**3. Pseudomorphic and metamorphic growth**

One of the main requirements for high quality heterostructure growth is the lattice constant of the growth material to be nearly the same as those of the substrate. In semiconductor alloys the lattice constant and band gap can be modified in a wide range. The lattice parameter difference may vary from nearly 0 to several per cent as in the cases of GaAs-AlAs and InAs-GaAs system, respectively. The growth of dilute nitride alloys is difficult because of the wide immiscibility range, a large difference in the lattice constant value and very small atom radius of N atoms. The growth of thick epitaxial layers creates many problems which absent in the quantum-well structures.

At the initial stage of the growth when the epitaxial layer is of different lattice constant than the substrate in-plane lattice parameter of the growth material will coherently strain in order to match the atomic spacing of the substrate. The elastic energy of deformation due to the misfit in lattice constant destroys the epilayer lattice. The substrate is sufficiently thick and it remains unstrained by the growth of the epitaxial layer. If the film is thin enough to remain coherent to the substrate, then in the plane parallel to the growth surface, the thin film will adopt the in-plane lattice constant of the substrate, i.e.*a*ll = *a*o , where *a*ll is the in-plane lattice constant of the layer and *a*o is the lattice constant of the substrate. This is the case of pseudomorphic growth, and the epitaxial layer is pseudomorphic. If the lattice constant of the layer is larger than that of the substrate as in the case of InGaAs on GaAs, under the pseudomorphic condition growth the lattice of the layer will be elastically compressed in the two in-plane directions. The lattice constant of the layer in the growth direction perpendicular to the interface (the so-called out-of plane direction) will be strained according the Poison effect and will be larger than the unstrained value and the layer lattice will tense in the growth direction. Schematically this situation is illustrated in Figure 3.1.

Fig. 3.1. Schematic presentation of atom arrangement for two materials with different cubic lattice constant: a) before growth; b) for pseudomorphic growth

In the case of the smaller lattice constant of the growth layer (GaAsN on GaAs for example), *a< a*o the layer will be elastically tensed in two in-plane directions and compressed in the growth directions (the out-of-plane lattice constant will be smaller than substrate lattice constant). Under pseudomorphic growth conditions the cubic lattice doesn't remain cubic: *a*ll = *a*<sup>o</sup> ≠ *a*⊥. The out -of-plane lattice constant could be determined from the equation:

$$a. \! = a \! [1 \text{-} D (a \! u / a \text{-} 1)] \tag{3.1}$$

Where:

72 Solar Cells – New Aspects and Solutions

Observations, analyses and measurements of LPE GaAs on the formation of nuclei and surface terraces show that nuclei grow into well-defined prismatic hillocks bounded by only {100} and {111} planes and they are unique to each substrate orientation, and hillocks tend to coalesce into chains and then into parallel surface terraces (Mattes & Route, 1974). The hillock boundaries may cause local strain fields and variation of the incorporation rates of impurities and dopants, or the local strain may getter or rejects impurities during annealing processes. This inhomogeneity may be suppressed by providing one single step source or by using substrates of well-defined small misorientation. The FM growth mode and such homogeneous layers can only be achieved by LPE or by VPE at very high growth

Only at low supersaturation, nearly zero misfit and small misorientation of the substrate the layer by-layer growth mode can be realized and used to produce low dislocation layers for ultimate device performance. Two-dimensional growth is desirable because of the need for multilayered structures with flat interfaces and smooth surfaces. A notable exception is the fabrication of quantum dot devices, which requires three-dimensional or SK growth of the dots. Even here it is desirable for the other layers of the device to grow in a two-dimensional mode. In all cases of heteroepitaxy, it is important to be able to control the nucleation and

One of the main requirements for high quality heterostructure growth is the lattice constant of the growth material to be nearly the same as those of the substrate. In semiconductor alloys the lattice constant and band gap can be modified in a wide range. The lattice parameter difference may vary from nearly 0 to several per cent as in the cases of GaAs-AlAs and InAs-GaAs system, respectively. The growth of dilute nitride alloys is difficult because of the wide immiscibility range, a large difference in the lattice constant value and very small atom radius of N atoms. The growth of thick epitaxial layers creates many

At the initial stage of the growth when the epitaxial layer is of different lattice constant than the substrate in-plane lattice parameter of the growth material will coherently strain in order to match the atomic spacing of the substrate. The elastic energy of deformation due to the misfit in lattice constant destroys the epilayer lattice. The substrate is sufficiently thick and it remains unstrained by the growth of the epitaxial layer. If the film is thin enough to remain coherent to the substrate, then in the plane parallel to the growth surface, the thin film will adopt the in-plane lattice constant of the substrate, i.e.*a*ll = *a*o , where *a*ll is the in-plane lattice constant of the layer and *a*o is the lattice constant of the substrate. This is the case of pseudomorphic growth, and the epitaxial layer is pseudomorphic. If the lattice constant of the layer is larger than that of the substrate as in the case of InGaAs on GaAs, under the pseudomorphic condition growth the lattice of the layer will be elastically compressed in the two in-plane directions. The lattice constant of the layer in the growth direction perpendicular to the interface (the so-called out-of plane direction) will be strained according the Poison effect and will be larger than the unstrained value and the layer lattice will tense in the growth direction. Schematically this

temperatures.

growth mode.

**3. Pseudomorphic and metamorphic growth** 

problems which absent in the quantum-well structures.

situation is illustrated in Figure 3.1.

*a*⊥ - out-of-plane lattice constant of the layer

*a*ll - in-plane lattice constant of the layer

*a* - lattice constant of the unstrained cubic epitaxial layer

*D* = 2*C12*/*C11* , where *C11* and *C12* are elastic constants of the grown layer

Beyond a given critical thickness *η*c when a critical misfit strain *ε* is exceeded, a transition from the elastically distorted to the plastically relaxed configuration occurs. In this case both mismatch component differ from zero: *a*ll≠ *a*o ≠ *a*⊥. The lattice constant misfit is:

$$f = \begin{pmatrix} a \ -a\_o \end{pmatrix} / a\_o$$

$$f\_\perp = (a\_\perp \cdot a\_o) / a\_o = (1 + D \cdot DR)f \tag{3.2}$$

$$f\_\parallel = (a\_\parallel \cdot a\_o) / a\_o = Rf$$

*R* is a relaxation rate. For pseudomorphic growth *R*=0, and for full strain relaxation *R* =1 If the epilayer is thicker than the critical thickness, there will be sufficient strain energy in the layer to create dislocations to relieve the excess strain. The layer has now returned to its unstrained or equilibrium lattice parameters in both the in-plane and out-of-plane directions and the film to be 100% relaxed. Figure 3.2 shows schematically how a misfit dislocation can relieve strain in the heteroepitaxial structure.

Dilute Nitride GaAsN and InGaAsN Layers Grown by Low-Temperature Liquid-Phase Epitaxy 75

Calculated values for critical thickness from People-Bean energy equilibrium and Matthews-

 

[ln( / ) 1] 4 (1 ) *c c <sup>b</sup> <sup>h</sup> h b*

The calculated values of People-Bean models are larger than that of the Matthews-Blakeslee model. The measurements of dislocation densities in many cases showed no evidence of misfit dislocations for layer considerable ticker than Matthews-Blakeslee limit and nearly close to the energy-equilibrium thickness limit. Layers with thicknesses above the People-Bean limit can be considered to be completely relaxed, whereas layers below Matthews-Blakeslee limit values fully strained. Layers with thicknesses between these limits are metastable. They could be free of dislocations after growth, but are susceptible to relaxation

For the semiconductor devices based on the thick metamorphic structure the influence of the misfit dislocations which are located at the interface on active region could be reduced by growing the additional barrier layers before active region growth. Threading dislocations, which propagate up through the structure, are the most trouble for electronic devices since they can create defect states such as nonradiative centres and destroy the device properties. There are a variety of techniques used to reduce the density of threading dislocations in a material. For planar structure a thick buffer layer with lattice parameter equal to that of the active layers is usually used for reduction of threading dislocations. However, these structures always have high threading dislocation densities. In most thick nearly relaxed heteroepitaxial layers, it is found that the threading dislocation density greatly exceeds that of the substrate. Some authors (Sheldon et al.1988, Ayers et al. 1992) are noted for a number of heteroepitaxial material systems that this dislocation density decreases approximately with the inverse of the thickness. The dislocation density could be reduced by postgrowth

A linearly graded buffers and graded superlattice also are effectively used for restricting dislocations to the plane parallel to the growth surface, and thus support the formation of misfit dislocation and suppress threading dislocation penetration in the active region.

The X-ray diffraction (XRD) method is an accurate nondestructive method for characterization of epitaxial structures. X-ray scans may be used for determination the

In XRD experiment a set of crystal lattice planes (hkl) is selected by the incident conditions

2*d*sinθB = nλ (3.1.1)

lattice parameter, composition, mismatch and thicknesses of semiconductor alloys.

and the lattice spacing *d*hkl is determined through the well-known Brag's law:

 *<sup>f</sup>* 

(3.3)

(3.4)

2 (1 ) ln( / ) 32 (1 ) *c c <sup>b</sup> <sup>h</sup> h b f* 

*f* is a lattice mismatch, *b= a* / 2 is a magnitude of Burgers vector

Blakeslee force balance models are:

*ν=C12 /*( *C12+ C11*) is Poison's ratio,

during later high-temperature processing.

**3.1 X-ray diffraction characterization** 

Where:

annealing.

Fig. 3.2. Schematic presentation of the atom arrangement for metamorphic growth

In actual films, there is usually some amount of partial relaxation, although it can be very small in nearly coherent layers and nearly 100% in totally relaxed layers. For the partially relaxed layer, the in-plane lattice constant has not relaxed to its unstrained value. So some mismatch is accommodated by elastic strain, but a portion of the mismatch is accommodated by misfit dislocations (plastic strain).

There are two widely used models for calculations the critical thickness values: the Matthews-Blakeslee mechanical equilibrium model (Matthews.& Blakeslee, 1974) and the People-Bean energy equilibrium model (People & Bean, 1985). The People-Bean energy equilibrium model requires the total energy being at its minimum under critical thickness. According this model the elastic energy is equal to the dislocation energy at the critical thickness if the total elastic energy of the system with fully coherent interface is larger than the sum of the total system energy for the reduced misfit, due to the generation of dislocations, and the associated dislocation energy, and then begins the formation of interfacial dislocations.

Generally, the Matthews-Blakeslee model based on stemming from force balance, is the most often used to describe strain relaxation in thin films system. The equilibrium model of Matthews-Blakeslee assumes the presence of threading dislocations from the substrate. It gives mathematical relation for critical thickness by examining the forces originating from both the misfit strain Fε and the tension of dislocation line FL. The critical thickness hc is defined as the thickness limit when the misfit strain force Fε is equal to the dislocation tension force FL( at hc Fε = FL). For layers ticker than the critical thickness, the threading segment begins to glide and creates misfit dislocations at the interface to relieve the mismatch strain. The dislocations can easily move if dislocation lines and the Burgers vectors belong to the easy glide planes as {111} planes in face-centred cubic crystals.

In III-V semiconductors, the relaxation is known to occur by the formation of misfit dislocations and /or stacking faults. The usual misfit dislocations that are considered are located along the intersection of the glide plane and the interface plane. In zinc-blende crystal structures, on (100) oriented substrates the glide planes intersect the interface (110) which provides the corresponding line directions of misfit dislocations in such structures. The component of 60 dislocations perpendicular to the line directions contributes to strain relaxation. The 60 Burgers vector is b= ½ *a*l 110 and has a length along the interface perpendicular to the line *a* / 2 .

Calculated values for critical thickness from People-Bean energy equilibrium and Matthews-Blakeslee force balance models are:

$$h\_c = \frac{b(l - \nu)}{32\pi f^2 (l + \nu)} \ln(h\_c / b) \tag{3.3}$$

$$h\_{\varepsilon} = \frac{b}{4\pi f (1+\nu)} [\ln(h\_{\varepsilon}/b) + 1] \tag{3.4}$$

Where:

74 Solar Cells – New Aspects and Solutions

Fig. 3.2. Schematic presentation of the atom arrangement for metamorphic growth

accommodated by misfit dislocations (plastic strain).

interfacial dislocations.

perpendicular to the line *a* / 2 .

In actual films, there is usually some amount of partial relaxation, although it can be very small in nearly coherent layers and nearly 100% in totally relaxed layers. For the partially relaxed layer, the in-plane lattice constant has not relaxed to its unstrained value. So some mismatch is accommodated by elastic strain, but a portion of the mismatch is

There are two widely used models for calculations the critical thickness values: the Matthews-Blakeslee mechanical equilibrium model (Matthews.& Blakeslee, 1974) and the People-Bean energy equilibrium model (People & Bean, 1985). The People-Bean energy equilibrium model requires the total energy being at its minimum under critical thickness. According this model the elastic energy is equal to the dislocation energy at the critical thickness if the total elastic energy of the system with fully coherent interface is larger than the sum of the total system energy for the reduced misfit, due to the generation of dislocations, and the associated dislocation energy, and then begins the formation of

Generally, the Matthews-Blakeslee model based on stemming from force balance, is the most often used to describe strain relaxation in thin films system. The equilibrium model of Matthews-Blakeslee assumes the presence of threading dislocations from the substrate. It gives mathematical relation for critical thickness by examining the forces originating from both the misfit strain Fε and the tension of dislocation line FL. The critical thickness hc is defined as the thickness limit when the misfit strain force Fε is equal to the dislocation tension force FL( at hc Fε = FL). For layers ticker than the critical thickness, the threading segment begins to glide and creates misfit dislocations at the interface to relieve the mismatch strain. The dislocations can easily move if dislocation lines and the Burgers

vectors belong to the easy glide planes as {111} planes in face-centred cubic crystals.

In III-V semiconductors, the relaxation is known to occur by the formation of misfit dislocations and /or stacking faults. The usual misfit dislocations that are considered are located along the intersection of the glide plane and the interface plane. In zinc-blende crystal structures, on (100) oriented substrates the glide planes intersect the interface (110) which provides the corresponding line directions of misfit dislocations in such structures. The component of 60 dislocations perpendicular to the line directions contributes to strain relaxation. The 60 Burgers vector is b= ½ *a*l 110 and has a length along the interface *ν=C12 /*( *C12+ C11*) is Poison's ratio,

*f* is a lattice mismatch, *b= a* / 2 is a magnitude of Burgers vector

The calculated values of People-Bean models are larger than that of the Matthews-Blakeslee model. The measurements of dislocation densities in many cases showed no evidence of misfit dislocations for layer considerable ticker than Matthews-Blakeslee limit and nearly close to the energy-equilibrium thickness limit. Layers with thicknesses above the People-Bean limit can be considered to be completely relaxed, whereas layers below Matthews-Blakeslee limit values fully strained. Layers with thicknesses between these limits are metastable. They could be free of dislocations after growth, but are susceptible to relaxation during later high-temperature processing.

For the semiconductor devices based on the thick metamorphic structure the influence of the misfit dislocations which are located at the interface on active region could be reduced by growing the additional barrier layers before active region growth. Threading dislocations, which propagate up through the structure, are the most trouble for electronic devices since they can create defect states such as nonradiative centres and destroy the device properties.

There are a variety of techniques used to reduce the density of threading dislocations in a material. For planar structure a thick buffer layer with lattice parameter equal to that of the active layers is usually used for reduction of threading dislocations. However, these structures always have high threading dislocation densities. In most thick nearly relaxed heteroepitaxial layers, it is found that the threading dislocation density greatly exceeds that of the substrate. Some authors (Sheldon et al.1988, Ayers et al. 1992) are noted for a number of heteroepitaxial material systems that this dislocation density decreases approximately with the inverse of the thickness. The dislocation density could be reduced by postgrowth annealing.

A linearly graded buffers and graded superlattice also are effectively used for restricting dislocations to the plane parallel to the growth surface, and thus support the formation of misfit dislocation and suppress threading dislocation penetration in the active region.

### **3.1 X-ray diffraction characterization**

The X-ray diffraction (XRD) method is an accurate nondestructive method for characterization of epitaxial structures. X-ray scans may be used for determination the lattice parameter, composition, mismatch and thicknesses of semiconductor alloys.

In XRD experiment a set of crystal lattice planes (hkl) is selected by the incident conditions and the lattice spacing *d*hkl is determined through the well-known Brag's law:

$$
\mathfrak{L}d\text{sinc}\theta\_{\mathbb{B}} = \mathfrak{n}\lambda\tag{3.1.1}
$$

Dilute Nitride GaAsN and InGaAsN Layers Grown by Low-Temperature Liquid-Phase Epitaxy 77

 *x* = (*a*(*x*) - *a*(B))/ (*a*(A) - *a*(B)) (3.1.4) If *a*(B) is the substrate lattice parameter, the composition *x* can be calculated from the

 *x* = *f*(*x*)/*f*(AB) (3.1.5)

In the case of GaAs1-xNx and InxGa1-xAs1-yNy dilute nitride alloys relationship between lattice

 *a*GaAs1-xNx = *x a*GaN *+* (1- *x*) *a*GaAs (3.1.6)

 *a* InxGa1-xAs1-yNy = *x ya*InN *+* (1- *x*)*y a*GaN + *x*(1- *y*) *a*InAs *+* (1- *x*) (1- *y*) *a*GaAs (3.1.7) The lattice parameter measurements method is one of the most accurate way to determine the composition, provided that the composition versus lattice parameter dependence is known. The comparison between composition values obtained from XRD and that, determined by other analytical techniques has allowed to measure the deviation from the

Table 1. presents the values of elastic constants and lattice parameters for GaAs, InAs, GaN,

compound GaAs InAs GaN InN

C11, GPa 118.79 83.29 293 187

C12, GPa 53.76 45.26 159 125

*a0*, nm 0.5653 0.60584 0.4508 0.4979

Low-temperature LPE is the most simple, low cost and safe method for high-quality III-V based heterostructure growth. It remains the important growth technique for a wide part of the new generations of optoelectronic devices, since the competing methods, MBE and MOCVD, are complicated and expensive although they offer a considerable degree of flexibility and growth controllability. The lowering the growth temperature for Al-Ga-As system provides the minimal growth rate values of 1–10 Å/s, and they are comparable with MBE and MOCVD growth values (Alferov et al, 1986). At the early stages of the process two-dimensional layer growth occurs, which ensures structure planarity and makes it

possible to obtain multilayer quantum well (QW) structures (Andreev et al, 1996).

Table 1. Elastic constants and lattice parameters for some III-V compounds

measurement misfit f(*x*) value:

linear Vegard's law in alloys.

InN binary compounds.

*f* (*x*) is the measured misfit value with respect to *a*(B) and

Parameter

**4. Low-temperature LPE growth** 

*f*(AB) is the misfit between compound A and compound B, used as reference.

parameters and composition assuming Vegard's law are the foolowing:

Where:

where n is the order of reflection and θB is the Brag angle

The crystal surface is the entrance and exit reference plane for the X-ray beams in Bragg scattering geometry and the incident and diffracted beams make the same angle with the lattice planes. Two types of rocking curve scan are used: symmetric when the Bragg diffraction is from planes parallel to crystal surface and asymmetric when the diffraction lattice planes are at angle φ to the crystal surface (Fig. 3.3).

Fig. 3.3. Symmetric and asymmetric reflections from crystal surface

Let *ω* be the incidence angle with respect to the sample surface of a monochromatic X-ray beam. By rocking a crystal through a selected angular range, centered on the Bragg angle of a given set of lattice planes a diffraction intensity profile I(*ω***)** is collected. For single layer heterostructure, the intensity profile will show two main peaks corresponding to the diffraction from the layer and substrate. The angular separation ∆*ω* of the peaks account for the difference ∆*dhkl* between the layer and substrate lattice spacing. XRD do not directly provide the strain value on the crystal lattice. Te measurable quantities being the lattice mismatches ∆*a*⊥/*a*o and ∆*a*ll/*a*o, i. e *f*<sup>⊥</sup> and *f*ll. The relationship between lattice mismatch components and misfit *f* with respect to substrate is:

$$f = f\_\perp \text{ (1-v)} / \text{(1+ v)} + 2 \text{ v} \, f\_\text{l} / \text{ (1+ v)} \tag{3.1.2}$$

where ν is the Poisson ratio

This is the basic equation for the strain and composition characterization of heterostructures for cubic lattice materials. In the case of semiconductor alloys AxB1-x the composition *x* can be obtained if the relationship between composition and lattice constant is known. Poisson ratio is also composition depending and the use of Poisson ratio ν is only valid for isotropic materials. For a cubic lattice, it can only be applied for high symmetric directions as (001), (011), (111), but Poison ratio may be different along different directions (ν ≈ 1/3 for the most semiconductors alloys).

XRD can easily be employed to measure the lattice parameter with respect the substrate used as a reference. The strain and the composition of layer can be accurately determined if the dependence of the lattice parameter with the composition is known, the accuracy being mainly due to the precise knowledge of the lattice parameter –composition dependence.

In many cases a good approximation of a such dependence is given by Vegard law, which assumes that in the alloy AxB1-x the lattice of the alloy is proportional to the stoichiometric coefficient *x*:

$$a \text{ (x)} = \text{xa(A)} + \text{(1-x)} \text{ a(B)}\tag{3.1.3}$$

From this equation the stoichiometric coefficient *x* is obtained:

$$\mathbf{x} = (a(\mathbf{x}) \cdot a(\mathbf{B})) / \text{ (}a(\mathbf{A}) \text{ - } a(\mathbf{B})\text{)}\tag{3.1.4}$$

If *a*(B) is the substrate lattice parameter, the composition *x* can be calculated from the measurement misfit f(*x*) value:

$$\mathbf{x} = f(\mathbf{x}) / f(\mathbf{AB}) \tag{3.1.5}$$

Where:

76 Solar Cells – New Aspects and Solutions

The crystal surface is the entrance and exit reference plane for the X-ray beams in Bragg scattering geometry and the incident and diffracted beams make the same angle with the lattice planes. Two types of rocking curve scan are used: symmetric when the Bragg diffraction is from planes parallel to crystal surface and asymmetric when the diffraction

ω θ 2 θ ω φ

Let *ω* be the incidence angle with respect to the sample surface of a monochromatic X-ray beam. By rocking a crystal through a selected angular range, centered on the Bragg angle of a given set of lattice planes a diffraction intensity profile I(*ω***)** is collected. For single layer heterostructure, the intensity profile will show two main peaks corresponding to the diffraction from the layer and substrate. The angular separation ∆*ω* of the peaks account for the difference ∆*dhkl* between the layer and substrate lattice spacing. XRD do not directly provide the strain value on the crystal lattice. Te measurable quantities being the lattice mismatches ∆*a*⊥/*a*o and ∆*a*ll/*a*o, i. e *f*<sup>⊥</sup> and *f*ll. The relationship between lattice mismatch

 *f* = *f*⊥ (1-ν)/(1+ ν) + 2 ν *f*ll/ (1+ ν) (3.1.2)

This is the basic equation for the strain and composition characterization of heterostructures for cubic lattice materials. In the case of semiconductor alloys AxB1-x the composition *x* can be obtained if the relationship between composition and lattice constant is known. Poisson ratio is also composition depending and the use of Poisson ratio ν is only valid for isotropic materials. For a cubic lattice, it can only be applied for high symmetric directions as (001), (011), (111), but Poison ratio may be different along different directions (ν ≈ 1/3 for the most

XRD can easily be employed to measure the lattice parameter with respect the substrate used as a reference. The strain and the composition of layer can be accurately determined if the dependence of the lattice parameter with the composition is known, the accuracy being mainly due to the precise knowledge of the lattice parameter –composition dependence. In many cases a good approximation of a such dependence is given by Vegard law, which assumes that in the alloy AxB1-x the lattice of the alloy is proportional to the stoichiometric

 *a* (*x*) = *xa*(A) + (1- *x*) *a*(B) (3.1.3)

θ

θ

where n is the order of reflection and θB is the Brag angle

lattice planes are at angle φ to the crystal surface (Fig. 3.3).

Fig. 3.3. Symmetric and asymmetric reflections from crystal surface

components and misfit *f* with respect to substrate is:

From this equation the stoichiometric coefficient *x* is obtained:

where ν is the Poisson ratio

semiconductors alloys).

coefficient *x*:

*f* (*x*) is the measured misfit value with respect to *a*(B) and

*f*(AB) is the misfit between compound A and compound B, used as reference.

In the case of GaAs1-xNx and InxGa1-xAs1-yNy dilute nitride alloys relationship between lattice parameters and composition assuming Vegard's law are the foolowing:

$$a\_{\text{CaAsJ}\cdot\text{xNx}} = \chi \, a\_{\text{CaN}} + \text{(1- }\chi\text{)}\, a\_{\text{CaAs}}\tag{3.1.6}$$

$$\mathcal{J}\text{ }\text{Im}\text{Ga}\text{1-a}\text{As}\text{1-y} \\ \text{N}\text{y} = \text{x } \text{y} \\ \text{a}\_{\text{InN}} + \text{(1-x)} \\ \text{y } a\_{\text{GaN}} + \text{x(1-y)} \\ \text{a}\_{\text{InAs}} + \text{(1-x)} \\ \text{(1-y)} \text{ a}\_{\text{GaAs}} \tag{3.1.7}$$

The lattice parameter measurements method is one of the most accurate way to determine the composition, provided that the composition versus lattice parameter dependence is known. The comparison between composition values obtained from XRD and that, determined by other analytical techniques has allowed to measure the deviation from the linear Vegard's law in alloys.

Table 1. presents the values of elastic constants and lattice parameters for GaAs, InAs, GaN, InN binary compounds.


Table 1. Elastic constants and lattice parameters for some III-V compounds

### **4. Low-temperature LPE growth**

Low-temperature LPE is the most simple, low cost and safe method for high-quality III-V based heterostructure growth. It remains the important growth technique for a wide part of the new generations of optoelectronic devices, since the competing methods, MBE and MOCVD, are complicated and expensive although they offer a considerable degree of flexibility and growth controllability. The lowering the growth temperature for Al-Ga-As system provides the minimal growth rate values of 1–10 Å/s, and they are comparable with MBE and MOCVD growth values (Alferov et al, 1986). At the early stages of the process two-dimensional layer growth occurs, which ensures structure planarity and makes it possible to obtain multilayer quantum well (QW) structures (Andreev et al, 1996).

Dilute Nitride GaAsN and InGaAsN Layers Grown by Low-Temperature Liquid-Phase Epitaxy 79

Fig. 4.2. Piston boat for growth of multilayer AlGaAs/GaAs heterostructures: 1, growth solution; 2, container for solution; 3, piston; 4, opening; 5, narrow slit; 6, substrate; 7, used

3 4 5 6 7 8

1 2

The substrate surface in this boat after the first wetting is always covered by a melt and this solves difficulties of wetting during the growth of AlGaAs heterostructures in the range 600-400 °C. The piston boat design is shown in Figure 4.2. In this boat the melts of different compositions are placed in containers which can move along the boat body. The liquid phase falls down into the piston chamber and squeezes throw narrow slit into the substrate which allows mechanical cleaning of oxides films from liquid phase and insures a good wetting. The crystallization is carried out from the melt 0.5-1 mm thick. After the growth of the layer liquid phase is removed from the substrate by squeezing of the next melt. The last liquid phase is swept from the surface by shifting the substrate holder out side the growth

The liquid phase can not remove completely from the surface structure and cause a poor morphology of the last grown layer. The excess melt could be remove from the substrate by using additional wash melt, which may either has a poor adhesion to the substrate or may be relatively easy remove with post-growth cleaning and etching in selective etchants. Authors (Mishurnyi at al, 2002) suggest an original method to complete remove the liquid solution after epitaxy. The remained liquid phase is pulled up into the space between the substrate and vertical plates made of the same materials as the substrate assembled very closely to the substrate surface. This method is very useful for growth of multilayer heterostructures not containing Al in modified slide boat because prevent mixing of any liquids remaining. For the most multicomponent alloys such as InGaAsP, InGaAsSb, InPAsSb etc., lattice constant is very sensitive to composition variation and the piston boat is not suitable for their growth because of mixing of two deferent solutions. Slide boats with different design are used for fabrication of complicated multilayer heterostructure on the base of these multicomponent alloys. In order to improve the control of layer thicknesses and uniformity it is necessary the growth to be carried out using a finite melt. In this boat the liquid phase after saturations is transferred into the additional containers or growth chamber with finite space for the liquid phase. Figure 4.3 shows a schematic slide boat for epitaxy growth from finite melt.A critical requirement for the most multicomponent alloys, instead of AlGaAs, AlGaP, is precise determination of the growth temperature. The

solution; 8, container for used solutions.

chamber.

The results of study the crystallization process in the temperature range 650-400 oC demonstrate precise layer composition and thickness controllability for the low-temperature LPE growth. A necessary requirements for successful devices fabrication is the optimal doping of the structure layers at low temperatures. The experiments (Milanova and Khvostikov, 2000) on doping using different type dopants covered large range of carrier concentrations: from 1016 to 1019 cm−3 for n Al*x*Ga1−*<sup>x</sup>*As layers (0<*x*<0.3); from 5×1017 cm−3 to well above 1019 cm−3 for p Al*x*Ga1−*<sup>x</sup>*As (0<*x*<0.3); and from 1016 to 1018 cm−3 for n- and p Al*x*Ga1−*<sup>x</sup>*As (0.5<*x*<0.9) layers. High quality multilayer heterostructures containing layers as thin as 2-20 nm, as well as several microns thick, with a smooth surface and flat interfaces have been grown by low-temperature LPE. The lowest absolute threshold current of 1.3mA (300 K) was obtained for buried laser diodes with a stripe width of ~ 1μm and cavity length of 125μm (Alferov et al, 1990).

High-efficiency solar cells for unconcentrated (Milanova et al, 1999) and concentrated solar cells (Andreev et al, 1999) have been fabricated by low-temperature LPE. The record conversion efficiency under ultra-high (>1000) concentration ratio solar radiation heve been achieved for GaAs single-junction solar cells based on multilayer AlGaAs/GaAs heterostructures (Algora et al, 2001).

The success of the LPE method is strongly depend on the graphite boat design used for epitaxy growth. The most widely used for LPE growth is a slide boat method. The conventional simple slide boat consists of a boat body in which are formed containers for liquid phase and a slider with one or more sits for the substrate (Fig. 4.1.). The slider moves the substrates under and out of the growth melt. This boat design has some disadvantages: the melt thicknesses is several millimeters and during growth from such semi-limited liquid-phase a portion of dissolved materials can not reach the substrate surface and forms stable seeds at a distance of 1 mm and more from the growth surface which deteriorate the planarity of the grown layer.

Fig. 4.1. Conventional slide boat for LPE growth: 1, body boat; 2, slider, 3, substrate.

Another drawback is the arising the defects on the layer surface due to the mechanical damage during its transfer from one melt to another. Also always on the surface of the melt present oxides films and it is difficult to completely removed these films even by long hightemperature baking. This is a critical problem for wetting of the substrate surface, especially for epitaxial process in Al-Ga-As system. A piston growth technique has been developed for LPE growth of AlGaAs heterostructures by Alferov at al (Alferov et al, 1975).

The results of study the crystallization process in the temperature range 650-400 oC demonstrate precise layer composition and thickness controllability for the low-temperature LPE growth. A necessary requirements for successful devices fabrication is the optimal doping of the structure layers at low temperatures. The experiments (Milanova and Khvostikov, 2000) on doping using different type dopants covered large range of carrier concentrations: from 1016 to 1019 cm−3 for n Al*x*Ga1−*<sup>x</sup>*As layers (0<*x*<0.3); from 5×1017 cm−3 to well above 1019 cm−3 for p Al*x*Ga1−*<sup>x</sup>*As (0<*x*<0.3); and from 1016 to 1018 cm−3 for n- and p Al*x*Ga1−*<sup>x</sup>*As (0.5<*x*<0.9) layers. High quality multilayer heterostructures containing layers as thin as 2-20 nm, as well as several microns thick, with a smooth surface and flat interfaces have been grown by low-temperature LPE. The lowest absolute threshold current of 1.3mA (300 K) was obtained for buried laser diodes with a stripe width of ~ 1μm and cavity length

High-efficiency solar cells for unconcentrated (Milanova et al, 1999) and concentrated solar cells (Andreev et al, 1999) have been fabricated by low-temperature LPE. The record conversion efficiency under ultra-high (>1000) concentration ratio solar radiation heve been achieved for GaAs single-junction solar cells based on multilayer AlGaAs/GaAs

The success of the LPE method is strongly depend on the graphite boat design used for epitaxy growth. The most widely used for LPE growth is a slide boat method. The conventional simple slide boat consists of a boat body in which are formed containers for liquid phase and a slider with one or more sits for the substrate (Fig. 4.1.). The slider moves the substrates under and out of the growth melt. This boat design has some disadvantages: the melt thicknesses is several millimeters and during growth from such semi-limited liquid-phase a portion of dissolved materials can not reach the substrate surface and forms stable seeds at a distance of 1 mm and more from the growth surface which deteriorate the

Fig. 4.1. Conventional slide boat for LPE growth: 1, body boat; 2, slider, 3, substrate.

LPE growth of AlGaAs heterostructures by Alferov at al (Alferov et al, 1975).

Another drawback is the arising the defects on the layer surface due to the mechanical damage during its transfer from one melt to another. Also always on the surface of the melt present oxides films and it is difficult to completely removed these films even by long hightemperature baking. This is a critical problem for wetting of the substrate surface, especially for epitaxial process in Al-Ga-As system. A piston growth technique has been developed for

3

2

1

of 125μm (Alferov et al, 1990).

planarity of the grown layer.

heterostructures (Algora et al, 2001).

Fig. 4.2. Piston boat for growth of multilayer AlGaAs/GaAs heterostructures: 1, growth solution; 2, container for solution; 3, piston; 4, opening; 5, narrow slit; 6, substrate; 7, used solution; 8, container for used solutions.

The substrate surface in this boat after the first wetting is always covered by a melt and this solves difficulties of wetting during the growth of AlGaAs heterostructures in the range 600-400 °C. The piston boat design is shown in Figure 4.2. In this boat the melts of different compositions are placed in containers which can move along the boat body. The liquid phase falls down into the piston chamber and squeezes throw narrow slit into the substrate which allows mechanical cleaning of oxides films from liquid phase and insures a good wetting. The crystallization is carried out from the melt 0.5-1 mm thick. After the growth of the layer liquid phase is removed from the substrate by squeezing of the next melt. The last liquid phase is swept from the surface by shifting the substrate holder out side the growth chamber.

The liquid phase can not remove completely from the surface structure and cause a poor morphology of the last grown layer. The excess melt could be remove from the substrate by using additional wash melt, which may either has a poor adhesion to the substrate or may be relatively easy remove with post-growth cleaning and etching in selective etchants. Authors (Mishurnyi at al, 2002) suggest an original method to complete remove the liquid solution after epitaxy. The remained liquid phase is pulled up into the space between the substrate and vertical plates made of the same materials as the substrate assembled very closely to the substrate surface. This method is very useful for growth of multilayer heterostructures not containing Al in modified slide boat because prevent mixing of any liquids remaining. For the most multicomponent alloys such as InGaAsP, InGaAsSb, InPAsSb etc., lattice constant is very sensitive to composition variation and the piston boat is not suitable for their growth because of mixing of two deferent solutions. Slide boats with different design are used for fabrication of complicated multilayer heterostructure on the base of these multicomponent alloys. In order to improve the control of layer thicknesses and uniformity it is necessary the growth to be carried out using a finite melt. In this boat the liquid phase after saturations is transferred into the additional containers or growth chamber with finite space for the liquid phase. Figure 4.3 shows a schematic slide boat for epitaxy growth from finite melt.A critical requirement for the most multicomponent alloys, instead of AlGaAs, AlGaP, is precise determination of the growth temperature. The

Dilute Nitride GaAsN and InGaAsN Layers Grown by Low-Temperature Liquid-Phase Epitaxy 81

Figure 5.1. shows the relationship between the lattice constant and band-gap energy in some III-V semiconductor alloys. In the case of InGaNAs adding In to GaAs increases the lattice constant, while adding N to GaAs decreases the lattice constant. In the same time the incorporation of In and N in GaAs leads to reduction of the band gap energy in the new alloy. Consequently, by adjusting the contents of In and N in quaternary InGaNAs alloys can be grown lattice-matched to GaAs layers because In and N have opposing strain effects on the lattice and make it possible to engineer a strain-free band gap layers suitable for different

0,45 0,50 0,55 0,60 0,65 0,70

Lattice constant, nm

Recently a development of the spectral splitting concentrator photovoltaic system based on a Fresnel lens and diachronic filters has a great promise to reach super high conversion efficiencies (Khvostiokov et al. 2010). Module efficiency nearly 50% is expected for the system with three single-junction solar cells connected in series with band gap of 1.88-1.42-1.0 eV. The development of three optimized AlGaAs, GaAs and InGaAsN based cells is the best combination for application in such system if PV quality of the quaternary

In this paper low-temperature LPE is proposed as a new growth method for dilute nitride materials. Because of its simplicity and low cost many experiments on GaInAsN and GaAsN growth under different condition and with different doping impurities could be made using LPE. The systematic study of their structural, optical and electrical properties by various methods make it possible to find optimized growth conditions for InGaAsN quaternary

GaAsN compounds were grown by the horizontal graphite slide boat technique for LPE on (100) semi-insulating or n-type GaAs substrates. A flux of Pd-membrane purified hydrogen at atmospheric pressure was used for experiments. No special baking of the system was done before epitaxy. Starting materials for the solutions consisted of 99.9999 % pure Ga, polycrystalline GaAs and GaN. The charged boat was heated at 750oC for 1 h in a purified H2 gas flow in order to dissolve the source materials and decrease the contaminants in the


GaAs

AlAs

 lattice matched InAs GaSb

GaAsN-

InN

Fig. 5.1. Relationship between lattice constant and bad gap energy for some III-V

GaN

applications.

semiconductor alloys

0,0

InGaAsN could be reached by LPE growth.

compounds lattice matched to GaAs substrate.

**5.1 Growth and characterization of GaAsN layers** 

0,5 1,0

1,5 2,0

Energy band gap, eV

2,5 3,0

3,5

temperature at the interface between the liquid phase and substrate can not be measured and common it is determined by measurements of the source component solubility (Mishurnyi et al, 1999) .

Fig. 4.3. Slide boat for growth from finite melt: 1, boat body with container for melts; 2, slider with container for finite melts; 3, slider for the substrates.

Slide boats with different design modification are used for growth of variety structures in different multicomponent system. A boat made of two different materials, sapphire (for body) and graphite (for slider), is suggested by Reynolds and Tamargo (Reynolds and Tamargo, 1984). This design reduces temperature variations around the perimeter of the substrate which contribute to unwanted 'edge' growth effects. Slide boats with narrowed melt contact for epitaxy of extremely thin epilayers have been used to grow active layer in single-quantum well lasers by (Alferov et al, 1985 ) and later by (Kuphal, 1991). Also a modified slide boat can be used for multilayer periodic structures growth (Arsent'ev et al, 1988). The use of two growth chambers with narrow slits makes it possible to produce such structures by means of repeated reciprocating movements of the slider with the substrate situated underneath these slits. Another variant of an LPE boat (Mishurnyi et la, 1997), which is a combination of the 'sliding' and 'piston' designs has been used successfully to grow InGaAsSb, AlGaAsSb and various multilayer structures on the basis of these materials.
