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Metamorphic semiconductor devices are commonly fabricated with linearly-graded buffer layers, but equilibrium modeling studies suggest that S-graded buffers, following a normal cumulative distribution function, may enable lower threading defect densities. The present work involves a study of threading dislocation density behavior in S-graded ZnS_xSe_1-x buffer layers for metamorphic devices on mismatched GaAs (001) substrates using a kinetic model for lattice relaxation and misfit-threading dislocation interactions. The results indicate that optimization of an S-graded buffer layer to minimize the surface threading dislocation density requires adjustment of the standard deviation parameter and cannot be achieved by varying the buffer thickness alone. Furthermore, it is possible to tailor the design of the S-graded buffer layer in such a way that the density of mobile threading dislocations at the surface vanishes. Nonetheless, the threading dislocation behavior in these heterostructures is quite complex, and a full understanding of their behavior will require further experimental and modeling studies.

Several simple models have been developed for the threading dislocation behavior in heteroepitaxial semiconductor materials. Tachikawa and Yamaguchi [Appl. Phys. Lett., 56, 484 (1990)] and Romanov et al. [Appl. Phys. Lett., 69, 3342 (1996)] described models for the annihilation and coalescence of threading dislocations in uniform-composition layers, and Kujofsa et al. [J. Electron. Mater., 41, 2993 (2013)] extended the annihilation and coalescence model to compositionally-graded and multilayered structures by including the misfit dislocation-threading dislocation interactions. However, an important limitation of these previous models is that they involve empirical parameters. The goal of this work is to develop a predictive model for annihilation and coalescence of threading dislocations which is based on the dislocation interaction length L_int. In the first case if only in-plane glide is considered the interaction length is equal to the length of misfit dislocation segments while in the second case glide and climb are considered and the interaction length is a function of the distance from the interface, the length of misfit dislocations, and the density of the misfit dislocations. In either case the interaction length may be calculated using a model for dislocation flow. Knowledge of the dislocation interaction length allows predictive calculations of the threading dislocation densities in metamorphic device structures and is of great practical importance. Here we demonstrate the latter model based on glide and climb. Future work should compare the two models to determine which is more relevant to typical device heterostructures.

Metamorphic semiconductor devices such as high electron mobility transistors (HEMTs), light-emitting diodes (LEDs), laser diodes, and solar cells are grown on mismatched substrates and typically exhibit a high degree of lattice relaxation. In order to minimize the incorporation of threading defects it is common to use a linearly-graded buffer layer to accommodate the mismatch between the substrate and device layers. However, some work has suggested that buffer layers with non-linear grading could offer superior performance in terms of limiting the surface density of threading defects. In this work, we have compared S-graded buffer layers with different orders and thicknesses. To do so we calculated the expected surface threading dislocation density for each buffer design assuming a GaAs (001) substrate. The threading dislocation densities were calculated using the L_MD model, in which the coefficient for second-order annihilation and coalescence reactions between threading dislocations is considered to be equal to the length of misfit dislocations.

Metamorphic realization of semiconductor devices has become increasingly important due to the great freedom it affords in layer compositions and thicknesses. However, metamorphic growth is often accompanied by the introduction of high densities of threading dislocation defects. This behavior may be understood by using an annihilation and coalescence model for the threading dislocation behavior which is based on the dislocation interaction length L_int. For its application we considered only glide of dislocations, so the interaction length was assumed to be equal to the length of misfit dislocation segments L_MD. The length of misfit segments was determined approximately by the Matthews, Mader, and Light model [J. Appl. Phys., 41, 3800 (1970)] for lattice relaxation, and was assumed to be independent of the distance from the interface. Within this framework we have applied the annihilation and coalescence model to chirped semiconductor superlattices to evaluate these superlattices as strainrelaxed buffers for metamorphic devices. In this work we have studied two basic types of InGaAs/GaAs chirped superlattice buffers: type I superlattices are compositionally modulated while type II superlattices are thickness modulated.

We conducted a modeling study of the threading dislocation behavior in chirped and unchirped InGaAs/GaAs (001) strained-layer superlattices (SLSs) using a Dodson & Tsao / Kujofsa & Ayers (DTKA) type plastic flow model. Four types of SLSs were investigated: type I was chirped using compositional modulation, type II was chirped using layer thickness modulation, type III was unchirped with alternating layers of InGaAs and GaAs, and type IV was unchirped with alternating layers of InGaAs having two different compositions. Generally the surface and average values of the dislocation density decreased with increasing total thickness. The dependence on top indium composition was more complex, due to dislocation compensation and multiplication effects, but for type II and IV superlattices, the average and surface threading dislocation densities increased in nearly monotonic fashion with top indium composition. Based on these results, the compositionally-modulated chirped (type I) and InGaAs/GaAs unchirped (type III) superlattices appear to be best suited as buffer layers for metamorphic devices, while the chirped superlattices with layer thickness modulation (type II) and InGaAs/InGaAs unchirped (type IV) superlattices appear to be poorly suited for use as buffer layers for devices containing high indium content.

Metamorphic semiconductor devices often utilize compositionally-graded buffer layers for the accommodation of the lattice mismatch with controlled threading dislocation density and residual strain. Linear or step-graded buffers have been used extensively in these applications, but there are indications that sublinear, superlinear, S-graded, or overshoot graded structures could offer advantages in the control of defect densities. In this work we compare linear, step-graded, and nonlinear grading approaches in terms of the resulting strain and dislocations density profiles using a state-of-the-art model for strain relaxation and dislocation dynamics. We find that sublinear grading results in lower surface dislocation densities than either linear or superlinear grading approaches.

Strained-layer superlattices (SLSs) have been used to modify the threading dislocation behavior in metamorphic semiconductor device structures; in some cases they have even been used to block the propagation of threading dislocations and are referred to in these applications as “dislocation filters.” However, such applications of SLSs have been impeded by the lack of detailed physical models. Here we present a “zagging and weaving” model for dislocation interactions in multilayers and strained-layer superlattices, and we demonstrate the use of this model to the threading dislocation dynamics in InGaAs/GaAs (001) structures containing SLSs.

Since the invention of dislocation sidewall gettering (DSG) in 2000 the technique has been applied extensively in infrared focal-plane arrays and flat-panel displays. However, development of DSG technology has been guided mostly by empirical trials due to the lack of detailed physical models. Here we demonstrate the application of a dislocation dynamics model to evaluate DSG approaches in both ZnS_ySe_1-y/GaAs (001) and InGa_xAs_1-x/GaAs (001) heterostructures. We find that the effectiveness of DSG is strongly dependent on composition in both material systems.

In this paper we describe state-of-the-art approaches to the modeling of strain relaxation and dislocation dynamics in InGaAs/GaAs (001) heterostructures. Current approaches are all based on the extension of the original Dodson and Tsao plastic flow model to include compositional grading and multilayers, dislocation interactions, and differential thermal expansion. Important recent break-throughs have greatly enhanced the utility of these modeling approaches in four respects: i) pinning interactions are included in graded and multilayered structures, providing a better description of the limiting strain relaxation as well as the dislocation sidewall gettering; ii) a refined model for dislocation-dislocation interactions including zagging enables a more accurate physical description of compositionally-graded layers and step-graded layers; iii) inclusion of back-and-forth weaving of dislocations provides a better description of dislocation dynamics in structures containing strain reversals, such as strained-layer superlattices or overshoot graded layers; and iv) the compositional dependence of the model kinetic parameters has been elucidated for the InGaAs material system, allowing more accurate modeling of heterostructures with wide variations in composition. We will describe these four key advances and illustrate their applications to heterostructures of practical interest.

Several simple models have been developed for the threading dislocation behavior in heteroepitaxial semiconductor materials. Tachikawa and Yamaguchi [Appl. Phys. Lett., 56, 484 (1990)] and Romanov et al. [Appl. Phys. Lett., 69, 3342 (1996)] described models for the annihilation and coalescence of threading dislocations in uniform-composition layers, and Kujofsa et al. [J. Electron. Mater., 41, 2993 (2013)] extended the annihilation and coalescence model to compositionally-graded and multilayered structures by including the misfit dislocation-threading dislocation interactions. However, an important limitation of these previous models is that they involve empirical parameters. The goal of this work is to develop a predictive model for annihilation and coalescence of threading dislocations which is based on the dislocation interaction length L_int. In the first case if only in-plane glide is considered the interaction length is equal to the length of misfit dislocation segments while in the second case glide and climb are considered and the interaction length is a function of the distance from the interface, the length of misfit dislocations, and the density of the misfit dislocations. In either case the interaction length may be calculated using a model for dislocation flow. Knowledge of the dislocation interaction length allows predictive calculations of the threading dislocation densities in metamorphic device structures and is of great practical importance. Here we demonstrate the latter model based on glide and climb. Future work should compare the two models to determine which is more relevant to typical device heterostructures.

Metamorphic semiconductor devices such as high electron mobility transistors (HEMTs), light-emitting diodes (LEDs), laser diodes, and solar cells are grown on mismatched substrates and typically exhibit a high degree of lattice relaxation. In order to minimize the incorporation of threading defects it is common to use a linearly-graded buffer layer to accommodate the mismatch between the substrate and device layers. However, some work has suggested that buffer layers with non-linear grading could offer superior performance in terms of limiting the surface density of threading defects. In this work, we have compared S-graded buffer layers with different orders and thicknesses. To do so we calculated the expected surface threading dislocation density for each buffer design assuming a GaAs (001) substrate. The threading dislocation densities were calculated using the L_MD model, in which the coefficient for second-order annihilation and coalescence reactions between threading dislocations is considered to be equal to the length of misfit dislocations.

Metamorphic realization of semiconductor devices has become increasingly important due to the great freedom it affords in layer compositions and thicknesses. However, metamorphic growth is often accompanied by the introduction of high densities of threading dislocation defects. This behavior may be understood by using an annihilation and coalescence model for the threading dislocation behavior which is based on the dislocation interaction length L_int. For its application we considered only glide of dislocations, so the interaction length was assumed to be equal to the length of misfit dislocation segments L_MD. The length of misfit segments was determined approximately by the Matthews, Mader, and Light model [J. Appl. Phys., 41, 3800 (1970)] for lattice relaxation, and was assumed to be independent of the distance from the interface. Within this framework we have applied the annihilation and coalescence model to chirped semiconductor superlattices to evaluate these superlattices as strain-relaxed buffers for metamorphic devices. In this work we have studied two basic types of InGaAs/GaAs chirped superlattice buffers: type I superlattices are compositionally modulated while type II superlattices are thickness modulated.

We conducted a modeling study of the threading dislocation behavior in chirped and unchirped InGaAs/GaAs (001) strained-layer superlattices (SLSs) using a Dodson & Tsao / Kujofsa & Ayers (DTKA) type plastic flow model. Four types of SLSs were investigated: type I was chirped using compositional modulation, type II was chirped using layer thickness modulation, type III was unchirped with alternating layers of InGaAs and GaAs, and type IV was unchirped with alternating layers of InGaAs having two different compositions. Generally the surface and average values of the dislocation density decreased with increasing total thickness. The dependence on top indium composition was more complex, due to dislocation compensation and multiplication effects, but for type II and IV superlattices, the average and surface threading dislocation densities increased in nearly monotonic fashion with top indium composition. Based on these results, the compositionally-modulated chirped (type I) and InGaAs/GaAs unchirped (type III) superlattices appear to be best suited as buffer layers for metamorphic devices, while the chirped superlattices with layer thickness modulation (type II) and InGaAs/InGaAs unchirped (type IV) superlattices appear to be poorly suited for use as buffer layers for devices containing high indium content.

Metamorphic semiconductor devices often utilize compositionally-graded buffer layers for the accommodation of the lattice mismatch with controlled threading dislocation density and residual strain. Linear or step-graded buffers have been used extensively in these applications, but there are indications that sublinear, superlinear, S-graded, or overshoot graded structures could offer advantages in the control of defect densities. In this work we compare linear, step-graded, and nonlinear grading approaches in terms of the resulting strain and dislocations density profiles using a state-of-the-art model for strain relaxation and dislocation dynamics. We find that sublinear grading results in lower surface dislocation densities than either linear or superlinear grading approaches.

Strained-layer superlattices (SLSs) have been used to modify the threading dislocation behavior in metamorphic semiconductor device structures; in some cases they have even been used to block the propagation of threading dislocations and are referred to in these applications as “dislocation filters.” However, such applications of SLSs have been impeded by the lack of detailed physical models. Here we present a “zagging and weaving” model for dislocation interactions in multilayers and strained-layer superlattices, and we demonstrate the use of this model to the threading dislocation dynamics in InGaAs/GaAs (001) structures containing SLSs.

Since the invention of dislocation sidewall gettering (DSG) in 2000 the technique has been applied extensively in infrared focal-plane arrays and flat-panel displays. However, development of DSG technology has been guided mostly by empirical trials due to the lack of detailed physical models. Here we demonstrate the application of a dislocation dynamics model to evaluate DSG approaches in both ZnS_ySe_1-y/GaAs (001) and InGa_xAs_1-x/GaAs (001) heterostructures. We find that the effectiveness of DSG is strongly dependent on composition in both material systems.

In this paper we describe state-of-the-art approaches to the modeling of strain relaxation and dislocation dynamics in InGaAs/GaAs (001) heterostructures. Current approaches are all based on the extension of the original Dodson and Tsao plastic flow model to include compositional grading and multilayers, dislocation interactions, and differential thermal expansion. Important recent breakthroughs have greatly enhanced the utility of these modeling approaches in four respects: i) pinning interactions are included in graded and multilayered structures, providing a better description of the limiting strain relaxation as well as the dislocation sidewall gettering; ii) a refined model for dislocation-dislocation interactions including zagging enables a more accurate physical description of compositionally-graded layers and step-graded layers; iii) inclusion of back-and-forth weaving of dislocations provides a better description of dislocation dynamics in structures containing strain reversals, such as strained-layer superlattices or overshoot graded layers; and iv) the compositional dependence of the model kinetic parameters has been elucidated for the InGaAs material system, allowing more accurate modeling of heterostructures with wide variations in composition. We will describe these four key advances and illustrate their applications to heterostructures of practical interest.