Analysis of Interface Control Methods for InAs/GaSb Type-Ⅱ Superlattice Materials Grown by MBE
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摘要: 本文系统地介绍了MBE外延生长InAs/GaSb Ⅱ类超晶格材料的界面控制方法，主要包括生长中断法、表面迁移增强法、Ⅴ族元素浸润法和体材料生长法。短波（中波）InAs/GaSb超晶格材料界面采用混合（mixed-like）界面，控制方法以生长中断法为主；长波（甚长波）超晶格材料界面采用InSb-like界面，控制方法采用表面迁移增强法（migration-enhanced epitaxy, MEE）或Sb soak法及体材料生长相结合。讨论分析了InAs/GaSb超晶格材料界面类型选择的依据，简述了界面控制具体实施理论，以及相关研究机构对于不同红外探测波段的超晶格材料界面类型及控制方法的选择。通过界面结构外延生长工艺设计即在界面控制方法的基础上进行快门顺序实验设计，有效地提高界面层的应力补偿效果，这对于长波、甚长波及双色（甚至多色）超晶格材料的晶体质量优化和器件性能提升具有重要意义。
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关键词:
- InAs/GaSb Ⅱ类超晶格 /
- InSb-like界面 /
- GaAs-like界面 /
- 生长中断法 /
- MEE
Abstract: This article systematically introduces interface control methods for the MBE growth of InAs/GaSb type-Ⅱ superlattice materials, including the interrupted growth epitaxy method, migration-enhanced epitaxy, V group element soak method, and bulk material growth method. The short-wavelength (mid-wavelength) InAs/GaSb superlattice material interface adopts a mixed-like interface, and the control method is mainly the interrupted growth epitaxy method, the long-wavelength (very long-wavelength) superlattice material interface adopts the InSb-like interface, and the control method adopts the migration-enhanced epitaxy (MEE) or Sb soak method combined with bulk material growth. The basis for selecting the interface type of InAs/GaSb superlattice material is discussed and analyzed, and the specific implementation theory of interface control is briefly described, along with the selection of interface types and control methods of superlattice materials in different infrared detection wavelength bands by related research institutions. To effectively improve the stress compensation effect of the interface layer, the interface structure epitaxial growth process design, that is, the experimental design of different shutter sequences based on the interface control method, was used. This is of great significance for the optimization of the crystal quality and device performance of long-wave, very long-wave, and two-color (even multi-color) superlattice materials. -
0. 引言
随着科技的发展，激光技术不仅在测距、遥感、通信等方面得到广泛的应用，而且在军事领域得到各国的重视，各类激光武器相继推出，例如激光制导武器、激光雷达等。激光近感探测根据激光束来感知目标，通过目标的回波信号来确定目标的距离和方位，其特点是方向性强、探测精度高、抗电磁干扰能力突出。战场环境中，烟雾对激光有散射和吸收的作用，从而引起能量的衰减，出现虚警和漏警的问题[1]。因此，对于激光在烟雾环境下后向散射特性的研究十分重要。
针对该问题，国内外科研人员进行了大量的研究。冯继青等[2]利用比尔朗伯定律和经典扩散方程建立烟雾环境下激光透过率模型，分析不同激光波长的透过率，但是该方法只考虑了单次散射，具有局限性。王红霞等[3]建立模型计算1.06 μm脉冲激光在烟雾中的传输，分析得到透过率与粒子粒径、烟雾厚度的关系，并且数值仿真脉冲激光在烟雾中的时间展宽特性。类成新等[4]研究激光在随机分布的烟尘团簇粒子的衰减特性，分析激光波长、入射角和粒子密度等参数对在烟尘中激光衰减的影响。李晓峰等[5]模拟研究在烟雾环境下不同波长激光在各个复折射率条件下的吸收、衰减和散射效应。Mori等[6]分析了非对称因子和Mie散射系数在烟雾中单次散射的变化特点。孟祥盛[7]利用偏振特性设计一种激光引信，该系统可以降低引信对烟雾后向散射信号的接收能力。陈慧敏等[8]建立烟雾后向散射模型，分析回波特性，将仿真结果与实测数值进行对比，验证模型的准确性。
本文根据Mie散射理论，运用Monte Carlo方法建立脉冲激光近感探测模型，设置不同距离的大小目标，在无干扰和烟雾干扰条件下仿真905 nm脉冲激光，分析回波波形特征。从而为激光近感探测抗烟雾干扰提供理论基础和新的思路。
1. 理论分析
1.1 烟雾的物理特性
战场上环境十分复杂，爆炸产生的烟雾粒子的主要成分是硫、碳、磷及其混合物。粒子的直径大小与爆炸强度、爆炸物成分和气候条件有关，爆炸产生的烟雾是瞬时的。烟雾也可以看作是气溶胶微粒，不仅爆炸会产生烟雾颗粒，人为释放烟雾气溶胶颗粒对制导武器系统是一种干扰[9]。本文选取发烟材料粒子的粒径大致分布在3~21 μm之间，烟雾粒子粒径分布如图 1所示。
1.2 Mie散射理论
Mie散射理论可用于各个方向同性的球体，但是对于形状不规则的粒子同样适用。Mie散射理论是研究大气中的气溶胶微粒与辐射光发生散射的经典理论，其散射的强度与频率二次方成正比，方向性较明显。假设入射光的强度为I0，散射距离为l，则散射光强I为[10]：
$$ I{\text{ = }}\frac{{{\lambda ^2}}}{{8{\pi ^2}}}\frac{{{i_1} + {i_2}}}{{{l^2}}}{I_0} $$ (1) 式中：i1、i2为强度函数，表达式为：
$$ \left\{ \begin{array}{l} {i_1} = {s_1}(m, \theta , \alpha ) \times {s_1}^ * (m, \theta , \alpha ) \hfill \\ {i_2} = {s_2}(m, \theta , \alpha ) \times {s_2}^ * (m, \theta , \alpha ) \hfill \\ \end{array} \right. $$ (2) 式中：m为散射体相对折射率；θ为散射角；s1、s2为散射光振幅函数，s1∗、s2∗分别为s1、s2的共轭函数，散射体尺度参数α的表达式为[11]：
$$ \alpha {\text{ = }}\frac{{2\pi r}}{\lambda } $$ (3) 式中：r是散射体的半径；λ为入射光波长。散射光振幅函数是无穷级数，可以取表达式的前10项来推演结果。因此，s1、s2具体展开式为：
$$ \left\{ \begin{array}{l} {s_1} = \sum\limits_{k = 1}^\infty {\frac{{2k + 1}}{{k(k + 1)}}[{a_k}{\pi _k} + {b_k}{\tau _k}]} \hfill \\ {s_2} = \sum\limits_{k = 1}^\infty {\frac{{2k + 1}}{{k(k + 1)}}[{a_k}{\tau _k} + {b_k}{\pi _k}]} \hfill \\ \end{array} \right. $$ (4) 式中：ak、bk表示为Mie散射系数，该系数和散射体相对折射率m及散射体尺度参数α相关。
烟雾粒子的散射系数Qsca和消光系数Qext的表达式分别为：
$$ \left\{ \begin{array}{l} {Q_{{\rm{sca}}}} = \frac{2}{{{\alpha ^2}}}\sum\limits_{k = 1}^\infty {(2k + 1)({{\left| {{a_k}} \right|}^2} + {{\left| {{b_k}} \right|}^2})} \hfill \\ {Q_{{\rm{ext}}}} = \frac{2}{{{\alpha ^2}}}\sum\limits_{k = 1}^\infty {(2k + 1){{\rm{Re}}} ({a_k} + {b_k})} \hfill \\ \end{array} \right. $$ (5) 不同相对折射率消光系数随尺度参数分布如图 2所示。
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图 2 不同相对折射率消光系数随尺度参数分布Figure 2. Distribution of extinction coefficient of different relative refractive indices with scale parameter如图 2所示，在选取的3种相对折射率下，消光系数随尺度参数的增加呈振荡衰减分布，最终趋于稳定值。相对折射率越大，震荡幅度越大。
光子与烟雾粒子发生碰撞后各个方向的散射强度用散射相函数来表示，该函数表达式为：
$$ P(\theta )=\frac{{\left|{S}_{1}(\theta )\right|}^{2}+{\left|{S}_{2}(\theta ）\right|}^{2}}{{\displaystyle \sum _{k=1}^{\infty }(2k+1)({\left|{a}_{k}\right|}^{2}+{\left|{b}_{k}\right|}^{2})}} $$ (6) 式中：S1(θ)、S2(θ)为散射光振幅函数。单个粒子散射相位函数与散射角关系如图 3所示。
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图 3 粒子散射相位函数与散射角关系Figure 3. Relationship between scattering phase function and scattering angle of particles2. 脉冲激光近感探测模型
构建本模型的主要思路是将发射的脉冲激光分解成大量光子，根据Mie散射理论和Monte Carlo方法模拟光子在烟雾中的运动轨迹，统计出发生散射后的抵达光电探测器的光子。脉冲激光近感探测模型分为3部分：激光发射模型、激光在烟雾中的传输模型、激光接收模型。
2.1 激光发射模型
激光器发出的脉冲激光为高斯脉冲，功率表达式为：
$$ P(t) = {P_0}\exp [ - \frac{{{{(t - \tau /2)}^2}}}{{{\tau ^2}/4\ln 2}}] $$ (7) 式中：P0为峰值功率；τ为高斯脉冲持续的时间。光子的发射点选择在激光的束腰处，该位置的光子服从高斯分布，因此可得光子的位置为：
$$ \left\{ \begin{array}{l} {x_t} = {\omega _0}{\xi _1} \hfill \\ {y_t} = {\omega _0}{\xi _2} \hfill \\ {z_t} = 0 \hfill \\ \end{array} \right. $$ (8) 式中：$ {\omega _0} = {\left( {\lambda {z_0}/\pi } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}} $为束腰半径；z0为瑞利长度；ξ1、ξ2为标准正态分布随机数。光子起始发射方向为：
$$ \left\{ \begin{array}{l} {u_{xt}} = \sin {\theta _t}\cos {\varphi _t} \hfill \\ {u_{yt}} = \sin {\theta _t}\sin {\varphi _t} \hfill \\ {u_{zt}} = \cos {\theta _t} \hfill \\ \end{array} \right. $$ (9) 式中：${\theta _t} = \left| {\left( {{\theta _0}/2} \right) \cdot {\zeta _3}} \right|$为光子发射方向的天顶角；θ0为光束发散角；ξ3为标准正态分布随机数；ϕt＝2π⋅ξ4为光子发射方向的方位角；ξ4为[0, 1]区间上的均匀分布随机数。
2.2 激光在烟雾中的传输模型
光子在烟雾环境中会与烟雾粒子发生碰撞，碰撞后光子的能量会发生变化，其变化为[12]：
$$ {E_1}{\text{ = }}\frac{{{Q_{{\rm{sca}}}}}}{{{Q_{{\rm{ext}}}}}}{E_0} $$ (10) 式中：E0为散射前光子能量；E1为散射后光子能量；Qsca和Qext分别为烟雾粒子的散射系数和消光系数，具体表达式参考1.2节。碰撞后，光子的方向也发生变化，其变化为：
$$ \left\{\begin{array}{l} u_{x s}^{\prime}=\frac{\sin \theta_{\text {sca }}}{\sqrt{1-u_{z s}^2}}\left(u_{x s} u_{z s} \cos \varphi_{\text {sca }}-u_{y s} \sin \varphi_{\text {sca }}\right)+u_{x s} \cos \theta_{\text {sca }} \\ u_{y s}^{\prime}=\frac{\sin \theta_{\text {sca }}}{\sqrt{1-u_{z s}^2}}\left(u_{y s} u_{z s} \cos \varphi_{\text {sca }}+u_{x s} \sin \varphi_{\text {sca }}\right)+u_{y s} \cos \theta_{\text {sca }} \\ u_{z s}^{\prime}=-\sin \theta_{\text {sca }} \cos \varphi_{\text {sca }} \sqrt{1-u_{z s}^2}+u_{z s} \cos \theta_{\text {sca }} \end{array}\right. $$ (11) 式中：(uxs, uys, uzs)为散射前的光子移动方向；(uxs′, uys′, uzs′)为散射后的光子移动方向；ϕsca为[0, 2π]均匀分布的散射方位角；θsca为散射天顶角。光子与烟雾粒子发生碰撞后，如果没有消亡（能量小于阈值），则继续朝新的方向移动，移动的距离为：
$$ \Delta s = - \frac{{\ln \varepsilon }}{{{\mu _t}}} $$ (12) 式中：ε为[0, 1]区间上均匀分布的随机数；μt为烟雾衰减系数。
2.3 激光接收模型
光子离开烟雾环境后，朝接收端光学系统移动，有一定的比例被光电探测器接收。若光子进入接收窗口，则有[13]：
$$ {({x_{\rm{f}}} - {d_{{\rm{tr}}}})^2} + y_{\rm{f}}^2 \leqslant R_{\rm{r}}^2 $$ (13) 式中：xf、yf为光子最后一次散射的位置；dtr为收发光轴间距；Rr为接收端镜头半径。同时，光子在进入接收端光学系统时，入射角需要满足接收视场角要求：
$$ {\theta _{{\rm{in}}}} \leqslant \frac{{{\theta _{{\rm{view}}}}}}{2} $$ (14) 式中：θin为光子入射角；θview为接收视场角。若满足上式，光子可看作是被光电探测器成功接收，成为回波光子。
3. 仿真结果与分析
3.1 仿真流程
烟雾环境下脉冲激光近感探测模型仿真流程图如图 4所示。大致流程如下：输入相关参数，对脉冲激光收发系统及烟雾模型初始化，光子与粒子发生碰撞后计算出光子的能量和位置，若光子在烟雾边界内且光子存活，重复碰撞直到光子进入光电探测器或者消失。当最后一个光子完成循环流程，计算出激光回波幅值。
3.2 仿真参数
选取大小两种目标，大目标为武装直升机和小型固定翼飞机。武装直升机机体长12.5 m，宽3.4 m，高3.94 m，主旋翼直径16.35 m；小型固定翼飞机长3.3 m，机身直径0.28 m，机翼长1.56 m，高为0.7 m。激光经过该目标的回波在一个周期内距离变化量大，实验中用反射率为0.9的白板代替；小目标为小尺寸靶弹，长为2 m，直径约为12 cm，激光经过该目标的回波在一个周期内距离变化量小，实验中用反射率为0.3的灰板代替。环境选取无干扰和烟雾干扰两种环境，仿真参数如表 1所示。
表 1 仿真参数Table 1. Simulation parametersSimulation parameters Value Laser wavelength/nm 905 Emission pulse width/ns 30 Emission beam divergence angle/mrad 5 Receiving field of view angle/mrad 21 Launching system diameter/mm 10 Receiving lens diameter/mm 30 Transmit-receive spacing/mm 35 Simulated photon number 106 Smoke particle size range/μm 3-18 Smoke complex index 1.75-0.43i Target surface Bloom Target reflectance 0.3(small target)
0.9(big target)Target distance/m 3(small target)
7(big target)3.3 结果分析
由图 5可知，取小目标和大目标的距离分别为3 m和7 m，比较小目标和大目标，作用距离增大，探测信号回波的幅值减小，即发射接收系统与目标之间的距离和探测信号回波幅值呈负相关。两者探测回波的前沿上升速率呈递增趋势。
由图 6可知，在烟雾干扰的环境下，对小目标和大目标取相同质量浓度的烟雾，探测回波信号和图 5相比有了明显的变化。脉冲激光会先探测到烟雾，因为烟雾对激光的反射率低，所以接收信号的幅值相对较小；当脉冲激光穿过烟雾到达目标表面，探测回波幅值相对较大，但是由于烟雾环境中粒子对激光的散射和吸收作用，引起能量的衰减，相比较于无干扰条件下，大小目标回波幅值有所降低。烟雾回波和目标回波的脉冲宽度相对于发射激光波形均有一定的展宽，但是前者的展宽程度大于后者。烟雾回波波形呈现前沿陡峭，后沿平缓的非对称特征，对于大目标而言，作用距离的增加，该特征变化得更加明显。因此激光近感探测系统在探测目标时，如果不加入任何抑制后向散射信号方法，烟雾后向散射信号和目标反射信号将会混合在一起，导致探测系统信噪比降低，进而造成系统虚警、漏警等一系列问题。
4. 结论
本文根据Mie散射理论，运用Monte Carlo方法建立脉冲激光近感探测模型，设置参数，仿真得到大小目标在有无烟雾干扰条件下的回波，分析回波的波形特征，得到如下结论：
① 无干扰情况下，发射接收系统与目标之间的距离和探测信号回波幅值呈负相关，目标回波前沿的上升速率均呈递增趋势。
② 烟雾干扰情况下，脉冲激光会先探测到烟雾回波后探测到目标回波且烟雾回波幅值小于目标回波幅值。烟雾回波和目标回波的脉冲宽度相对于发射激光波形均有一定的展宽，但前者的展宽程度要大于后者，烟雾回波波形呈现前沿陡峭，后沿平缓的非对称特征，对于大目标而言，作用距离的增加，该特征变化得更加明显。
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图 1 6.1 Å材料体系的晶格常数、禁带宽度和能带排列
Figure 1. The lattice constant, bandgap and energy band alignment for these 6.1Å family materials
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图 2 界面控制方法快门顺序[28]
Figure 2. The shutter sequence based on the interface control method
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图 3 超晶格样品在外延生长时快门开关顺序示意图[68]
Figure 3. Diagram of the shutter sequence during epitaxy growth of InAs/GaSb superlattice samples
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图 4 超晶格一个周期生长的快门顺序[58]
Figure 4. The shutter sequence of a periodic growth of InAs/GaSb superlattices
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图 5 在界面控制方法不变的基础上进行不同快门顺序设计[68]
Figure 5. The experimental design of different shutter sequences based on the interface control method
表 1 国内相关科研机构所采用的不同探测波段的超晶格界面类型与控制方法
Table 1 The interface types and control methods of InAs/GaSb superlattices in different detection wavelength bands adopted byrelated research institutions in China
Research institutions in China InAs/GaSb SLs structure (band) Interface types and interface control methods Year Institute of Semiconductors 4ML InAs/8MLGaSb SLs (short wave- length) Mixed-like interface; if InSb-like interface is formed (MEE method) 2008[69] 50 periods of 4MLInAs/8MLGaSb SLs (short-wavelength) InAs-on-GaSb interface adopt interrupted growth epitaxy method; GaSb-on-InAs interface (InSb-like interface) adopts Sb soak method 2009[70] InAs/GaSb (4ML/8ML) SLs and InAs/GaSb(8ML/8ML) SLs Interrupted growth epitaxy method (a combination of unprotected interruption with bulk material growth method or conventional molecular beam epitaxy) Long-wavelength SLs PIN structure InSb interface; mixed-like interface: InAs-on-GaSb interface adopts GaAs-Like (As soak), GaSb- on-InAs interface adopts InSb-Like (a combination of bulk material growth, unprotected interruption and V group element soak) 2011[71] Long-wavelength SLs Pin device: absorption layer consists of 15.2ML InAs/10ML GaSb SLs or absorption layer consists of 16.2ML InAs/10.75ML GaSb SLs InSb interface 2012[72] Mid-wavelength SLs (7ML InAs/7ML GaSb) Interrupted growth epitaxy method 2012[22] Long-wavelength SLs (12ML InAs+0.8ML InSb/8ML GaSb+0.8 ML InSb) InSb-like interface (MEE method) Shanghai Institute of Technical Physics 9ML InAs/12ML GaSb SLs p-i-n structure (Mid-wavelength) InSb interface (MEE method) 2011[74] 15ML InAs/7ML GaSb SLs PBIN structure InSb interface (MEE method) 2013[75] 50 periods of 12ML InAs/12ML GaSb SLs InSb-like interface (MEE method) 2014[68] 
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表 2 国外相关科研机构所采用的不同探测波段的超晶格界面类型与控制方法
Table 2 The interface types and control methods of InAs/GaSb superlattices in different detection wavelength bands adopted byforeign related research institutions
Foreign Research Institutions InAs/GaSb SLs structure (band) Interface types and interface control methods Year Université de Montpellier and Northwestern University An InAs/GaSb heterojunction allows a layer by layer growth mode InSb-like interface (MEE method) 2000[39] Université de Montpellier 10MLInAs/10MLGaSb SLs GaSb-on-InAs interface (InSb interface) adopts a combination of bulk material growth method and unprotected interrupted growth epitaxy method (conventional molecular beam epitaxy) 2004[26] University of New Mexico 13ML InAs/7ML GaSb SLs (~8-μm cutoff wavelength(300 K)) GaSb-on-InAs interface (InSb interface) adopts bulk material growth method or Sb-soak 2008[62] Absorption region of NBN detector: 322 periods of [1s As Soak time/13ML InAs/0.45ML InSb/7MLGaSb] SLs InSb interface (bulk material growth method) Absorption region of NBN detector: 13ML InAs/0.73ML InSb/7ML GaSb SLs (300 periods), contact layer: 13ML InAs (Si)/0.73ML InSb/7ML GaSb SLs InSb interface (bulk material growth method) 2010[49] Naval Research Laboratory(NRL) 40 periods of SLs structure: 8ML InAs/12ML GaSb and 1ML InSb or GaAs (8-12-l), as well as 8-8-1 and 12-8-1 Using MEE method to change the interface type[73] Institute of Electron Technology, Poland 9ML InAs/9ML GaSb SLs InAs-on-GaSb interface adopts GaAs-like (As soak); GaSb-on-InAs interface adopts InSb-like (Sb soak) 2011[67]
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