Patent Publication Number: US-2023155292-A1

Title: Semiconductor element

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation of International Patent Application No. PCT/JP2021/026676, filed on Jul. 15, 2021, which claims the benefit of Japanese Patent Application No. 2020-126353, filed on Jul. 27, 2020, both of which are hereby incorporated by reference herein in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a semiconductor element that oscillates or detects a terahertz wave. 
     Background Art 
     As a current-injection-type light source that generates terahertz waves, which are electromagnetic waves in a frequency range of at least 30 GHz and not more than 30 THz, an oscillator, in which a semiconductor element having an electromagnetic gain of terahertz waves and a resonator are integrated, has been known. In particular, an oscillator, in which a resonant tunneling diode (RTD) and an antenna are integrated, is expected to be used as a semiconductor element that operates at room temperature in a frequency range around 1 THz. 
     Non Patent Literature (NPL) 1 describes a terahertz wave oscillator in which an RTD and a slot antenna resonator are integrated on a semiconductor substrate. In NPL 1, a double-barrier-type RTD including an InGaAs quantum well layer and an AlAs tunnel barrier layer epitaxially grown on an InP substrate is used. The oscillator using such an RTD can implement oscillation of terahertz waves at room temperature in a region in which differential negative resistance is obtained in voltage-current (V-I) characteristics. 
     Patent Literature (PTL) 1 describes a terahertz wave antenna array in which a plurality of oscillators each having an RTD and an antenna integrated therein are arranged on the same substrate. The antenna array described in PTL 1 can enhance antenna gain and power by synchronizing adjacent antennas with each other. NPL 2 describes a configuration in which adjacent antennas are connected to each other by a chip resistor to achieve mode stabilization. 
     However, since the number of modes (the number of resonance frequency bands) to be synchronized increases in conjunction with an increase in the number of antennas (the number of negative resistance elements) in the antenna array, it becomes more difficult for the element to stabilize generation or detection of terahertz waves as the number of antennas increases. Consequently, there are cases in which the element including a plurality of antennas cannot efficiently generate or detect a terahertz wave because there are a plurality of modes to be synchronized. 
     With the foregoing in view, it is an object of the present invention to implement more efficient generation or detection of a terahertz wave by an element including a plurality of antennas. 
     CITATION LIST 
     Patent Literature 
     PTL 1: Japanese Patent Application Publication No. 2014-200065 
     Non Patent Literature 
     NPL 1: Jpn.J.Appl.Phys., Vol. 47, No. 6 (2008), pp. 4375-4384 
     NPL 2: IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 42, NO. 4, APRIL 1994 
     NPL 3: J.Appl.Phys., Vol. 103, 124514 (2008) 
     NPL 4: J Infrared Milli Terahz Waves (2014) 35:425-431 
     SUMMARY OF THE INVENTION 
     The first aspect of the invention is a semiconductor element comprising: an antenna array that is provided with a plurality of antennas each including a semiconductor layer having an electromagnetic wave gain or carrier nonlinearity with respect to a terahertz wave; and a coupling line that synchronizes adjacent antennas in the antenna array with each other at a frequency of the terahertz wave, wherein the coupling line includes a plurality of first regions connected to the adjacent antennas respectively and a second region provided between the plurality of first regions, wherein the second region has impedance different from impedance of each of the first regions, and wherein the second region has a loss larger than a loss of the individual first region at a frequency other than a resonance frequency of the antenna array. 
     The second aspect of the invention is a semiconductor element comprising: an antenna array that is provided with a plurality of antennas each including a semiconductor layer having an electromagnetic wave gain or carrier nonlinearity with respect to a terahertz wave; and a coupling line that synchronizes adjacent antennas in the antenna array with each other at a frequency of the terahertz wave, wherein the coupling line includes first regions connected to the adjacent antennas respectively and a second region provided between the first regions, wherein the second region has impedance different from impedance of each of the first regions, and wherein a loss difference between the individual first region and the second region at a resonance frequency of the antenna array is smaller than a loss difference between each of the first regions and the second region at a frequency other than the resonance frequency of the antenna array. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS.  1 A to  1 D  illustrate semiconductor element circuits according to Embodiment 1; 
         FIGS.  2 A to  2 D  illustrate configurations of a semiconductor element  100 ; 
         FIGS.  3 A to  3 C  illustrate a configuration of the semiconductor element  100 ; 
         FIGS.  4 A and  4 B  illustrate an analysis result of the semiconductor element  100 ; 
         FIGS.  5 A to  5 D  illustrate a configuration of a semiconductor element  200 . 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Embodiment 1 
     Hereinafter, a semiconductor element  100  according to Embodiment 1 will be described. The semiconductor element  100  generates (oscillates) or detects a terahertz wave (an electromagnetic wave in a frequency range of at least 30 GHz and not more than 30 THz) having a frequency (resonance frequency; oscillation frequency) f THz . In the following description, an example in which the semiconductor element  100  is used as an oscillator will be described. The length of each component in a lamination direction of the semiconductor element  100  is referred to as “thickness” or “height”. 
     Description of Circuit Configuration of Semiconductor Element 
     First, a circuit configuration of the semiconductor element  100  will be described below.  FIG.  1 A  illustrates an equivalent circuit of the semiconductor element  100 .  FIG.  1 D  illustrates an equivalent circuit of bias circuits V a  and V b  included in the semiconductor element  100 . 
     The semiconductor element  100  includes an antenna array provided with a plurality of antennas. In the present embodiment, the semiconductor element  100  includes an antenna array in which an antenna  100   a  and an antenna  100   b  are provided adjacent to each other. The antenna  100   a  serves as both a resonator for resonating terahertz waves and a radiator for transmitting or receiving terahertz waves and includes a semiconductor  102   a  therein for generating or detecting terahertz waves (electromagnetic waves). The antenna  100   b  has the same configuration as that of the antenna  100   a . Hereinafter, the configuration of the antenna  100   a  will be described in detail, and detailed descriptions of the same constituent elements of the antenna  100   b  as those of the antenna  100   a  will be omitted. 
     While the semiconductor element  100  provided with two antennas will be described in the present embodiment, the number of antennas may be three or more. For example, an array in which antennas are arranged in a 3×3 matrix or a linear array in which three antennas are linearly arranged in a vertical or horizontal direction may be used. The semiconductor element  100  may have an antenna array in which antennas are arranged in an m×n matrix (m≥2, n≥2). These antennas may be arranged at a pitch that is an integer multiple of the wavelength of the terahertz wave having a frequency f THz . 
     In the following description, at each end of the reference numerals of constituent members belonging to the antenna  100   a  and the antenna  100   b , an alphabet indicating the corresponding antenna is added. More specifically, “a” is added to the end of the reference numerals of the constituent member included in the antenna  100   a , and “b” is added to the end of the reference numerals of the constituent member included in the antenna  100   b.    
     As illustrates in  FIG.  1 A , in the antenna  100   a , the semiconductor  102   a , a resistor R a , which is determined by radiation and a conductive loss of the antenna, and LC components (a capacitor C a  and an inductor L a ), which is determined by a structure, are connected in parallel. In addition, a bias circuit V a  for supplying a bias signal to the semiconductor  102   a  is connected in parallel with the semiconductor  102   a.    
     The semiconductor  102   a  has an electromagnetic wave gain or carrier nonlinearity (nonlinearity of a current corresponding to a voltage change in current-voltage characteristics) with respect to a terahertz wave. In the present embodiment, a resonant tunneling diode (RTD), which is a typical semiconductor having an electromagnetic wave gain in a frequency band of the terahertz wave, is used as the semiconductor  102   a . The semiconductor  102   a  includes a circuit in which differential negative resistance and diode capacitance of the RTD are connected in parallel (not illustrated). 
     Similarly to the antenna  100   a , the antenna  100   b  is constituted by a circuit in which a semiconductor  102   b , a resistor R b , LC components (C b  and L b ), and a bias circuit V b  are connected in parallel. Each antenna individually transmits or receives a terahertz wave having a frequency f THz . 
     The bias circuit V a  includes a power supply for supplying a bias signal to the semiconductor  102   a  of the antenna  100   a  and a stabilization circuit, and the bias circuit V b  includes a power supply for supplying a bias signal to the semiconductor  102   b  of the antenna  100   b  and a stabilization circuit. As illustrated in  FIG.  1 D , the bias circuits V a  and V b  include a shunt resistor  121 , a wiring  122 , a power supply  123 , and a capacitor  124  respectively. 
     The shunt resistor  121  is connected in parallel with the semiconductor  102   a / 102   b . The capacitor  124  is connected in parallel with the shunt resistor  121 . The power supply  123  supplies a current needed for driving the semiconductor  102   a / 102   b  and adjusts a bias signal corresponding to the semiconductor  102   a / 102   b . When an RTD is used for the semiconductor  102   a / 102   b , the bias signal is selected from voltages in a differential negative resistance region of the RTD. The shunt resistor  121  and the capacitor  124  of the bias circuit V a /V b  reduces parasitic oscillation of a relatively low resonance frequency (typically in a frequency band from DC to 10 GHz) caused by the bias circuit V a /V b . 
     Adjacent antennas  100   a  and  100   b  are coupled to each other by a coupling line  109 . The coupling line  109  reduces occurrence of multi-mode resonance and realizes efficient generation or detection of a terahertz wave. Hereinafter, a configuration of the coupling line  109  will be described in more detail. 
     Description of Configuration of Coupling Line 
     The coupling line  109  includes a plurality of first regions connected to the respective adjacent antennas and a second region provided between the plurality of first regions. More specifically, the coupling line  109  includes a first region  1091   a  connected to the antenna  100   a , a first region  1091   b  connected to the antenna  100   b , and a second region  1092  provided between the first regions  1091   a  and  1091   b.    
     The second region  1092  has impedance different from that of the first regions  1091   a  and  1091   b , and a loss of the second region  1092  is larger than that of the first regions  1091   a  and  1091   b  at a frequency other than the resonance frequency of the antenna array. 
     In addition, a loss difference between the first regions  1091   a  and  1091   b  and the second region  1092  at a resonance frequency of the antenna array is smaller than a loss difference between the first regions  1091   a  and  1091   b  and the second region  1092  at a frequency other than the resonance frequency of the antenna array. At the resonance frequency of the antenna array, a loss difference between the first regions  1091   a  and  1091   b  and the second region  1092  may be smaller than a predetermined threshold. As the predetermined threshold, a value that indicates that there is practically no difference between the losses can be adopted. 
     Further, when the phase of a component in the resonance frequency of the antenna array is shifted in the electromagnetic field that synchronizes the adjacent antennas  100   a  and  100   b , the loss of the second region  1092  is larger than that of the first regions  1091   a  and  1091   b  for such a component. 
     As described above, since the coupling line  109  includes the second region  1092  having impedance different from that of the first regions  1091   a  and  1091   b , only a frequency other than a desired operating frequency f THz  of the terahertz wave and an out-of-phase component of the operating frequency f THz  are selectively lost. As a result, occurrence of resonance (multi-mode resonance) in a plurality of frequency bands and asynchronization due to a phase shift between the antennas are reduced. 
     From the viewpoint of the radiation efficiency of the antenna, the second region  1092  is preferably disposed (connected) at a position corresponding to the antinode of the electric field of a terahertz wave having a resonance frequency f THz  standing in the coupling line  109 . Here, the “position corresponding to the antinode of the electric field of a terahertz wave having a resonance frequency f THz  standing in the coupling line  109 ” refers to, for example, a position where the electric field intensity of the terahertz wave having the resonance frequency f THz  standing in the coupling line  109  is maximized. In other words, the position refers to a position where the current intensity of the terahertz wave having the resonance frequency f THz  standing in the coupling line  109  decreases by approximately one digit. 
     The impedance of the second region  1092  of the coupling line  109  is selected to be a value in a range from a value equal to or slightly smaller than an absolute value of the differential negative resistance of the connected semiconductors  102   a  and  102   b  to a value approximately 100 times the absolute value. Considering that a typical value of the negative resistance of the RTD used in the terahertz band is in a range of 0.1 to 1000Ω, the value of the impedance of the second region  1092  is set in a range of 0.1 to 100 kΩ. 
       FIG.  1 B  illustrate s a modification of the equivalent circuit of the semiconductor element  100 . In this example, a thin-film resistor R c  is connected between the first regions  1091   a  and  1091   b , which are transmission lines, as an upper conductor of the second region  1092 . A value for the resistor R c  is selected to be a value in a range from a value equal to or slightly smaller than an absolute value of the differential negative resistance of the connected semiconductors  102   a  and  102   b  to a value approximately 100 times the absolute value. Considering that a typical value of the negative resistance of the RTD used in the terahertz band is in a range of 0.1 to 1000Ω, the value of the resistor R c  is set in a range of 1 to 100 kΩ. 
       FIG.  1 C  illustrates an equivalent circuit of a semiconductor element  200  as a modification of the present embodiment. The semiconductor element  200  has an antenna  200   a  including a semiconductor  202   a  and an antenna  200   b  including a semiconductor  202   b  that are coupled to each other by a coupling line  209 . In the present modification, the coupling line  209  includes first regions  2091   a   1 ,  2091   a   2 ,  2091   b   1 , and  2091   b   2  and a second region  2092  provided between the first regions  2091   a   2  and  2091   b   2 . 
     The coupling line  209  is connected to shunt elements  230   a  and  230   b  connected in parallel with semiconductors  202   a  and  202   b , respectively. Since the shunt elements  230   a  and  230   b  are arranged in this manner, short circuit is achieved for a terahertz wave having a frequency other than a desired operating frequency f THz  of the terahertz wave so that the impedance of the semiconductor element  200  is lowered at such a frequency. 
     As described in the present modification, by disposing the shunt elements in addition to having the second region  2092  that has impedance different from that of the first regions, the effect of reducing the occurrence of resonance (multi-mode resonance) in a plurality of frequency bands is further enhanced. 
     From the viewpoint of radiation efficiency of the antennas, the shunt elements  230   a  and  230   b  are preferably disposed (connected) at positions corresponding to the nodes of the electric field of a terahertz wave having a resonance frequency f THz  standing in the coupling line  109 . Here, the “positions corresponding to the nodes of the electric field of a terahertz wave having a resonance frequency f THz  standing in the coupling line  209 ” refer to, for example, positions where the electric field intensity of the terahertz wave having the resonance frequency f THz  standing in the coupling line  209  decreases by approximately one digit. 
     As illustrated in  FIG.  1 C , the shunt elements  230   a  and  230   b  each include a resistor R d  and a capacitor C d  connected in series. A value for the resistor R d  is selected to be a value equal to or slightly smaller than an absolute value of the combined differential negative resistance of the semiconductors  202   a  and  202   b  connected in parallel. Further, a value of the capacitor C d  is set to have impedance equal to or slightly lower than an absolute value of the combined differential negative resistance of the semiconductors  202   a  and  202   b  connected in parallel. That is, it is preferable that each of the values of the resistor R d  and the capacitor C d  be set to have impedance lower than an absolute value of the negative resistance (impedance) corresponding to the gains of the semiconductors  202   a  and  202   b . Considering that a typical value of the negative resistance of the RTD used in the terahertz band is in a range of 0.1 to 1000Ω, the value of the resistor R d  is set in a range of 0.1 to 1000 Ω. To obtain a shunt effect in a frequency range from 10 GHz to 1000 GHz, the value of the capacitor C d  is typically set in a range of 0.1 to 1000 pF. The condition of the impedance of the resistor R d  and the capacitor C d  with respect to the negative resistance of the RTD is satisfied in a frequency band lower than the resonance frequency f THZ . 
       FIGS.  2 A to  2 D  illustrate specific configurations of the coupling line  109  of the semiconductor element according to Embodiment 1. The coupling line  109  is constituted by a microstrip line having a structure in which a dielectric layer  104  is sandwiched between an upper conductor (third conductor layer) laminated on the dielectric layer  104  and a first conductor layer  106  serving as GND. In the semiconductor element  100 , in order to synchronize adjacent antennas with each other at the resonance frequency f THz , the antennas are coupled by DC coupling. That is, third layers  110   a  and  110   b , which are upper conductors of the coupling line  109  that couple the antennas  100   a  and  100   b , are directly connected to patch conductors of the antennas  100   a  and  100   b  (second conductor layers  103   a  and  103   b  in  FIG.  3 A ). In the semiconductor element  100 , the third conductor layers  110   a  and  110   b  and the second conductor layers  103   a  and  103   b  are formed in the same layer. 
       FIG.  2 A  illustrates a configuration example of the coupling line  109 . In the present example, the first regions  1091   a  and  1091   b  in the coupling line  109  are the microstrip line and have a structure in which the dielectric layer  104  is sandwiched between the third conductor layers  110   a  and  110   b  and the first conductor layer  106 . The second region  1092  is a stripline and has a structure in which the dielectric layer  104  is sandwiched between the upper conductor of the third conductor layer (resistance layer)  151  and the first conductor layer  106 . The resistance layer  151  is disposed between the third conductor layers  110   a  and  110   b  and is electrically and physically connected to each of the third conductor layers  110   a  and  110   b , thereby forming the coupling line  109  (microstrip line) that couples the antennas  100   a  and  100   b.    
     Since the upper conductors of the first regions  1091   a  and  1091   b  are low-resistance conductor layers and the upper conductor of the second region  1092  is a high-resistance resistor, the second region  1092  has impedance higher than that of the first regions  1091   a  and  1091   b  and has a large loss at a high frequency. Typically, the effect of the present disclosure can be obtained when the impedance of the second region  1092  is on the order of 2 times to 100 times the impedance of the first regions  1091   a  and  1091   b . For example, the value of the impedance is set in a range of 1 to 100 kΩ. 
     Conventionally, the coupling line is composed of lines having the same characteristic impedance and does not have a function of selecting a frequency. However, in the semiconductor element  100  according to the present disclosure, lines having different impedance are arranged depending on the electric field distribution of the lines so that a loss is selectively given at a frequency other than a specific frequency and phase. 
       FIG.  2 B  illustrates another configuration example of the coupling line  109 . In the present example, the upper conductor of the second region is a conductor layer  152  that is made of the same material as the third conductor layers  110   a  and  110   b  and is thin and narrow. The conductor layer  152  is disposed between the third conductor layers  110   a  and  110   b  and electrically connected to each of the third conductor layers  110   a  and  110   b . In this case, too, since the resistance of the conductor layer  152  is higher, the second region  1092  has impedance higher than that of the first regions  1091   a  and  1091   b  and has a larger loss at a high frequency. As long as the second region  1092  has higher impedance, the conductor layer  152  may have a configuration that only satisfies either the condition that the conductor layer  152  is thinner or the condition that the conductor layer  152  is narrower compared with the third conductor layers  110   a  and  110   b.    
       FIG.  2 C  illustrates still another configuration example of the coupling line  109 . The coupling line  109  of the present example includes dielectrics  104   a  and  104   b  each having a small loss at a high frequency in the first regions  1091   a  and  1091   b , respectively, and a dielectric  104   c  having a large loss at a high frequency in the second region  1092 . Specifically, the dielectric  104   c  in the second region  1092  is made of a material having a larger loss at a high frequency compared with the dielectrics  104   a  and  104   b  in the first regions  1091   a  and  1092   b . In this configuration, too, the second region  1092  has impedance higher than that of the first regions  1091   a  and  1091   b  and has a larger loss at a high frequency. 
       FIG.  2 D  illustrates still another configuration example of the coupling line  109 . The coupling line  109  of the present example includes thick dielectrics  104   a  and  104   b  in the first regions  1091   a  and  1091   b , respectively, and includes a thin dielectric  104   c  in the second region  1092 . Typically, each of the dielectrics  104   a  and  104   b  preferably has a layer thickness in a range of 1 to 30 μm. Typically, the dielectric  104   c  preferably has a layer thickness in a range of 0.01 to 1 μm, which is thinner than the dielectrics  104   a  and  104   b . As described above, the second region  1092  is a line having a low-impedance structure that generates a leakage electric field due to a capacitance structure in which the thin dielectric  104   c  is sandwiched between a conductor  153  and the first conductor layer  106 . By using such a low-impedance line as the second region  1092 , a configuration in which the loss of the second region  1092  is larger than that of the first regions  1091   a  and  1091   b  can be realized. Typically, the dielectric  104   c  preferably has a thickness in a range of 0.01 to 1 μm. 
     Description of Structure of Semiconductor Element 
     A specific structure of the semiconductor element  100  will be described with reference to  FIGS.  3 A to  3 C .  FIG.  3 A  is a top view of the semiconductor element  100 .  FIG.  3 B  is a cross-sectional view of the semiconductor element  100 , taken along line A-A′ in  FIG.  3 A , and  FIG.  3 C  is a cross-sectional view of the semiconductor element  100 , taken along line B-B′ in  FIG.  3 A . 
     The antenna  100   a  includes a substrate  113 , a first conductor layer  106 , a semiconductor layer  115   a , an electrode  116   a , a conductor  117   a , a dielectric layer  104 , and a second conductor layer  103   a . As illustrated in  FIG.  3 B , the antenna  100   a  has a configuration in which the dielectric layer  104  composed of three layers of a first dielectric layer  1041 , a second dielectric layer  1042 , and a third dielectric layer  1043  is sandwiched between two conductors, which are the first conductor layer  106  and the second conductor layer  103   a . Such a configuration is known as a microstrip antenna. In the present embodiment, an example in which the antennas  100   a  and  100   b  are used as patch antennas, which are typical microstrip resonators, will be described. 
     The second conductor layer  103   a  is a patch conductor of the antenna  100   a  and is disposed so as to face the first conductor layer  106  via the dielectric layer  104  (semiconductor layer  115   a ). The second conductor layer  103   a  is electrically connected to the semiconductor layer  115   a . The antenna  100   a  is set to be a resonator in which the second conductor layer  103   a  has a width of λ THz /2 in an A-A′ direction (resonance direction). The first conductor layer  106  is a ground conductor and is electrically grounded. Here, λ THz  is an effective wave length of a terahertz wave resonating in the dielectric layer  104  of the antenna  100   a  and is expressed by λ THz =λ 0 ×ε r   −1/2 , where λ 0  is a wave length of the terahertz wave in vacuum, and ε r  is an effective relative permittivity of the dielectric layer  104 . 
     The semiconductor layer  115   a  corresponds to the semiconductor  102   a  of the equivalent circuit illustrated in  FIG.  1 A  and includes an active layer  101   a  constituted by a semiconductor having an electromagnetic wave gain or carrier nonlinearity with respect to a terahertz wave. In the present embodiment, an example in which an RTD is used as the active layer  101   a  will be described. Hereinafter, the active layer  101   a  will be described as an RTD  101   a.    
     The semiconductor layer  115   a  is disposed on the first conductor layer  106  laminated on the substrate  113 , and the semiconductor layer  115   a  and the first conductor layer  106  are electrically connected to each other. Note that the semiconductor layer  115   a  and the first conductor layer  106  are preferably connected to each other with low resistance so that ohmic loss is reduced. 
     The RTD  101   a  has a resonant tunneling structure layer including a plurality of tunnel barrier layers. The RTD  101   a  has a multi-quantum-well structure in which a quantum-well layer is provided between a plurality of tunnel barriers and terahertz waves are generated by intersubband transition of carriers. The RTD  101   a  has an electromagnetic wave gain in a frequency range of terahertz waves based on a photon-assisted tunneling phenomenon in a differential negative resistance region of current-voltage characteristics and self-oscillates in the differential negative resistance region. The RTD  101   a  is disposed at a position shifted from the center of gravity of the second conductor layer  103   a  by 40% in the resonance direction (that is, the A-A′ direction). 
     The antenna  100   a  is an active antenna in which the semiconductor layer  115   a  including the RTD  101   a  and a patch antenna are integrated. A frequency f THz  of the terahertz wave oscillated singly from the antenna  100   a  is determined as the resonance frequency for all parallel resonance circuits in each of which the reactance of the patch antenna and the reactance of the semiconductor layer  115   a  are combined. Specifically, based on the equivalent circuit of the oscillator described in NPL 1, a frequency that satisfies an amplitude condition expressed by Equation (1) and a phase condition expressed by Equation (2) is determined as the resonance frequency f THz  for the resonance circuit in which the admittance of the RTD and the admittance of the antenna (Y RTD  and Y aa ) are combined. 
         Re[Y   RTD   ]+Re[Y   aa ]≤0  (1)
 
         Im[Y   RTD   ]+Im[Y   aa ]=0  (2)
 
     In the above equations, Y RTD  represents the admittance of the semiconductor layer  115   a , Re represents a real part, and Im represents an imaginary part. Since the semiconductor layer  115   a  includes the RTD  101   a , which is a negative resistance semiconductor element, as an active layer, Re[Y RTD ] has a negative value. Y aa  represents the total admittance of the antenna  100   a  viewed from the semiconductor layer  115   a . Therefore, the components R a , C a , and L a  of the antenna in the equivalent circuit in  FIG.  1 A  are the main circuit elements of Y aa , and the differential negative resistance and diode capacitance of the semiconductor  102   a  are the main circuit elements of Y RTD . 
     As another example of the active layer  101   a , a quantum-cascade laser (QCL) having a multi-layer structure of several hundreds to several thousands of semiconductor layers may be used. In this case, the semiconductor layer  115   a  is a semiconductor layer including a QCL structure. As the active layer  101   a , a negative resistance semiconductor element such as a Gunn diode or an impact avalanche and transit time (IMPATT) diode, which is often used in a millimeter-wave band, may be used. In addition, as the active layer  101   a , a high-frequency element such as a transistor having one terminal terminated may be used. For example, a heterojunction bipolar transistor (HBT), a compound semiconductor-based field-effect transistor (FET), a high-electron-mobility transistor (HEMT), or the like is preferable. Further, as the active layer  101   a , a differential negative resistance of a Josephson device using a superconductor may be used. 
     The desirable dielectric layer  104  is capable of forming a thick film (typically, a film having a thickness of 3 μm or more), has a low loss and low permittivity in a terahertz band, and has excellent fine processability (processability by planarization or etching). In a microstrip resonator such as a patch antenna, by increasing the thickness of the dielectric layer  104 , conductor loss can be reduced, and radiation efficiency can be improved. The thicker the dielectric layer  104  is, the greater the radiation efficiency becomes. However, if the dielectric layer  104  is too thick, multi-mode resonance occurs. Therefore, the thickness of the dielectric layer  104  is preferably one-tenth or less of the oscillation wavelength. 
     Miniaturization of the diode and higher current density are needed to achieve higher frequency and higher output of the oscillator. For this reason, the dielectric layer  104  is also expected to reduce leakage current and to take measures against migration as an insulating structure of the diode. In the present embodiment, to satisfy these objects, the dielectric layer  104  includes a first dielectric layer  1041  and a second dielectric layer  1042 , which are two types of dielectric layers made of different materials. 
     An organic dielectric material such as BCB (benzocyclobutene, manufactured by the Dow Chemical Company, ε r1 =2, where, ε r1  is relative permittivity of the first dielectric layer  1041 ), polytetrafluoroethylene, or polyimide is preferably used for the first dielectric layer  1041 . The first dielectric layer  1041  may be made of an inorganic dielectric material such as a TEOS oxide film or spin-on-glass, which can be formed to be relatively thick and has low permittivity. 
     The second dielectric layer  1042  is expected to have an insulating property (a property of behaving as an insulator or a high-resistance resistor that does not conduct electricity with respect to a DC voltage), a barrier property (a property of preventing diffusion of a metal material used for an electrode), and processability (a property of being processable with submicron accuracy). To satisfy these properties, an inorganic insulating material such as silicon oxide (ε r2 =4), silicon nitride (ε r2 =7), aluminum oxide, or aluminum nitride is preferably used for the second dielectric layer  1042 . Here, ε r2  is relative permittivity of the second dielectric layer  1042 . 
     From the viewpoint of impedance matching between the antenna and air (space), it is preferable that the permittivity difference between the antenna and the air be small. Thus, the first dielectric layer  1041  is preferably made of a material that is different from that of the second dielectric layer  1042  and that has relative permittivity lower than that of the second dielectric layer  1042  (ε r1 &lt;ε r2 ). 
     The electrode  116   a  is disposed on the opposite side of the semiconductor layer  115   a  from the side on which the first conductor layer  106  is disposed. The electrode  116   a  and the semiconductor layer  115   a  are electrically connected to each other. The semiconductor layer  115   a  and the electrode  116   a  are embedded in the second dielectric layer  1042  (the second dielectric layer  1042  and the third dielectric layer  1043 ). More specifically, the peripheries of the semiconductor layer  115   a  and the electrode  116   a  are covered with the second dielectric layer  1042  (the second dielectric layer  1042  and the third dielectric layer  1043 ). 
     The conductor layer ohmically connected to the semiconductor layer  115   a  is suitable for the electrode  116   a  to reduce ohmic loss and RC delay caused by series resistance. When the electrode  116   a  is used as an ohmic electrode, for example, Ti/Pd/Au, Ti/Pt/Au, AuGe/Ni/Au, TiW, Mo, ErAs, or the like is suitably used as the material of the electrode  116   a.    
     In addition, when the region of the semiconductor layer  115   a  that is in contact with the electrode  116   a  is a semiconductor doped with an impurity at a high concentration, the contact resistance can be further reduced, which is suitable for achieving higher output and higher frequency. Since an absolute value of negative resistance indicating the magnitude of a gain of the RTD  101   a  used in a terahertz band is typically on the order of 1 to 100Ω, the loss of electromagnetic waves may be reduced to 1% or less. Thus, the contact resistance in the ohmic electrode may be reduced to 1Ω or less as a target. 
     In addition, in order to operate in the terahertz band, the width of the semiconductor layer  115   a  electrode  116   a ) is set to approximately 0.1 to 5 μm as a typical value. Thus, the resistivity is set to 10Ω·μm 2  or less, and the contact resistance is suppressed to a range of 0.001 to several Ω. As another embodiment, the electrode  116   a  may be made of metal that is not ohmic but Schottky-connected. In this case, a contact interface between the electrode  116   a  and the semiconductor layer  115   a  exhibits a rectifying property, and the antenna  100   a  has a suitable configuration to be a detector for terahertz waves. In the following description of the present embodiment, an ohmic electrode is used as the electrode  116   a.    
     In the lamination direction from the RTD 101   a , as illustrated in  FIG.  2 B , the first conductor layer  106 , the semiconductor layer  115   a , the electrode  116   a , the conductor  117   a , and the second conductor layer  103   a  are laminated in this order from the substrate  113  side. 
     The conductor  117   a  is formed inside the dielectric layer  104 , and the second conductor layer  103   a  and the electrode  116   a  are electrically connected via the conductor  117   a . If the width of the conductor  117   a  is too large, the resonance characteristics of the antenna  100   a  are deteriorated, and the radiation efficiency is reduced due to an increase in parasitic capacitance. Therefore, it is preferable that the conductor  117   a  have a width that does not interfere with the resonance electric field, that is, typically, λ/10 or less is suitable. Further, the width of the conductor  117   a  can be reduced to such an extent that the series resistance is not increased, that is, to approximately twice the skin depth, as a guide. Considering that the series resistance is reduced to a level not exceeding 1Ω, the width of the conductor  117   a  is typically in a range of at least 0.1 μm and not more than 20 μm, as a guide. 
     A structure that electrically connects upper and lower layers, as with the conductor  117   a , is called a via. The first conductor layer  106  and the second conductor layer  103   a  serve not only as members that constitute the patch antenna but also as electrodes for injecting a current into the RTD  101   a  by being connected to the via. The conductor  117   a  is preferably made of a material having a resistivity of 1×10 −6 Ω·m or less. Specifically, metals and metallic compounds such as Ag, Au, Cu, W, Ni, Cr, Ti, Al, an AuIn alloy, and TiN are preferably used as the material of the conductor  117   a.    
     The second conductor layer  103   a  is connected to lines  108   a   1  and  108   a   2 . The lines  108   a   1  and  108   a   2  are lead lines each connected to a bias line including the bias circuit V a . The width of each of the lines  108   a   1  and  108   a   2  is set to be narrower than that of the second conductor layer  103   a . Here, the width refers to a width in the resonance direction (=A-A′ direction) of an electromagnetic wave in the antenna  100   a . For example, the width of the line  108   a   1 / 108   a   2  is preferably equal to or less than one-tenth of the effective wave length λ. (λ/10 or less) of the terahertz wave having the resonance frequency f THz  standing in the antenna  100   a . This is because, from the viewpoint of improving the radiation efficiency, it is preferable that the lines  108   a   1  and  108   a   2  have such dimensions and be disposed at such positions that do not interfere with the resonance electric field in the antenna  100   a.    
     The lines  108   a   1  and  108   a   2  are preferably disposed at nodes of the electric field of a terahertz wave having a resonance frequency f THz  standing in the antenna  100   a . The lines  108   a   1  and  108   a   2  have impedance sufficiently higher than an absolute value of the differential negative resistance of the RTD  101   a  in the frequency band near the resonance frequency f THz . In other words, the lines  108   a   1  and  108   a   2  are connected to the antenna so as to have high impedance with respect to the RTD at the resonance frequency f THz . In this case, each antenna of the semiconductor element  100  is isolated (separated) from the antenna  100   a  in a path via a bias line including the lines  108   a   1  and  108   a   2  and the bias circuit V a  at the frequency f THz . As a result, the current of the resonance frequency f THz  induced in each antenna is prevented from acting (affecting) on another adjacent antenna via the bias line. In addition, this configuration also reduces the interference between the electric field of the resonance frequency f THz  standing in the antenna  100   a  and these power feeding members. 
     Each of the bias circuits V a  and V b  includes the shunt resistor  121 , the wiring  122 , the power supply  123 , and the capacitor  124  (see  FIG.  1 D ). The wiring  122  is illustrated as an inductor in  FIG.  1 D  because the wiring  122  always includes a parasitic inductance component. The power supply  123  supplies bias signals needed to drive the RTD  101   a  and the RTD  101   b . The voltage of the bias signal is typically selected from the voltage in the RTD differential negative resistance region used in the RTDs  101   a  and  101   b . In the case of the antenna  100   a , the bias voltages from the bias circuits V a  and V b  are supplied to the RTD  101   a  in the antenna  100   a  via the lines  108   a   1  and  108   a   2 . 
     Here, the shunt resistor  121  and the capacitor  124  of each of the bias circuits V a  and V b  serve to reduce parasitic oscillation at a relatively low resonance frequency (typically in a frequency band from DC to 10 GHz) caused by the bias circuits V a  and V b . A value of the shunt resistor  121  is selected to be a value equal to or slightly smaller than an absolute value of the combined differential negative resistance of the RTDs  101   a  and  101   b  connected in parallel. Similarly to the shunt resistor  121 , a value of the capacitor  124  is also set to have impedance equal to or slightly lower than an absolute value of the combined differential negative resistance of the RTDs  101   a  and  101   b  connected in parallel. That is, by providing these shunt elements, a bias circuit  120  is set to have impedance lower than an absolute value of the combined negative resistance corresponding to the gain in a frequency band from DC to 10 GHz. Generally, it is preferable that the capacitor  124  have a large value within the range described above, and in the present embodiment, a capacitance of approximately several tens of pF is used. The capacitor  124  is a de-coupling capacitor and may use, for example, a metal-insulator-metal (MIM) structure in which the antenna  100   a  and the substrate are integrally formed. 
     Description of Antenna Array 
     The semiconductor element  100  has an antenna array in which two antennas  100   a  and  100   b  are E-plane coupled. Each antenna individually oscillates a terahertz wave having a frequency f THz . Adjacent antennas are mutually coupled by the coupling line  109  and are mutually injection-locked at the resonance frequency f THz  of the terahertz wave. 
     The mutual injection locking means that all of the plurality of self-excited oscillators oscillate in pull-in synchronization by interaction. For example, the antenna  100   a  and the antenna  100   b  are mutually coupled by the coupling line  109 . “Mutually coupled” refers to a phenomenon in which a current induced in a certain antenna acts on another adjacent antenna and changes transmission and reception characteristics of each other. By synchronizing the mutually coupled antennas with the same phase or the opposite phase, the electromagnetic field between the antennas is strengthened or weakened by the mutual injection-locking phenomenon, and the increase or decrease of the antenna gain can be adjusted. 
     The oscillation condition of the semiconductor element  100  having the antenna array can be determined based on the condition for mutual injection-locking in a configuration in which two or more individual RTD oscillators are coupled, which is described in J.Appl.Phys.,Vol.103,124514 (2008) (Non Patent Literature 3). Specifically, the oscillation condition of the antenna array in which the antenna  100   a  and the antenna  100   b  are coupled by the coupling line  109  will be considered. In this case, two oscillation modes of positive-phase mutual injection locking and opposite-phase mutual injection locking occur. The oscillation condition of the positive-phase mutual injection locking oscillation mode (even mode) is expressed by Equations (4) and (5), and the oscillation condition of the opposite-phase mutual injection locking oscillation mode (odd mode) is expressed by Equations (6) and (7). 
       Positive phase (even mode): frequency f=f even   
     
       
      
       Y 
       even 
       =Y 
       aa 
       +Y 
       ab 
       +Y 
       RTD 
      
     
         Re ( Y   even )≤0  (4)
 
         Im ( Y   even )=0  (5)
 
       Opposite phase (odd mode): frequency f=f odd   
     
       
      
       Y 
       odd 
       =Y 
       aa 
       +Y 
       ab 
       +Y 
       RTD 
      
     
         Re ( Y   odd )≤0  (6)
 
         Im ( Y   odd )=0  (7)
 
     In the above equations, Y ab  represents mutual admittance between the antenna  100   a  and the antenna  100   b . Y ab  is proportional to a coupling constant representing the strength of coupling between the antennas. Ideally, it is preferable that the real part of −Y ab  be large and the imaginary part be zero. In the semiconductor element  100  of the present embodiment, the coupling is performed under the condition of the positive-phase mutual injection locking, and the resonance frequency f THz ≈f even . Similarly, the other antennas are coupled by the coupling line  109  so as to satisfy the condition of the positive-phase mutual injection locking described above. 
     The coupling line  109  is constituted by a microstrip line having a structure in which the dielectric layer  104  is sandwiched between the third conductor layer  110  laminated on the dielectric layer  104  and the first conductor layer  106 . In the semiconductor element  100 , the antennas are coupled by DC coupling. In order to synchronize the antennas with each other at the resonance frequency f THz , the third conductor layer  110 , which is the upper conductor of the coupling line  109  that couples the antenna  100   a  and the antenna  100   b , is directly connected to the second conductor layer  103   a  and to the second conductor layer  103   b . In the semiconductor element  100 , the third conductor layer  110  and the second conductor layers  103   a  and  103   b  are formed in the same layer. 
     With such a structure including the coupling line  109 , the adjacent antennas  100   a  and  100   b  are coupled to each other and operate in synchronization with each other at the frequency f THz  of the terahertz wave oscillated. In the antenna array synchronized by DC coupling, since the adjacent antennas can be synchronized by strong coupling, a synchronization operation by pull-in is easily performed, and variations in frequency and phase of each antenna are less likely to occur. 
     In the semiconductor element  100 , the antenna array and the coupling line  109  are formed on the same substrate. The coupling line  109  is constituted by a microstrip line having a structure in which the dielectric layer  104  is sandwiched between the third conductor layers  110   a ,  110   b , and  110   c  as well as conductor layers  152   a  and  152   b  and the first conductor layer  106  serving as GND. The third conductor layer  110   a , the conductor layer  152   a , the third conductor layer  110   b , the conductor layer  152   b , and the third conductor layer  110   c  are formed of the same material (Ti/Au (=5/300 nm)) in the same layer and are connected in this order. Each of the third conductor layers  110   a ,  110   b , and  110   c  is 10 μm wide and 150 μm long, and a microstrip line having a characteristic impedance of 50Ω is formed. Each of the conductor layers  152   a  and  152   b  is 1 μm wide and 3 μm long, and a microstrip line having a characteristic impedance of 100Ω is formed. 
     The conductor layers  152   a  and  152   b  are disposed at positions corresponding to the antinodes of the electric field of a terahertz wave having a resonance frequency f THz  standing in the coupling line  109 . The microstrip line having the conductor layers  152   a  and  152   b , which correspond to the second region  1092 , as the upper conductors has impedance higher than that of the first regions and is configured such that only a frequency other than the operating frequency f THz  and an out-of-phase component of the operating frequency f THz  are selectively lost. 
     In the semiconductor element  100 , the antennas are coupled by DC coupling so as to synchronize the antennas with each other at the resonance frequency f THz . That is, the third conductor layers  110   a  and  110   b , which are upper conductors of the coupling line  109  that couples the antennas  100   a  and  100   b , are directly connected to the second conductor layers  103   a  and  103   b , respectively, which are patch conductors of the antennas  100   a  and  100   b . In the semiconductor element  100 , the third conductor layers  110   a  and  110   b  and the second conductor layers  103   a  and  103   b  are formed in the same layer. 
     Here, the “positions corresponding to the antinodes of the electric field of a terahertz wave having a resonance frequency f THz  standing in the coupling line  109 ” refer to, for example, positions where the electric field intensity of the terahertz wave having the resonance frequency f THz  standing in the coupling line  109  is maximized. In other words, the positions refer to positions where the current intensity of the terahertz wave having the resonance frequency f THz  standing in the coupling line  109  decreases by approximately one digit. As a result, occurrence of resonance (multi-mode resonance) in a plurality of frequency bands other than the frequency f THz  and asynchronization due to phase shift between the antennas are reduced. If the dimension of each of the conductor layers  152   a  and  152   b  is too large, the resonance characteristics of the high-frequency electric field of the frequency f THz  propagating through the coupling line are deteriorated, and the radiation efficiency is reduced due to a conductive loss. Therefore, it is preferable that the conductor layers  152   a  and  152   b  each have a width and length as small as possible and have a dimension that does not interfere with the resonance electric field, that is, typically, λ/10 or less is suitable. 
     Description of Comparison with Conventional Semiconductor Element 
       FIG.  4 A  illustrates a comparison of analysis results between the impedance of the semiconductor element  100  according to the present embodiment and the impedance of a conventional semiconductor element. In the conventional semiconductor element, a coupling line does not have the second regions  152   a  and  152   b  having different impedance. For this analysis, HFSS manufactured by ANSYS, Inc., which is a high-frequency electromagnetic field solver using a finite element method, is used. Impedance Z corresponds to the inverse of Y aa , which is the admittance of the entire structure of the antenna  100   a . Z (100Ω) represents the impedance Z in the case where the second regions  152   a  and  152   b  have different impedance as in the present embodiment. Z (no resistance) represents the impedance Z in the conventional case. Re and Im represent a real part and an imaginary part, respectively, and resonance occurs at a frequency at which the impedance of the imaginary part is 0. 
     As illustrated in  FIG.  4 A , multi-peaks have occurred in the impedance of the conventional structure, and resonance modes are likely to occur in two frequency bands near 0.42 THz and 0.52 THz. In contrast, only a single peak has occurred at a desired resonance frequency f THz =0.48 THz in the impedance of the semiconductor element  100  according to the present embodiment, that is, occurrence of multi-mode resonance is reduced. In addition, it can be seen that the semiconductor element  100  according to the present embodiment also provides an effect of suppressing the occurrence of resonance at the lower frequency band (0.3 THz or lower). 
       FIG.  4 B  illustrates an analysis example of mutual injection locking between the RTD  101   a  of the antenna  100   a  and the RTD  101   b  of the antenna  100   b  in the semiconductor element  100  according to the present invention. The horizontal axis represents time for 10 cycles, and the vertical axis represents normalized amplitude of voltages input to the RTD  101   a  and the RTD  101   b . It can be seen that, even if there is a slight phase difference, by using the semiconductor element  100  of the present invention, the electromagnetic waves oscillated by the two RTDs gradually overlap in the same phase with time, and mutual injection locking starts. 
     In the semiconductor element  100 , since the second region  1092  having different impedance is disposed in the coupling line  109 , only a frequency other than a desired operating frequency f THz  of the terahertz wave and an out-of-phase component of the operating frequency f THz  are selectively lost. As a result, multi-mode resonance in a relatively high frequency band (typically from 10 GHz to 1000 GHz) can be suppressed, and only the resonance at the desired operating frequency fTHz of the terahertz wave can be selectively stabilized. 
     Therefore, according to the present embodiment, even when the number of antennas in the antenna array is increased, a single mode operation at the operating frequency f THz  of the terahertz wave can be performed. As a result, the upper limit of the number of antennas to be arranged can be increased, and an effect of significant improvement in directivity and front strength accompanying an increase in the number of arrays can be expected. Therefore, according to the present embodiment, it is possible to provide the semiconductor element capable of efficiently generating or detecting a terahertz wave. 
     Modification 1 
     A semiconductor element  200  according to Modification 1 will be described with reference to  FIGS.  5 A to  5 D .  FIGS.  5 A to  5 D  illustrate the semiconductor element  200  according to Modification 1.  FIG.  5 A  is a top view of the semiconductor element  200 .  FIG.  5 B  is a cross-sectional view of the semiconductor element  200 , taken along line A-A′ in  FIG.  5 A .  FIG.  5 C  is a cross-sectional view of the semiconductor element  200 , taken along line B-B′ in  FIG.  5 A .  FIG.  5 D  is a cross-sectional view of the semiconductor element  200 , taken along line C-C′ in  FIG.  5 A . 
     The semiconductor element  200  includes an antenna array in which two antennas of antennas  200   a  and  200   b  are H-plane coupled. The semiconductor element  200  includes an antenna array in which antennas are coupled by AC coupling (capacitance coupling). In the configuration and structure of the antennas  200   a  and  200   b , detailed descriptions of portions similar to those of the antennas  100   a  and  100   b  in the semiconductor element  100  will be omitted. 
     As illustrated in  FIG.  5 B , a coupling line  209  is constituted by a microstrip line having a structure in which a dielectric layer  204  and a fourth dielectric layer  2044  are sandwiched between a third conductor layer  210  and a first conductor layer  206 . The dielectric layer  204  includes a first dielectric layer  2041 , a second dielectric layer  2042 , and a third dielectric layer  2043 . Second conductor layers  203   a  and  203   b  are formed in a layer between the third conductor layer  210  and the first conductor layer  206 . The third conductor layer  210 , which is the upper conductor of the coupling line  209  that couples the antenna  200   a  and the antenna  200   b , overlaps the second conductor layers  203   a  and  203   b  by a length x=5 μm near the radiation end when viewed from the lamination direction (in a plan view). In the overlapping portion, the second conductor layers  203   a  and  203   b , the fourth dielectric layer  2044 , and the third conductor layer  210  are laminated in this order. Thus, a metal-insulator-metal (MIM) capacitance structure in which the second conductor layers  203   a  and  203   b  and the third conductor layer  210  sandwich the fourth dielectric layer  2044  is formed. A DC open state is formed between the second conductor layer  203   a  and the second conductor layer  203   b , and the magnitude of the coupling is small in a low-frequency range below the resonance frequency f THz  so that inter-element isolation is ensured. The magnitude of the coupling between the antennas in the band of the resonance frequency f THz  can be adjusted by the capacitance. 
     In the semiconductor element  200 , shunt elements  2301  and  2302  are connected to the coupling line  209 . The shunt elements  2301  and  2302  are connected to the coupling line  209  through vias  2141  and  2142 , respectively. The vias  2141  and  2142  are connected to the third conductor layer  210  at nodes of the high-frequency electric field of the resonance frequency f THz  standing in the coupling line  209 . As a result, short-circuiting can be achieved at a frequency other than the resonance frequency f THz  of the terahertz wave so that occurrence of multi-mode resonance is reduced. 
     The third conductor layer  210  of the coupling line  209  and resistor layers  2191  and  2192  laminated on the first dielectric layer  2041  are connected to each other through the vias  2141  and  2142  formed in the fourth dielectric layer  2044 . The resistor layers  2191  and  2192  are connected to fourth conductor layers  2181  and  2182  laminated on the third dielectric layer  2043  through vias  2071  and  2072  formed in the first dielectric layer  2041 . 
     An MIM capacitance structure in which the third dielectric layer  2043  is sandwiched between the fourth conductor layers  2181  and  2182  and the first conductor layer  206  is formed. Such an AC coupling structure that can weaken the coupling between the antennas leads to reduction of the transmission loss between the antennas, and the radiation efficiency of the antenna array is expected to be improved. There are cases where the vias  2071  and  2072  have a large width because the vias  2071  and  2072  are formed inside the first dielectric layer  2041  having a relatively large thickness. However, by disposing the vias  2071  and  2072  at the locations away from the coupling line  209  as in the present modification, even if the vias  2071  and  2072  have a large width (typically λ/10 or more), interference with the resonance electric field of the antenna is suppressed. As a result, the antenna gain can be improved. 
     In  FIGS.  5 A and  5 D , first regions  2091   a  and  2091   b  of the coupling line  209  are microstrip lines having a structure in which the dielectric layer  204  is sandwiched between the third conductor layers  210   a  and  210   b  and the first conductor layer  206 . A second region  2092  is a microstrip line having a structure in which the dielectric layer  204  is sandwiched between the upper conductor of a resistance layer  251  and the first conductor layer  206 . The resistance layer  251  is disposed between the third conductor layers  210   a  and  210   b  and electrically and physically connected to each other to form the coupling line  209  (microstrip line). The third conductor layers  210   a  and  210   b  are made of Ti/Au, whereas the resistance layer  251  is made of a material (TiW) having a high resistivity. Therefore, the second region  2092  has higher impedance and larger loss than the first regions  2091   a  and  2091   b.    
     EXAMPLE 1 
     As Example 1, a specific configuration of the semiconductor element  100  according to Embodiment 1 will be described with reference to  FIGS.  3 A to  3 C . The semiconductor element  100  is a semiconductor device capable of single mode oscillation in a frequency band of 0.45 to 0.50 THz. 
     RTDs  101   a  and  101   b  have a multi-quantum well structure of InGaAs/AlAs lattice-matched on an InP substrate  113 , and in the present example, an RTD having a double-barrier structure is used. The semiconductor heterostructure of this RTD is described in J Infrared Milli Terahz Waves (2014) 35:425-431 (Non Patent Literature 4). The RTDs  101   a  and  101   b  have current-voltage characteristics in which, as measured values, peak current density is 9 mA/μm 2  and differential negative conductance per unit area is 10 mS/μm 2 . 
     An antenna  100   a  has a mesa structure that includes a semiconductor layer  115   a , which includes the RTD  101   a , and an electrode  116   a , which is an ohmic electrode. In the present example, a circular mesa structure having a diameter of 2 μm is formed. The magnitude of the differential negative resistance of the RTD  101   a  is approximately −30Ω per diode. In this case, the differential negative conductance (GRTD) of the semiconductor layer  115   a  including the RTD  101   a  is estimated to be approximately 30 mS, and the diode capacitance (C RTD ) of the RTD  101   a  is estimated to be approximately 10 fF. 
     The antenna  100   a  is a patch antenna having a structure in which a dielectric layer  104  is sandwiched between a second conductor layer  103   a , which is a patch conductor, and a first conductor layer  106 , which is a ground conductor. The semiconductor layer  115   a  including the RTD  101   a  is integrated in the antenna  100   a . The antenna  100   a  is a square patch antenna in which one side of the second conductor layer  103   a  is 150 μm, and a resonator length L of the antenna is 150 μm. As the second conductor layer  103   a  and the first conductor layer  106 , a metallic layer mainly formed of an Au thin film having low resistivity is used. 
     The dielectric layer  104  is disposed between the second conductor layer  103   a  and the first conductor layer  106 . The dielectric layer  104  includes three layers of a first dielectric layer  1041 , a second dielectric layer  1042 , and a third dielectric layer  1043 . The first dielectric layer  1041  is formed of 5 μm-thick BCB (benzocyclobutene, manufactured by the Dow Chemical Company, ε r1 =2). The second dielectric layer  1042  is formed of 2 μm-thick SiO 2  (plasma CVD, ε r2 =4). The third dielectric layer  1043  is formed of 0.1 μm-thick SiN x  (plasma CVD, C r3 =7). That is, in the present example, the three dielectric layers included in the dielectric layer  104  are made of different materials. 
     The first conductor layer  106  includes a Ti/Pd/Au layer (20/20/200 nm) and a semiconductor formed of an n+−InGaAs layer (100 nm) having an electronic concentration of 1×10 18  cm −3  or more. In the first conductor layer  106 , the metal and the semiconductor are connected to each other by low-resistance ohmic contact. 
     The electrode  116   a  is an ohmic electrode formed of a Ti/Pd/Au layer (20/20/200 nm). The electrode  116   a  is connected by low-resistance ohmic contact to the semiconductor formed of an n+−InGaAs layer (100 nm) that is formed in the semiconductor layer  115   a  and has an electronic concentration of 1×10 18  cm −3  or more. 
     In the structure around the RTD  101   a  in the lamination direction, the substrate  113 , the first conductor layer  106 , the semiconductor layer  115   a  including the RTD  101   a , the electrode  116   a , a conductor  117   a , and the second conductor layer  103   a  are laminated in this order from the substrate  113  side and are electrically connected to each other. The conductor  117   a  is formed of a conductor containing Cu (copper). 
     The RTD  101   a  is disposed at a position shifted by 40% (60 μtm) from the center of gravity of the second conductor layer  103   a  in the resonance direction (A-A′ direction). The input impedance at the time of feeding a high-frequency wave from the RTD to the patch antenna is determined by the position of the RTD  101   a  in the antenna  100   a . The second conductor layer  103   a  is connected to lines  1081   a   1  and  108   a   2 . 
     The lines  108   a   1  and  108   a   2  are formed of a metallic layer including Ti/Au (=5/300 nm) laminated on the first dielectric layer  1041  and connected to bias circuits V a  and V b . The antenna  100   a  is designed to be able to obtain oscillation of a power of 0.2 mW at a frequency f THz =0.48 THz by setting a bias in the negative resistance region of the RTD  101   a . The lines  108   a   1  and  108   a   2  are each composed of a metallic layer pattern including Ti/Au (=5/300 nm) having a length of 75 μm in the resonance direction (=A-A′ direction) and a width of 10 μm. The lines  108   a   1  and  108   a   2  are each connected to the second conductor layer  103   a  at the center in the resonance direction (=A-A′ direction) and at the edge in the B-B′ direction of the second conductor layer  103   a . The connection positions correspond to nodes of the electric filed of a terahertz wave of a frequency f THz  standing at the antenna  100   a.    
     The semiconductor element  100  includes an antenna array in which two antennas of the antenna  100   a  and the antenna  100   b  are aligned in an electric field direction (=E-plane direction) of radiated electromagnetic waves and are coupled to each other. The individual antenna is designed to singly oscillate a terahertz wave having a frequency f THz  and is arranged at a pitch of 340 μm in the A-A′ direction. The adjacent antennas are mutually coupled by a coupling line  109  including a third conductor layer  110  made of Ti/Au (=5/300 nm). More specifically, the second conductor layer  103   a  and the second conductor layer  103   b  are connected by the third conductor layer  110 , which is 5 μm wide and 190 μm long. The antenna  100   a  and the antenna  100   b  are mutually injection-locked at the resonance frequency f THz =0.48 THz in a state where the phases are aligned with each other (positive phase) to oscillate. 
     In the semiconductor element  100 , the coupling line  109  is constituted by a microstrip line having a structure in which the dielectric layer  104  is sandwiched between third conductor layers  110   a ,  110   b , and  110   c  and conductor layers  152   a  and  152   b  and the first conductor layer  106  serving as GND. The third conductor layer  110   a , the conductor layer  152   a , the third conductor layer  110   b , the conductor layer  152   b , and the third conductor layer  110   c  are formed of the same material (Ti/Au (=5/300 nm)) in the same layer and are connected in this order. Each of the third conductor layers  110   a ,  110   b , and  110   c  is 10 μm wide and 150 μm long. Each of the conductor layers  152   a  and  152   b  is 1 μm wide and 3 μm long, and the microstrip line having a characteristic impedance of 20Ω is formed. 
     The conductor layers  152   a  and  152   b  are disposed at positions corresponding to the antinodes of the electric field of a terahertz wave having a resonance frequency f THz  standing in the coupling line  109 . The microstrip line having the conductor layers  152   a  and  152   b , which correspond to the second region  1092 , as the upper conductors has impedance higher than that of the first regions and is configured such that only a frequency other than the operating frequency f THz  and an out-of-phase component of the operating frequency f THz  are selectively lost. The third dielectric layer  1043  is formed of 0.1 μm-thick silicon nitride (ε r3 =7). Here, the frequency band in which a frequency other than the operating frequency f THz  and an out-of-phase component of the operating frequency f THz  are selectively lost is, for example, from 10 GHz to 1000 GHz. 
     Power is supplied to the semiconductor element  100  from the bias circuits V a  and V b , and normally, a bias voltage in a differential negative resistance region is applied so as to supply a bias current. In the case of the semiconductor element  100  disclosed in the present example, radiation of a terahertz electromagnetic wave of 0.4 mW at a frequency of 0.48 THz is obtained by an oscillation operation in a negative resistance region. 
     As described above, according to the present example, compared with the related art, the loss of the electromagnetic wave can be further reduced, and the terahertz wave can be oscillated or detected with higher efficiency. 
     Other Examples 
     While the preferred embodiments and examples of the present invention have thus been described, the present invention is not limited to these embodiments and examples, and various modifications and variations can be made without departing from the gist of the present invention. For example, in the above embodiments and examples, the descriptions have been made assuming the case where carriers are electrons. However, the present invention is not limited thereto, and positive holes may be used. In addition, the materials of the substrate and the dielectrics may be selected depending on the application, and a semiconductor such as silicon, gallium arsenide, indium arsenide, or gallium phosphide, or a resin such as glass, ceramic, polytetrafluoroethylene, or polyethylene terephthalate can be used. The above-described structures and materials in the embodiments and examples may be appropriately selected in accordance with a desired frequency or the like. 
     Further, in the above-described embodiments and examples, the square patch antenna is used as the resonator for the terahertz wave. However, the shape of the resonator is not limited thereto, and for example, a resonator having a structure using a patch conductor with a polygonal shape such as a rectangular shape and a triangular shape, a circular shape, an elliptical shape, or the like may be used. 
     The number of differential negative resistance elements integrated in the semiconductor element is not limited to one, and a resonator having a plurality of differential negative resistance elements may be used. The number of lines is not limited to one, and a plurality of lines may be used. 
     In the above description, the double-barrier RTD made of InGaAs/AlAs grown on the InP substrate has been described as an RTD. However, the present invention is not limited to these structures and material systems, and other structures and combinations of materials may be used. For example, an RTD having a triple-barrier quantum well structure or an RTD having a multiple-barrier quantum well structure having four or more barriers may be used. 
     In addition, each of the following combinations may be used as the material of the RTD. 
     GaAs/AlGaAs/ and GaAs/AlAs, InGaAs/GaAs/AlAs formed on a GaAs substrate
 
InGaAs/InAlAs, InGaAs/AlAs, InGaAs/AlGaAsSb formed on an InP substate
 
InAs/AlAsSb and InAs/AlSb formed on an InAs substrate
 
SiGe/SiGe formed on an Si substrate
 
     According to the present invention, more efficient generation or detection of a terahertz wave can be realized by an element including a plurality of antennas. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.