JP6259325B2 - Quantum cascade laser - Google Patents

Description

  The present invention relates to a quantum cascade laser using intersubband transition in a quantum well structure.

  Light in the mid-infrared wavelength region (for example, wavelength 3 to 30 μm) is an important wavelength region in the spectroscopic analysis field. In recent years, quantum cascade lasers (QCLs) have attracted attention as high-performance semiconductor light sources in such a wavelength region (see, for example, Patent Documents 1 to 3).

  Quantum cascade lasers are monopolar laser elements that use a level structure with subbands formed in a semiconductor quantum well structure and generate light by electronic transition between subbands. High-efficiency and high-power operation can be realized by cascading the quantum well light-emitting layers serving as active regions in multiple stages. The cascade coupling of the quantum well light-emitting layers is realized by alternately stacking the quantum well light-emitting layers and the injection layers using an electron injection layer for injecting electrons into the emission upper level.

JP-A-10-144959 Japanese Patent No. 5127430 JP 2009-206340 A

M. Yamanishi et al., "Theory of the Intrinsic Linewidth of Quantum-Cascade Lasers: HiddenReason for the Narrow Linewidth and Line-Broadening by Thermal Photons", IEEE Journal of Quantum Electronics Vol.44 No.1 (2008), pp. 12-29 L. Tombez et al., "Temperature dependence of the frequency noise in a mid-IR DFB quantumcascade laser from cryogenic to room temperature", Opt. Express Vol.20 No.7 (2012), pp.6851-6859 S. Bartalini et al., "Measuring frequency noise and intrinsic linewidth of a room-temperatureDFB quantum cascade laser", Opt. Express Vol.19 No.19 (2011), pp.17996-18003 I. Galli et al., "Comb-assisted subkilohertz linewidth quantum cascade laser for high-precision mid-infrared spectroscopy", Appl. Phys. Lett. Vol.102 (2013), pp.121117-1-121117-4 L. Tombez et al., "Physical Origin of Frequency Noise and Linewidth in Mid-IR DFB QuantumCascade Lasers", Conference Paper CLEO: Science and InnovationsMid-infrared QCL's (CM1K), San Jose, California United States, June 9-14, 2013 G. D. Domenico et al., "Simple approach to the relation between laser frequency noise and laserline shape", Appl. Opt. Vol.49 No.25 (2010), pp.4801-4807

  The quantum cascade laser is originally supposed to have a very narrow spectral line width of, for example, about 260 Hz. However, when actually used in a free-running state, such a narrow spectral line width cannot be obtained, and this line width extends, for example, to about 400 kHz (room temperature operation).

  This increase in line width causes voltage noise due to carrier fluctuations in the laser element to produce output fluctuations and temperature fluctuations, thereby changing the refractive index in the laser elements and causing oscillation wavelength fluctuations. It is by doing. In other words, the cause of spectral fluctuations in quantum cascade lasers is voltage noise (electrical fluctuations) in the laser element, and another way of viewing it is current noise obtained by dividing voltage noise by the differential resistance of the element. (See Non-Patent Documents 1 to 3).

  Here, one of the main uses of the quantum cascade laser is spectral spectroscopy by absorption. In such spectroscopic measurement, the spectral line width of the laser light determines the measurement accuracy. Therefore, it is very important to narrow the spectral line width of the laser element, but the conventional quantum cascade laser cannot obtain a sufficiently narrow line width as described above. In addition, fluctuations and disturbances in the laser element as described above also cause intensity fluctuations in the laser output. Non-Patent Document 4 describes a configuration using a feedback loop as a technique for suppressing spectrum fluctuation. However, such a configuration requires a very large apparatus and is not practical.

  The present invention has been made to solve the above problems, and provides a quantum cascade laser capable of reducing the spectral line width by suppressing the influence of electrical fluctuations in the laser element. For the purpose.

によって決まるミニバンド内での電荷分布の重心位置ｚ_ｃからの距離が３．６ｎｍ以下の位置を中心位置とし、４．４ｎｍ以下の半値全幅を有する添加量分布で添加されていることを特徴とする。ただし、上記式（１）において、ｚはレーザ素子における半導体積層方向でのミニバンド内の電子の位置、Ｅ_ｉはミニバンドに含まれるｉ番目の準位（ｉ番目のサブバンド）のエネルギー、Ψ_ｉ（ｚ）はミニバンドに含まれるｉ番目の準位の規格化された波動関数、Ｔ_ｅは活性層内での電子温度、ｋ_Ｂはボルツマン定数である。
In order to achieve such an object, the quantum cascade laser according to the present invention includes (1) a semiconductor substrate, and (2) a unit laminate body provided on the semiconductor substrate and including a quantum well light emitting layer and an injection layer in multiple stages. And an active layer having a cascade structure in which quantum well light-emitting layers and injection layers are alternately stacked, and (3) a unit stacked body included in the active layer has a sub-structure based on the quantum well structure. The band level structure includes at least a light emission upper level and a miniband including a plurality of levels each functioning as a light emission lower level or a relaxation level, and (4) a light emission upper level in a quantum well light emitting layer. Light is generated by the intersubband transition of electrons from the level to the lower emission level, and the electrons that have undergone the intersubband transition are transferred to the quantum well light emitting layer of the subsequent unit stack via the relaxation level in the miniband. And injected (5) injection layer, n (n is an integer of 4 or more) is configured to include a barrier layer and the well layer of the miniband, viewed contains a level of the I-number (I is an integer of 4 or more), In the injection layer, an impurity for supplying electrons is added to a single well layer or a single barrier layer among n barrier layers and well layers constituting the injection layer. At the same time, an impurity for supplying electrons in the injection layer is expressed by the following formula (1).

Characterized in that the distance from the gravity center position z _c of the charge distribution within the miniband centered position following positions 3.6 nm, and is added in amount distribution having the following FWHM 4.4 nm determined by And However, in the above formula (1), z is an electronic position within the miniband in a semiconductor lamination direction of the laser element, E _i is the energy of the i-th level included in the miniband (i th sub-band) Ψ _i (z) is the normalized wave function of the i-th level included in the miniband, _Te is the electron temperature in the active layer, and k _B is the Boltzmann constant.

  In the quantum cascade laser described above, in the subband level structure in the unit laminate structure composed of the light emitting layer and the injection layer, the light emitting upper level and a plurality of levels functioning as the light emitting lower level or the relaxation level, respectively. And the injection layer includes four or more (n) barrier layers and well layers, and the miniband includes four or more (I) subband levels. It is composed by.

In such a configuration, the centroid position z _c of the charge distribution in the miniband determined by the above formula (1) is obtained for the impurity for supplying electrons (carriers) added to a predetermined position in the injection layer. reference, the distance from the gravity center position z _c is the center position (barycentric position) of the following positions 3.6 nm, are configured to add an impurity in amount distribution having the following FWHM 12 nm. In this way, by adding impurities in an additive amount distribution that satisfies a predetermined condition with respect to the center of gravity of the charge distribution in the miniband, the influence of electrical fluctuations in the laser element is suppressed, and the spectral line width Can be made narrower.

  Here, in the above-described quantum cascade laser, for the semiconductor layer to which the impurity is added in the injection layer, the impurity is a single layer among the n barrier layers and the well layers constituting the injection layer in the injection layer. Preferably, it is added in one well layer or in a single barrier layer. Alternatively, the impurity may be added over the adjacent well layers and barrier layers among n barrier layers and well layers constituting the injection layer in the implantation layer.

  Regarding the width of the impurity addition amount distribution, it is preferable that the impurity is added in the additive amount distribution having a full width at half maximum of 4.4 nm or less in the injection layer. Thereby, the influence of the electrical fluctuation in the laser element can be further suppressed.

Also, the position of the added weight distribution of impurities in the implanted layer, impurities, added weight distribution distance from the gravity center position z _c of the charge distribution within the miniband centered position following positions 1.2nm It is preferable that it is added. Even with such a configuration, it is possible to further suppress the influence of electrical fluctuation in the laser element.

  Further, in the quantum cascade laser described above, the active layer has a plurality of types of unit stacks having different quantum well structures as the unit stack, and the impurity additive distribution in the injection layer is that of the unit stack. It is good also as a structure set for every kind. In this way, by adding impurities with an addition amount distribution corresponding to the quantum well structure in each unit stack, the influence of electrical fluctuations in laser elements having active layers with various configurations is suitably suppressed. be able to.

  According to the quantum cascade laser of the present invention, in the subband level structure in the unit laminate structure composed of the light emitting layer and the injection layer, a plurality of light emitting upper levels and a plurality of light emitting lower levels and relaxation levels respectively functioning. A mini-band including a plurality of levels, an injection layer including four or more barrier layers and a well layer, a mini-band including four or more subband levels, In the structure, an impurity for supplying electrons is added in an additive amount distribution having a full width at half maximum of 12 nm or less, with the center position being a position where the distance from the center of gravity of the charge distribution in the miniband is 3.6 nm or less. By doing so, the influence of electrical fluctuations in the laser element can be suppressed, and the spectral line width can be narrowed.

It is a figure which shows schematically the basic composition of a quantum cascade laser. It is a figure which shows an example of the subband level structure in the active layer of a quantum cascade laser. (A), (b) It is a figure which shows typically about the addition of the impurity for supplying an electron in the injection layer of an active layer. It is a graph which shows an example of the semiconductor laminated structure which comprises a quantum cascade laser. It is a chart which shows an example of composition of an upper injection layer, an active layer, and a lower injection layer. It is a graph which shows an example of a structure of the unit laminated body for 1 period in an active layer. It is a figure which shows an example of the structure of the unit laminated body in an active layer, and a subband level structure. It is a graph which shows the other example of a structure of the unit laminated body for 1 period in an active layer. (A), (b) It is a figure shown about the addition position of the impurity in an injection layer, and an impurity level. It is a graph which shows the frequency dependence of noise power. It is a graph which shows the temperature dependence of VNPSD about the element I and II. 3 is a graph showing the temperature dependence of VNPSD for device III. 10 is a graph showing the temperature dependence of VNPSD for device IV. (A), (b) It is a figure shown about the electric charge distribution in a miniband. (A), (b) It is a figure shown about the electric charge distribution in a miniband. It is a graph which shows the impurity addition width | variety dependence of the noise suppression amount. It is a graph which shows about the change of the temperature dependence of VNPSD by the position shift of an impurity addition position. It is a perspective view which shows an example of a specific structure of a quantum cascade laser. It is a graph which shows the other example of a structure of an upper injection layer, an active layer, and a lower injection layer. It is a graph which shows the other example of a structure of the unit laminated body for 1 period in an active layer. It is a figure shown about the structure of the unit laminated body in an active layer, a subband level structure, and an impurity level. It is a figure shown about (a) temperature dependence of VNPSD, and (b) electric charge distribution in a miniband. It is a graph which shows the other example of a structure of the unit laminated body for 1 period in an active layer. It is a figure shown about (a) temperature dependence of VNPSD, and (b) electric charge distribution in a miniband. It is a figure shown about (a) temperature dependence of VNPSD, and (b) electric charge distribution in a miniband. It is a figure shown about the half value full width in the addition amount distribution of an impurity.

  Hereinafter, embodiments of the quantum cascade laser according to the present invention will be described in detail with reference to the drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted. Further, the dimensional ratios in the drawings do not necessarily match those described.

  FIG. 1 is a diagram schematically showing a basic configuration of a quantum cascade laser according to the present invention. The quantum cascade laser 1A of the present embodiment is a monopolar type laser element that generates light by utilizing electronic transition between subbands in a semiconductor quantum well structure. This quantum cascade laser 1 </ b> A includes a semiconductor substrate 10 and an active layer 15 formed on the semiconductor substrate 10.

  The active layer 15 has a cascade structure in which quantum well light-emitting layers used for light generation and electron injection layers used for injection of electrons into the light-emitting layer are alternately stacked in multiple stages. Specifically, a semiconductor multilayer structure composed of a quantum well light emitting layer and an injection layer is used as a unit laminated body 16 for one period, and the unit laminated body 16 is laminated in multiple stages, whereby an active layer 15 having a cascade structure is formed. It is configured. The number of unit laminates 16 including the quantum well light emitting layer and the injection layer is appropriately set according to the specific configuration, characteristics, and the like of the laser element. The active layer 15 is formed directly on the semiconductor substrate 10 or via another semiconductor layer.

  FIG. 2 is a diagram showing an example of a subband level structure in the active layer of the quantum cascade laser shown in FIG. As shown in FIG. 2, each of the plurality of unit stacked bodies 16 included in the active layer 15 is configured by a quantum well light emitting layer 17 and an electron injection layer 18. The light emitting layer 17 and the injection layer 18 are formed to have a predetermined quantum well structure including a quantum well layer and a quantum barrier layer, respectively. Thereby, in the unit laminated body 16, the subband level structure which is an energy level structure by a quantum well structure is formed.

Specifically, the injection layer 18 includes n barrier layers and well layers, where n is an integer of 4 or more. In addition, as schematically shown in FIG. 2 by the impurity level L _imp , impurities for supplying carriers (electrons) necessary for the light emission operation in the laser element are given in the injection layer 18 to a predetermined level. It is added in an addition amount distribution having an addition position and an addition width. The configuration conditions and the like to be satisfied by the impurity addition amount distribution in the injection layer 18 will be described in detail later.

As shown in FIG. 2, the unit laminated body 16 in the present embodiment has a light emission upper level L _up that is a level related to light emission and a plurality of lower energy than the light emission upper level in the subband level structure. And a miniband MB including a plurality of levels (a plurality of subbands). Specifically, the miniband MB is configured by I subband levels that function as the emission lower level L _low or the relaxation level L _r , respectively, where I is an integer of 4 or more.

Here, the emission lower level L _low is a level related to emission together with the emission upper level L _up . Further, the relaxation level L _r is a level used for relaxation and transport of electrons from the lower emission level L _low to the quantum well light emitting layer 17b of the subsequent unit stacked body. The I subband levels constituting these minibands MB are generated due to the quantum well structure of the n barrier layers and well layers of the injection layer 18 or, further, the barrier layers and well layers of the light emitting layer 17. Is done.

Further, in the subband level structure shown in FIG. 2, in addition to the above-described emission upper level L _up and miniband MB, a high energy level L _h having higher energy than the emission upper level is provided. . In this configuration example, the high energy level L _h functions as a light emission upper level (second light emission upper level) together with the level L _up .

  In the unit laminated body 16 shown in FIG. 2, an injection that becomes a barrier against electrons injected from the injection layer 18 a to the light emitting layer 17 between the light emitting layer 17 and the injection layer 18 a in the previous unit laminated body. An injection barrier layer 161 is provided. An extraction barrier layer for electrons from the light emitting layer 17 to the injection layer 18 is provided between the light emitting layer 17 and the injection layer 18 as necessary.

In such a subband level structure, electrons e ⁻ from the relaxation level L _r in the mini-band MB in the preceding injection layer 18 a enter the light emitting layer 17 through the injection barrier layer 161 by the resonant tunneling effect. Injected. Thus, carriers necessary for the light emission operation are supplied to the second light emission upper level (high energy level) L _h and the light emission upper level L _up .

The electrons injected into the emission upper level L _up and the second emission upper level L _h transition to one or more emission lower levels L _low included in the miniband MB. At this time, Light hν having a wavelength corresponding to the energy difference between the subband levels of the levels L _up and L _h and the lower level L _low is generated and emitted. In FIG. 2, only the light emission transition from the upper levels L _up and L _h to the lower level L _low on the highest energy side in the miniband MB is shown for the sake of easy viewing. The illustration of the transition to the level is omitted.

Electrons transition to the emission lower level L _low, in miniband MB including the emission lower level L _low and the relaxation level L _r, LO phonon scattering, electron - by miniband within relaxed through an electron scattering, Relaxed at high speed. As a result, an inversion distribution is formed between the upper levels L _up and L _h and the lower level L _low . In addition, electrons relaxed and transported in the miniband MB are cascade-injected into the emission upper levels L _up and L _h in the light emitting layer 17b at the subsequent stage.

  By repeating such electron injection, light emission transition, and relaxation in the plurality of unit laminated bodies 16 constituting the active layer 15, cascade light generation occurs in the active layer 15. That is, by stacking a large number of quantum well light-emitting layers 17 and injection layers 18, electrons move one after another in the cascade 16 in a cascade manner, and light hν at the time of transition between subbands in each laminate 16. Is generated. Further, such light is resonated in the optical resonator of the laser 1A, so that laser light having a predetermined wavelength is generated.

Note that the subband level structure in the unit stack 16 constituting the active layer 15 of the quantum cascade laser 1A is not limited to the configuration shown in FIG. 2, and various configurations may be used specifically. For example, the high energy level L _h may function as an injection level for injecting electrons into the emission upper level L _up instead of the second emission upper level. Moreover, this high energy level L _h may not be provided if not needed. For the lower emission level L _low , the miniband MB is configured as a relaxation miniband including a plurality of relaxation levels L _r , and separately from the miniband MB, one or more lower emission levels L _low are set. It is good also as a structure to provide.

  In the quantum cascade laser 1A having the configuration illustrated in FIGS. 1 and 2, as described above, the spectral line width is wider than the original due to voltage noise (electric fluctuation) in the laser element. The inventor of the present application has considered electrical fluctuations in the element of such a quantum cascade laser. Hereinafter, voltage noise that causes deterioration of the spectral line width in the quantum cascade laser will be described.

The voltage noise seen in the element of the quantum cascade laser is 1 / f _N type (f _N is a noise frequency) so-called flicker noise (Non-patent Document 3). In general, flicker noise is considered to be caused by an electrical random phenomenon in which electrons are trapped by surface states or defects, or the trapped electrons are released. For example, RTS (Random Telegraph Signal) Interpreted by the model.

  The inventor of the present application considered the quantum cascade laser by taking the above-described concept of carrier trapping and release. In the following, the spatial concepts such as impurity addition position, spatial expansion, electron position and expansion within the miniband are all of the multiple quantum well structure constituting the laser element unless otherwise specified. The concept in the stacking direction (direction perpendicular to the stacking surface) is shown, and no particular limitation is imposed on the direction parallel to the stacking surface.

The inventor of the present application relaxes the electrons extracted from the light emitting layer 17 in the active layer 15 of the quantum cascade laser 1A having the multi-layer stacked structure of the unit laminated body 16 composed of the light emitting layer 17 and the injection layer 18, thereby Impurity level L due to impurities doped in the injection layer 18 to supply electrons serving as carriers to the active layer 15 and the miniband MB transported to the light emitting layer 17b (see FIG. 2) through the latter 18 We focused on the relationship with _imp .

FIG. 3 is a diagram schematically showing the addition of impurities for supplying electrons in the injection layer 18 of the active layer 15 in the quantum cascade laser 1A. 3A and 3B, L _imp indicates an impurity level, and L _{1 to} L ₅ indicate a plurality of levels (a plurality of subbands) constituting the miniband MB.

The electron e ⁻ is stochastically excited from the impurity level L _imp to the level in the mini-band MB, and forms an electron distribution determined by the normalized wave function and Boltzmann distribution in an instant. Further, an ionized donor having a positive charge is formed in the impurity level L _imp emptied by the excitation of electrons, and an electron having a negative charge exists in the miniband MB. At this time, if the ionized donor and the electrons are spatially separated, a charge dipole having a dipole length Z (see FIG. 3B) is formed, and an electric field is thereby generated. Further, as an opposite process, a phenomenon occurs in which electrons e ⁻ in the miniband MB are trapped by ionized donors which are stochastically empty impurity levels L _imp . In this process, the charge dipole formed as described above disappears.

Thus, the electric field changes due to the emission and trapping of electrons e ⁻ from the impurity level L _imp provided in the injection layer 18. Such a change in voltage due to electron emission and trapping process becomes voltage noise in the quantum cascade laser 1A. As shown in FIG. 3, the polarity and size of the charge dipole formed in the injection layer 18 depends on where the negative charge distribution due to electrons is formed relative to the position of the generated positive ionization donor. Come different.

  Here, a case where only a single impurity exists in the injection layer 18 is considered. In this case, the size of the average charge dipole generated by the electrons excited from the impurities can be considered. In addition, if the charge dipoles having different polarities generated by the electron distribution in the miniband MB are well balanced, the size of the charge dipole can be reduced to zero on average. That is, in this case, the voltage noise in the element of the quantum cascade laser 1A can be made zero.

In other words, the average charge dipole size is the size of the charge dipole generated by the centroid of the charge distribution produced by the excited electrons and the doped impurities. Therefore, if the center of gravity of the charge distribution of excited electrons is not spatially separated from the impurity addition position, excitation of electrons from the impurity level L _imp to the miniband MB, or from the miniband MB to the impurity Even if the trapping of electrons to the level L _imp is repeated, a charge dipole is not substantially formed, and the voltage noise thereby becomes zero.

  Next, let us consider a case where, in addition to the single impurity described above, another impurity exists at another spatially separated position. The electrons excited from this impurity to the miniband MB are also instantly relaxed as before, and form an electron distribution determined by the normalized wave function and Boltzmann distribution. Therefore, the charge distribution formed in the miniband MB does not change no matter what position the impurities are excited from.

  In this case, the charge dipoles generated by the first and second impurities added at spatially separated positions and the center of the charge distribution in the miniband MB are averaged to be zero. It is not possible. This is because the first and second impurities are independent events having completely independent excitation and trapping processes. In this case, the voltage noise in the laser element must be evaluated as an integrated value of noise power caused by each impurity. The noise power is an amount obtained by squaring the noise voltage generated by the charge dipole, and is an amount having no polarity. Therefore, the noise power is always added.

Therefore, as a method for minimizing the noise power in a situation where a large number of carriers (electrons) are required for the operation of the laser element, it is preferable to add (dope) a large number of impurities at positions that are not separated as far as possible. . In such a configuration, since the spatial position of the impurity level L _imp due to each of a large number of impurities added to the implantation layer 18 is hardly different, the polarities and sizes of dipoles formed by the impurities are considered to be substantially the same. It is done. Therefore, if the noise power is minimized for a certain impurity, the noise power can be kept small even if the noise power is added.

  From the above consideration, as the structure of the quantum cascade laser for minimizing the voltage noise, which is the square root of the noise power, the impurity is locally added to a specific semiconductor layer and addition position in the injection layer 18. It can be seen that the doping structure is optimal. Further, in the case where the impurities are added in a spatially widened manner in the implantation layer 18, the impurities are added to as narrow a region as possible, and the center position (center of gravity position) of the impurity addition amount distribution, It is understood that it is important for reducing the voltage noise to make the position of the center of gravity of the charge distribution formed in the miniband MB as close as possible.

のように見積もった。 The inventor of the present application has proceeded analytically with the above consideration, and the voltage noise power spectral density (VNPSD) generated in the quantum cascade laser element when impurities are doped only at a specific position is expressed as follows. Equation (2)

Estimated as follows.

ｅ：素電荷
Ｚ（ｚ_ｉｍｐ）：ダイポール長
ε_０：真空の誘電率
ε_ｓ：活性層の比誘電率
Ｓ：活性層の水平方向の面積
Ｍ：カスケード構造の段数
ｎ_ｉｍｐ：カスケード構造１段当たりの不純物面密度
ｆ（Ｅ_ｉｍｐ，Ｅ_Ｆ，Ｔ_ｅ）：不純物準位の電子分布関数
Ｅ_ｉｍｐ：不純物準位のエネルギー
Ｅ_Ｆ：注入層にあるミニバンドに対する擬似フェルミエネルギー
Ｔ_ｅ：活性層内での電子温度（〜格子温度）
Ｉ：ミニバンドに含まれるサブバンドの数
τ_ｅＬ：不純物準位からのミニバンドへの放出最長時間（レートの逆数）
τ_ｅＳ：不純物準位からのミニバンドへの放出最短時間
Ｅ_ｉ：ミニバンドに含まれるｉ番目のサブバンド端のエネルギー
ｚ：半導体積層構造の積層方向での空間的位置（ミニバンド内の電子の位置）
ｚ_ｉｍｐ：不純物準位の積層方向での空間的位置
Ψ_ｉ：ミニバンドに含まれるｉ番目のサブバンドの規格化された波動関数
ｆ_Ｎ：ノイズ周波数
ｍ^＊：電子の有効質量
ｋ_Ｂ：ボルツマン定数 Here, the voltage noise power spectral density is an amount indicating how much the voltage noise power is per band 1 Hz at each noise frequency. Moreover, in said Formula (2), each symbol, a formula, etc. are as follows, respectively.

e: Elementary charge Z (z _imp ): Dipole length ε ₀ : Vacuum dielectric constant ε _s : Relative permittivity of active layer S: Horizontal area of active layer M: Number of stages of cascade structure n _imp : One stage of cascade structure Impurity surface density per contact f (E _imp , E _F , T _e ): Impurity level electron distribution function E _imp : Impurity level energy E _F : Pseudo Fermi energy T _e for the miniband in the injection layer: Active layer Electron temperature (~ lattice temperature)
I: Number of subbands included in miniband τ _eL : Maximum emission time from impurity level to miniband (reciprocal of rate)
τ _eS : Minimum emission time from impurity level to miniband E _i : Energy at the edge of the i-th subband included in the miniband z: Spatial position in the stacking direction of the semiconductor stacked structure (electrons in the miniband Position of)
z _imp : spatial position of impurity levels in the stacking direction ψ _i : normalized wave function of the i-th subband included in the miniband f _N : noise frequency m ^* : effective electron mass k _B : Boltzmann constant

ただし、上記の式（７）において、ｐ（ｚ_ｉｍｐ）は、添加位置ｚ_ｉｍｐに不純物が存在する確率である。 Here, in the above formula (2), VNPSD is calculated under the condition of δ doping in which an impurity is added to one addition position z _imp . When the impurity level (addition position) is spatially widened, VNPSD can be obtained by the following equation (7) obtained by further integrating equation (2) with z _imp .

However, in the above formula (7), p (z _imp ) is the probability that an impurity exists at the addition position z _imp .

In the VNPSD equation (2), if the dipole length Z (z _imp ) = 0 at the addition position z _imp , the value of VNPSD is S _v (f _N ) = 0 regardless of the noise frequency f _N. Further, the dipole length Z (z _imp ), which is a function of the impurity addition position z _imp , is incorporated in the VNPSD equation as a square, and when the impurity addition position is spread spatially, the noise power Can be seen to increase.

Note that the formula VNPSD (2), the probability density of the transition of the impurity level probability density function of the transition from the _{L imp} to the miniband MB _{p e} (τ _e), and from the miniband MB to impurity level _{L imp} The function p _c (τ _c ) is calculated as being proportional to the reciprocal of the emission time τ _e from the impurity level to the miniband and the capture time τ _c from the miniband to the impurity level, respectively. The distribution of electrons to each level in the miniband MB is calculated according to the Boltzmann distribution at the electron temperature _Te , but this has been confirmed experimentally and is widely known. ing. In addition, in the cascade structure stacked in multiple stages, the structure of the injection layer in each stage is the same.

In the above formula, dipole length _{Z (z imp)} is set to the position _{z imp} impurity level _{L imp,} wave functions are normalized shows electron existence probability at the position z with the miniband MB [psi (z) Determined by the product of the square of. Further, f (E _imp , E _F , T _e ) indicates the probability that electrons exist in the impurity level, and the electrons that can be excited from the impurity level to the miniband at the electron temperature T _e in the active layer 15. Has determined the number of. Further, {1-f (E _imp , E _F , T _e )} indicates a probability that electrons are not present in the impurity level, and how many electrons in which the impurity level exists in the miniband can be received. Have decided. The VNPSD in equation (2) is the square of these dipole lengths Z (z _imp ), f (E _imp , E _F , T _e ), and {1−f (E _imp , E _F , T _e )} And product.

Here, the normalized wave function Ψ (z) is determined including not only the multiple quantum well structure in the active layer 15 of the cascade structure but also the influence of the operating voltage during the laser oscillation operation. Further, the denominator of the above equation (2) is due to the consideration of the transition probability density functions p _e (τ _e ) and p _c (τ _c ) between the impurity level L _imp and the miniband MB. It can be understood from the above description that the VNPSD equation (2) basically takes this form.

In addition, as described above, the spatial coordinates such as z _imp and z in the formula (2) are coordinates in a direction (stacking direction, z-axis direction) perpendicular to the stack surface of the quantum well structure in the active layer 15. is there. The square of the normalized wave function | Ψ (z) | ² represents the probability density for one electron integrated in the x-axis direction and the y-axis direction orthogonal to the z-axis at the position z in the z-axis direction. ing.

添加位置ｚ_ｉｍｐにある不純物と、ミニバンドＭＢ内にある電子とによって生成されるダイポール長Ｚ（ｚ_ｉｍｐ）を示す上記の式（３）は、ミニバンドＭＢ内での電子分布を示す式（８）に位置ｚを乗じた式（１０）

によって求められるミニバンドＭＢ内での電荷分布（電子分布）の重心位置ｚ_ｃを、不純物の添加位置ｚ_ｉｍｐを座標の基準として表現したものとなっている。 The electron distribution indicating the probability that electrons are distributed at the position z in the stacking direction in the miniband MB, and the resulting charge distribution are expressed by the following equations (8) and (9).

The above equation (3) showing the dipole length Z (z _imp ) generated by the impurity at the addition position z _imp and the electrons in the miniband MB is an equation showing the electron distribution in the miniband MB ( 8) Multiplying position z (10)

Gravity position z _c of the charge distribution (electron distribution) within the miniband MB obtained by, has become a representation of a feed point z _imp impurities as reference coordinates.

This means that when the center of gravity position z _c of the charge distribution coincides with the impurity addition position z _imp , the dipole length Z (z _imp ) becomes zero, so that no electric field is generated by the dipole and voltage noise is generated. Indicates that there will be no more. In addition, with respect to the expression (7) in the case where the impurity addition position is spatially expanded, the integration is performed by multiplying the dipole length Z (z _imp ) at the impurity addition position z _imp by the impurity existence probability p (z _imp ). This means that the dipole length Z is calculated by weighting the gravity center of the impurity. Therefore, necessarily, in a case where the center-of-gravity position z _c of the charge distribution in the miniband MB, the center position of the added weight distribution of impurities (gravity center position) and is coincident, so that the voltage noise is suppressed.

As described above, in the quantum cascade laser 1 </ _b > A according to the present embodiment, the impurities for supplying electrons in the injection layer 18 with respect to the barycentric position z _c of the charge distribution in the miniband MB determined by the above formula (10). Add so that the added amount distribution satisfies a predetermined condition. Specifically, in the injection layer 18, the impurity supplying electrons, the distance from the gravity center position z _c of the charge distribution within the miniband MB is centered position following positions 3.6 nm, 12 nm or less in half It is set as the structure added with the addition amount distribution which has a full width (FWHM: Full Width at Half Maximum). The above conditions required for the impurity addition amount distribution will be specifically described later.

  The effect of the quantum cascade laser 1A according to the present embodiment will be described.

In the quantum cascade laser 1A of the above embodiment, in the subband level structure in the unit stacked body 16 composed of the light emitting layer 17 and the injection layer 18, the emission upper level L _up and the emission lower level L _low or respectively It is provided and the mini-band MB that includes a plurality of levels, which functions as a relaxation level L _r. In addition, in the quantum well structure in the unit stacked body 16, the injection layer 18 includes four or more (n) barrier layers and well layers. Further, the miniband MB is composed of four or more (I) subband levels.

In such a configuration, the gravity center position z _c of the charge distribution in the miniband MB determined by the above formula (10) is referred to for the impurity for supplying electrons added to a predetermined position in the injection layer 18. and, the distance from the gravity center position z _c is the center position (barycentric position) of the following positions 3.6 nm, are configured to add an impurity in amount distribution having the following FWHM 12 nm. In this way, by adding impurities in an additive amount distribution that satisfies a predetermined condition with respect to the center of gravity of the charge distribution in the miniband, the influence of electrical fluctuations in the laser element is suppressed, and the spectral line width Can be made narrower.

  Here, in the quantum cascade laser described above, for the semiconductor layer to which the impurity is added in the injection layer 18, the impurity is included in the n barrier layers and well layers constituting the injection layer 18 in the injection layer 18. Thus, it is preferable that the dopant is added in a single well layer or a single barrier layer. Alternatively, the impurity may be added to the implanted layer 18 over the adjacent well layers and barrier layers among the n barrier layers and well layers that constitute the implanted layer 18. However, in any of these cases, the distribution of the added amount of impurities needs to satisfy the above-described conditions.

  In addition, with respect to the width of the impurity addition amount distribution, it is preferable that the impurity is added in the addition amount distribution having a full width at half maximum of 4.4 nm or less in the injection layer 18. Thereby, the influence of the electrical fluctuation in the laser element can be further suppressed.

The addition for the location of the added weight distribution of impurities in the implanted layer 18, impurity, the distance from the gravity center position z _c of the charge distribution within the miniband MB is centered position following positions 1.2nm It is preferable to add by quantity distribution. Even with such a configuration, it is possible to further suppress the influence of electrical fluctuation in the laser element.

  Further, in the quantum cascade laser 1A described above, the active layer 15 has a plurality of types of unit stacks having different quantum well structures as the unit stack 16, and the impurity additive distribution in the injection layer 18 is as follows. It is good also as a structure set individually for every kind of unit laminated body 16. FIG. As described above, by adding impurities by setting an addition amount distribution corresponding to the type of quantum well structure in each unit stacked body 16 to a plurality of types of unit stacked bodies, active layers 15 having various configurations can be formed. The influence of the electric fluctuation in the laser element can be suitably suppressed.

  Evaluation of VNPSD (Voltage Noise Power Spectral Density) shown in the above formulas (2) and (7), and the validity of the above condition for the impurity addition amount distribution in the injection layer 18 obtained based on the evaluation formula A study was made using a specific laser element. FIG. 4 is a chart showing a specific example of the semiconductor multilayer structure constituting the quantum cascade laser 1A. In the chart shown below, the “u” type indicates an undoped type. Further, specifically, Si is added as an n-type impurity.

In the configuration example shown in FIG. 4, an n ⁺ type InP substrate 50 having a carrier concentration of 5 × 10 ¹⁸ (/ cm ³ ) and a thickness of 350 μm is used as the semiconductor substrate 10. 5 μm InP lower cladding layer 51, 10.0 nm thick InGaAs / AlInAs lower graded layer 52, 0.25 μm thick InGaAs lower guide layer 53, InGaAs / AlInAs lower injection layer 25, and unit laminate 16 are formed in multiple stages. 2. Laminated InGaAs / AlInAs active layer 15, InGaAs / AlInAs upper injection layer 20, 0.25 μm thick InGaAs upper guide layer 54, 10.0 nm thick InGaAs / AlInAs upper graded layer 55, and thickness By stacking 5 μm InP upper cladding layer 56 in order, the quantum cascade laser Child structure is formed. The carrier concentration in each semiconductor layer is as shown in FIG.

In the present configuration example, an InP second contact layer 57 having a thickness of 0.5 μm and a carrier concentration of 3 × 10 ¹⁸ (/ cm ³ ), a thickness of 0.02 μm, and a carrier concentration is further formed on the upper cladding layer 56. A 5 × 10 ¹⁸ (/ cm ³ ) InP first contact layer 58 and a cap layer 59 having a thickness of 0.01 μm and a carrier concentration of 1 × 10 ¹⁹ (/ cm ³ ) are provided.

FIG. 5 is a chart showing an example of the configuration of the upper injection layer 20, the active layer 15, and the lower injection layer 25 in the quantum cascade laser shown in FIG. FIG. 6 is a chart showing an example of the configuration of the unit laminate body 16 for one cycle in the active layer 15. In this configuration example, the upper injection layer 20 is composed of AlInAs barrier layers 201 to 204 and InGaAs well layers 211 to 213, and impurities are added at a carrier concentration of 3 × 10 ¹⁷ (/ cm ³ ) in the well layer 213. ing. The lower injection layer 25 includes AlInAs barrier layers 251 to 255 and InGaAs well layers 261 to 264. In the well layer 264, impurities are added at a carrier concentration of 3 × 10 ¹⁷ (/ cm ³ ).

FIG. 6 shows the configuration of the unit laminate 16 of the active layer 15 in the quantum cascade laser element (element I) having the structure I. In the configuration of the element I, the light emitting layer 17 in the unit stacked body 16 includes four AlInAs barrier layers 161 to 164 and InGaAs well layers 171 to 174. The injection layer 18 is composed of seven AlInAs barrier layers 181 to 187 and InGaAs well layers 191 to 197. In the seventh well layer 197, impurities are added at a carrier concentration of 3 × 10 ¹⁷ (/ cm ³ ). Has been.

  The active layer 15 in this configuration example is configured by stacking unit laminated bodies 16 including a light emitting layer 17 and an injection layer 18 in 40 cycles. Of the 40 unit stacked bodies 16 constituting the active layer 15, in the uppermost unit stacked body 16, the barrier layer 161 of the light emitting layer 17 is replaced with the barrier layer 204 of the upper injection layer 20. Further, in the lowermost unit laminated body 16, the injection layer 18 is replaced with the lower injection layer 25.

FIG. 7 is a diagram showing the configuration of the unit laminate body 16 and the subband level structure in the active layer 15 of the element I shown in FIG. In this configuration example, the unit stacked body 16 has a light emission upper level L _up , a high energy level L _h that functions as a second light emission upper level, and a miniband MB in its subband level structure. (See FIG. 2).

FIG. 8 shows the configuration of the unit laminate 16 of the active layer 15 in the quantum cascade laser element (element II) having the structure II. In the configuration of the element II, the light emitting layer 17 in the unit stacked body 16 includes four AlInAs barrier layers 161 to 164 and InGaAs well layers 171 to 174. The injection layer 18 is composed of seven AlInAs barrier layers 181 to 187 and InGaAs well layers 191 to 197. In the fourth well layer 194, impurities are added at a carrier concentration of 3 × 10 ¹⁷ (/ cm ³ ). Has been. Note that the structure of the element II is the same as that of the element I except for the impurity addition position.

FIG. 9 is a diagram showing the impurity addition position z _imp and the impurity level L _imp in the injection layer 18 for the elements I and II having the above-described structure. In FIG. 9A, the well layer to which the impurity is added in the injection layer 18 and the energy position of the impurity level are shown by graphs. In FIG. 9B, the impurity addition position z _imp and the impurity level energy E _imp are shown in a chart.

Here, the impurity addition position z _imp is based on the end of the injection barrier layer 161 adjacent to the injection layer 18 on the well layer 171 side, as shown in the graph of FIG. The energy E _imp of the impurity level is based on the energy positions indicated by black circles and one-dot chain lines in FIG. 9A. Further, in FIG. 9, in addition to the element I for adding impurities to the seventh well layer 197 and the element II for adding impurities to the fourth well layer 194, impurities are added to the sixth well layer 196, which will be described later. For the element III to be added and the element IV to which an impurity is added to the fifth well layer 195, the impurity addition position z _imp and the impurity level L _imp are also shown.

With respect to the quantum cascade laser having the above-described configuration, a laser element having a ridge structure was manufactured, and VNPSD was measured by performing frequency analysis of noise voltage, and VNPSD was evaluated by calculation using the above-described evaluation formula. In the calculation results for VNPSD shown below, τ _eS = 0.1 _μs , τ _eL = 100 ms, ε _s = 14, M = 40, n _imp = 1.0 × 10 ¹¹ cm ⁻ for each parameter value. ² and a numerical value of S = 1.4 × 10 ⁻⁴ cm ² are used. In the calculation using the formula (2) for δ doping, the calculation is performed assuming that the impurity is localized at the center of the well layer. The bias voltage applied to the active layer 15 is 35 kV / cm.

FIG. 10 is a graph showing the frequency dependence of noise power. In this graph, the horizontal axis indicates the frequency (Hz), and the vertical axis indicates the noise power (V ² / Hz). Further, the graph of FIG. 10 shows the measurement result of VNPSD of the element I at an electron temperature of 180K. Here, together with the measurement results, the noise frequency f _N is an order of magnitude higher becomes the VNPSD shows an order of magnitude down line by broken lines, the measurement result of VNPSD is, it can be confirmed that becomes 1 / f _N noise .

FIG. 11 is a graph showing the temperature dependence of VNPSD for elements I and II. In this graph, the horizontal axis indicates the electron temperature (K), and the vertical axis indicates VNPSD (V ² / Hz). Further, the graph of FIG. 11 shows the experimental measurement result and theoretical calculation result in the element I, and the experimental measurement result and theoretical calculation result in the element II for VNPSD at the noise frequency f _N = 100 Hz. It shows. As shown in FIG. 11, the measurement results and calculation results for VNPSD agree fairly well, and the validity of the above-described evaluation formula can be confirmed.

The graph of FIG. 11 shows the data at the noise frequency f _N = 100 Hz. As can be seen from FIG. 10, the measured VNPSD has a characteristic of 1 / f _N , and the evaluation formula (2) because that is the functional form of the 1 / _{f N,} not match happens to noise frequency 100 Hz.

In FIG. 11, the temperature dependence of VNPSD calculated using the evaluation formula (2) shows that in the device II (E _imp = 0.2154 eV), VNPSD indicating electrical noise at the operating temperature of the electron temperature of 550K. Is very strongly suppressed. On the other hand, for the element I (E _imp = 0.1563 eV), there is no temperature region where VNPSD is strongly suppressed.

FIG. 12 shows the calculation of the temperature dependence of VNPSD for the element III (E _imp = 0.1745 eV) having the same element structure and the impurity addition position z _imp being the position of the sixth well layer 196 shown in FIG. It is a graph which shows a result. In this configuration, VNPSD is strongly suppressed at an operating temperature of 150K.

FIG. 13 shows the calculation of the temperature dependence of VNPSD for the element IV (E _imp = 0.1950 eV) having the same element structure and the impurity addition position z _imp being the position of the fifth well layer 195 shown in FIG. It is a graph which shows a result. In this configuration, the VNPSD is strongly suppressed at the operating temperature of 300K when the calculation result with δ doping is seen.

In addition, the broken line shown in the graph of FIG. 13 has shown VNPSD assumed when there is no suppression of noise. Further, in the graph of FIG. 11, in the case of the element II, VNPSD tends to be remarkably lowered on the extremely low temperature side. This is due to a decrease in the probability f (E _imp , E _F , T _e ) that electrons exist in the impurity level L _imp at an extremely low temperature, and not due to a decrease in the charge dipole.

  In each case of the devices I, II, III, and IV, the electron distribution (charge distribution) in the miniband, the position of the center of gravity, and the spatial position of the impurity addition are examined. 14 (a), 14 (b), 15 (a), and 15 (b) respectively show the quantum well structure (FIG. 7, FIG. 7) for the charge distribution (electron distribution) in the miniband MB. It is a graph shown with FIG. 9 (a). In these graphs, the horizontal axis indicates the position (nm) in the stacking direction, and the vertical axis indicates the energy (eV) for the quantum well structure or the number of carriers (au) for the electron distribution. The bias voltage applied to the active layer 15 is 35 kV / cm as described above.

The graph of FIG. 14A shows the electron distribution at the electron temperature 0K in the miniband and the position of the center of gravity (indicated by an arrow) for the element I. In this configuration, the electronic distribution The more low temperature is, but biased towards small energy, even in 0K, centroid position z _c of the electron distribution is in the position of 8.0nm as viewed from the injection barrier layer. In the element I, the impurity addition position is z _imp = 5.3 nm in the seventh well layer 197 of the injection layer 18 and is largely deviated from the center position of the electron distribution. Therefore, with this configuration, the charge dipole cannot be canceled and noise is not suppressed.

The graph in FIG. 14B shows the electron distribution at the electron temperature of 550 K in the miniband and the position of the center of gravity of the element II. The element II has a configuration in which the impurity addition position is z _imp = 22.8 nm and the VNPSD is minimum at an electron temperature of 550 K. In this case, the center of gravity position z _c is certain even in the miniband electron distribution. Similarly to the impurity addition position z _imp , the position is 22.8 nm.

The graph of FIG. 15A shows the electron distribution at the electron temperature of 150 K in the miniband and the position of the center of gravity of the element III. The element III has a configuration in which the impurity addition position is z _imp = 11.4 nm and the VNPSD is minimum at 150 K. However, even in this case, the center of gravity position of the miniband electron distribution is 11.4 nm. is there.

The graph of FIG. 15B shows the electron distribution at the electron temperatures of 250 K, 300 K, and 350 K in the miniband and the position of the center of gravity for the element IV. The element IV has a configuration in which the impurity addition position is z _imp = 17.1 nm and the VNPSD is minimum at 300 K. Even in this case, the center of gravity position at 300 K is 17.1 nm for the miniband electron distribution. In position. Further, regarding the electron distribution at the electron temperatures of 250K and 350K that are not 300K at which VNPSD is minimized, the positions of the centers of gravity are 15.7 nm and 18.4 nm, respectively, which coincide with the impurity addition positions. Absent.

The discussion so far has mainly discussed and calculated the configuration of δ doping in which impurities are locally added to one addition position z _imp in a specific semiconductor layer in the injection layer 18. On the other hand, in an actual laser element, the impurity addition amount distribution has a certain width and spread in the stacking direction. In FIG. 13 showing the temperature dependence of VNPDS in the element IV with respect to such an impurity addition width, in addition to the calculation result of δ doping, an expression (7 The calculation results using) are shown.

  Specifically, in the graph of FIG. 13, the impurity addition width is 0 nm (δ doping), 0.6 nm, 1.2 nm, 1.8 nm, in order from the bottom in the graph of the solid line in the graph position at 300 K. The temperature dependence of VNPSD is shown for 2.4 nm, 3.0 nm, 3.6 nm, 5.0 nm, 6.0 nm, 8.0 nm, 10.0 nm, 12.0 nm, and 14.0 nm. Moreover, the broken line graph in FIG. 13 shows VNPSD assumed when there is no noise suppression as described above.

によって定義して、不純物の添加幅（ドーピング層の厚さ）と、ノイズ抑制量との関係について調べた。 As can be seen from the graph of FIG. 13, in a state where noise is not suppressed, VNPSD shows a function that gradually changes with temperature. Therefore, the noise suppression amount (Suppression) is expressed by the following equation (11) for the data shown in FIG.

The relationship between the impurity addition width (doping layer thickness) and the noise suppression amount was examined.

  FIG. 16 is a graph showing the dependency of the noise suppression amount on the impurity addition width. In this graph, the horizontal axis indicates the impurity addition width (nm), and the vertical axis indicates the above-described noise suppression amount. Moreover, the broken line graph in FIG. 16 shows VNPSD when the addition width is 0 nm (δ doping). In this data, when the addition width is 14 nm, suppression of noise cannot be confirmed, but when the addition width is less than that, it is understood that VNPSD is suppressed. Therefore, with respect to the addition width in the impurity addition amount distribution, it is preferable to add the impurity in an addition amount distribution having a full width at half maximum of 12 nm or less.

  In particular, in the data of FIG. 16, noise suppression of about one digit is achieved with the addition width of 4.4 nm, and considering that noise suppression of one digit or more is a high noise suppression effect, It becomes the limit of spread. Considering this point, it is preferable that the impurity is added in an additive amount distribution having a full width at half maximum of 4.4 nm or less. Here, in the InGaAs material system having the above configuration example, 0.6 nm corresponds to the thickness of one lattice layer. In this case, the spread of about seven lattice layers is considered to be the limit of the impurity spread for obtaining a very effective noise suppression effect.

Next, the positional shift of the addition position in the impurity addition amount distribution will be considered. As described above, the impurity addition position z _imp is preferably added with the center of gravity position z _c of the charge distribution in the miniband as the center position. However, with respect to this addition position, even if there is a positional deviation within a certain range, a noise suppression effect can be obtained.

FIG. 17 is a graph showing changes in the temperature dependence of VNPSD due to the displacement of the impurity addition position. In this graph, the horizontal axis indicates the electron temperature (K), and the vertical axis indicates VNPSD (V ² / Hz). Further, in the graph of FIG. 17, regarding the element IV having a structure in which the noise is minimum at around 300 K, the change in the temperature dependence of VNPSD and the electron in the position shift of the addition position within the range of +4.8 nm to −4.8 nm It shows the change in noise suppression effect at a temperature of 300K.

In the calculation results shown in FIG. 17, since δ doping is impossible in an actual device, the calculation was performed for the case where impurities were added with an addition width of 0.6 nm corresponding to the lattice constant of InGaAs. Moreover, the broken line graph in FIG. 17 indicates VNPSD assumed when noise is not suppressed at the noise frequency f _N = 100 Hz.

According to this data, the position shift (distance of the addition position from the center of gravity position) of the impurity addition position (center position of the addition amount distribution) z _imp from the center of gravity position z _c of the charge distribution in the miniband is 3.6 nm. If it is below, it will be understood that VNPSD is suppressed at 300K. In particular, considering that noise suppression of one digit or more is a high noise suppression effect, the position shift of the impurity addition position z _imp from the center of gravity position z _c of the charge distribution in the miniband should be 1.2 nm or less. Is preferred.

  A specific configuration example of the quantum cascade laser having the above configuration will be further described. FIG. 18 is a perspective view showing an example of a specific configuration of the quantum cascade laser. In the quantum cascade laser 1B shown in FIG. 18, an InP lower cladding layer 51, an InGaAs / AlInAs lower graded layer 52, an InGaAs lower guide layer 53, an InGaAs / AlInAs lower injection layer 25, on an InP substrate 50 (semiconductor substrate 10). The InGaAs / AlInAs active layer 15, the InGaAs / AlInAs upper injection layer 20, the InGaAs upper guide layer 54, the InGaAs / AlInAs upper graded layer 55, the InP upper cladding layer 56, and the InP second contact, in which the unit laminates 16 are stacked in multiple stages. The element structure of the quantum cascade laser 1B is formed by sequentially stacking the layer 57, the InP first contact layer 58, and the InGaAs cap layer 59. Of these semiconductor layers, the structure of each layer except the upper injection layer 20, the active layer 15, and the lower injection layer 25 is the same as that shown in FIG.

  In the configuration example shown in FIG. 18, in such a semiconductor stacked structure, all the semiconductor layers thereabove are etched leaving a width w = 14 μm so that the lower cladding layer 51 immediately above the InP substrate 50 is exposed. The exposed side surface is covered with an insulating layer 60 made of SiN. A contact hole is formed in the insulating layer 60 on the cap layer 59 having a ridge structure, and an electrode structure 61 is provided for the contact hole.

  The electrode structure 61 has a structure in which a contact electrode extending from an Au electrode having a thickness of 300 nm electrically connected to the contact layer is led out to the insulating layer 60 on the exposed lower cladding layer 51 to form a bonding pad. ing. In this configuration example, the ridge length of the ridge structure is, for example, 1 = 1 mm.

FIG. 19 is a chart showing configurations of the upper injection layer 20, the active layer 15, and the lower injection layer 25 in the first embodiment. FIG. 20 is a chart showing a configuration of the unit laminate body 16 for one cycle in the active layer 15 in the first embodiment. FIG. 21 is a diagram showing the configuration of the unit laminate structure 16 in the active layer 15 of Example 1 shown in FIG. 20 and the subband level structure. FIG. 21 also shows the impurity level L _imp together with the subband level structure including the emission upper level L _up and the miniband MB. The bias voltage applied to the active layer 15 is 35 kV / cm.

The present Example 1 corresponds to the structure of the element III in which the impurity is added to the sixth well layer 196 of the injection layer 18 (see FIG. 9), and the specific impurity addition amount distribution is shown in FIG. It is like that. That is, in Example 1, the sixth well layer 196 having a thickness of 3.6 nm is divided into three regions having a thickness of 1.5 nm, 0.6 nm, and 1.5 nm, respectively. Impurity Si is added at a carrier concentration of 1.8 × 10 ¹⁸ (/ cm ³ ) only in the central region.

FIG. 22 is a diagram showing device characteristics of the quantum cascade laser having the configuration of the first embodiment. FIG. 22 (a) shows the temperature dependence of VNPSD in noise frequency 100 Hz, the electron temperature _{T e} of the active layer 15 is noise becomes minimum when the 150K, noise suppression effect of two orders of magnitude is obtained ing. FIG. 22B shows the electron distribution at 150 K in the miniband and the centroid position thereof, and the centroid position of the electron distribution is 11.4 nm which coincides with the impurity addition position.

  FIG. 23 is a chart showing a configuration of the unit laminate body 16 for one cycle in the active layer 15 in the second embodiment. In the second embodiment as well, the basic semiconductor multilayer structure of the quantum cascade laser and the configurations of the upper injection layer 20 and the lower injection layer 25 are the same as those in the first embodiment.

Example 2 corresponds to the structure of the element IV in which impurities are added to the fifth well layer 195 of the injection layer 18 (see FIG. 9). The specific impurity distribution of the impurities is shown in FIG. It is like that. That is, in Example 2, the fifth well layer 195 having a thickness of 3.6 nm is divided into three regions having a thickness of 1.5 nm, 0.6 nm, and 1.5 nm, respectively. Impurity Si is added at a carrier concentration of 1.8 × 10 ¹⁸ (/ cm ³ ) only in the central region.

FIG. 24 is a diagram illustrating element characteristics of the quantum cascade laser having the configuration of the second embodiment. FIG. 24 (a) is shows the temperature dependence of VNPSD in noise frequency 100 Hz, the electron temperature _{T e} of the active layer noise at 300K is the minimum. FIG. 22B shows the electron distribution at 300 K in the miniband and the centroid position thereof, and the centroid position of the electron distribution is 17.1 nm, which coincides with the impurity addition position.

  Here, the relationship between voltage noise and frequency fluctuation in the mid-infrared quantum cascade laser, that is, the full width at half maximum of the spectral line will be described (see Non-Patent Documents 2 and 6).

ただし、上記式（１２）において、ｆ_ｃは下記の式（１３）で与えられる。

Ｎ_{ｆｌｉｃｋｅｒ}は、ノイズ周波数１Ｈｚにおけるレーザ周波数ノイズパワースペクトル密度である。また、Ｔ_ｗは、計測における積分時間である。この式から、スペクトル線幅は周波数ノイズと密接に関係し、周波数ノイズが２桁減少すれば、スペクトル線幅は１桁減少することがわかる。 In Non-Patent Document 6, the full width at half maximum δν of the spectral line width of the laser frequency is obtained by the following equation (12) when the frequency noise indicates a 1 / f _n type function form, that is, N _flicker / f _n. It is shown.

However, in the above equation (12), _fc is given by the following equation (13).

N _flicker is a laser frequency noise power spectral density at a noise frequency of 1 Hz. _Tw is an integration time in measurement. From this equation, it can be seen that the spectral line width is closely related to the frequency noise, and if the frequency noise is reduced by two digits, the spectral line width is reduced by one digit.

4 and 5 of Non-Patent Document 2 show the relationship between the frequency noise power spectral density and the temperature of the same element, and the relationship between the current noise power spectral density and the temperature. According to this, the frequency fluctuation is almost constant in the temperature range of 200 K to 270 K, and is 7 × 10 ⁶ Hz ² / Hz at a noise frequency of 3 kHz. The current noise power spectral density corresponding to this is also substantially constant in the same temperature region, and is 6 × 10 ⁻¹⁷ A ² / Hz at a noise frequency of 3 kHz.

Assuming that the conversion coefficients δν / δi representing the frequency change with respect to the current change are the same, and using the 1 / f _n relationship, these values are converted into values at a noise frequency of 100 Hz corresponding to T _w = 10 ms. respectively and ^{2.1 × 10 8 Hz 2 /Hz,1.8×10 -15} a 2 / Hz. When this number to the _{original, N flicker} becomes 2.1 × ¹⁰ 10 Hz, and the when determining the _{f c} from the above formula (13) and 193KHz. Furthermore, when the full width at half maximum δν of the spectral line width of the laser frequency at T _w = 10 ms is obtained from the equation (12), it can be estimated as 939 kHz.

On the other hand, in the above embodiment according to the present invention, when an impurity is added with an addition width of 0.6 nm in FIG. 13, a voltage noise power spectral density (VNPSD) of 4 × 10 ⁻¹⁸ V ² / Hz at a noise frequency of 100 Hz. However, since the differential resistance of the element is about 10Ω, the current noise power spectral density is 4 × 10 ⁻²⁰ A ² / Hz. This fluctuation is about 1/45000 smaller than the fluctuation described in the literature.

This also indicates that N _flicker is 1/45000. Since the full width at half maximum of the spectral line is proportional to the square root of N _flicker , it can be estimated that the full width at half maximum of the spectral line is 4.43 kHz. Furthermore, considering the influence on the spectral line width by the term [ln (f _c T _w )] ^1/2 in Equation (12), a very narrow full width at half maximum of 2.39 kHz is expected at room temperature. It is shown that.

  A specific configuration of the quantum cascade laser will be further described. In the above-described embodiments and examples, the active layer 15 has a structure in which the unit stacked body 16 having the light emitting layer 17 and the injection layer 18 having the same structure is stacked in multiple stages. However, such a configuration of the active layer 15 may be configured such that the unit laminate 16 has a plurality of types of unit laminates having different quantum well structures and subband level structures.

ここで、式（１４）において、添え字のｊは、複数段の単位積層体のうちでｊ段目の単位積層体についてのパラメータを示している。また、上記の式（１４）において、ダイポール長Ｚ（ｚ_{ｉｍｐ，ｊ}）は、下記の式（１５）

によって表される。 Further, in the configuration having a plurality of types of unit laminate bodies 16 as described above, the impurity addition amount distribution (addition position and addition width) in the injection layer 18 is individually set for each type of unit laminate body 16. Is preferred. In this case, for example, the above-described evaluation formula (7) of VNPSD becomes the following generalized formula (14).

Here, in the formula (14), the subscript j indicates a parameter for the j-th unit laminated body among the plurality of unit laminated bodies. In the above equation (14), the dipole length Z (z _{imp, j} ) is expressed by the following equation (15):

Represented by

ダイポール長Ｚ（ｚ_{ｉｍｐ，ｊ}）を示す上記の式（１５）は、ミニバンド内での電子分布を示す式（１６）に位置ｚを乗じた式（１７）

によって求められるミニバンド内での電荷分布（電子分布）の重心位置ｚ_ｃ，ｊを、不純物の添加位置ｚ_{ｉｍｐ，ｊ}を座標の基準として表現したものとなっている。 In the j-th unit stacked body in the active layer, an electron distribution indicating the probability that electrons are distributed at the position z in the stacking direction within the miniband is represented by the following formula (16).

The above equation (15) indicating the dipole length Z (z _{imp, j} ) is obtained by multiplying the equation (16) indicating the electron distribution in the miniband by the position z.

The center-of-gravity position z _{c, j} of the charge distribution (electron distribution) in the miniband obtained by the above expression is expressed using the impurity addition position z _{imp, j} as the coordinate reference.

This means that, in the arbitrary j-th unit laminate constituting the active layer, when the center of gravity position z _{c, j} of the charge distribution coincides with the impurity addition position z _{imp, j} , the dipole length Z (z _{imp, j} ) is zero, which indicates that no electric field is generated by the dipole and no voltage noise is generated.

The position of impurity addition in the injection layer will be further described. In the above-described embodiments and examples, an impurity is added to a single addition position z _imp in the injection layer. On the other hand, considering a configuration in which impurities are added to a plurality of addition positions in the injection layer, such a configuration cannot provide a sufficient noise suppression effect.

FIG. 25 shows (a) the temperature dependence of VNPSD and (b) the charge in the miniband when δ-doped impurities are doped in half at two positions of the addition position z _imp = 9.6 nm and 24.6 nm. It is a figure shown about distribution. Here, for VNPSD, the calculation results obtained using the evaluation formula (7) are shown. In this case, the gravity center position of the impurity added to the two positions is 17.1 nm corresponding to the impurity addition position in the element IV, but the noise including 300 K at which the noise is minimized in the element IV is included. The inhibitory effect is not obtained.

  That is, in the configuration in which the first and second impurities are added to the spatially separated addition positions as described above, the first and second impurities are excited and trapped completely independent of each other as described above. Therefore, the charge dipoles generated by each of the first and second impurities and the center of the charge distribution in the miniband cannot be canceled. Moreover, in the said structure, since the spread (addition width) of impurity addition is as wide as 15 nm, it turns out that noise cannot be suppressed at all.

  The full width at half maximum of the added amount distribution when impurities are added to a plurality of addition positions is defined as shown in FIG. That is, as shown in the graph D1, when an impurity is δ-doped at two addition positions, the full width at half maximum is the interval D2 between the two addition positions. Further, as shown in graph D6, when impurities are added to two addition positions with a certain width, the full width at half maximum is the value at the outer position where the half value of the peak is obtained in each addition amount distribution. The interval D7.

  The quantum cascade laser according to the present invention is not limited to the above-described embodiments and configuration examples, and various modifications are possible. For example, FIG. 2 shows an example of the subband level structure in the unit stacked body 16 of the active layer 15. Specifically, various configurations other than those in FIG. 2 may be used. In general, a unit stack includes at least a light emission upper level and a miniband including a plurality of levels each functioning as a light emission lower level or a relaxation level in a subband level structure of the quantum well structure. If you do.

  In the above configuration example, an InP substrate is used as the semiconductor substrate and the active layer is configured by InGaAs / AlInAs. However, in addition to such a material system, various configurations are specifically used. good. As such a semiconductor material system, various material systems such as GaAs / AlGaAs, InAs / AlGaSb, AlGaN / GaN, and Si / SiGe can be used.

  In the above configuration example, the configuration in which impurities are added to a single well layer among the barrier layer and the well layer that configure the injection layer is not limited to such a configuration. The impurity may be added in the barrier layer or over the adjacent well layer and barrier layer. However, even in the case of these configurations, the impurity addition amount distribution needs to satisfy the above-described conditions for the addition position and the addition width.

  INDUSTRIAL APPLICABILITY The present invention can be used as a quantum cascade laser capable of reducing the spectral line width by suppressing the influence of electrical fluctuations in the laser element.

DESCRIPTION OF SYMBOLS 1A, 1B ... Quantum cascade laser, 10 ... Semiconductor substrate, 15 ... Active layer, 16 ... Unit laminated body, 17 ... Quantum well light emitting layer, 18 ... Injection layer, 161 ... Injection barrier layer, 162-164 ... Barrier layer, 171 ˜174 ... well layer, 181-187 ... barrier layer, 191-197 ... well layer, 20 ... upper injection layer, 25 ... lower injection layer,
50 ... InP substrate, 51 ... InP lower cladding layer, 52 ... InGaAs / AlInAs lower graded layer, 53 ... InGaAs lower guide layer, 54 ... InGaAs upper guide layer, 55 ... InGaAs / AlInAs upper graded layer, 56 ... InP upper portion Cladding layer, 57 ... InP second contact layer, 58 ... InP first contact layer, 59 ... InGaAs cap layer, 60 ... insulating layer, 61 ... electrode structure,
L _up ... upper emission level, L _h ... high energy level (second emission upper level, injection level), MB ... miniband, L _low ... lower emission level, L _r ... relaxation level, L _imp ... impurity levels.

Claims (4)

A semiconductor substrate;
A cascade structure in which the quantum well light-emitting layers and the injection layers are alternately stacked is formed by stacking unit stacks of quantum well light-emitting layers and injection layers in multiple stages, which are provided on the semiconductor substrate. An active layer,
The unit stacked body has at least a light emission upper level and a miniband including a plurality of levels each functioning as a light emission lower level or a relaxation level in the subband level structure of the quantum well structure,
Light is generated by an intersubband transition of electrons from the upper emission level to the lower emission level in the quantum well light emitting layer, and the electrons that have undergone the intersubband transition have the relaxation level in the miniband. And then injected into the quantum well light-emitting layer of the subsequent unit laminate body,
The injection layer is n (n is an integer of 4 or more) is configured to include a barrier layer and the well layer of the miniband, viewed contains a level of the number I (I is an integer of 4 or more), the In the injection layer, an impurity for supplying electrons is added to a single well layer or a single barrier layer among the n barrier layers and well layers constituting the injection layer. And
In the injection layer, said impurity for supplying electrons, the following formula (1)

(Where z is the position of the electron in the miniband in the stacking direction, E _i is the energy of the i th level included in the mini band, and ψ _i (z) is the i th level included in the mini band. normalized wave function of level, T _e is the electron temperature in the active layer, k _B is the distance from the gravity center position z _c of the charge distribution within the miniband depends Boltzmann constant) 3.6 nm A quantum cascade laser characterized in that the quantum cascade laser is added in an additive amount distribution having a full width at half maximum of 4.4 nm or less with the following position as a central position. In the injection layer, said impurity, the distance from the gravity center position z _c of the charge distribution within the miniband is added in the amount distribution centered position following positions 1.2nm quantum cascade laser according to claim 1 Symbol mounting features. The active layer has a plurality of types of unit stacks having different quantum well structures as the unit stack,
3. The quantum cascade laser according to claim 1, wherein the distribution of the added amount of the impurity in the injection layer is set for each type of the unit stacked body.   In the injection layer, the impurity is added into the single well layer, the single well layer is divided into three regions, and the impurity is added only in the central region. The quantum cascade laser according to any one of claims 1 to 3, wherein

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