Semiconductor epitaxial structure design involves the selection of quantum wells, waveguide design, and doping optimization.For 915-nm lasers, the quantum wells can use 5-8 nm compressive strain material In(x)GaAs, and the content of In component needs to be adjusted according to the thickness of the used quantum well to ensure that the lasing wavelength is around 915 nm.In addition to the quantum well material, the height of the barrier has a significant influence on the performance of the device because the barrier height affects the internal quantum efficiency and temperature characteristics of the device.In order to examine the exact relationship between the barrier height and the quantum efficiency within the device, a numerical model of internal quantum efficiency based on traveling wave amplification is developed.This model considers the photon flux density at different locations in the resonator, the carrier concentration in the quantum wells, thermionic emission, etc., to calculate the number of radiatively recombined carriers among.Fig. 1 shows the relationship between the internal quantum efficiency and the barrier Al content based on our traveling wave amplification model.It can be found from the calculation that for the 915 nm high-power laser, the internal quantum efficiency reaches 99% when the content of the Al component in the Al(x)GaAs material exceeds 0.23.Based on the above calculation, the quantum well structure we selected is In0.10GaAs/Al0.23GaAs.
图 1 内量子效率与量子阱势垒材料Al组份含量之间的关系
Figure 1. Relationship between internal quantum efficiency and Al component content of quantum well barrier materials
半导体外延结构设计涉及到量子阱的选取、波导设计以及掺杂优化等。对于915 nm激光来说, 量子阱可选用5~8 nm的压应变材料In(x)GaAs材料, 其中In组份含量需要根据所采用的量子阱厚度做必要的调整, 以保证激射波长为915 nm左右。除量子阱材料外, 势垒的高度对器件的性能影响至关重要, 因为势垒高度影响器件的内量子效率以及温度特性。为了考察势垒高度与器件内量子效率之间的精确关系, 我们发展出一种基于行波放大的内量子效率计算模型, 模型中考虑了在谐振腔中不同位置的光子通量密度、量子阱内的载流子浓度、热电子发射等, 从而计算出受激复合的载流子占注入载流子的比例。该计算模型是我们自己首次提出的一种计算方法, 尚未查阅到类似的文献。图 1是根据我们的行波放大模型计算的内量子效率与势垒Al组份含量之间的关系。由计算可见, 对于915 nm高功率激光来说, 当Al(x)GaAs材料中Al组份含量超过0.23时, 内量子效率达到99%。基于上述计算, 我们选取的量子阱结构为In0.10GaAs/Al0.23GaAs。
After the quantum well material is determined, the material structure design should be performed according to actual application requirements, and its main purpose is to find a waveguide structure that satisfies the laser operating parameters(such as a suitable quantum well confinement factor).This is because the material structure of the semiconductor laser is essentially a typical one-dimensional waveguide structure, i.e., a low refractive index under clad layer, a high refractive index waveguide core, and a low refractive index upper cladding layer in the material growth direction in turn.In this way, light waves can be transmitted in a guided wave manner in the growth plane.The waveguide structure generally has two different design ideas:one is a traditional narrow-waveguide single-mode design[10, 14], and the other is a popular large-cavity structure design in high-power lasers.The advantage of the large-cavity structure is that the optical loss can be designed to be very low because of the small overlap of the light field and the material doped region, so that free carrier absorption(FCA) and inter-valence band absorption(IVBA) can be minimized.The waveguide design calculates the mode field distribution of light in the waveguide in the vertical direction(i.e., growth direction) according to the refractive index distribution of the given epitaxial structure.Then, the parameters related to the device performance including the quantum well confinement factor Г, far field distribution, normalized power density, etc.are calculated by the mode field distribution.The mode field distribution in the optical waveguide needs to solve the following Helmholtz equation derived from the Maxwell electromagnetic equations:
量子阱材料确定后, 需要根据实际应用需求进行材料结构设计, 其主要目的是找出满足激光工作参数(如合适的量子阱限制因子)的波导结构。这是因为半导体激光器的材料结构本质上是一典型的一维波导结构, 即在材料生长方向上, 先后是低折射率的下包层, 高折射率的波导核以及低折射率的上包层。这样光波可以在生长面内以导波的方式进行传播。波导结构一般有两种不同的设计思路:其一为传统的窄波导单模设计[10, 14], 其二是在高功率激光中颇为流行的大光腔结构设计。大光腔结构的优点是光损耗可以被设计得非常低, 因为光场和材料掺杂区域重叠很小, 如此一来, 自由载流子吸收(FCA)以及价带间的空穴跃迁引起的吸收(IVBA)可以被降低到最小程度。波导设计是根据给定的外延结构的折射率分布计算光在波导中垂直方向(亦即生长方向)的模场分布, 然后通过模场分布计算出与器件性能相关的参数包括量子阱限制因子Г、远场分布、归一化的功率密度等。光波导中的模场分布需要求解从麦克斯韦尔电磁方程组推导而来的下述亥尔姆霍尔兹方程:
This equation is actually an eigenvalue equation, which means that the effective refractive index of the waveguide mode can only take a specific discrete value, and each eigenvalue(effective refractive index value) corresponds to a mode field distribution.For a single mode waveguide, only the fundamental mode exists, and correspondingly, there are multiple waveguide modes for the multimode waveguide.
这一方程式实际上是一本征值方程, 意味着波导模式的有效折射率只能取特定的分立值, 每一个本征值(有效折射率值)对应一个模场分布。对于单模波导来说, 只存在基模, 与此相对应, 多模波导存在多个波导模式。
In equation (1), represents the electric field strength of light waves,
(λ0 is wavelength in vacuum) is the free space wave number, n(x) is the refractive index distribution of the epitaxial structure in the growth direction, and the refractive index distribution of the material depends on the change of the material composition in the growth direction.Fig. 5 shows the refractive index changes along the growth direction of the material structure designed in this paper, the dispersion relationship of AlGaAs materials refer to , and ne is the effective refractive index of the desired waveguide mode.The mode field distribution within the waveguide can be calculated using the transfer matrix method(TMM).In order to calculate the mode gain, considering that the mode field distribution is only partially overlapping with the active region, the concept of the quantum well confinement factor has been introduced.The quantum well confinement factor Г is defined as the ratio of the distribution of the light field intensity of the waveguide mode(proportional to E2) at the quantum well to the total area distribution, i.e.:
, (λ0为真空中的波长)是自由空间波数, n(x)是外延结构在生长方向上的折射率分布, 而材料的折射率分布取决于生长方向上的材料组份变化(图 5给出了本文设计的材料结构沿生长方向上的折射率变化, AlGaAs材料的色散关系参见文献), ne是所求的波导模式的有效折射率。波导内的模场分布可非常容易地用转移矩阵法(TMM)进行计算。考虑到模场分布与有源区只是部分重叠, 为了计算模式增益, 人们引入了量子阱限制因子这一概念。量子阱限制因子Г被定义为波导模式的光场强度(正比于E2)在量子阱处的分布占整个区域分布的比例, 即: (2)
The threshold current of chip can be expressed as:
Where Nth is the carrier concentration in the quantum well when the threshold condition is reached, e is the electron charge amount; A, B, C are non-radiative recombination coefficient, spontaneous emission coefficient, and Auger recombination coefficient, respectively.By comparing with a large number of experimental test data, we fit the A, B, C coefficient values at 915 nm to approximately 5×10-7 s-1, 7×10-10 cm3/s, 1×10-30 cm6/s, respectively.d, w, L are the quantum well thickness, the width of the chip current injection region, and the cavity length, respectively, and η is the carrier quantum well implantation efficiency, which can be further expressed as η=1-ηe, ηe is the probability that carriers escape the quantum well.The following equation solves A in equation (3):
式中, Nth为到达阈值条件时量子阱内的载流子浓度, e为电子电荷量, A、B、C分别为非辐射复合、自发辐射以及俄歇复合系数。通过与大量实验测试数据比较, 我们拟合出915 nm时的A、B、C系数取值分别大约为5×10-7 s-1、7×10-10 cm3/s、1×10-30 cm6/s。d、w、L分别为量子阱厚度、芯片电流注入区宽度以及腔长, η为载流子的量子阱注入效率, 可以进一步表示为η=1-ηe, ηe为载流子逃逸出量子阱的几率。式(3)中的Nth需要求解下方程:
Equation (4) describes the device reaching the threshold condition when the gain and loss obtained are balanced and the photons go back and forth within the cavity, where g(Nth) is the material gain of the quantum well.The calculation can be referred to Ref..α is the cavity loss, RA and RH are the reflectivity of the two facets.The left side of equation (4) is the mode gain of the light, and the first term on the right side of the equation is the internal loss(we will then see the dependence of the loss on material doping).The second term is loss related to the mirror loss.
方程(4)意味着当光子在腔内往返一周时所获得的增益与损耗达到平衡时, 器件达到阈值条件, 式中, g(Nth)是量子阱的材料增益, 其计算可以参考文献, α为腔内光损耗, RA、RH分别为两个腔面镀膜的反射率。式(4)等式左边为光的模式增益, 而等式右边第一项为腔内光损耗(随后我们将会看到损耗与材料掺杂之间的依赖关系), 第二项为与腔面透光有关的损耗。
The divergence angle of the beam, that is, the far field distribution and the near field distribution constitute a Fourier transform, and it is also necessary to consider the refraction of light at the interface between the semiconductor and the air.Fig. 2-Fig. 4 shows the relationship among quantum well confinement factor, beam divergence angle(full width at half maximum(FWHM)), normalized power density and the total waveguide thickness(the total thickness of the SCH layer) in the case of symmetric waveguides where the aluminum component of the waveguide layer is 0.06, 0.09, and 0.12 respectively higher than the aluminum component of the cladding layer.In this paper, the normalized power density refers to the peak power density corresponding to a 100 μm wide active area chip output power of 10 W.It can be seen from the figure that all three parameters obtain the highest value at a certain SCH thickness and after the highest point, the above parameters decrease with the increase of the SCH thickness.The reason for the existence of the maximum value of the quantum well confinement factor Г is that, as the thickness of the SCH increases, the light-restricting ability of the waveguide increases, and the mode field value of the waveguide at the quantum well increases.After reaching the highest point, the thickness of the SCH increases further.As a result, the mode field size increases, eventually resulting in a decrease in the field value of the mode at the quantum well.It should be pointed out that, unlike low-power communication laser chips, the design of high-power laser chips mainly considers whether the highest possible output power can be obtained, and the actual output power is limited by the highest power density that the bulk material and the facet coating can withstand.Therefore, in a high-power semiconductor laser design, the normalized power density value should be reduced as much as possible.In this paper, the normalized power density value is about 10 MW/cm2.
光束发散角亦即远场分布与近场分布构成傅里叶变换关系, 同时还需要考虑到光在半导体与空气界面处的光折射。图 2~图 4为在对称波导情形时, 波导层的铝组份分别比包层铝组份高0.06、0.09和0.12三种情况下的量子阱限制因子、光束发散角(半高全宽值:FWHM)、以及归一化功率密度与波导总厚度(SCH层总厚度)之间的关系。在本论文中, 归一化功率密度是指100 μm条宽的有源区芯片输出功率为10 W时所对应的峰值功率密度。由图可见, 3个参量均在某一SCH厚度处取得最高值, 过了最高点后, 上述参量随SCH厚度的增加而减小。量子阱限制因子Г存在最大值的原因在于:随着SCH厚度的增加, 波导对光的限制能力随之增强, 在量子阱处的波导模场值增大, 当达到最高点后, SCH厚度的进一步增加, 导致了模场尺寸的增大, 从而导致了量子阱处的模式的场值的减小。需要指出的是, 不同于低功率通讯激光芯片, 高功率激光芯片设计的主要考虑在于获得尽可能高的输出功率, 而实际的输出功率受芯片材料以及腔面镀膜材料所能承受的最高功率密度限制, 所以实际上在高功率半导体激光设计中, 应尽可能降低归一化的功率密度值。在我们的设计中我们取归一化功率密度值为10 MW/cm2左右。
It should be noted that Fig. 2-Fig. 4 are calculated for symmetric waveguides.In order to increase the efficiency of the device as much as possible, we adopt a dual asymmetrical waveguide design based on the calculation of symmetric waveguides, that is:1)the aluminum composition of the P-type AlGaAs material is higher than that of the N-type AlGaAs material; 2)the quantum well is placed asymmetrically in the SCH waveguide as shown in Fig. 5.Fig. 5-Fig. 6 show the calculated waveguide near-field and far-field distributions.From the near-field distribution, it can be seen that about 72% of the light field is on the side of the N-type region.The asymmetrical distribution of the light field allows us to simultaneously reduce internal losses and electrical resistance to a minimum.This is because considering light absorption, the cross-section of electrons is only about half of that of holes, and the mobility of electrons in Al(x)GaAs(when x < 0.45) is much higher than that of holes.
图 5 双非对称波导结构(线1)以及对应的光场分布(线2)
Figure 5. Double unsymmetrical waveguide structure(line 1) and corresponding light field distribution(line 2)
需要指出的是, 图 2~图 4是针对对称波导进行计算的。为了尽可能提高器件的效率, 我们在对称波导计算的基础上, 采用了双非对称波导设计:即(1)P型AlGaAs材料的铝组份比N型AlGaAs材料的铝组份要高一些; (2)量子阱在SCH波导中是非对称的放置, 如图 5所示。图 5~图 6给出了计算的波导近场与远场分布。从近场分布可以看出, 大约72%的光场处于N型区域一边。光场的非对称分布使得我们能够同时将腔内损耗以及芯片电阻降低到最小程度。这是因为, 电子对光的吸收截面大约只有空穴对光的吸收截面的一半左右, 另外, 电子在Al(x)GaAs材料中(当x < 0.45)的迁移率要远远高于空穴的迁移率。
After optimization of the waveguide, doping optimization should be considered because doping not only affects the series resistance of the chip but also affects the optical loss of the laser resonator.For shallowly etched waveguide, the scattering loss of the light at the material interface is negligible, so that the internal optical loss is completely determined by the absorption of free carriers and that of holes in the valence band transition.This means that as long as electrons and holes exist within the scope of the light field, absorption by the above mechanism will occur.Thus, the optical loss of the semiconductor laser is composed of three parts:one is the light absorption caused by electrons and holes in the quantum well, because the carrier concentration in the quantum well generally exceeds 1×1018 cm-3 during normal operation of the device; the second is the electron-induced absorption of light in the n-type region; the third is the light absorption caused by holes in the p-type doped region.Therefore, the total light loss and the resistance per unit area of the material and doping distribution can be expressed as:
波导优化完毕之后, 随后的设计考虑是掺杂优化, 因为掺杂不仅影响芯片的串联电阻, 而且也影响激光谐振腔的光损耗。在波导为浅刻蚀情形下, 光在材料界面处的散射损耗可以忽略不计, 从而腔内的光损耗完全取决于自由载流子吸收以及空穴在价带间跃迁引起的吸收, 这就意味着在光场所及的范围内, 只要存在电子与空穴, 上述机理引起的吸收就会发生。基于上述理由, 半导体激光器的光损耗由三部分组成:其一为量子阱内的电子与空穴引起的光吸收, 因为在器件正常工作时, 量子阱内的载流子浓度一般会超过1×1018 cm-3; 其二为n型区域的电子引起的光吸收; 其三为p型掺杂区域内的空穴引起的光吸收。所以, 光的总损耗以及材料的单位面积电阻与掺杂分布可表示为:
Where Γ is quantum well confinement factor, Nth is the carrier concentration in the quantum well when the device reaches the threshold, I(x)(the dimension is cm-1) is a normalized light field distribution whose integral over the entire growth direction is 1, indicating that the intensity distribution of the light field in the material growth direction, which is proportional to the square of the field strength E, and the field strength can be obtained by solving the aforementioned equation (1).Cfc, Civba(in cm2) are the absorption cross-sections of the free carriers electrons and holes, respectively, Nd, Na are the doping concentration distributions of donor and acceptor atoms, μe, μh are the mobility of electrons and holes in the material, e is the electron charge.In equation (5), the first term indicates light absorption due to carriers in the quantum well, and the second and third terms are the optical losses in the n-type doped region and the p-type doped region, respectively.In equation (6), the first and second terms are the resistances of the n-type region and the p-type region, respectively.The actual calculations show that for a 915 nm high-power laser structure using a large optical cavity, the light loss caused by the doping of the epitaxial layer can be reduced to below 0.2/cm through doping optimization, and the resistance per unit area of the device can be reduced to below 6.0×10-5 Ω·cm2.
式中, Γ为量子阱限制因子, Nth为器件达到阈值时量子阱内的载流子浓度, I(x)(量纲为cm-1)是归一化的光场分布, 其在整个生长方向上的积分为1, 表示光场在材料生长方向上的强度分布, 与场强E的平方成正比, 而场强可以由求解前述的方程(1)而得到。Cfc、Civba(单位为cm2)分别为自由载流子电子与空穴的吸收截面, Nd、Na分别为施主与受主原子的掺杂浓度分布, μe、μh分别为电子与空穴在材料中的迁移率, e为电子电荷量。在(5)式中, 第一项表示量子阱内的载流子引起的光吸收, 第二与第三项分别为n型掺杂区域与p型掺杂区域内的光损耗。在式(6)中, 第一与第二项分别是n型区域与p型区域的电阻。实际计算表明, 对于采用大光腔的915 nm高功率激光结构, 经过掺杂优化, 外延层掺杂引起的光损耗α可以减小到0.2/cm以下, 同时器件的单位面积电阻可以降低到6.0×10-5 Ω·cm2以下。
Appropriate cavity length for the required output power is to be calculated by device design.Careful consideration has been given to thermal issues during packaging for cavity length calculations.A three-dimensional numerical analysis method is adopted to analyze the heat dissipation typically used for packaging of 915 nm fiber laser pump modules to calculate the thermal resistance of the entire package module.The calculation assumes that the chip′s electrical injection region has a width of 95 μm and is soldered to the AlN heat sink with a thickness of 350 μm(this type of package is called COS) in the form of P-face down.The AlN heat sink is then welded on a 2 mm thick copper block.Equations (7) and (8) give the relationship of the thermal resistance of the package module varies with the length of the laser cavity and the corresponding change in the junction temperature, respectively:
器件设计主要计算对于要求的输出功率时所需要的合适腔长。腔长计算时需要仔细考虑封装时的热问题。我们采用三维数值分析方法分析了典型的用于915 nm光纤激光泵浦模块热封装的热场分布, 从中计算出整个封装模块的热阻。在计算中, 假定芯片的电注入区宽度为95 μm并以P面朝下的形式被焊接在厚度为350 μm的AlN热沉上(这一封装形式被称之为COS), 随后AlN热沉再被焊接在2 mm厚的铜块上。式(7)与式(8)分别给出了上述封装模块的热阻随激光器腔长的变化关系以及对应的结温变化:
where L is the cavity length of the laser which is given in centimeters.The dimension of the thermal resistance is K/W, Q is the thermal power(in Watt) generated by the chip.ΔT is the chip junction temperature rises, which is given in K.After the high-power laser is fabricated, the facets are coated as required.The reflectivity of the rear facet coating is usually greater than 95%.The reflectivity of the front facet coating(i.e., the light exiting facet) is optimized based on the epitaxial structure, device cavity length, and light output power.This is because the reflectance affects both the device′s threshold current and the external quantum efficiency.Using the self-developed semiconductor laser design software, the dependences of device′s electro-optical conversion efficiency(WPE) and the output power on the device cavity length and front-facet reflectivity at an injected current of 12 A and at room temperature at 25 ℃ are calculated(see Fig. 7-Fig. 8).In this calculation model, the calculations to be performed include:discrete energy levels in quantum well structures and their corresponding quantum wells, material gain and spontaneous emission coefficient, optical waveguide and its quantum well limiting factor, and heat dissipation of packaged modules and corresponding thermal resistance, light-current-voltage(L-I-V) characteristics, etc.From the simulation results, it can be seen that the electro-optical conversion efficiency at a cavity length of 4.8 mm reaches 67% when the AR film reflectivity is about 1%, and the output power exceeds 13 W.In the case of the fixed front-facet reflectance, due to the interaction between the parameters of mirror loss, electrical resistance and thermal resistance, the output power will decreases as the cavity length increases, while the electro-optical conversion efficiency increases as the cavity length increases.
图 7 输出功率与腔长以及AR膜反射率之间的关系
Figure 7. Relationship between output power, cavity length and reflectivity of antireflection(AR) layer
图 8 电光转换效率与腔长以及AR膜反射率之间的关系
Figure 8. Relationship between electro-optical conversion efficiency, cavity length, and reflectivity of antireflection(AR) layer
式中, L为激光器的腔长, 单位为厘米, 热阻的量纲为K/W, Q为芯片产生的热功率, 单位为瓦, ΔT为芯片结温升高量, 单位为K。高功率激光器制作完毕后, 需要根据需要对腔面进行镀膜处理, 后腔面的反射率通常大于95%, 而前腔面(即出光面)的反射率需要根据外延结构、器件腔长以及出光功率大小进行优化。这是因为腔面反射率会同时影响器件的阈值电流以及外量子效率。利用我们自己研发出的半导体激光器设计软件, 我们计算了器件在25 ℃室温下, 当注入电流为12 A时的电光转换效率(WPE)以及输出功率与前腔面抗反射膜(antireflection coating)反射率和腔长之间的关系(见图 7, 图 8)。在我们的计算模型中, 所需要进行的计算包括:量子阱结构及其对应的量子阱内的分立能级计算, 材料增益以及自发辐射系数计算、光波导及其量子阱限制因子计算、封装模块的热分析及其对应的热阻计算, 光—电流—电压(L-I-V)特性计算等。由仿真计算可以看出, 腔长为4.8 mm时的电光转换效率在AR膜反射率为1%左右时达到67%, 而输出功率超过13 W。在相同AR膜反射率情况下, 因为腔面光提取效率、电阻以及热阻等参量之间的相互作用, 导致输出功率随腔长增加而减小, 而电光转换效率却随腔长增加而增大。