about 5×10 13  cm −3  to 1×10 14  cm −3  is formed in the active region  10 . Then, boron (B) ions for threshold voltage control at an implant dose of about 0.5×10 13  cm −2  to 1×10 13  cm −2  are further implanted into the entire surface of the active region  10  with an implant energy of about 30 kev through the protective oxide film  53 . 
   Next, as shown in  FIG. 16B , the first resist pattern  91  is removed and then the second resist pattern  92  having an opening over the drain formation region of the active region  10  is formed on the semiconductor substrate  51 . By using the formed second resist pattern  92  as a mask, boron (B) ions are implanted in two steps with different acceleration voltages. In the first step, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the gate oxide film  54  with an implant energy of about 30 keV, whereby the first heavily doped p-type impurity layer  56  is formed in the drain formation region. In the second step, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the gate oxide film  54  with an implant energy of about 15 keV, whereby the second heavily doped p-type impurity layer  56  having a junction depth shallower than that of the first heavily doped impurity layer  56  is formed in the drain formation region. 
   Then, as shown in  FIG. 16C , the second resist pattern  92  is removed and the resist pattern  93  for masking the source formation region and the end portion of the heavily doped impurity layer  56  closer to the source formation region is formed on the semiconductor substrate  51 . By using the formed third resist pattern  93  as a mask, dry etching is performed with respect to the semiconductor substrate  51 , thereby forming the recessed portion  51   a  in the drain formation region of the semiconductor substrate  51 . At this time, the dimension of the depletion control layer  56   a  in the direction of the gate length, which will be formed from the heavily doped impurity layer  56  in the subsequent step, can be optimized by adjusting the amount of masking the end portion of the first heavily doped impurity layer  56  closer to the source formation region. 
   Next, as shown in  FIG. 16D , arsenic (As) ions at an implant dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 10 keV by using the third resist pattern  93  as a mask, whereby the lightly doped n-type drain region  38  is formed in the drain formation region. 
   At this time, the concentration of the p-type impurity in the portion of the first heavily doped p-type impurity layer  56  underlying the sidewall  57  is lowered by the compensating effect exerted by the n-type impurity implanted during the formation of the lightly doped drain region  58 . What results is the depletion control layer  56   a  composed of the first heavily doped p-type impurity layer  56  and formed in the stepped portion  51   b  of the recessed portion  51   a  in the semiconductor substrate  51  closer to the control gate electrode  55  to extend from a position located under the control gate electrode  55  and at a distance from the upper corner of the stepped portion  51   b  toward the lower corner of the stepped portion  51   b  and adjoin the lightly doped drain region  58  without reaching the step side region. 
   At the same time, the high-electric-field forming layer  71   a  which is lower in concentration than the first heavily doped impurity layer  56  due to the compensating effect during the formation of the lightly doped drain region  58  can be formed from the second heavily doped p-type impurity layer  71  to be located between the upper corner of the stepped portion  51   b  and the depletion control layer  56   a.    
   Next, as shown in  FIG. 17A , the third resist pattern  93  and the protective oxide film  53  are removed, whereby the stepped portion  51   b  composed of the upper surface of the semiconductor substrate  51 , i.e., the first surface region  59  serving as the upper stage, the second surface region  60  serving as the lower stage, and the step side region  61  connecting the upper and lower stages is exposed. 
   Next, as shown in  FIG. 17B , the gate oxide film  54  serving as the first insulating film is formed on the exposed surface of the semiconductor substrate  51  including the stepped portion  51   b . Then, the first polysilicon film  63 A, the silicon dioxide film  67 A as the second insulating film, and the second polysilicon film  55 A are deposited by, e.g., CVD over the entire surface of the gate oxide film  54 . The silicon dioxide film  67 A may also be formed as a thermal oxide film. 
   Next, as shown in  FIG. 17C , a fourth resist pattern  94  including the pattern for the gate electrode which covers up the stepped portion  51   b  is formed on the second polysilicon film  55 A. By using the formed fourth resist pattern  94  as a mask, anisotropic etching is performed with respect to the second polysilicon film  55 A, the silicon dioxide film  67 A, and the first polysilicon film  63 A, thereby forming the floating gate electrode  63 B composed of the first polysilicon film  63 A, the capacitance insulating film  67 B composed of the silicon dioxide film  67 A, and the floating gate electrode  55 B composed of the second polysilicon film  55 A. The gate oxide film  54  between the semiconductor substrate  51  and the floating gate electrode  63 B functions as the tunnel film. 
   Next, as shown in  FIG. 17D , the fourth resist pattern  94  is removed. Then, as shown in  FIG. 18 , the fifth resist pattern  95  having an opening over the source formation region and the drain formation region is formed. By using the formed fifth resist pattern  95  and the control gate electrode  55 B as a mask, arsenic (As) ions are implanted into the semiconductor substrate  51  so that the heavily doped source region  65  is formed in the first surface region  59  of the semiconductor substrate  51  and the heavily doped drain region  66  is formed in the area of the second surface region  60  of the semiconductor substrate  51  connecting to the lightly doped drain region  58 , whereby the memory element in the stacked-gate nonvolatile semiconductor memory device is completed. 
   Thus, in accordance with the method for fabricating the nonvolatile semiconductor memory device of the fourth-embodiment, the first heavily doped p-type impurity layer  56  and the second heavily doped impurity layer  71  having a junction shallower than that of the first heavily doped impurity layer  56  are formed in the drain formation region of the semiconductor substrate  51 . Then, the recessed portion  51   a  is formed in the semiconductor substrate  51  by masking the respective end portions of the first and second heavily doped impurity layer  56  and  71  closer to the source region, whereby the stepped portion  51   b  using the portion of the semiconductor substrate  51  underlying the sidewall  57  as the first surface region (upper stage) and using the bottom surface of the recessed portion  51   a  as the second surface region  60  (lower stage) is formed. In subsequently forming the lightly doped drain region  58  by implantation in the second surface region  60 , the depletion control layer  56   a  having a desired impurity profile and located discretely in spaced apart and opposing relation to the upper corner of the stepped portion  51   b  to adjoin the lightly doped drain region  58  can be formed reliably by the compensating effect exerted on the first heavily doped impurity layer  56 . In addition, the high-electric-field forming layer  71   a  composed of the second heavily doped impurity layer  71  and having a desired impurity profile can be formed between the upper corner of the stepped portion  51   b  and the depletion control layer  56   a.    
   Although the fourth embodiment has formed the first and second heavily doped impurity layers  56  and  71  by performing the two consecutive-steps of ion implantation using the same second resist pattern  91  and thereby formed different impurity profiles desired in the respective heavily doped impurity layers, it will easily be appreciated that the desired impurity profiles can also be achieved in the first and second heavily doped impurity layers  56  and  71  even if the first and second steps of ion implantation are performed by using different mask patterns. 
   Embodiment 5 
   A fifth embodiment of the present invention will be described with reference to the drawings. 
   Each of the first to fourth embodiments described above has provided the depletion control layer  33  located discretely in spaced apart and opposing relation to the stepped portion  16  in the semiconductor substrate  11  such that a carrier path in the channel region formed under the floating gate electrode  23  during, e.g., a write operation is formed along the step side region  15  and carriers flow through the high electron temperature region generated under the stepped portion  16 , thereby improving the efficiency with which carriers are injected into the floating gate electrode  23 . 
   By contrast, the fifth embodiment applies, to the semiconductor substrate, a substrate voltage of a polarity opposite to that of the drain voltage during a write operation instead of providing the depletion control layer  33  of the conductivity type opposite to that of the drain region such that the carrier path in the channel region is formed along the step side region  15 . 
   The present embodiment will be described herein below by using split-gate and stacked-gate nonvolatile semiconductor memory devices shown in  FIGS. 19A and 19B , respectively. 
     FIGS. 19A and 19B  show respective cross-sectional structures of memory elements in the nonvolatile semiconductor memory devices according to the present embodiment, of which  FIG. 19A  shows the split-gate type and  FIG. 19B  shows the stacked-gate type. In  FIG. 19A , the description of the same components as shown in  FIG. 1  will be omitted by retaining the same reference numerals. In  FIG. 19B , the description of the same components as shown in  FIG. 11  will be omitted by retaining the same reference numerals. 
   First, as shown in  FIG. 19A , the nonvolatile semiconductor memory device according to the fifth embodiment features the heavily doped impurity region  35  which is higher in the concentration of a p-type impurity than the semiconductor substrate  11  and formed in the upper corner of the stepped portion  16  as well as a negative voltage applied to the substrate during a write operation. 
   The heavily doped impurity region  35  has the effect of increasing the electron temperature in the step side region  15  and controlling the threshold voltage of the memory element. 
   In such a heavily doped impurity region  35 , depletion is less likely to occur so that the channel is less likely to be formed and electrons are more likely to flow in the vicinity of the interface between the heavily doped impurity region  35  and the semiconductor substrate  11 . Since the electrons flow along a path at a distance from the upper and lower corners of the stepped portion, they flow directly into the drain electrode  32  without passing through the high electron temperature region generated in the vicinity of the lower corner of the stepped portion and do not contribute to the injection of carriers into the floating gate electrode  23 . 
   In the present embodiment, therefore, a negative voltage, e.g., a voltage on the order of −1.0 V to −5.0 V is applied to the semiconductor substrate  11  during a write operation such that the electrons flow expansively toward the step side region  15  to form a path of carriers flowing toward the high electron temperature region generated in the vicinity of the lower corner of the stepped portion  16 . 
   This is because the application of a negative voltage to the semiconductor substrate  11  formed with the stepped portion  16  provides the region in the vicinity of the upper corner of the stepped portion  16  with the same effect as achieved when a potential at the floating gate electrode  23  is relatively increased so that the electrons are attracted to the surface of the semiconductor substrate  11 . As a result, the carrier path can be formed in the region enclosed with the upper corner of the stepped portion  16  as shown in  FIG. 3A  without providing the depletion control layer  33 . 
   Since the nonvolatile semiconductor memory device according to the present embodiment is increased in current density only during the application of the substrate potential, power consumption when a write operation is not performed can be reduced significantly. 
   As shown in  FIG. 19B , the stacked-gate nonvolatile semiconductor memory device can also achieve effects equal to those achieved by the split-gate nonvolatile semiconductor memory device shown in  FIG. 19A  if the heavily doped impurity region  35  which is higher in the concentration of a p-type impurity than the semiconductor substrate  11  is formed in the upper corner of the stepped portion  16  and a negative voltage is applied to the substrate during a write operation. 
   In a nonvolatile semiconductor memory device provided with the depletion control layer  33  as shown in each of the first to fourth embodiments also, the efficiency of carrier injection can further be improved by applying the substrate voltage during a write operation. 
   Even in a nonvolatile semiconductor memory device in which the heavily doped impurity region  35  is not provided in the upper corner of the stepped portion  16  also, the efficiency of carrier injection can also be improved by applying a negative substrate voltage during a write operation. 
   Although each of the memory elements according to the first to fifth embodiments has been described as an n-channel element, the same effects are achievable with a p-channel element in which each of the source and drain regions has the p-type conductivity. In this case, the depletion control layer has the n-type conductivity opposite to the conductivity type of the drain region and the substrate voltage applied during a write operation has the positive polarity. 
   Although the present embodiment has described the effects achieved by the application of the substrate voltage during a write operation, the same effects are achievable by properly changing the drain voltage or the control gate voltage. 
   Embodiment 6 
   A sixth embodiment of the present invention will be described with reference to the drawings. 
     FIG. 20  shows a cross-sectional structure of a memory element in a split-gate nonvolatile semiconductor memory device according to the sixth embodiment. In  FIG. 20 , the description of the same components as used in the first embodiment and shown in  FIG. 1  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 20 , the nonvolatile semiconductor memory device according to the sixth embodiment features the source region  31  which is composed of a middle-concentration layer  31   a  formed at the end portion closer to the channel region and a high-concentration layer  31   b  formed externally of and having a higher impurity concentration than the middle-concentration layer  31   a  as well as a drain region  32  which is composed of a low-concentration layer  32   a , the middle-concentration layer  32   b , and the high-concentration layer  32   c  such that their impurity concentrations are progressively outwardly higher with distance from the channel region. The end portion of the low-concentration layer  32   a  closer to the channel region is formed to adjoin the depletion control layer  33 . 
   A description will be given herein below to exemplary data write, erase, and read operations performed with respect to the device of the present embodiment with reference to  FIGS. 21A and 21B . 
   First, during the data write operation shown in  FIG. 21A , a voltage of about 4.0 V to 7.0 V is applied to the control gate electrode  21 , a voltage of 0 V is applied to the source region (not shown), and a voltage of 4.0 to 6.0 V is applied to the drain region  32 . As a result, hot electrons are generated in the vicinity of the corner of the step side region  15  and injected into the floating gate electrode  23  through the step side region  15 . 
   Next, during the data erase operation shown in  FIG. 21B , a voltage of −5.0 V is applied to the control gate electrode  21 , a voltage of about 4.0 V to 7.0 V is applied to the drain region  32 , and a voltage of 0 V is applied to the source region (not shown), whereby the electrons accumulated in the floating gate electrode  23  are extracted in the direction indicated by the arrow toward the drain region  32  through the third insulating film  25  serving as the tunnel oxide film due to a FN tunneling phenomenon. 
   During the data read operation, a voltage of about 1.0 V to 3.0 V is applied to the source region, a voltage of 0 V is applied to the drain region  32 , and a voltage of about 2.0 V to 4.0 V is applied to the control gate electrode  21  or, alternatively, a voltage of 1.0 V to 3.0 V is applied to the drain region  32 , a voltage of 0 V is applied to the source region, and a voltage of about 2.0 V to 4.0 V is applied to the control gate electrode  21 , whereby a read current different in value depending on an amount of charge accumulated in the floating gate electrode  23  is read to the source region or the drain region. 
   Thus, the nonvolatile semiconductor memory device according to the sixth embodiment has the stepped portion  16  in which the source region  32  is formed in the first surface region  13  serving as the upper stage and the drain region  32  is formed in the second surface region  1  serving as the lower stage. In addition, the p-type depletion control layer  33  is formed within the semiconductor substrate  11  to be located at a position adjacent the stepped portion  16  and not reaching each of the first surface region  14  and the step side region  15 . Since the depletion control layer  33  has the end portion closer to the drain region  32  in contact with the low-concentration layer  32   a  of the drain region  32 , a current path flowing toward the high electron temperature region generated in the vicinity of the lower corner of the step side region  15  is generated during a write operation. Consequently, electrons which have become hot electrons in the vicinity of the step side region  15  pass through the step side region  15  to be injected into the floating gate electrode  23 . This achieves a high efficiency with which the channel electrons are injected into the floating gate electrode  23 . 
   In the sixth embodiment, the drain region  32  is composed of the low-concentration layer  32   a , the middle-concentration layer  32   b , and the high-concentration layer  32   c  having impurity concentrations which are progressively higher with distance from the channel region. In other words, the drain region  32  has the concentration of an n-type impurity which is progressively lower with approach toward the channel region. Since the middle-concentration layer  32   b  lower in impurity concentration than the high-concentration layer  32   c  is provided in the region  32   d  underlying the floating gate electrode  23 , the intensity of an electric field in the vicinity of the region  32   d  is reduced during an erase operation so that hot holes generated at the pn junction interface of the region  32   d  are reduced. This prevents the lowering of the reliability of the third insulating film  25  as the tunnel film. 
   Although the sixth embodiment has formed the source region  31  composed of the middle-concentration layer  31   a  and the high-concentration layer  31   b  as shown in  FIG. 20 , the source region  31  may be formed to have a uniform concentration. 
   It will easily be appreciated that equal effects are also achievable with a split-gate flash memory unformed with the stepped portion  16 . 
   A description will be given herein below to a method for fabricating the nonvolatile semiconductor memory device thus constituted with reference to the drawings. 
     FIGS. 22A to 24D  show the cross-sectional structures of the nonvolatile semiconductor memory device according to the sixth embodiment in the individual process steps of the fabrication method therefor. 
   First, as shown in  FIG. 22A , the isolation layer  52  having, e.g., a trench isolation structure is formed in the semiconductor substrate  51  composed of p-type silicon. Then, the first resist pattern  91  having a pattern for forming a p-type well region in the active region  10  is formed on the semiconductor substrate  51 . Subsequently, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 300 keV by using the first resist pattern  91  as a mask, whereby the p-type well region having a near-surface impurity concentration of about 5×10 13  cm −3  to 1×10 14  cm −3  is formed in the active region  10 . Then, boron (B) ions for threshold voltage control at an implant dose of about 0.5×10 13  cm −2  to 1×10 13  cm −2  are further implanted into the entire surface of the active region  10  with an implant energy of about 30 keV. 
   Next, as shown in  FIG. 22B , the first resist pattern  91  is removed and then the gate oxide film  54  as the first insulating film is formed on the active region  10  by CVD or thermal oxidation. Thereafter, the first polysilicon film is deposited by, e.g., CVD over the entire surface of the semiconductor substrate  51 . The deposited first polysilicon film is patterned by photolithography to form the control gate electrode  55  composed of polysilicon. Subsequently, the second resist pattern  92  having an opening over the drain formation region of the active region  10  is formed on the semiconductor substrate  51 . By using the formed second resist pattern  92  and the control gate electrode  55  as a mask, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the gate oxide film  54  with an implant energy of about 15 keV, whereby the heavily doped p-type impurity layer  56  is formed in the drain formation region. 
   Then, as shown in  FIG. 22C , the second resist pattern  92  is removed. Thereafter, the BPSG film is deposited by CVD over the entire surface of the semiconductor substrate  51 . Subsequently, anisotropic etching is performed with respect to the deposited BPSG film to form the sidewalls  57  composed of the BPSG film on the side surfaces of the control gate electrode  55 . By adjusting the thickness of the deposited BPSG film, the distance between the side surface of the control gate electrode  55  and the stepped portion, which will be formed in the semiconductor substrate  51  in the subsequent step, can be determined by self alignment. 
   Next, as shown in  FIG. 22D , the third resist pattern  93  having an opening over the drain formation region is formed on the semiconductor substrate  51 . By using the formed third resist pattern  93 , the gate electrode  55 , and the sidewalls  57  as a mask, dry etching is performed with respect to the semiconductor substrate  51 , thereby forming the recessed portion  51   a  in the drain formation region of the semiconductor substrate  51 . 
   Next, as shown in  FIG. 23A , boron (B) ions as a p-type impurity and arsenic (As) ions as an n-type impurity are implanted sequentially by using the third resist pattern  93 , the gate electrode  55 , and the sidewalls  57  as a mask. As a result, the boron ions and the arsenic ions compensate for, i.e., offset each other in the vicinity of the stepped portion in the semiconductor substrate  51  to form the depletion control layer  56   a  composed of the heavily doped p-type impurity layer  56  and formed in the stepped portion  51   b  of the recessed portion  51   a  in the semiconductor substrate  51  closer to the control gate electrode  55  to extend from a position located under the control gate electrode  55  and at a distance from the upper corner of the stepped portion  51   b  toward the lower corner of the stepped portion  51   b  and adjoin the lightly doped drain region  58  without reaching the step side region. At this time, the boron ions are implanted at a dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2 , with an implant energy of about 25 keV, and at an angle of about 30° with respect to a normal to the substrate surface. On the other hand, the arsenic ions are implanted at a dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  with an implant energy of about 10 keV, and at an angle of about 0° with respect to a normal to the substrate surface. 
   Next, as shown in  FIG. 23B , the third resist pattern  93  is removed and then the sidewalls  57  and the exposed portion of the gate oxide film  54  are removed by wet etching, whereby the stepped portion  51   b  composed of the first surface region  59  serving as the upper stage, the second surface region  60  serving as the lower stage, and the step side region  61  connecting the upper and lower stages and the side surface of the control gate electrode  55  are exposed. 
   Next, as shown in  FIG. 23C , the thermal oxide film  62  serving as the second and third insulating films is formed on the exposed surface of the semiconductor substrate  51  including the stepped portion  51   b  and on the surface of the control gate electrode  55 . The thermal oxide film  62  may also be a silicon dioxide film formed by CVD or the like. 
   Next, as shown in  FIG. 23D , the second polysilicon film is deposited by, e.g., CVD over the entire surface of the semiconductor substrate  51  including the control gate electrode  55 . By performing anisotropic etching with respect to the deposited second polysilicon film, the floating gate electrode  63  composed of polysilicon, capacitively coupled to the side surface of the control gate electrode  55  closer to the stepped portion  51   b  with the thermal oxide film  62  interposed therebetween, and opposed to the second surface region  60  with the thermal oxide film  62  interposed therebetween is formed by self alignment so as to cover up the stepped portion  51   b . The region of the thermal oxide film  62  sandwiched between the floating gate electrode  63  and the semiconductor substrate  51  functions as the tunnel film. 
   Subsequently, phosphorus (P) ions are implanted into the semiconductor substrate  51  by using the control gate electrode  55  and the floating gate electrode  63  as a mask, whereby a moderately doped source region  68  is formed in the region of the semiconductor substrate  51  opposite to the floating gate electrode  63  relative to the control gate electrode  55  and a middle-concentration drain region  69  is formed in the region of the semiconductor substrate  51  closer to the floating gate electrode  63 . At this time, the phosphorus ions are implanted at a dose of, e.g., about 5×10 12  cm −2  to 5×10 13  cm −2  and with an implant energy of about 20 keV. 
   Next, as shown in  FIG. 24A , the insulating film  64  composed of a silicon dioxide or the like is formed over the entire surface of the semiconductor substrate  51 . The formed insulating film is then etched to form insulating film sidewalls  72  on the respective side surfaces of the control gate electrode  55  and the floating gate electrode  63 . 
   Next, as shown in  FIG. 24B , arsenic (As) ions are implanted into the semiconductor substrate  51  by using the control gate electrode  55 , the floating gate electrode  63 , and the insulating film sidewalls  72  as a mask so that the heavily doped source region  65  is formed in the region of the semiconductor substrate  51  opposite to the floating gate electrode  63  relative to the control gate electrode  55  and the heavily doped drain region  66  is formed in the region of the semiconductor substrate  51  closer to the floating gate electrode  63  than to the control gate electrode  55  and connecting to the moderately doped drain region  69 , whereby the memory element in the nonvolatile semiconductor memory device is completed. The arsenic ions are implanted here at an implant dose of, e.g., about 1×10 15  cm −2  to 5×10 15  cm −2  and with an implant energy of about 40 keV. 
   Thus, the fabrication method according to the sixth embodiment allows the formation of the p-type depletion control layer  56   a  in the vicinity of the stepped portion  51   b  of the p-type semiconductor substrate  51  and ensures the formation of the drain region composed of the lightly doped drain region  58 , the moderately doped drain region  69 , and the heavily doped drain region  66  in which the concentrations of the n-type impurities are progressively higher with distance from the channel region. 
   Variation of Embodiment 6 
   A variation of the sixth embodiment will be described with reference to the drawings. 
     FIG. 25  shows a cross-sectional structure of a memory element in a split-gate nonvolatile semiconductor memory device according to the variation of the sixth embodiment. In  FIG. 25 , the description of the same components as used in the sixth embodiment and shown in  FIG. 20  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 25 , the nonvolatile semiconductor memory device according to the variation of the sixth embodiment features the high-electric-field forming layer  34  formed in the upper corner of the stepped portion  16  in place of the depletion control layer and containing a p-type impurity diffused therein. The concentration of a p-type impurity in the high-electric-field forming layer  34  has been adjusted to be higher than the concentration of the p-type impurity in the semiconductor substrate  11 . The end portion of the high-electric-field forming layer  34  closer to the drain region  32  is in contact with the low-concentration layer  32   a.    
   With the p-type high-electric-field forming layer  34  provided between the upper corner of the stepped portion  16  and the low-concentration layer  32   a  of the drain region  32 , an energy level in the step side region  15  has a sharper gradient due to a pn junction portion composed of the interface between the high-electric-field forming layer  34  and the drain region  32 . As a result, a high electric field is generated at the interface between the high-electric-field forming layer  34  and the low-concentration layer  32   a , so that an electron temperature in the vicinity of the lower corner of the stepped portion  16  is further increased. This increases the number of electrons in the channel that have become hot electrons and remarkably improves the efficiency with which the electrons are injected into the floating gate electrode  23 . 
   The present variation can be implemented by adjusting an implant acceleration voltage and a dose during the implantation of boron (B) ions shown in  FIG. 22B  or during the implantation of boron (B) ions and arsenic (As) ions shown in  23 A, e.g., by increasing the dose of the boron ions implanted at the angle shown in  FIG. 23A . It is also possible to perform only the step of implanting the boron (B) ions and the arsenic (As) ions shown in  FIG. 23A  without performing the implantation of the boron (B) ions shown in  FIG. 22B . 
   Although the present variation has also formed the source region  31  composed of the middle-concentration layer  31   a  and the high-concentration layer  31   b , the source region  31  may also be formed to have a uniform concentration. 
   Equal effects are also achievable with a split-gate flash memory unformed with the stepped portion  16 . 
   Embodiment 7 
   A seventh embodiment of the present invention will be described with reference to the drawings. 
     FIG. 26  shows a cross-sectional structure of a memory element in a split-gate nonvolatile semiconductor memory device according to the seventh embodiment. In  FIG. 26 , the description of the same components as used in the sixth embodiment and shown in  FIG. 20  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 26 , the nonvolatile semiconductor memory device according to the seventh embodiment features a short-channel-effect suppressing region  36  which is composed of a p-type impurity region and formed in a portion of the first surface region  13  underlying the outer peripheral portion of the source region  31  so as to cover the junction interface of the source region  31  with the semiconductor substrate  11 . Since the p-type short-channel-effect suppressing region  36  is provided between the n-type source region  31  and the channel region, the intensity of an electric field between the source region  31  and the drain region  32  is reduced, which suppresses a short-channel effect and allows device size reduction. 
   A description will be given herein below to a method for fabricating the nonvolatile semiconductor memory device thus constituted with reference to the drawings. 
     FIGS. 27A to 29  show the cross-sectional structures of the nonvolatile semiconductor memory device according to the first embodiment in the individual process steps of the fabrication method therefor. 
   First, as shown in  FIG. 27A , the isolation layer  52  having, e.g., a trench isolation structure, is formed in the semiconductor substrate  51  composed of p-type silicon. Then, the first resist pattern  91  having a pattern for forming a p-type well region in the active region  10  is formed on the semiconductor substrate  51 . Subsequently, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 300 keV by using the first resist pattern  91  as a mask, whereby the p-type well region having a near-surface impurity concentration of about 5×10 13  cm −3  to 1×10 14  cm −3  is formed in the active region  10 . Then, boron (B) ions for threshold voltage control at an implant dose of, e.g., 0.5×10 13  cm −2  to 1×10 13  cm −2  are further implanted into the entire surface of the active region  10  with an implant energy of about 30 keV. 
   Next, as shown in  FIG. 27B , the first resist pattern  91  is removed and then the gate oxide film  54  as the first insulating film is formed on the active region  10  by CVD or thermal oxidation. Thereafter, the first polysilicon film is deposited by, e.g., CVD over the entire surface of the semiconductor substrate  0 . 51 . The deposited first polysilicon film is patterned by photolithography to form the control gate electrode  55  composed of polysilicon. Subsequently, the second resist pattern  92  having an opening over the drain formation region of the active region  10  is formed on the semiconductor substrate  51 . By using the formed second resist pattern  92  and the control gate electrode  55  as a mask, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the gate oxide film  54  with an implant energy of about 15 keV, whereby the heavily doped p-type impurity layer  56  is formed in the drain formation region. 
   Then, as shown in  FIG. 27C , the second resist pattern  92  is removed. Thereafter, the BPSG film is deposited by CVD over the entire surface of the semiconductor substrate  51 . Subsequently, anisotropic etching is performed with respect to the deposited BPSG film to form the sidewalls  57  composed of the BPSG film on the side surfaces of the control gate electrode  55 . By adjusting the thickness of the deposited BPSG film, the distance between the side surface of the control gate electrode  55  and the stepped portion, which will be formed in the semiconductor substrate  51  in the subsequent step, can be determined by self alignment. 
   Next, as shown in  FIG. 27D , the third resist pattern  93  having an opening over the drain formation region is formed on the semiconductor substrate  51 . By using the formed third resist pattern  93 , the gate electrode  55 , and the sidewalls  57  as a mask, dry etching is performed with respect to the semiconductor substrate  51 , thereby forming the recessed portion  51   a  in the drain formation region of the semiconductor substrate  51 . 
   Next, as shown in  FIG. 28A , boron (B) ions as a p-type impurity and arsenic (As) ions as an n-type impurity are implanted sequentially by using the third resist pattern  93 , the gate electrode  55 , and the sidewalls  57  as a mask. As a result, the boron ions and the arsenic ions compensate for each other in the vicinity of the stepped portion in the semiconductor substrate  51  to form the depletion control layer  56   a  composed of the heavily doped p-type impurity layer  56  and formed in the stepped portion  51   b  of the recessed portion  51   a  in the semiconductor substrate  51  closer to the control gate electrode  55  to extend from a position located under the control gate electrode  55  and at a distance from the upper corner of the stepped portion  51   b  toward the lower corner of the stepped portion  51   b  and adjoin the lightly doped drain region  58  without reaching the step side region. At this time, the boron ions are implanted at a dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  with an implant energy of about 25 keV, and at an angle of about 30° with respect to a normal to the substrate surface. On the other hand, the arsenic ions are implanted at a dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  with an implant energy of about 10 keV, and at an angle of about 0° with respect to a normal to the substrate surface. 
   Next, as shown in  FIG. 28B , the third resist pattern  93  is removed and then the sidewalls  57  and the exposed portion of the gate oxide film  54  are removed by wet etching, whereby the stepped portion  51   b  composed of the first surface region  59  serving as the upper stage, the second surface region  60  serving as the lower stage, and the step side region  61  connecting the upper and lower stages and the side surface of the control gate electrode  55  are exposed. Subsequently, the fourth resist pattern  94  having an opening over the source formation region of the active region  10  is formed. By using the formed fourth resist pattern  94  and the gate electrode  55  as a mask, boron ions at a dose of, e.g., about 0.5×10 13  cm −2  to 5×10 13  cm −2  are implanted into the semiconductor substrate  50  with an implant energy of about 30 keV and at an angle of about 30° relative to a normal to the substrate surface, whereby a p-type short-channel-effect suppressing layer  70  is formed. 
   Next, as shown in  FIG. 28C , the fourth resist pattern  94  is removed. Then, the thermal oxide film  62  serving as the second and third insulating films is formed on the exposed surface of the semiconductor substrate  51  including the stepped portion  51   b  and on the surface of the control gate electrode  55 . The thermal oxide film  62  may also be a silicon dioxide film formed by CVD or the like. 
   Next, as shown in  FIG. 28D , the second polysilicon film is deposited by, e.g., CVD over the entire surface of the semiconductor substrate  51  including the control gate electrode  55 . By performing anisotropic etching with respect to the deposited second polysilicon film, the floating gate electrode  63  composed of polysilicon, capacitively coupled to the side surface of the control gate electrode  55  closer to the stepped portion  51   b  with the thermal oxide film  62  interposed therebetween, and opposed to the second surface region  60  with the thermal oxide film  62  interposed therebetween is formed by self alignment so as to cover up the stepped portion  51   b . The region of the thermal oxide film  62  sandwiched between the floating gate electrode  63  and the semiconductor substrate  51  functions as the tunnel film. 
   Next, as shown in  FIG. 29 , the fifth resist pattern  95  having an opening over the source formation region and the drain formation region is formed. By using the formed fifth resist pattern, the control gate electrode  55 , and the floating gate electrode  63  as a mask, arsenic (As) ions are implanted into the semiconductor substrate  51  so that the heavily doped source region  65  is formed in the region of the semiconductor substrate  51  opposite to the floating gate electrode  63  relative to the control gate electrode  55  and internal of the short-channel-effect suppressing layer  70  and the heavily doped drain region  66  is formed in the region of the semiconductor substrate  51  closer to the floating gate electrode  63  than to the control gate electrode  55  and connecting to the lightly doped drain region  58 , whereby the memory element in the nonvolatile semiconductor memory device is completed. 
   Thus, the fabrication method according to the seventh embodiment allows the formation of the p-type depletion control layer  56   a  in the vicinity of the stepped portion  51   b  of the p-type semiconductor substrate  51  and ensures the formation of the p-type short-channel-effect suppressing layer  70  covering from beneath the junction interface of the heavily doped n-type source region  65 . 
   It will easily be appreciated that the effect of suppressing a short-channel effect is also achievable with a split-gate flash memory unformed with the stepped portion  16 . 
   Variation of Embodiment 7 
   A variation of the seventh embodiment will be described with reference to the drawings. 
     FIG. 30  shows a cross-sectional structure of a memory element in a split-gate nonvolatile semiconductor memory device according to the variation of the seventh embodiment. In  FIG. 30 , the description of the same components as used in the seventh embodiment and shown in  FIG. 26  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 30 , the nonvolatile semiconductor memory device according to the variation of the seventh embodiment features the high-electric-field forming layer  34  formed in the upper corner of the stepped portion  16  in place of the depletion control layer and containing a p-type impurity diffused therein. The concentration of a p-type impurity in the high-electric-field forming layer  34  has been adjusted to be higher than the concentration of the p-type impurity in the semiconductor substrate  11 . The end portion of the high-electric-field forming layer  34  closer to the drain region  32  is in contact with the low-concentration layer  32   a.    
   With the p-type high-electric-field forming layer  34  provided between the upper corner of the stepped portion  16  and the low-concentration layer  32   a  of the drain region  32 , an energy level in the step side region  15  has a sharper gradient due to a pn junction portion composed of the interface between the high-electric-field forming layer  34  and the drain region  32 . As a result, a high electric field is generated at the interface between the high-electric-field forming layer  34  and the low-concentration layer  32   a , so that an electron temperature in the vicinity of the lower corner of the stepped portion  16  is further increased. This increases the number of electrons in the channel that have become hot electrons and remarkably improves the efficiency with which the electrons are injected into the floating gate electrode  23 . 
   The present variation can be implemented by adjusting an implant acceleration voltage and a dose during the implantation of boron (B) ions shown in  FIG. 27B  or during the implantation of boron (B) ions and arsenic (As) ions shown in  28 A. It is also possible to perform only the step of implanting the boron (B) ions and the arsenic (As) ions shown in  FIG. 28A  without performing the implantation of the boron (B) ions shown in  FIG. 27B . 
   Embodiment 8 
   An eighth embodiment of the present invention will be described with reference to the drawings. 
     FIG. 31  shows a cross-sectional structure of a memory element in a stacked-gate nonvolatile semiconductor memory device according to the eighth embodiment. In  FIG. 31 , the description of the same components as used in the third embodiment and shown in  FIG. 11  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 31 , the nonvolatile semiconductor memory device according to the eighth embodiment features the source region  31  which is composed of the middle-concentration layer  31   a  formed at the end portion closer to the channel region and the high-concentration layer  31   b  formed externally of and having a higher impurity concentration than the middle-concentration layer  31   a  as well as the drain region  32  which is composed of the low-concentration layer  32   a , the middle-concentration layer  32   b , and the high-concentration layer  32   c  such that their impurity concentrations are progressively outwardly higher with distance from the channel region. The end portion of the low-concentration layer  32   a  closer to the channel region is formed to adjoin the depletion control layer  33 . 
   In the arrangement, the depletion control layer  33  containing a p-type impurity at a high concentration is not depleted during a write operation. Instead, the portion of the semiconductor substrate  11  enclosed with the first surface region  13 , the step side region  15 , and the depletion control layer  33  is depleted to function as a channel, similarly to the third embodiment. This causes electrons in the channel to flow expansively toward the step side region and improves the efficiency with which carriers are injected into the floating gate electrode  23 A. 
   Since the middle-concentration layer  32   b  lower in impurity concentration than the high-concentration layer  32   c  is provided in the region underlying the floating gate electrode  23 A, the intensity of an electric field in the vicinity of the underlying region is reduced during an erase operation so that hot holes generated at the adjacent pn junction interface are reduced. This prevents the lowering of the reliability of the third insulating film  25  as the tunnel film. 
   Although the eighth embodiment has formed the source region  31  composed of the middle-concentration layer  31   a  and the high-concentration layer  31   b  as shown in  FIG. 31 , the source region  31  may be formed to have a uniform concentration. 
   It will easily be appreciated that equal effects are also achievable with a stacked-gate flash memory unformed with the stepped portion  16 . 
   A description will be given herein below to a method for fabricating the nonvolatile semiconductor memory device thus constituted with reference to the drawings. 
     FIGS. 32A to 34B  show the cross-sectional structures of the nonvolatile semiconductor memory device according to the eighth embodiment in the individual process steps of the fabrication method therefor. 
   First, as shown in  FIG. 32A , the isolation layer  52  having e.g., a trench isolation structure, is formed on a semiconductor substrate  51  composed of p-type silicon. Then, the first resist pattern  91  having a pattern for forming a p-type well region in the active region  10  is formed on the semiconductor substrate  51 . Subsequently, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 300 kev by using the first resist pattern  91  as a mask, whereby the p-type well region having a near-surface impurity concentration of about 5×10 13  cm −3  to 1×10 14  cm −3  is formed in the active region  10 . Then, boron (B) ions for threshold voltage control at an implant dose of, e.g., 0.5×10 13  cm −2  to 1×10 13  cm −2  are further implanted into the entire surface of the active region  10  with an implant energy of about 30 keV. 
   Next, as shown in  FIG. 32B , the first resist pattern  91  is removed. Then, the second resist pattern  92  having an opening over the drain formation region of the active region  10  is formed on the semiconductor substrate  51 . By using the formed second resist pattern  92  as a mask, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the protective insulating film  53  with an implant energy of about 15 keV, whereby the heavily doped p-type impurity layer  56  is formed in the drain formation region. 
   Next, as shown in  FIG. 32C , the second resist pattern  92  is removed. Then, the third resist pattern  93  for masking the source formation region and the end portion of the heavily doped impurity layer  56  closer to the source formation region is formed on the semiconductor substrate  51 . By using the formed third resist pattern  93  as a mask, dry etching is performed with respect to the semiconductor substrate  51 , thereby forming the recessed portion  51   a  in the drain formation region of the semiconductor substrate  51 . At this time, the dimension of the depletion control layer  56   a  in the direction of the gate length, which will be formed from the heavily doped impurity layer  56  in the subsequent step, can be optimized by adjusting the amount of masking (overlapping) the end portion of the heavily doped impurity layer  56  closer to the source formation region. 
   Next, as shown in  FIG. 32D , boron (B) ions as a p-type impurity and arsenic (As) ions as an n-type impurity are implanted sequentially by using the third resist pattern  93  as a mask. As a result, the boron ions and the arsenic ions compensate for each other in the vicinity of the stepped portion in the semiconductor substrate  51  to form the depletion control layer  56   a  composed of the heavily doped p-type impurity layer  56  and formed in the stepped portion  51   b  of the recessed portion  51   a  in the semiconductor substrate  51  closer to the control gate electrode  55  to extend from a position located under the control gate electrode  55  and at a distance from the upper corner of the stepped portion  51   b  toward the lower corner of the stepped portion  51   b  and adjoin the lightly doped drain region  58  without reaching the step side region. At this time, both of the boron ions and the arsenic ions are implanted at a dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  and with an implant energy of about 10 kev, while only the boron ions are implanted at an angle of about 30°. 
   Next, as shown in  FIG. 33A , the third resist pattern  93  is removed, whereby the stepped portion  51   b  composed of the upper surface of the semiconductor substrate  51 , i.e., the first surface region  59  serving as the upper stage, the second surface region  60  serving as the lower stage, and the step side region  61  connecting the upper and lower stages is exposed. 
   Next, as shown in  FIG. 33B , the gate oxide film  54  serving as the first insulating film is formed on the exposed surface of the semiconductor substrate  51  including the stepped portion  51   b . Then, the first polysilicon film  63 A, the silicon dioxide film  67 A serving as the second insulating film, and the second polysilicon film  55 A are deposited by, e.g., CVD over the entire surface of the gate oxide film  54 . The silicon dioxide film  67 A may also be formed as the thermal oxide film. 
   Next, as shown in  FIG. 33C , the fourth resist pattern  94  including a pattern for a gate electrode which covers up the stepped portion  51   b  is formed on the second polysilicon film  55 A. By using the formed fourth resist pattern  94  as a mask, anisotropic etching is performed with respect to the second polysilicon film  55 A, the silicon dioxide film  67 A, and the first polysilicon film  63 A, thereby forming the floating gate electrode  63 B composed of the first polysilicon film  63 A, the capacitance insulating film  67 B composed of the silicon dioxide film  67 A, and the floating gate electrode  55 B composed of the second polysilicon film  55 A. The gate oxide film  54  between the semiconductor substrate  51  and the floating gate electrode  63 B functions as the tunnel film. 
   Next, as shown in  FIG. 33D , the fourth resist pattern  94  is removed. Then, the fifth resist pattern  95  having an opening over the source formation region and the drain formation region is formed. By using the formed fifth resist pattern  95  and the control gate electrode  55 B as a mask, arsenic (As) ions are implanted into the semiconductor substrate  51  so that the moderately doped source region  68  is formed in the first surface region  59  of the semiconductor substrate  51  and the moderately doped drain region  69  is formed in the area of the second surface region  60  of the semiconductor substrate  51  connecting to the lightly doped drain region  58 . 
   Next, as shown in  FIG. 34A , the insulating film  64  composed of a silicon dioxide or the like is formed over the entire surface of the semiconductor substrate  51 . Then, the formed insulating film is etched to form the insulating film sidewalls  72  on the respective side surfaces of the floating gate electrode  63 B and the control gate electrode  55 B. 
   Next, as shown in  FIG. 34B , a sixth resist pattern  96  having an opening over the source formation region and the drain formation region is formed and arsenic (As) ions are implanted into the semiconductor substrate  51  by using the formed sixth resist pattern  96 , the control gate electrode  55 , and the insulating film sidewalls  72  as a mask so that the heavily doped source region  65  is formed in the area of the first surface region  59  of the semiconductor substrate  51  connecting to the moderately doped source region  68  and the heavily doped drain region  66  is formed in the area of the second surface region  60  of the semiconductor substrate  51  connecting to the moderately doped drain region  69 , whereby the memory element in the nonvolatile semiconductor memory device is completed. 
   Thus, the fabrication method according to the eighth embodiment allows the formation of the p-type depletion control layer  56   a  in the vicinity of the stepped portion  51   b  in the p-type semiconductor substrate  51  and ensures the formation of the drain region composed of the lightly doped drain region  58 , the moderately doped drain region  60 , and the heavily doped drain region  66  in which the concentrations of the n-type impurities are progressively higher with distance from the channel region. 
   Variation of Embodiment 8 
   A variation of the eighth embodiment will be described with reference to the drawings. 
     FIG. 35  shows a cross-sectional structure of a memory element in a stacked-gate nonvolatile semiconductor memory device according to the variation of the eighth embodiment. In  FIG. 35 , the description of the same components as used in the eighth embodiment and shown in  FIG. 31  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 35 , the nonvolatile semiconductor memory device according to the variation of the sixth embodiment features the high-electric-field forming layer  34  formed in the upper corner of the stepped portion in place of the depletion control layer and containing a p-type impurity diffused therein. The concentration of a p-type impurity in the high-electric-field forming layer  34  has been adjusted to be higher than the concentration of the p-type impurity in the semiconductor substrate  11 . The end portion of the high-electric-field forming layer  34  closer to the drain region  32  is in contact with the low-concentration layer  32   a.    
   With the p-type high-electric-field forming layer  34  provided between the upper corner of the stepped portion  16  and the low-concentration layer  32   a  of the drain region  32 , an energy level in the step side region  15  has a sharper gradient due to a pn junction portion composed of the interface between the high-electric-field forming layer  34  and the drain region  32 . As a result, a high electric field is generated at the interface between the high-electric-field forming layer  34  and the low-concentration layer  32   a , so that an electron temperature in the vicinity of the lower corner of the stepped portion  16  is further increased. This increases the number of electrons in the channel that have become hot electrons and remarkably improves the efficiency with which the electrons are injected into the floating gate electrode  23 . 
   The present variation can be implemented by adjusting an implant acceleration voltage and a dose during the implantation of boron (B) ions shown in  FIG. 32B  or during the implantation of boron (B) ions and arsenic (As) ions shown in  FIG. 32D . It is also possible to perform only the step of implanting the boron (B) ions and the arsenic (As) ions shown in  FIG. 32D  without performing the implantation of the boron (B) ions shown in  FIG. 32B . 
   Although the present variation has also formed the source region  31  composed of the middle-concentration layer  31   a  and the high-concentration layer  31   b , the source region  31  may also be formed to have a uniform concentration. 
   Equal effects are also achievable with a stacked-gate flash memory unformed with the stepped portion  16 . 
   Embodiment 9 
   A ninth embodiment of the present invention will be described with reference to the drawings. 
     FIG. 36  shows a cross-sectional structure of a memory element in a stacked-gate nonvolatile semiconductor memory device according to the ninth embodiment. In  FIG. 36 , the description of the same components as used in the eighth embodiment and shown in  FIG. 31  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 36 , the nonvolatile semiconductor memory device according to the ninth embodiment features the short-channel-effect suppressing region  36  which is composed  15  of a p-type impurity region and formed in a portion of the first surface region  13  underlying the outer peripheral portion of the source region  31  so as to cover the junction interface between the source region  31  and the semiconductor substrate  11 . Since the p-type short-channel-effect suppressing region  36  is provided between the n-type source region  31  and the channel region, the intensity of an electric field between the source region  31  and the drain region  32  is reduced, which suppresses a short-channel effect and allows device size reduction. 
   A description will be given herein below to a method for fabricating the nonvolatile semiconductor memory device thus constituted with reference to the drawings. 
     FIGS. 37A to 39  show the cross-sectional structures of the nonvolatile semiconductor memory device according to the ninth embodiment in the individual process steps of the fabrication method therefor. 
   First, as shown in  FIG. 37A , the isolation layer  52  having, e.g., a trench isolation structure, is formed in the semiconductor substrate  51  composed of p-type silicon. Then, the first resist pattern  91  having a pattern for forming a p-type well region in the active region  10  is formed on the semiconductor substrate  51 . Subsequently, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 300 keV by using the first resist pattern  91  as a mask, whereby the p-type well region having a near-surface impurity concentration of about 5×10 13  cm −3  to 1×10 14  cm −3  is formed in the active region  10 . Then, boron (B) ions for threshold voltage control at an implant dose of, e.g., 0.5×10 13  cm −2  to 1×10 13  cm −2  are further implanted into the entire surface of the active region  10  with an implant energy of about 30 keV. 
   Next, as shown in  FIG. 37B , the first resist pattern  91  is removed. Then, the second resist pattern  92  having an opening over the drain formation region of the active region  10  is formed on the semiconductor substrate  51 . By using the formed second resist pattern  92  as a mask, boron (B) ions at an implant dose of, e.g., about 0.5×10 13  cm −2  to 1×10 14  cm −2  are implanted into the semiconductor substrate  51  through the protective insulating film  53  with an implant energy of about 15 keV, whereby the heavily doped p-type impurity layer  56  is formed in the drain formation region. 
   Next, as shown in  FIG. 37C , the second resist pattern  92  is removed. Then, the third resist pattern  93  for masking the source formation region and the end portion of the heavily doped impurity layer  56  closer to the source formation region is formed on the semiconductor substrate  51 . By using the formed third resist pattern  93  as a mask, dry etching is performed with respect to the semiconductor substrate  51 , thereby forming the recessed portion  51   a  in the drain formation region of the semiconductor substrate  51 . At this time, the dimension of the depletion control layer  56   a  in the direction of the gate length, which will be formed from the heavily doped impurity layer  56  in the subsequent step, can be optimized by adjusting the amount of masking (overlapping) the end portion of the heavily doped impurity layer  56  closer to the source formation region. 
   Next, as shown in  FIG. 37D , boron (B) ions as a p-type impurity and arsenic (As) ions as an n-type impurity are implanted sequentially by using the third resist pattern  93  as a mask. As a result, the boron ions and the arsenic ions compensate for each other in the vicinity of the stepped portion in the semiconductor substrate  51  to form the depletion control layer  56   a  composed of the heavily doped p-type impurity layer  56  and formed in the stepped portion  51   b  of the recessed portion  51   a  in the semiconductor substrate  51  closer to the control gate electrode  55  to extend from a position located under the control gate electrode  55  and at a distance from the upper corner of the stepped portion  51   b  toward the lower corner of the stepped portion  51   b  and adjoin the lightly doped drain region  58  without reaching the step side region. At this time, both of the boron ions and the arsenic ions are implanted at a dose of, e.g., about 0.5×10 14  cm −2  to 5×10 14  cm −2  and with an implant energy of about 10 keV, while only the boron ions are implanted at an angle of about 30°. 
   Next, as shown in  FIG. 38A , the third resist pattern  93  is removed, whereby the stepped portion  51   b  composed of the upper surface of the semiconductor substrate  51 , i.e., the first surface region  59  serving as the upper stage, the second surface region  60  serving as the lower stage, and the step side region  61  connecting the upper and lower stages is exposed. 
   Next, as shown in  FIG. 38B , the gate oxide film  54  serving as the first insulating film is formed on the exposed surface of the semiconductor substrate  51  including the stepped portion  51   b . Then, the first polysilicon film  63 A, the silicon dioxide film  67 A serving as the second insulating film, and the second polysilicon film  55 A are deposited by, e.g., CVD over the entire surface of the gate oxide film  54 . The silicon dioxide film  67 A may also be formed as the thermal oxide film. 
   Next, as shown in  FIG. 38C , the fourth resist pattern  94  including a pattern for a gate electrode which covers up the stepped portion  51   b  is formed on the second polysilicon film  55 A. By using the formed fourth resist pattern  94  as a mask, anisotropic etching is performed with respect to the second polysilicon film  55 A, the silicon dioxide film  67 A, and the first polysilicon film  63 A, thereby forming the floating gate electrode  63 B composed of the first polysilicon film  63 A, the capacitance insulating film  67 B composed of the silicon dioxide film  67 A, and the floating gate electrode  55 B composed of the second polysilicon film  55 A. The gate oxide film  54  between the semiconductor substrate  51  and the floating gate electrode  63 B functions as the tunnel film. 
   Next, as shown in  FIG. 38D , the fifth resist pattern  95  having an opening over the source formation region of the active region  10  is formed on the semiconductor substrate  51 . By using the formed fifth resist pattern  95  and the gate electrode  55 B as a mask, boron ions at a dose of, e.g., about 0.5×10 13  cm −2  to 5×10 13  cm −2  are implanted into the semiconductor substrate  51  with an implant energy of about 30 keV, whereby the p-type short-channel-effect suppressing layer  70  is formed in the source formation region. 
   Next, as shown in  FIG. 39 , the fifth resist pattern  95  is removed and then the sixth resist pattern having an opening over the source formation region and the drain formation region is formed. By using the formed sixth resist pattern  96  and the control gate electrode  55 B as a mask, arsenic (As) ions are implanted into the semiconductor substrate  51  so that the heavily doped source region  65  is formed in the area of the first surface region  51  of the semiconductor substrate  51  internal of the short-channel-effect suppressing layer  70  and the heavily doped drain region  66  is formed in the area of the second surface region  60  of the semiconductor substrate  51  connecting to the lightly doped drain region  58 , whereby the memory element in the stacked-gate nonvolatile semiconductor memory device is completed. 
   Thus, the fabrication method according to the ninth embodiment allows the formation of the p-type depletion control layer  56   a  in the vicinity of the stepped portion  51   b  in the p-type semiconductor substrate  51  and ensures the formation of the p-type short-channel-effect suppressing layer  70  covering from beneath the junction interface of the heavily doped n-type source region  65 . 
   It will easily be appreciated that the effect of suppressing a short-channel effect is also achievable with a stacked-gate flash memory unformed with the stepped portion  16 . 
   Variation of Embodiment 9 
   A variation of the ninth embodiment will be described with reference to the drawings. 
     FIG. 40  shows a cross-sectional structure of a memory element in a stacked-gate nonvolatile semiconductor memory device according to the variation of the ninth embodiment. In  FIG. 40 , the description of the same components as used in the ninth embodiment and shown in  FIG. 36  will be omitted by retaining the same reference numerals. 
   As shown in  FIG. 40 , the nonvolatile semiconductor memory device according to the variation of the ninth embodiment features the high-electric-field forming layer  34  formed in the upper corner of the stepped portion in place of the depletion control layer and containing a p-type impurity diffused therein. The concentration of a p-type impurity in the high-electric-field forming layer  34  has been adjusted to be higher than the concentration of the p-type impurity in the semiconductor substrate  11 . The end portion of the high-electric-field forming layer  34  closer to the drain region  32  is in contact with the low-concentration layer  32   a.    
   With the p-type high-electric-field forming layer  34  provided between the upper corner of the stepped portion  16  and the low-concentration layer  32   a  of the drain region  32 , an energy level in the step side region  15  has a sharper gradient due to a pn junction portion composed of the interface between the high-electric-field forming layer  34  and the drain region  32 . As a result, a high electric field is generated at the interface between the high-electric-field forming layer  34  and the low-concentration layer  32   a , so that an electron temperature in the vicinity of the lower corner of the stepped portion  16  is further increased. This increases the number of electrons in the channel that have become hot electrons and remarkably improves the efficiency with which the electrons are injected into the floating gate electrode  23 . 
   The present variation can be implemented by adjusting an implant acceleration voltage and a dose during the implantation of boron (B) ions shown in  FIG. 37B  or during the implantation of boron (B) ions and arsenic (As) ions shown in  FIG. 37D . It is also possible to perform only the step of implanting the boron (B) ions and the arsenic (As) ions shown in  FIG. 37D  without performing the implantation of the boron (B) ions shown in  FIG. 37B . 
   Embodiment 10 
   A tenth embodiment of the present invention will be described with reference to the drawings. 
   The tenth embodiment relates to a method for controlling a nonvolatile semiconductor memory device according to the present invention, which is a method for bias application used to extract electrons accumulated in a floating gate electrode therefrom (erase operation). 
     FIGS. 41A and 41B  show cross-sectional structures of, e.g., the split-gate nonvolatile semiconductor memory device according to the seventh embodiment in which the region in the vicinity of the stepped portion  16  is enlarged. In  FIGS. 41A and 41B , the description of the same components as shown in  FIG. 26  will be omitted by retaining the same reference numerals. 
   In  FIG. 41A , exemplary erase bias conditions are such that a voltage applied to the control gate electrode  21  is −6 V to −8 V and a voltage applied to the drain region  32  is 5 V to 6 V. Under such conditions, hot holes are generated in the region  11   a  of the semiconductor substrate  11  underlying the low-concentration layer  32   a  of the drain region  32 . 
   Under the foregoing erase bias conditions, the hot holes generated under the drain region  32  may flow in the direction indicated by the arrow A to be captured in the end portion of the first insulating film  22  as the gate insulating film, the second insulating film  24  as the capacitance insulating film, or the third insulating film  25  as the tunnel insulating film closer to the control gate electrode  21 . If the hot holes are captured in such places, a read current is reduced in value because of their proximity to the channel region. 
   In  FIG. 41B , therefore, the tenth embodiment has used erase bias conditions such that, e.g., a voltage applied to the control gate electrode  21  is −4 V to −5 V and a voltage applied to the drain region  32  is 6 V to 7 V. In short, the control gate bias is reduced and the drain bias is increased. As a result, the hot holes generated in the region  11   a  underlying the low-concentration layer  32   a  of the drain region  32  flow in the direction indicated by the arrow B, i.e., toward the portion of the third insulating film (tunnel film)  25  underlying the floating gate electrode  23  to be captured in the portion of the third insulating film  25  at a distance from the channel region. Since the hot holes are thus captured in the portion at a distance from the channel region, the influence given to the read current value can be reduced. 
   The bias conditions according to the tenth embodiment greatly change depending on the design rules for the device and are not limited to the foregoing voltage range. 
   Although the present embodiment has described the split-gate flash memory having the stepped portion  16 , it will be appreciated that equal effects are achievable with a split-gate flash memory unformed with the stepped portion  16 .