Patent Publication Number: US-2023143585-A1

Title: Semiconductor device

Description:
TECHNICAL FIELD 
     The present disclosure relates to a semiconductor device. 
     BACKGROUND ART 
     A high-output semiconductor device operating at a high frequency is adopted for a communication system using wireless communication, for example, satellite communication. A transistor using a nitride semiconductor is adopted as the semiconductor device, which enhances the performance of the semiconductor device. 
     In the transistor using a nitride semiconductor, two types of compound semiconductors having different band gaps form a heterojunction. A two-dimensional carrier gas (2DCG) is induced at the heterojunction interface (hereinafter referred to as “hetero interface”). The two-dimensional carrier gas is a general name for the two-dimensional electron gas (2DEG) and: the two-dimensional hole gas (2DHG). 
     A high electron mobility transistor (hereinafter referred to as “HEMT”) uses the two-dimensional carrier gas. The HEMT has high output and operates at high frequencies. 
     In recent years, as the digitization of communication and the progress in bit rate, there is a demand for reduction in distortion of communication systems. In order to meet such a demand, it is necessary not only to apply a distortion compensation circuit but also to improve the linearity of HEMT per se. 
     The mutual conductance of the HEMT has a non-linearity that increases once with an increase in a drain current and then sharply decreases after reaching a peak value. Shortening the gate length of the HEMT for increasing the frequency increases the non-linearity. In order to solve the increase in non-linearity, various studies have been conducted using the techniques developed for semiconductor devices using silicon. 
     For example, Non-Patent Document 1 discloses a structure with reference to a multi-gate element. A similar structure is also disclosed in Patent Document 4. In the structure (hereinafter, tentatively referred to as “buried gate arrangement structure”), a plurality of gate electrodes each having a columnar shape are arranged and buried in one direction in an epitaxial layer forming the hetero interface. The plurality of gate electrodes are connected to each other at positions separated from the epitaxial layer. In the buried gate arrangement structure, a depleted layer spreads on the side surfaces and bottom surfaces of the buried gate electrodes, and the channels are closed in the epitaxial layer located between the buried gate electrodes. 
     For example, Patent Document 1, Patent Document 2, and Patent Document 3 disclose a structure in which a channel is narrowed (hereinafter, tentatively referred to as a “narrow channel structure”). In the narrow channel structure, a gate electrode is adhered and formed on an epitaxial layer processed into a fine wire form. In the narrow channel structure, the area where the epitaxial layer is in contact with the source electrode and the drain electrode is small, and the contact resistance is large. The length of the epitaxial layer in the direction connecting the drain electrode and the source electrode is shortened to reduce the contact resistance. 
     PRIOR ART DOCUMENTS 
     Patent Document(s) 
     
         
         [Patent Document 1] Japanese Patent Application Laid-Open No. 2009-212291 
         [Patent Document 2] Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2016-512927 
         [Patent Document 3] Japanese Patent Application Laid-Open No. 5-275436 
         [Patent Document 4] Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2020-526921 
       
    
     Non-Patent Document(s) 
     
         
         [Non-Patent Document 1] K. Shinohara et. al, “GaN-Based Field-Effect Transistors With Laterally Gated Two-Dimensional Electron Gas”, IEEE Electron Device Lett. 39-3, 417, 2018. 
       
    
     SUMMARY 
     Problem to be Solved by the Invention 
     In a transistor having a gate electrode, it is desired that the concentration of the electric field (the electric field being concentrated) is relaxed in the vicinity of the gate electrode from the viewpoint of the breakdown voltage of the transistor. For example, a so-called field plate structure is used for the relaxation. The field plate structure is considered to increase the electrostatic capacitance between the gate electrode and the other electrodes (e.g., the gate-drain capacitance and the gate-source capacitance). 
     Means to Solve the Problem 
     According to the present disclosure, a semiconductor device includes a semiconductor layer group including a first nitride semiconductor layer and a second nitride semiconductor layer laminated in a first direction, a plurality of gate electrodes, each of which being in contact with the second nitride semiconductor layer in a second direction different from the first direction and is arranged along the second direction, a conductor electrically connecting the plurality of gate electrodes and located away from the semiconductor layer group, a source electrode opposite to the plurality of gate electrodes in a third direction different from both the first direction and the second direction and conducting with the first nitride semiconductor layer, a drain electrode opposite to the source electrode via the plurality of gate electrodes in the third direction and conducting with the first nitride semiconductor layer, and a first layer located between the plurality of gate electrodes and the drain electrode in the third direction and in contact with the plurality of gate electrodes, and in contact with the second nitride semiconductor layer in the second direction. The first nitride semiconductor layer and the second nitride semiconductor layer form a heterojunction, and a two-dimensional carrier gas is induced in the first nitride semiconductor layer. The first nitride semiconductor layer and the second nitride semiconductor layer form a Schottky junction with each of the plurality of gate electrodes. The first layer is any of an insulator, an intrinsic semiconductor, and a semiconductor having a conductivity type opposite to that of the second nitride semiconductor layer, and suppresses induction of the two-dimensional carrier gas in the first nitride semiconductor layer opposite to the first layer in the first direction. 
     Effects of the Invention 
     A semiconductor device having a high breakdown voltage is provided. 
     The objects, features, aspects, and advantages of the present disclosure will become more apparent from the following detailed description and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    A perspective view illustrating a structure of a semiconductor device according to a first embodiment. 
         FIG.  2    A plan view illustrating the structure of the semiconductor device according to the first embodiment. 
         FIG.  3    A cross-sectional view illustrating a cross section of the semiconductor device according to the first embodiment at the position AA of  FIG.  2   . 
         FIG.  4    A cross-sectional view illustrating a cross section of the semiconductor device according to the first embodiment at the position BB of  FIG.  2   . 
         FIG.  5    A cross-sectional view illustrating a cross section of the semiconductor device according to the first embodiment at the position CC of  FIG.  2   . 
         FIG.  6    A plan view illustrating the structure of the semiconductor device according to a second embodiment. 
         FIG.  7    A cross-sectional view illustrating a cross section of the semiconductor device according to the second embodiment at the position AA of  FIG.  6   . 
         FIG.  8    A plan view illustrating a structure of a semiconductor device according to a third embodiment. 
         FIG.  9    A cross-sectional view illustrating a cross section of the semiconductor device according to the third embodiment at the position AA of  FIG.  8   . 
         FIG.  10    A plan view illustrating a structure of a semiconductor device according to a fourth embodiment. 
         FIG.  11    A cross-sectional view illustrating a cross section of the semiconductor device according to the fourth embodiment at the position AA of  FIG.  10   . 
         FIG.  12    A plan view illustrating a structure of a semiconductor device according to a fifth embodiment. 
         FIG.  13    A cross-sectional view illustrating a cross section of the semiconductor device according to the fifth embodiment at the position AA of  FIG.  12   . 
         FIG.  14    A plan view illustrating a structure of a semiconductor device according to a sixth embodiment. 
         FIG.  15    A cross-sectional view illustrating a cross section of the semiconductor device according to the sixth embodiment at the position AA of  FIG.  14   . 
         FIG.  16    A plan view illustrating a structure of a semiconductor device according to a seventh embodiment. 
         FIG.  17    A cross-sectional view illustrating a cross section of the semiconductor device according to the seventh embodiment at the position AA of  FIG.  16   . 
         FIG.  18    A plan view illustrating a structure of a semiconductor device according to an eighth embodiment. 
         FIG.  19    A cross-sectional view illustrating a cross section of the semiconductor device according to the eighth embodiment at the position AA of  FIG.  18   . 
         FIG.  20    A cross-sectional view illustrating a cross section of the semiconductor device according to the eighth embodiment at the position CC of  FIG.  18   . 
         FIG.  21    A plan view illustrating a structure of a semiconductor device according to a ninth embodiment. 
         FIG.  22    A cross-sectional view illustrating a cross section of the semiconductor device according to the ninth embodiment at the position AA of  FIG.  21   . 
         FIG.  23    A cross-sectional view illustrating a cross section of the semiconductor device according to the ninth embodiment at the position BB of  FIG.  21   . 
         FIG.  24    A cross-sectional view illustrating a cross section of the semiconductor device according to the ninth embodiment at the position CC of  FIG.  21   . 
         FIG.  25    A cross-sectional view illustrating a structure of a semiconductor device according to a tenth embodiment. 
         FIG.  26    A cross-sectional view illustrating a modification structure of a semiconductor device according to the tenth embodiment. 
         FIG.  27    A cross-sectional view illustrating a structure of a semiconductor device according to an eleventh embodiment. 
         FIG.  28    A diagram illustrating a band structure of a semiconductor device according to a twelfth embodiment. 
         FIG.  29    A plan view illustrating the gate electrode. 
     
    
    
     DESCRIPTION OF EMBODIMENT(S) 
     For any of the semiconductor devices illustrated in the following embodiments, the main part of the field effect transistor is illustrated. In addition to the following disclosure, the field effect transistor is used with an element isolation region, wiring connected to an electrode, and a via hole being formed. The illustrations in the following embodiments do not preclude that the semiconductor device according to the present disclosure is applied to an element other than a field effect transistor. 
     First Embodiment 
     [Structure and Operation] 
       FIG.  1    is a perspective view illustrating a structure of a semiconductor device  101  according to a first embodiment. The directions X, Y, and Z added in  FIG.  1    are different from each other, and the plane parallel to both of the directions X and Y is unparalleled to the direction Z. In the disclosure, the case where the directions X, Y, and Z are orthogonal to each other is illustrated. 
     For convenience, a second element on a direction Z side when viewed from a first element is described as being above the first element. The first element is described as being below the second element. In the present disclosure, terms “upper” and “lower” are indicating the relative positional relationship of components, and are terms not necessarily based on the direction of gravity.  FIG.  1    illustrates a cross section of the semiconductor device  101  perpendicular to the direction Y and a cross section perpendicular to the direction X. 
     In the following, the length along the direction X may be simply referred to as “length”″, the length along the direction Y may be referred to as “width”, and the length along the direction Z may be referred to as “thickness”. 
       FIG.  2    is a plan view illustrating a structure of the semiconductor device  101 .  FIG.  2    is a plan view of the semiconductor device  101  as viewed in the direction opposite to the direction Z in the range illustrated in  FIG.  1   . 
       FIG.  3    is a cross-sectional view illustrating a cross section of the semiconductor device  101  at the position AA of  FIG.  2   .  FIG.  4    is a cross-sectional view illustrating a cross section of the semiconductor device  101  at the position BB of  FIG.  2   .  FIG.  5    is a cross-sectional view illustrating a cross section of the semiconductor device  101  at the position CC of  FIG.  2   . 
     The semiconductor device  101  includes a semiconductor layer group  4 , a source electrode  5 , a drain electrode  6 , gate electrodes  8 , a conductor  9 , and first layers  10 . The semiconductor layer group  4  includes nitride semiconductor layers  2  and  3  laminated along the direction Z. The nitride semiconductor layers  2  and  3  are, for example, epitaxial layers epitaxially grown on a substrate  1 . In the present disclosure, the description is made that the substrate  1  is included in the semiconductor layer group  4 . 
     The semiconductor device  101  further includes a protective film  14 . For ease of understanding, the protective film  14  is omitted in  FIGS.  1  and  2   . In  FIG.  2   , the conductor  9  is drawn by a two-dot chain line. 
     The number of gate electrodes  8  is plural, and they are arranged in the direction Y. Each of the gate electrodes  8  is in contact with the nitride semiconductor layer  3  in the direction Y. For example, a gate electrode  8  has surfaces  8   c  and  8   d . The surface  8   c  appears on the direction Y side of the gate electrode  8  having the surface  8   c . The surface  8   d  appears on the opposite side of the direction Y of the gate electrode  8  having the surface  8   d . The gate electrode  8  has a surface  8   e  and the surface  8   e  appears on the opposite side of the direction Z of the gate electrode  8  having the surface  8   e . It can also be said that in the semiconductor layer group  4 , a groove  7  is open in which a part of the gate electrode  8  is buried. 
     In the present disclosure, each of the gate electrodes  8  extends through the nitride semiconductor layer  3  in the direction opposite to the direction Z and reaches the nitride semiconductor layer  2 . In this case, the surfaces  8   c  and  8   d  also contact the nitride semiconductor layer  2  in the direction Y. 
     The conductor  9  is located away from the semiconductor layer group  4 . The conductor  9  electrically connects the gate electrodes  8  to each other. In the present disclosure, the conductor  9  has a shape extending along the direction Y above the semiconductor layer group  4 . 
     The source electrode  5  is opposite to the gate electrodes  8  in direction X. The drain electrode  6  is apart from and opposite to the source electrode  5  via the gate electrodes  8  in the direction X. The source electrode  5 , the gate electrodes  8 , and the drain electrode  6  are arranged in this order in the direction X. The gate electrodes  8  have a surface  8   b  on the source electrode  5  side. The gate electrodes  8  have a surface  8   a  on the source electrode  6  side. 
     The source electrode  5  and the drain electrode  6  conduct with the nitride semiconductor layer  2 . In the semiconductor device  101 , the case is illustrated where the source electrode  5  and the drain electrode  6  extend through the nitride semiconductor layer  3  from above the nitride semiconductor layer  3  and reach the nitride semiconductor layer  2 . 
     The number of the first layers  10  is plural, and the first layers  10  exist corresponding to the gate electrodes  8 . The first layers  10  are located between the gate electrodes  8  and the drain electrode  6  in the direction X and are in contact with the gate electrodes  8 . In the semiconductor device  101 , the first layers  10  are in contact with the surfaces  8   a  and the drain electrode  6 . The first layers  10  are in contact with the nitride semiconductor layer  3  in the direction Y. 
     In the semiconductor device  101 , the case is illustrated where the first layers  10  extend through the nitride semiconductor layer  3  from above the nitride semiconductor layer  3  and reach the nitride semiconductor layer  2 . Although in the drawing, the shape of the first layer  10  protruding in the direction Z side from the nitride semiconductor layer  3  is illustrated, such protrusion is not essential. 
     The first layer  10  has a function of relaxing the concentration of the electric field as described later. The first layer  10  is, for example, an insulator. 
     The nitride semiconductor layer  2  and the nitride semiconductor layer  3  form a heterojunction. The nitride semiconductor layers  2  and  3  form a Schottky junction with the gate electrode  8 . 
     The formation of the heterojunction induces a two-dimensional carrier gas on the nitride semiconductor layer  2  side of the hetero interface located between the nitride semiconductor layer  2  and the nitride semiconductor layer  3 . In the semiconductor device  101 , the two-dimensional carrier gas is used for the current flowing between the source electrode  5  and the drain electrode  6  (so-called “drain current”). The current is controlled by the relationship of the voltages applied between the source electrode  5 , the drain electrode  6 , and the gate electrodes  8 . Such control per se is known and will not be described in detail in the present disclosure. 
     In the following, the case will be described where the two-dimensional carrier gas is a two-dimensional electron gas as an example unless otherwise specified. For example, the nitride semiconductor layer  2  and the nitride semiconductor layer  3  both have an n-type conductivity type. 
     A plurality of gate electrodes  8  connected to each other by the conductor  9  are arranged in the semiconductor device  101 . Electrons moving from the source electrode  5  pass along the direction X between adjacent gate electrodes  8  lying along the direction Y and head toward the drain electrode  6 . 
     Depleted layers derived from the Schottky junctions are formed in the nitride semiconductor layers  2  and  3  interposed between the gate electrodes  8  in the direction Y. The width of the depleted layer is controlled by the voltage applied between the gate electrode  8  and the source electrode  5 . Controlling the width of the depleted layer contributes to controlling the drain current. When the semiconductor device  101  is adopted as a switching element, the width of the depleted layer is controlled to control the On/Off of the semiconductor device  101 . 
     For example, when a voltage that is negative with respect to the source electrode  5  (hereinafter, also simply referred to as “negative voltage”) is applied to the gate electrodes  8 , the depletion layers spread from the surfaces  8   b ,  8   c ,  8   d , and  8   e  of the gate electrodes  8  into the nitride semiconductor layers  2  and  3 . The spreading of the depleted layers close the channels in the nitride semiconductor layers  2  and  3  interposed between the gate electrodes  8  in the direction Y, to turn off the semiconductor device  101 . 
     Arranging the gate electrodes  8  separately in the direction Y contributes to reducing the gate-drain capacitance and the gate-source capacitance of the semiconductor device  101 . The reduction enhances the linearity in operation of the semiconductor device  101 . 
     In a region opposite to the first layer  10  in the direction Z, the induction of two-dimensional electron gas in the nitride semiconductor layer  2  is suppressed. Such suppression makes the distance supporting the voltage between the gate electrode  8  and the drain electrode  6  becomes substantially long. The longer the distance, the smaller the electric field between the gate electrode  8  and the drain electrode  6  becomes, and the more the concentration of the electric field on the drain electrode  6  side of the gate electrode  8  is relaxed. 
     The first layer  10  relaxes the concentration of the electric field on the drain electrode  6  side of the gate electrode  8 . Such relaxation increases the breakdown voltage of the semiconductor device  101 . Increasing the breakdown voltage contributes to increasing the power output by the semiconductor device  101 . A region where the first layer  10  intervenes between the nitride semiconductor layer  2  and the gate electrode  8  is present and this also contributes to the reduction of the leakage current (so-called “gate leak current”) in the gate electrode  8  of the semiconductor device  101 . 
     When the induction of two-dimensional electron gas in the nitride semiconductor layer  2  is suppressed, the gate-drain capacity and the source-drain capacity are reduced. The reduction of these capacitances contributes to the improvement of drain efficiency and power load efficiency. 
     The first layers  10  are located between the gate electrodes  8  and the drain electrode  6  in the direction X. The first layers  10  are not required to be aligned with the gate electrodes  8  in the direction Y. The drain current flows through the nitride semiconductor layer  2  by the two-dimensional electron gas in the nitride semiconductor layer  2  in the region interposed between the gate electrodes  8  (for example, position BB) arranged in the direction Y. The first layer  10  relaxes the concentration of the electric field on the drain electrode  6  side of the gate electrode  8  even though the first layer  10  does not exist in the region. The degree of freedom for the position of first layer  10  allows it to easily avoid a decrease in drain current. Degradation of the drain current of the semiconductor device  101  caused by the first layer  10  being located between the gate electrode  8  and the drain electrode  6  in the direction X and being in contact with the gate electrode  8  is less likely to happen. When the first layer  10  is juxtaposed with the gate electrode  8  in the direction Y, On/Off switching of the transistor may be prevented. 
     The protective film  14  covers the semiconductor layer group  4 . The protective film  14  contributes to making the semiconductor device  101  less susceptible to the impact from the outside of the semiconductor device  101 . The protective film  14  exposes an upper portion of each of the source electrode  5 , the drain electrode  6 , and the gate electrodes  8 . Above the protective film  14 , the conductor  9  connects the plurality of gate electrodes  8  to each other. The protective film  14  may also cover the conductor  9 . The substrate  1  and the protective film  14  are not essential for the operation of the semiconductor device  101 . 
     In the narrow channel structure illustrated in Patent Document 1, Patent Document 2, and Patent Document 3, in addition to the gate structure adopting Schottky junction, the Metal-Insulator-Semiconductor (MIS) gate structure is also proposed. 
     In the MIS gate structure, an insulating film is located between the gate electrode and the semiconductor layer. Typically, in a transistor having a MIS gate structure, a gate leakage current thereof is reduced. Further, the MIS gate structure contributes to expanding the range of controlling the gate voltage in the forward direction in the transistor in which the structure is adopted. Such contribution improves the power output by the transistor. 
     When the MIS gate structure is adopted in the buried gate arrangement structure of Non-Patent Document 1, the depleted layer does not spread in the lateral direction of the gate electrode, and the transistor does not operate. 
     In the semiconductor device  101  according to the first embodiment, the gate electrodes  8  form a Schottky junction with the nitride semiconductor layers  2  and  3 . The semiconductor device  101  has a structure different from the MIS structure having a narrow channel structure, the difference being the depleted layer spreading in the direction Y in which the gate electrodes  8  are arranged. 
     The drain electrode  6  side of the gate electrodes  8  being in contact with the first layers  10  is a structure different from that of the buried gate arrangement structure of Non-Patent Document 1. The first layers  10  contribute to the reduction in gate leak current. 
     [Modification of Structure] 
     An other nitride semiconductor layer may exist any of between the nitride semiconductor layer  2  and the nitride semiconductor layer  3 , between the substrate  1  and the nitride semiconductor layer  2 , and on the opposite side of the nitride semiconductor layer  2  on the nitride semiconductor layer  3  (on the direction Z side to the nitride semiconductor layer  3 ). 
     For example, a nitride semiconductor layer using aluminum nitride (AlN) as a base material is arranged as a spacer layer between the nitride semiconductor layer  2  and the nitride semiconductor layer  3 . For example, the nitride semiconductor layer using AlN as a base material is arranged as a nucleation layer between the substrate  1  and the nitride semiconductor layer  2 . For example, a nitride semiconductor layer using GaN as a base material is arranged as a cap layer on the nitride semiconductor layer  3 . 
     Two-dimensional electron gas moves and drain current flows. The two-dimensional electron gas flows through the nitride semiconductor layer  2 . The source electrode  5  and the drain electrode  6  need only be electrically connected to the nitride semiconductor layer  2  and do not need to extend through the nitride semiconductor layer  3 . For example, the source electrode  5  may be located on the nitride semiconductor layer  3 . In this case, for example, the nitride semiconductor layers  2  and  3  are doped with a concentration at which ohmic contact is established between the nitride semiconductor layers  2  and  3  and the source electrode  5 . Similar arrangement and doping may be adopted for the drain electrode  6 . 
     The first layer  10  does not need to extend through the nitride semiconductor layer  3 . Suppressing the induction of two-dimensional electron gas in the nitride semiconductor layer  2  in the region opposite to the first layer  10  does not presuppose that the first layer  10  is in contact with the nitride semiconductor layer  2 . 
     For example, there is a case where the first layer  10  is in contact with at least the nitride semiconductor layer  3  in the direction Y and is not necessarily in contact with the nitride semiconductor layer  2 . When the induction of two-dimensional electron gas on the semiconductor layer group  4  side (opposite to the direction Z) with respect to the first layer  10  is suppressed, the function of relaxing the concentration of the electric field is obtained by the first layer  10 . Even if the nitride semiconductor layer  3  is interposed between the first layer  10  and the nitride semiconductor layer  2  in the direction Z, the thinness of the nitride semiconductor layer  3  suppresses the induction of the two-dimensional electron gas in the nitride semiconductor layer  2  in some cases. 
     As illustrated in the semiconductor device  101 , the contact of the first layer  10  with the nitride semiconductor layer  2  contributes to suppressing the induction of two-dimensional electron gas in the nitride semiconductor layer  2  in the region opposite to the first layer  10 . 
     The existence of the first layer  10  downward from (on the opposite side to the direction Z) the position in the direction Z of the two-dimensional electron gas induced in the region where the first layer  10  is not formed, for example, the position BB, is advantageous in terms of suppressing the induction of two-dimensional electron gas. 
     The gate electrodes  8  do not need to extend through the nitride semiconductor layer  3 . For example, the nitride semiconductor layer  3  may be interposed between the gate electrodes  8  and the nitride semiconductor layer  2 . Even in this case, the depletion layer extends along the direction Y by applying a negative voltage to the gate electrodes  8 . 
     As illustrated in the semiconductor device  101 , the extension of the gate electrodes  8  below the two-dimensional electron gas contributes to facilitating mutual contact between adjacent depleted layers in the direction Y. 
     [Component Specifications] 
     Examples of the material of the substrate  1  include silicon carbide (SiC), Si, gallium nitride (GaN), AlN, and sapphire. 
     Examples of the materials of the nitride semiconductor layers  2  and  3  include In x Al y Ga (1-x-y) N(0≤x≤1, 0≤y≤1, 0≤x+y≤1). The nitride semiconductor may be undoped, or may have a p-type conductivity type or an n-type conductivity type. For example, in order to have an n-type conductivity type, silicon is ion-implanted into a nitride semiconductor and this is subject to heat treatment to activate the silicon as a donor. The composition of the compound of the nitride semiconductor and the concentration of doping do not need to be constant with respect to the position, and may change continuously or stepwise. 
     The structure in which the nitride semiconductor layer  2  and the nitride semiconductor layer  3  are laminated is a structure in which two-dimensional electron gas is generated by heterojunction. For example, GaN is an example of the material of the nitride semiconductor layer  2 , and Al 0.25 Ga 0.75 N is an example of the material of the nitride semiconductor layer  3 . 
     The thickness thick enough for electrons to flow suffices for the thickness of the nitride semiconductor layer  2 . For example, the thickness of the nitride semiconductor layer  2  is 200 nm. The thickness thick enough for inducing the two-dimensional electron gas in the nitride semiconductor layer  2  suffices for the thickness of the nitride semiconductor layer  3 . For example, the thickness of the nitride semiconductor layer  3  is 15 nm. 
     The distance along the direction X between the source electrode  5  and the drain electrode  6  is, for example, 2.0 μm. 
     Obtaining ohmic contact both between the source electrode  5  and the semiconductor layer group  4  and between the drain electrode  6  and the semiconductor layer group  4  contributes to the reduction in the on-resistance of the semiconductor device  101 . For example, both the source electrode  5  and the drain electrode  6  are formed using a single layer or a lamination layer containing a metal exemplified by Ti, Al, and Au. 
     For example, both the gate electrodes  8  and the conductor  9  are formed using a single layer or a lamination layer containing a metal exemplified by Ni, Pt, and Au. 
     A gap between the gate electrodes  8  along the direction Y and the thickness of the gate electrodes  8  are set so that adjacent depleted layers in the direction Y come into contact with each other by applying a negative voltage to the gate electrodes  8 . 
     For example, the gate electrode  8  is square in plan view, the width and length of the gate electrode  8  are both 150 nm, and the thickness of the portion in contact with the semiconductor layer group  4  is 60 nm. For example, the distance between the gate electrodes  8  along the direction Y is 250 nm. The gaps between the plurality of gate electrodes  8  arranged in direction Y do not need to be equal to each other. 
     The arrangement of the plurality of gate electrodes  8  at equal intervals simplifies the creation of a mask used for, for example, photolithography when forming grooves  7  in the semiconductor layer group  4 . This simplicity improves the uniformity of the structure of the gate electrodes  8 . 
     The width of the first layer  10  may be wider than the width of the gate electrode  8 . The width of the first layer  10  being the same as the width of the gate electrode  8  or smaller than the width of the gate electrode  8  contributes to obtaining a large drain current. 
     In the thickness of the first layer  10  and the thickness of the gate electrode  8 , one of which may be larger than the other or equal to each other in their portions in contact with the semiconductor layer group  4 . 
     In the semiconductor device  101 , the first layers  10  are in contact with not only the gate electrodes  8  but also with the drain electrode  6 . The length of the first layer  10  is, for example, 1.5 μm. The width of the first layer  10  is, for example, 150 nm. The first layers  10  are arranged at a distance of, for example, 250 nm in the direction Y. The thickness of the first layer  10  is, for example, 60 nm in its portion in contact with the semiconductor layer group  4 . 
     The adoption of an insulator as the material of the first layers  10  contributes to relaxing the concentration of the electric field described above. Examples of the material of the first layer  10  include Al 2 O 3 , silicon nitride (SiN), and SiO 2 . Air may be adopted for the first layer  10 . 
     Alternatively, the first layer  10  may be obtained by losing the conductivity of the surface of the semiconductor layer group  4  on the direction Z side. For example, by implanting Ar into the semiconductor layer group  4 , the conductivity of the nitride semiconductor layer  3  or the nitride semiconductor layer  2  can be lost and they can be converted into an insulator. 
     Any material that suppresses the induction of two-dimensional electron gas in the nitride semiconductor layer  2  in the region opposite to the first layer  10  can be used as the first layer  10 . From this point of view, the first layer  10  may be formed of a semiconductor having the same conductivity type as the nitride semiconductor layer  3 . For example, a nitride semiconductor layer having a lower doping concentration than the nitride semiconductor layer  3  and having the same conductivity type can be adopted as the first layer  10 . 
     The effect of suppressing two-dimensional electron gas from being induced due to the first layer  10  is higher in a case where any of an insulator, a semiconductor having a conductivity type opposite to that of the nitride semiconductor layer  3 , and an intrinsic semiconductor is adopted for the first layer  10  than in a case where a semiconductor having the same conductivity type as the nitride semiconductor layer  3  is adopted for the first layer  10 . The case where a semiconductor having a conductive type opposite to that of the nitride semiconductor layer  3  is adopted for the first layer  10  will also be described in the twelfth embodiment. 
     When a conductor is adopted for the first layer  10 , the effect of relaxing the concentration of the electric field is small even if the two-dimensional electron gas is not induced in the nitride semiconductor layer  2 . It is considered that when a conductor is adopted for the first layer  10 , the first layer  10  conducts with the gate electrode  8  and substantially functions as the gate electrode  8 . When a conductor is adopted for the first layer  10 , the gate electrode  8  and the drain electrode  6  conduct to each other. Such conduction hinders the operation of the transistor. 
     It can be said that at least a part of the first layer  10  is buried in the semiconductor layer group  4  as with the gate electrode  8 . For example, the first layers  10  may be formed by forming grooves in the semiconductor layer group  4  and performing deposition to fill the grooves. For example, the grooves and the grooves  7  are concurrently formed. Such concurrent formation contributes to the reduction in damage given to the semiconductor layer group  4 . Either the formation of the first layers  10  or the formation of the gate electrodes  8  may be performed first. 
     For example, the gate electrodes  8  and the conductor  9  are obtained by sputtering. For example, the gate electrodes  8  and the conductor  9  are obtained by chemical vapor deposition (CVD). 
     The protective film  14  having insulating property contributes to avoiding a short circuit between the source electrode  5 , the drain electrode  6 , and the gate electrodes  8 . Examples of the material of the protective film  14  include SiN, Al 2 O 3 , SiO 2 , and resin. The protective film  14  does not need to be a single layer. The protective film  14  may be a laminated film including a first film that suppresses surface trapping in the nitride semiconductor layer  3  and a second film that is arranged on the first film to obtain moisture resistance. 
     Second Embodiment 
       FIG.  6    is a plan view illustrating a structure of a semiconductor device  102  according to a second embodiment.  FIG.  6    illustrates the same range as that illustrated in  FIG.  2    for the semiconductor device  101 . In  FIG.  6   , the same positions AA, BB, and CC as those illustrated in  FIG.  2    are also illustrated. In  FIG.  6   , the protective film  14  is omitted, and the conductor  9  is drawn by a two-dot chain line. 
       FIG.  7    is a cross-sectional view illustrating a cross section of the semiconductor device  102  at the position AA of  FIG.  6   . The cross section of the semiconductor device  102  at the position BB of  FIG.  6    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  102  at the position CC of  FIG.  6    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     The semiconductor device  102  has a structure in which second layers  12  are added to the semiconductor device  101 . 
     The number of the second layers  12  is plural, and the second layers  12  exist corresponding to the gate electrodes  8 . The second layers  12  are located between the gate electrodes  8  and the source electrode  5  in the direction X and are in contact with the gate electrodes  8 . In the semiconductor device  102 , the second layers  12  are in contact with the surfaces  8   b  and the source electrode  5 . The second layers  12  are in contact with the nitride semiconductor layer  3  in the direction Y. 
     In the semiconductor device  102 , the case is illustrated where the second layers  12  extend through the nitride semiconductor layer  3  from above the nitride semiconductor layer  3  and reach the nitride semiconductor layer  2 . Although in the drawing, the shape of the second layer  12  protruding in the direction Z side from the nitride semiconductor layer  3  is illustrated, such protrusion is not essential. 
     The second layer  12  is formed of, for example, an insulator or a semiconductor, as with the first layers  10 . As with the first layer  10 , the semiconductor is preferably an intrinsic semiconductor or has a conductivity type opposite to that of the nitride semiconductor layer  3 . 
     The positions of the second layers  12  in the direction Z may be selected in the same manner as the positions of the first layers  10  in the direction Z. For example, in the direction Z, the nitride semiconductor layer  3  may be interposed between the second layers  12  and the nitride semiconductor layer  2 . The second layers  12  may extend through the nitride semiconductor layer  3  in the direction Z and are in contact with the nitride semiconductor layer  2 . The second layer  12  may exist downward from the position in the direction Z of the two-dimensional electron gas induced in the region where the second layer  12  is not formed, for example, the position BB. The positions of the second layers  12  in the direction Z may be different from positions of the first layers  10  in the direction Z. 
     In a region opposite to the second layer  12  in the direction Z, the induction of two-dimensional electron gas in the nitride semiconductor layer  2  is suppressed. Such suppression reduces gate-source capacitance and source-drain capacitance. The reduction of these capacitances contributes to the improvement of drain efficiency and power load efficiency. 
     For example, when a charged human body is in contact with the semiconductor device  102 , electrostatic discharge (ESD) occurs (for example, refer to JEDEC standards JESD22-A114 human body model (HBM) test in electrostatic breakdown). The static electricity causes an increase in the electric field at the source electrode  5 . The second layer  12  relaxes the concentration of the electric field on the source electrode  5  side of the gate electrode  8 . Such relaxation contributes to reducing the potential of electrostatic discharge of the semiconductor device  102 . 
     As with the first layer  10 , the second layer  12  relaxes the concentration of the electric field on the source electrode  5  side of the gate electrode  8  even though it does not exist in the region interposed between the gate electrodes  8  arranged in the direction Y (for example, the position BB). The degree of freedom for the position of second layer  12  allows it to easily avoid a decrease in drain current. Degradation of the drain current of the semiconductor device  102  caused by the second layer  12  being located between the gate electrode  8  and the source electrode  5  in the direction X and being in contact with the gate electrode  8  is less likely to happen. 
     As the material of the second layer  12 , for example, the examples given as the material of the first layer  10  are adopted. The material of the first layer  10  and the material of the second layer  12  do not need to match. The matching of the material of the first layer  10  and the material of the second layer  12  contributes to the easy formation of the first layer  10  and the second layer  12 . 
     Third Embodiment 
       FIG.  8    is a plan view illustrating a structure of a semiconductor device  103  according to a third embodiment.  FIG.  8    illustrates the same range as that illustrated in  FIG.  2    for the semiconductor device  101 . In  FIG.  8   , the same positions AA, BB, and CC as those illustrated in  FIG.  2    are also illustrated. In  FIG.  8   , the protective film  14  is omitted, and the conductor  9  is drawn by a two-dot chain line. 
       FIG.  9    is a cross-sectional view illustrating a cross section of the semiconductor device  103  at the position AA of  FIG.  8   . The cross section of the semiconductor device  103  at the position BB of  FIG.  8    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  103  at the position CC of  FIG.  8    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     The semiconductor device  103  differs from the semiconductor device  101  in that the length of the first layer  10  is shorter than the distance between the gate electrode  8  and the drain electrode  6 . In the semiconductor device  103 , the nitride semiconductor layers  2  and  3  are interposed between the first layer  10  and the drain electrode  6  along the direction X. 
     In the semiconductor device  101 , electrons directed from between the gate electrodes  8  to the drain electrode  6  move between adjacent first layers  10  in the direction Y. In the semiconductor device  103 , electrons directed from between the gate electrodes  8  to the drain electrode  6  move not only between the adjacent first layers  10  in the direction Y but also in the region interposed between the first layers  10  and the drain electrode  6 . Compared with the semiconductor device  101 , the semiconductor device  103  has a wider region of two-dimensional electron gas that contributes to the drain current, and a large drain current is obtained. The large drain current increases the power output by the transistor realized by the semiconductor device  101  and enhances efficiency. 
     Fourth Embodiment 
       FIG.  10    is a plan view illustrating a structure of a semiconductor device  104  according to a fourth embodiment.  FIG.  10    illustrates the same range as that illustrated in  FIG.  2    for the semiconductor device  101 . In  FIG.  10   , the same positions AA, BB, and CC as those illustrated in  FIG.  2    are also illustrated. In  FIG.  10   , the protective film  14  is omitted, and the conductor  9  is drawn by a two-dot chain line. 
       FIG.  11    is a cross-sectional view illustrating a cross section of the semiconductor device  104  at the position AA of  FIG.  10   . The cross section of the semiconductor device  104  at the position BB of  FIG.  10    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  104  at the position CC of  FIG.  10    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     The semiconductor device  104  differs from the semiconductor device  102  in that the length of the first layer  10  is shorter than the distance between the gate electrode  8  and the drain electrode  6  and the length of the second layer  12  is shorter than the distance between the gate electrode  8  and the source electrode  5 . 
     The semiconductor device  104  has a structure in which second layers  12  are added to the semiconductor device  103 . The second layers  12  are located between the gate electrodes  8  and the source electrode  5  in the direction X and are in contact with the gate electrodes  8 . In the semiconductor device  104 , the second layers  12  are in contact with the surfaces  8   b . The length of the second layer  12  is shorter than the distance between the gate electrode  8  and the source electrode  5 . Above said second layer  12  may be added to the semiconductor device  101 . 
     In the semiconductor device  104 , along the direction X, the nitride semiconductor layers  2  and  3  are interposed between the first layer  10  and the drain electrode  6  and the nitride semiconductor layers  2  and  3  are interposed between the second layer  12  and the source electrode  5 . 
     In the semiconductor device  102 , electrons directed from between the source electrode  5  to the gate electrode  8  move between adjacent second layers  12  in the direction Y. In the semiconductor device  104 , electrons directed from the source electrode  5  to between the gate electrodes  8  move not only between the adjacent second layers  12  in the direction Y but also in the region interposed between the second layers  12  and the drain electrode  6 . 
     Compared with the semiconductor device  102 , the semiconductor device  104  has a wider region of two-dimensional electron gas that contributes to the drain current, and a large drain current is obtained. 
     Compared with the semiconductor device  103 , the semiconductor device  104  relaxes the concentration of the electric field on the source electrode  5  side of the gate electrode  8 . 
     Fifth Embodiment 
       FIG.  12    is a plan view illustrating a structure of a semiconductor device  105  according to a fifth embodiment.  FIG.  12    illustrates the same range as that illustrated in  FIG.  2    for the semiconductor device  101 . In  FIG.  12   , the same positions AA, BB, and CC as those illustrated in  FIG.  2    are also illustrated. In  FIG.  12   , the protective film  14  is omitted, and the conductor  9  is drawn by a two-dot chain line. 
       FIG.  13    is a cross-sectional view illustrating a cross section of the semiconductor device  105  at the position AA of  FIG.  12   . The cross section of the semiconductor device  105  at the position BB of  FIG.  12    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  105  at the position CC of  FIG.  12    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     Compared with the semiconductor device  103 , the semiconductor device  105  has a feature that the width of the first layer  10  on the drain electrode  6  side is narrower than the width thereof on the gate electrode  8  side. The length of the first layer  10  along the direction Y decreases as it is away from the gate electrode  8  along the direction X. For example, the width of the first layer  10  coincides with the width of the surface  8   a  at the position where it is in contact with the surface  8   a , and is narrower as it is closer to the drain electrode  6 . 
     As with the semiconductor device  103 , also in the semiconductor device  105 , electrons directed from the source electrode  5  to between the gate electrodes  8  move not only between the adjacent second layers  12  in the direction Y but also in the region interposed between the second layers  12  and the drain electrode  6 . When the electrons move from between the gate electrodes  8  toward the direction X, they spread and move toward both the direction Y and the opposite side of the direction Y. The first layers  10  in the semiconductor device  105  are less likely to hinder the spread of the electrons than the first layers  10  in the semiconductor device  104 . 
     Compared with the semiconductor device  103 , the semiconductor device  105  is less likely to hinder the move of the two-dimensional electron gas that contributes to the drain current, and a large drain current is obtained. 
     As the shape of the first layer  10 , a shape whose width is narrowed stepwise toward the direction X may be adopted. Adopting a shape having a narrower width in a linear or curved toward the direction X as a shape of the first layer  10  is advantageous from the viewpoint of widening the place where the electric field is concentrated and relaxation of the concentration. 
     A structure in which the width of the drain electrode  6  side of the first layer  10  is narrower than the width thereof on the gate electrode  8  side can be adoptable to any structure of the semiconductor devices  101  to  104  and contributes to obtaining a large drain current. 
     Sixth Embodiment 
       FIG.  14    is a plan view illustrating a structure of a semiconductor device  106  according to a sixth embodiment.  FIG.  14    illustrates the same range as that illustrated in  FIG.  2    for the semiconductor device  101 . In  FIG.  14   , the same positions AA, BB, and CC as those illustrated in  FIG.  2    are also illustrated. In  FIG.  14   , the protective film  14  is omitted, and the conductor  9  is drawn by a two-dot chain line. 
       FIG.  15    is a cross-sectional view illustrating a cross section of the semiconductor device  106  at the position AA of  FIG.  14   . The cross section of the semiconductor device  106  at the position BB of  FIG.  14    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  106  at the position CC of  FIG.  14    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     The semiconductor device  106  has a structure in which second layers  12  are added to the semiconductor device  105 . The second layers  12  are located between the gate electrodes  8  and the source electrode  5  in the direction X and are in contact with the gate electrode  8 . In the semiconductor device  106 , the second layers  12  are in contact with the surfaces  8   b . The length of the second layer  12  is shorter than the distance between the gate electrode  8  and the source electrode  5 . The width of the second layer  12  on the source electrode  5  side is narrower than the width thereof on the gate electrode  8  side. 
     Compared with the semiconductor device  104 , the semiconductor device  106  has a feature that the width of the first layer  10  on the drain electrode  6  side is narrower than the width thereof on the gate electrode  8  side and the width of the second layer  12  on the source electrode  5  side is narrower than the width thereof on the gate electrode  8  side. 
     The length of the first layer  10  along the direction Y decreases as it is away from the gate electrode  8  along the direction X. For example, the width of the first layer  10  coincides with the width of the surface  8   a  at the position where it is in contact with the surface  8   a , and is narrower as it is closer to the drain electrode  6 . 
     The length of the second layer  12  along the direction Y increases as it nears the gate electrode  8  along the direction X. For example, the width of the second layer  12  coincides with the width of the surface  8   b  at the position where it is in contact with the surface  8   b , and is narrower as it is closer to the source electrode  5 . 
     Compared with the semiconductor device  105 , the semiconductor device  106  relaxes the concentration of the electric field on the source electrode  5  side of the gate electrode  8 . 
     As with the semiconductor device  104 , also in the semiconductor device  106 , electrons directed from the source electrode  5  to between the gate electrodes  8  move not only between the adjacent second layers  12  in the direction Y but also in the region interposed between the second layers  12  and the drain electrode  6 . When the electrons move from the drain electrode  6  to between the gate electrodes  8  toward the direction X, they narrow and move toward both direction Y and the opposite side of direction Y. The second layers  12  in the semiconductor device  106  are less likely to hinder the narrowing of the electrons than the second layers  12  in the semiconductor device  104 . 
     Compared with the semiconductor device  104 , the semiconductor device  106  is less likely to hinder the move of the two-dimensional carrier gas that contributes to the drain current, and a large drain current is obtained. 
     As the shape of the second layer  12 , a shape whose width is widened stepwise toward the direction X may be adopted. Adopting a shape having a wider width in a linear or curved toward the direction X as a shape of the second layer  12  is advantageous from the viewpoint of widening the place where the electric field is concentrated and relaxation of the concentration. 
     The structure in which the length of the second layer  12  along the direction Y increases as it nears the gate electrode  8  along the direction X is applicable to any of the semiconductor devices  101  to  105 . 
     Seventh Embodiment 
       FIG.  16    is a plan view illustrating a structure of a semiconductor device  107  according to a seventh embodiment.  FIG.  16    illustrates the same range as that illustrated in  FIG.  2    for the semiconductor device  101 . In  FIG.  16   , the same positions AA, BB, and CC as those illustrated in  FIG.  2    are also illustrated. In  FIG.  16   , the protective film  14  is omitted, and the conductor  9  is drawn by a two-dot chain line. 
       FIG.  17    is a cross-sectional view illustrating a cross section of the semiconductor device  107  at the position AA of  FIG.  16   . The cross section of the semiconductor device  107  at the position BB of  FIG.  16    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  107  at the position CC of  FIG.  16    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     The semiconductor device  107  has a structure in which fourth layers  16  are added to the semiconductor device  103 . 
     The number of the fourth layers  16  is plural, and the fourth layers  16  exist corresponding to the gate electrodes  8 . The fourth layers  16  are located between the first layers  10  and the drain electrode  6  in the direction X and are in contact with both the first layers  10  and the drain electrode  6 . The fourth layers  16  are in contact with the nitride semiconductor layer  3  in the direction Y. 
     In the semiconductor device  107 , the case is illustrated where the fourth layers  16  extend through the nitride semiconductor layer  3  from above the nitride semiconductor layer  3  and reach the nitride semiconductor layer  2 . Although in the drawing, the shape of the fourth layer  16  protruding in the direction Z side from the nitride semiconductor layer  3  is illustrated, such protrusion is not essential. 
     The fourth layer  16  is formed of, for example, an insulator or a semiconductor, as with the first layer  10 . As with the first layers  10 , the semiconductor is preferably an intrinsic semiconductor or has a conductivity type opposite to that of the nitride semiconductor layer  3 . The fourth layer  16  has a function of relaxing the concentration of the electric field similar to the first layer  10 . 
     The positions of the fourth layers  16  in the direction Z may be selected in the same manner as the positions of the first layers  10  in the direction Z. For example, in the direction Z, the nitride semiconductor layer  3  may be interposed between the fourth layers  16  and the nitride semiconductor layer  2 . The fourth layers  16  may extend through the nitride semiconductor layer  3  in the direction Z and are in contact with the nitride semiconductor layer  2 . The fourth layer  16  may exist downward from the position in the direction Z of the two-dimensional electron gas induced in the region where the fourth layer  16  is not formed, for example, the position BB. The positions of the fourth layers  14  in the direction Z may be different from positions of the first layers  10  in the direction Z. 
     The permittivity of the fourth layer  16  is smaller than the permittivity of the first layer  10 . A high permittivity facilitates the relaxation of the concentration of the electric fields. The relaxation of the concentration of the electric field contributes to increasing the power output by the semiconductor device  107 . Low permittivity makes it easy to reduce gate-drain capacitance and source-drain capacitance. The reduction of these capacitances contributes to the improvement of drain efficiency and power load efficiency. 
     The electric field is prone to concentrate as it is closer to the gate electrode  8 ; therefore, the higher permittivity of the first layer  10  closer to the gate electrode  8  than the fourth layer  16  is advantageous in terms of reduction in the gate-drain capacitance and the source-drain capacitance and relaxation of the concentration of the electric field. 
     Assuming that the fourth layer  16  is regarded as a part of the first layer  10 , it can be said that the semiconductor device  107  has a structure where the permittivity of the first layer  10  gradually decreases toward the direction X according to the semiconductor device  101 . According to the first layer  10  in the semiconductor device  101 , the permittivity of three or more types may gradually decrease in the first layer  10 . The permittivity of the first layer  10  may decrease continuously toward the direction X. 
     Similar to the semiconductor device  103 , the fourth layers  16  do not are in contact with the drain electrode  6 , and the nitride semiconductor layer  3  may be interposed between the fourth layers  16  and the drain electrode  6 . 
     The structure in which the permittivity of the first layer  10  decreases toward the direction X is applicable to any of the semiconductor devices  101  to  107 , and contributes to the reduction of the gate-drain capacitance and the source-drain capacitance and the relaxation of the concentration of the electric field. 
     In the semiconductor devices  102 ,  104 , and  106 , the permittivity of the second layer  12  may decrease toward the direction opposite to the direction X. Such a feature contributes to the reduction in the gate-source capacitance and source-drain capacitance. 
     Eighth Embodiment 
       FIG.  18    is a plan view illustrating a structure of a semiconductor device  108  according to an eighth embodiment.  FIG.  18    illustrates the same range as that illustrated in  FIG.  2    for the semiconductor device  101 . In  FIG.  18   , the same positions AA, BB, and CC as those illustrated in  FIG.  2    are also illustrated. In  FIG.  18   , the protective film  14  is omitted, and the conductor  9  is drawn by a two-dot chain line. 
       FIG.  19    is a cross-sectional view illustrating a cross section of the semiconductor device  108  at the position AA of  FIG.  18   . The cross section of the semiconductor device  108  at the position BB of  FIG.  18    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   .  FIG.  20    is a cross-sectional view illustrating a cross section of the semiconductor device  108  at the position CC of  FIG.  18   . 
     The semiconductor device  108  has a structure in which third layers  13  are added to the semiconductor device  103 . The third layers  13  are in contact with the surfaces  8   e.    
     As the material of the third layer  13 , for example, the examples given as the material of the first layer  10  are adopted. The material of the first layer  10  and the material of the third layer  13  do not need to match. The matching of the material of the first layer  10  and the material of the third layer  13  contributes to the easy formation of the first layer  10  and the third layer  13 . 
     The third layers  12  are located between the gate electrodes  8  and the semiconductor layer group  4  in the direction Z and are in contact with the gate electrodes  8 . In  FIGS.  19  and  20   , the third layer  13  is located between the surface  8   e  and the nitride semiconductor layer  2  in direction Z. The third layer  13  relaxes the concentration of the electric field on the surface  8   e  side of the gate electrode  8 . The third layer  13  being located between the gate electrode  8  and the nitride semiconductor layer  2  contributes to the reduction of the gate leak current. 
     The suppression described above is not directly related to the contact of the third layer  13  with the first layer  10 . The third layers  13  contacting the first layers  10  makes it easier to concurrently form the third layers  13  and the first layers  10 , for example, between the formation of the grooves  7  and the formation of the gate electrodes  8 , for example, between the formation of the grooves  7  and the formation of the gate electrodes  8 . 
     The third layer  13  is addable to any of the semiconductor devices  101  to  107 , and this contributes to the reduction of the gate leak current. 
     Ninth Embodiment 
       FIG.  21    is a plan view illustrating a structure of a semiconductor device  109  according to a ninth embodiment.  FIG.  21    illustrates the same range as that illustrated in  FIG.  2    for the semiconductor device  101 . In  FIG.  21   , the same positions AA, BB, and CC as those illustrated in  FIG.  2    are also illustrated. In  FIG.  21   , the protective film  14  is omitted, and the conductor  9  is drawn by a two-dot chain line. 
       FIG.  22    is a cross-sectional view illustrating a cross section of the semiconductor device  109  at the position AA of  FIG.  21   .  FIG.  23    is a cross-sectional view illustrating a cross section of the semiconductor device  109  at the position BB of  FIG.  21   .  FIG.  24    is a cross-sectional view illustrating a cross section of the semiconductor device  109  at the position CC of  FIG.  21   . 
     The semiconductor device  109  differs from the semiconductor device  103  in the configuration of the nitride semiconductor layers  2  and  3 . Specifically, the nitride semiconductor layer  2  includes nitride semiconductor layers  21 ,  22 , and  23 , and the nitride semiconductor layer  3  includes nitride semiconductor layers  31 ,  32 , and  33 . 
     The nitride semiconductor layer  21  and the nitride semiconductor layer  31  form a heterojunction. The nitride semiconductor layer  31  and the nitride semiconductor layer  22  form a heterojunction. The nitride semiconductor layer  22  and the nitride semiconductor layer  32  form a heterojunction. The nitride semiconductor layer  32  and the nitride semiconductor layer  23  form a heterojunction. The nitride semiconductor layer  23  and the nitride semiconductor layer  33  form a heterojunction. 
     Assuming the nitride semiconductor layer  21  is regarded as the nitride semiconductor layer  2  in the semiconductor device  103 , it can be said that the semiconductor device  109  has a structure in which the nitride semiconductor layers  31 ,  22 ,  32 ,  23 , and  33  are added, as the nitride semiconductor layer  3 , on the semiconductor layer group  4  in the semiconductor device  103  in this order toward the direction Z. 
     Assuming the nitride semiconductor layers  21  and  31  are regarded as the nitride semiconductor layers  2  and  3 , respectively, in the semiconductor device  103 , it can be said that the semiconductor device  109  has a structure in which the nitride semiconductor layers  22 ,  32 ,  23 , and  33  are added on the semiconductor layer group  4  in the semiconductor device  103  in this order toward the direction Z. 
     Assuming the nitride semiconductor layers  21 ,  31 , and  22  are regarded as the nitride semiconductor layer  2  in the semiconductor device  103 , it can be said that the semiconductor device  109  has a structure in which the nitride semiconductor layers  32 ,  23 , and  33  are added, as the nitride semiconductor layer  3 , on the semiconductor layer group  4  in the semiconductor device  103  in this order toward the direction Z. 
     Assuming the nitride semiconductor layers  21 ,  31 ,  22 ,  32 , and  23  are regarded as the nitride semiconductor layer  2  in the semiconductor device  103 , it can be said that the semiconductor device  109  has a structure in which the nitride semiconductor layer  33  is added, as the nitride semiconductor layer  3 , on the semiconductor layer group  4  in the semiconductor device  103  on the direction Z side. 
     It can be said that the nitride semiconductor layer  2  includes a plurality of nitride semiconductor layers (tentatively referred to as “first sublayers” in the present disclosure), the nitride semiconductor layer  3  has a plurality of nitride semiconductor layers (tentatively referred to as “second sublayers” in the present disclosure), and the first sublayers and the second sublayers are alternately laminated. 
     It can also be said that the semiconductor layer group  4  has a plurality of nitride semiconductor layers  21 ,  22 , and  23  and a plurality of nitride semiconductor layers  31 ,  32 , and  33 , and they are alternately laminated. 
     Two-dimensional carrier gas is induced in the heterojunction. In the semiconductor device  109 , regions where the two-dimensional carrier gas is induced exist at a plurality of positions along the direction Z. The existence of a plurality of regions where the two-dimensional carrier gas is induced contributes to increasing the amount of the two-dimensional carrier gas that contributes to the drain current in the semiconductor device  109 . The semiconductor device  109  obtains a larger drain current than the semiconductor device  103 . 
     The laminated structure including the nitride semiconductor layers  21 ,  31 ,  22 ,  32 ,  23 , and  33  may be obtained by a periodic superlattice structure. The number of such layers may be further increased, or the nitride semiconductor layers  23  and  33  may be omitted. 
     The composition, doping concentration, and film thickness of the nitride semiconductor layers  21 ,  22 , and  23  may be the same as each other, or may be different from each other. The composition, doping concentration, and film thickness of the nitride semiconductor layers  31 ,  32 , and  33  may be the same as each other, or may be different from each other. 
     Such a laminated structure in the nitride semiconductor layers  2  and  3  is applicable to any of the semiconductor devices  101  to  108 , and contributes to obtaining a large drain current. 
     Tenth Embodiment 
       FIG.  25    is a cross-sectional view illustrating a structure of a semiconductor device  110  according to a tenth embodiment. The plan view of the semiconductor device  110  appears in the same manner as, for example, the plan view of the semiconductor device  103  according to the third embodiment (see  FIG.  8   ). In this case,  FIG.  25    illustrates a cross section of the semiconductor device  110  at a position corresponding to the position AA illustrated in  FIG.  8   . The cross section of the semiconductor device  110  at a position corresponding to the position BB illustrated in  FIG.  8    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  110  at a position corresponding to the position CC illustrated in  FIG.  8    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     Or, the plan view of the semiconductor device  110  appears in the same manner as, for example, the plan view of the semiconductor device  105  according to the fifth embodiment (see  FIG.  12   ). In this case,  FIG.  25    illustrates a cross section of the semiconductor device  110  at a position corresponding to the position AA illustrated in  FIG.  12   . The cross section of the semiconductor device  110  at a position corresponding to the position BB illustrated in  FIG.  12    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  110  at a position corresponding to the position CC illustrated in  FIG.  12    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     In the semiconductor device  110 , the length (thickness) of the first layer  10  along the direction Z decreases as it is away from the gate electrode  8  in the first layer  10  along the direction X, as compared with the semiconductor devices  103  and  105 . For example, the position, in the direction Z, of a surface  10   e  of the first layer  10  opposite to in the direction Z coincides with the position of the surface  8   e  in the direction Z at the position in contact with the gate electrode  8 , and it goes toward the direction Z as it nears the drain electrode  6 . 
       FIG.  26    is a cross-sectional view illustrating a structure of a modification of the semiconductor device  110 .  FIG.  26    illustrates a cross section of the modification at the same position as the cross section illustrated in  FIG.  25   . In  FIG.  25   , the surface  10   e  has a shape in which the absolute value of the inclination of the surface  10   e  with respect to the direction X in a cross-sectional view only increases toward the direction X. The surface  10   e  in  FIG.  26    has a portion where the absolute value decreases toward the direction X. 
     Both the first layer  10  having the cross section illustrated in  FIG.  25    and the first layer  10  having the cross section illustrated in  FIG.  26    are advantageous from the viewpoint of widening the place where the electric field is concentrated and relaxation of the concentration in the same manner as the semiconductor devices  105  and  106 . As the shape of the first layer  10 , a shape whose thickness decreases stepwise toward the direction X may be adopted. 
     A structure in which the thickness of the drain electrode  6  side of the first layer  10  decreases as it is away from the gate electrode  8  can be adoptable to any structure of the semiconductor devices  101  to  109  and contributes to obtaining a large drain current. 
     The concentration of the electric field is prone to occur at the end of the gate electrode  8  on the drain electrode  6  side, for example, the surface  8   a , and not near the two-dimensional electron gas. From this point of view, the variation of the thickness of the first layer  10  not only in the nitride semiconductor layer  2  but also in the nitride semiconductor layer  3  as described above contributes to relaxation of the concentration of the electric field. 
     Eleventh Embodiment 
       FIG.  27    is a cross-sectional view illustrating a structure of a semiconductor device  111  according to an eleventh embodiment. The plan view of the semiconductor device  111  appears in the same manner as the plan view of the semiconductor device  104  according to the fourth embodiment (see  FIG.  10   ). In this case,  FIG.  27    illustrates a cross section of the semiconductor device  111  at a position corresponding to the position AA illustrated in  FIG.  10   . The cross section of the semiconductor device  111  at a position corresponding to the position BB illustrated in  FIG.  10    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  111  at a position corresponding to the position CC illustrated in  FIG.  10    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     Or, the plan view of the semiconductor device  111  appears in the same manner as the plan view of the semiconductor device  106  according to the sixth embodiment (see  FIG.  14   ). In this case,  FIG.  27    illustrates a cross section of the semiconductor device  111  at a position corresponding to the position AA illustrated in  FIG.  14   . The cross section of the semiconductor device  111  at a position corresponding to the position BB illustrated in  FIG.  14    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  4   . The cross section of the semiconductor device  111  at a position corresponding to the position CC illustrated in  FIG.  14    appears in the same manner as the cross section of the semiconductor device  101  illustrated in  FIG.  5   . 
     In the semiconductor device  111 , the length (thickness) of the second layer  12  along the direction Z increases as it nears the gate electrode  8  along the direction X, as compared with the semiconductor devices  104  and  106 . For example, the position, in the direction Z, of a surface  12   e  of the second layer  12  opposite to the direction Z coincides with the position of the surface  8   e  in the direction Z at the position in contact with the gate electrode  8 , and it goes toward the direction Z as it nears the source electrode  5 . 
     The second layer  12  having such a cross section is advantageous from the viewpoint of widening the place where the electric field is concentrated and relaxation of the concentration in the same manner as the semiconductor device  106 . 
     As the shape of the second layer  12 , a shape whose thickness increases stepwise toward the direction X may be adopted. In  FIG.  27   , the surface  12   e  has a shape in which the absolute value of the inclination of the surface  12   e  with respect to the direction X in a cross-sectional view only decreases toward the direction X. The surface  12   e  may have a portion where the absolute value increases toward the direction X. 
     A structure in which the thickness of the source electrode  5  side of the second layer  12  increases as it nears the gate electrode  8  can be adoptable to any structure of the semiconductor devices  101  to  110  and contributes to obtaining a large drain current. 
     Twelfth Embodiment 
     In the present embodiment, the first layer  10  is a semiconductor having a conductivity type opposite to the conductivity type of the nitride semiconductor layer  3 . For example, the conductivity type of the nitride semiconductor layer  3  is n-type, and a semiconductor having a p-type conductivity type is adopted for the first layer  10 . The first layer  10  in which such a semiconductor is adopted is adoptable in any structure of the semiconductor devices  101  to  111 . 
       FIG.  28    is a diagram illustrating a band structure of a semiconductor device according to a twelfth embodiment.  FIG.  28    illustrates the band structure of the nitride semiconductor layer  3  at specific positions in the directions Y and Z. The specific position is the position where the first layer  10  exists in the direction Y, and corresponds to the above-mentioned position AA. The specific position is the position (depth) where the nitride semiconductor layer  3  exists in the direction Z. 
     On the horizontal axis, a region R 8  where the gate electrode  8  exists at the specific position (the boundary opposite to the direction X is omitted), a region R 10  where the first layer  10  exists at the specific position, a region R 3  where the nitride semiconductor layer  3  exists at the specific position exists, and a region R 6  where the drain electrode  6  exists at the specific position (the boundary on the direction X side is omitted) are illustrated. Potential energy for electrons is adopted on the vertical axis. 
     The bottom Ec 1  of the conduction band and the top Ev 1  of the valence band of the nitride semiconductor layer  3  are illustrated when the source electrode  5 , the drain electrode  6 , and the gate electrode  8  have the same potential. The bottom Ec 2  of the conduction band and the top Ev 2  of the valence band of the nitride semiconductor layer  3  is illustrated when the source electrode  5  and the drain electrode  6  have the same potential and the potential of the gate electrode  8  is positive with respect to the potentials of the source electrode  5  and the drain electrode  6 . 
     When the potential of the gate electrode  8  becomes positive with respect to the potential of the drain electrode  6 , the following phenomena occur: holes are implanted from the first layer  10  having a p-type conductivity type to the nitride semiconductor layer  2  having an n-type conductivity type; potentials for holes decreases in nitride semiconductor layer  3 ; and the implanted holes approach the nitride semiconductor layer  3  which has a low potential for holes and function as a two-dimensional hole gas. 
     The two-dimensional hole gas functions as a carrier in the drain current in the same manner as the two-dimensional electron gas; therefore, the occurrence of the above-mentioned phenomenon contributes to the increase in the drain current. The increase in the drain current improves the current drive capability and improves the linearity of mutual conductance due to conductivity modulation. The improvement of the linearity of the mutual conductance contributes to the reduction in distortion of the communication system using the semiconductor device according to the present embodiment. 
     A pn junction is formed at the interface between the first layer  10  and the nitride semiconductor layer  3 . The pn junction generates electrostatic capacitance due to the depleted layer and reduces the electrostatic capacitance between the gate electrode  8  and the drain electrode  6 . Such reduction in capacitance contributes to at least any of improvement of drain efficiency and improvement of power added efficiency in power conversion using the semiconductor device according to the present embodiment. 
     Similarly, for both the second layer  12  in the semiconductor devices  102 ,  104 ,  106 , and  111  and the third layer  13  in the semiconductor device  108 , adopting a semiconductor having a conductivity type opposite to the conductivity type of the nitride semiconductor layer  3  allows to obtain either or both of the improvements and contributions described above. 
     Modifications for Surfaces  8   a ,  8   b ,  8   c , and  8   d    
       FIG.  29    is a plan view of the gate electrode  8  as viewed along the direction opposite to the direction Z. In  FIG.  29   , a case where the gate electrode  8  exhibits a circular shape in plan view is illustrated. For example, the gate electrode  8  exhibits a cylinder. The structure of such a gate electrode  8  is disclosed in, for example, Non-Patent Document 1. 
     The virtual lines J, K, L, and M pass through the center  8   f  of the gate electrode  8  in plan view. The virtual line J is parallel to the direction X, and is parallel to the direction in which the source electrode  5  and the drain electrode  6  are aligned. The virtual line K is parallel to the direction Y, and is parallel to the direction in which the plurality of gate electrodes  8  are aligned. Both the virtual lines L and M have an inclination of 45 degrees with respect to the directions X and Y. The virtual line L goes to direction Y as it goes to direction X. 
     The virtual lines L and M are the boundaries of the regions  8   ar  and  8   br  of the gate electrode  8 . The region  8   ar  is located more on the direction X side than the region  8   br  is. In  FIG.  29   , the regions  8   ar  and  8   br  are illustrated by thick lines for better visibility. 
     For example, the region  8   ar  is treated as the surface  8   a . The first layer  10  is in contact with the gate electrode  8  without extending over the region  8   ar . For example, the region  8   br  is treated as the surface  8   b . The second layer  12  is in contact with the gate electrode  8  without extending over the region  8   br.    
     The first layer  10  is in contact with the gate electrode  8  within a range, in a plan view, of 45° or less in both positive and negative to a direction from the source electrode  5  to the drain electrode  6 . 
     The second layer  12  is in contact with the gate electrode  8  within a range, in a plan view, of 45° or less in both positive and negative to the direction from the source electrode  5  to the drain electrode  6 . 
     The embodiments can be combined, appropriately modified or omitted. 
     While the disclosure has been illustrated and described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is therefore understood that numerous modifications can be devised. 
     EXPLANATION OF REFERENCE SIGNS 
     
         
         
           
               2 ,  3 ,  21  to  23 ,  31  to  33  nitride semiconductor layer,  4  semiconductor layer group,  5  source electrode,  6  drain electrode,  8  gate electrode,  9  conductor,  10  first layer,  12  second layer,  13  third layer,  100  to  111  semiconductor device, X, Y, Z direction.