in the last two decades , a large research effort has been devoted to quantum dots ( qds ) , the quantum wires , qd chains , nanoholes and pits [ 1 - 8 ] due to their modified density of states , fascinating optoelectronic properties and device applications for lasers , photodetectors and other electronic devices . among quantum dots , pits and wires fabrication techniques , the self - organized stranski 
krastanow method   is an important one by which dislocation - free dots , elongated islands and wires can be produced . indeed , above a certain critical thickness , the growth mode switches from the conventional layer - by - layer ( i.e. , two - dimensional , 2d ) to a 3d growth mode due to the accumulation of the elastic energy in the strained layer that , first , partially relaxes by spontaneously nucleating small islands of strained material and , later , by creating misfit dislocations .
the elastic strain caused by lattice mismatch can also be relaxed by the formation of undulations , pits and their combination [ 5 - 8 ] .
depending on the growth conditions , the elastic strain can be relaxed by the formation of either quantum wires and quantum dots , or even unique island 
extensive experimental results suggest that surface morphologies are relying on growth conditions and matrix materials . on the basis of an atomistic model
, it is shown that the energy change due to the step formation is negative or positive depending upon the sign of the misfit
. the step formation energy can even be negative for compressive misfit stress in the heterolayer , while it is definitely positive for tensile misfit stress .
this conclusion is in contrast to the classical model where the step energy is always positive and independent of the sign of the misfit .
the step formation energy influences the critical thickness and the energy barrier for dislocation nucleation . using a simple atomistic simulation
, it is shown that the critical thickness depends upon the sign of the misfit .
for example , it changes from 4 nm for ge films on si(100 ) substrates to 6 nm for si films on ge(100 ) substrates having the same misfit .
the investigations of the surface morphology evolution of strained inas / gaas films at different growth conditions   demonstrated that there are at least three different strain relaxation mechanisms for the same material system .
that is , depending on the growth conditions , the elastic strain can be relaxed by the formation of either quantum wires or quantum dots , or even unique island  pit pairs .
. both the island height and the pit depth can be much greater than the average layer thickness .
this suggests that considerable mass transport from substrate into the islands is taking place during the growth .
however , during heteroepitaxy , when the layer becomes sufficiently thick , the pits are eventually filled up either by the lateral overgrowth or by the expanding islands , forming nearly pure island morphology at the surface .
the detailed analysis of the surface dynamics during phase transitions of gaas(100 )   and unusual role of the substrate at droplet - induced gaas / algaas qd pairs growth   also confirm this assumption . from the industrial point of view , the narrow band gap iii 
v semiconductor materials like inas , gasb , insb and their ternary and quaternary alloys are particularly interesting and useful since they are potentially promising to access mid - infrared and far infrared wavelength regions .
these materials would provide the next generation of leds , lasers and photodiodes for applications such as infrared gas sensors , for molecular spectroscopy , thermal imaging , photovoltaic ( pv )   and thermo - photovoltaic cells ( tpv ) .
the application of the inassbp and other similar quaternary materials opens up interesting physical and technological prospects for the dirigible growth of qds , the pits and dots  pits cooperative systems .
independent variations of the third and fourth components provide corresponding sign of the misfit ; i.e. , providing the tensile or compressive misfit stress .
at the first case , elastic strain will be relaxed by the formation of qds , but at the second one  by the pits . in this article , an example of inassbp quaternary qds , the pits and dots  pits cooperative structure growth on inas(100 ) substrates by lpe , as well as the interaction and surface morphology of the dots  pits combinations are presented and investigated .
the samples are grown by lpe using a slide - boat crucible . to ensure a high purity of the epitaxial layers ,
the inas(100 ) substrates have a 11 mm diameter are undoped , with a background electron concentration of n = 2  10 cm .
the inas0,742 sb0,08 p0,178 quaternary alloy used here as basis composite is conveniently lattice - matched to inas .
the lpe growth solution components  undoped inas , undoped inp and sb ( 6 n ) are solved in a in ( 7 n ) solution that has been first homogenized for 1 h at t = 580 c and then 3 h at the initial growth temperature of t = 550 c to equilibrate the system thermodynamically . to expect the strain - induced qds and pits formation , the undoped and supersaturated by antimony and phosphorus liquid phase was used to provide a different sign of lattice mismatch up to 4% between the inas substrate and inassbp epilayer . to initiate the growth of qds and pits ,
an oversaturation of the liquid phase is developed by decreasing the initial growth temperature up to 2 c at the slower ramp rate .
the high - resolution scanning electron microscope ( sem - edxa  fei nova 600dual beam ) is used to study the strain - induced inassbp qds 
1 ) that the pits ( large and small ) like the islands primarily formed into truncated  reverse  pyramids . the edxa measurements shown that , at first , either islands or pits edges have a quaternary composition and that on average , they are enriched by antimony and by phosphorus , respectively . in our inassbp quaternary experimental system , the nucleation mechanism of qds and the exposure of wetting layer ( and inas substrate ) at pits are quite interesting , but very complicated for explanation result . from a physical perspective
, we have assumed that simultaneous nucleation of the islands and pits are occurring due to variable curvature ( the tensile or compressive local perturbations ) of the wetting layer .
we suggest that at the perturbed sites , the wetting layer surface is strained , and the depositing material will prefer not to remain at these sites , but rather diffuse away .
after that occurs , the strain relaxation is performed at the adatoms ( sb and p ) surface diffusion in opposite directions , leaving behind the islands and the pits on the surface . in this scenario , corners or edges of the pits and islands
are the most preferred sites to attach newly deposited materials , because at these regions , the strain energy is most relieved .
the islands ( or pits ) at these relaxed regions will grow rapidly at the expense of the material around the pits ( or dots ) .
the fact that the  large  pits are deeper ( up to 100 nm and more ) than the wetting layer thickness implies that the arsenic atoms are also  pumped  out from the substrate and probably replaced by the phosphorus atoms . the similar cooperative nucleation of the dots  pits pairs was detected at the growth of inas qds on gaas substrate , gaas / algaas qd pairs   and at the growth of in 0.53 ga0.47 as layers on inp(001 ) substrate .
the effect of island density on pit nucleation in in0.27 ga0.73 as films grown on gaas(001 ) substrate is discussed in .
large  pits banded by the quantum wires in order to be confident , we calculated the gibbs free energy of inassbp quaternary alloy , as well as separately of inas - insb , inas - inp and insb - inp ternary alloys .
we found that at t = 550 c ( our growth temperature ) , the gibbs energy has the minimal value at x = 0.39 for inas1xsbx and at y = 0.52 for inas1ypy alloys .
otherwise , for the insb1zpz ternary alloy at the same temperature , the sufficiently wide immiscibility gap is exist at 0.05 < z < 0.97 . in this concentration range , the gibbs energy increases ( from the both sides ) and the mixing of these binary compounds becomes energetically not preferable .
this result marginally proves our assumption that at the nucleation of inassbp quaternary dots and pits , the surface diffusion of the antimony and phosphorus in opposite direction has to be energetically more preferable .
in addition , note that with the increasing of the liquid phase initial concentration , the islands and pits shape transformation from the truncated pyramids to ellipsoidal and globe shape was detected .
figure 2a displays the sem and afm images of the inassbp unencapsulated dots  pits cooperative structure in plain view for the surface area of s = 4 m . in this figure
the qds and pits are clearly visible and quite uniformly distributed over the substrate surface .
figures 1b , 1c and 2b2d show that cooperative nucleation of the dots  pits structures is occurring . in
pits are banded by quantum wires and that the qds are banded by pits ( in the form of  nano - camomile  ) .
b , c and d  enlarged view of the mentioned by red , blue and green ovals related regions .
white ovals  qds , black ovals  pits our statistical explorations show that the  small  qds average density ranges from 0.8 to 2  10 cm , with heights and widths dimensions from 2 to 20 nm and 5 to 45 nm , respectively .
the average density of the  small  pits is equal to ( 610 )  10 cm with dimensions of 540 nm in width and depth .
surface density of the  large  dots and pits is less by almost on two orders of magnitude .
small  qds and pit amount , and surface density versus their average diameter calculated from the surface of s = 4 m is detected and displayed in fig .
dependence of the inassbp strain - induced qds and pits amount ( a , b ) and surface density ( c , d ) versus their average diameter ( s = 4 m ) .
 slezov approximations we used the fourier transform infrared spectrometry ( ftir  nicolet / nexus ) to investigate the transmission spectra ( see fig .
4 ) of an unencapsulated inassbp dots  pits cooperative structure at room temperature . as a test sample
the result shows the displacement of the absorption edge toward the long wavelength region from  = 3.44 m ( for test sample ) to    = 3.85 m , as well as the enlargement of the absorption spectrum up to  = 2.75 m short wavelength region .
we assume that this effect is the result of the absorption by the qds through the permitted energy sub - band .
pits cooperative structure grown on inas(100 ) substrate schematic diagram showing the type ii inassbp / inas qds is presented in fig .
1 . whereis the planck constant , is the light holes effective mass , is the average diameter of qds andis the integer .
the similar approach was applied in . for our experimental system ( at light holes confinements ) ,   ( at ) ,   ( at ) , sub - band depth .
numerical value for the light holes effective mass for our inas1xysbxpy quaternary system was calculated by the linear approximation of the corresponding values for binary compounds at x = 0.04 and y = 0.08 .
schematic view of the zone diagram showing the type ii inassbp / inas qds  pits cooperative structure .
numerical values for b , c , d and e energies are approximate and based on ftir measurements and calculations finally , note that at the growth of diode heterostructures with the quantum dots and pits inside p  n junction spatial charge region , the main challenge to overcome is providing the lateral overgrowth of the pits ( providing  reverse  qds ) and keeping the dots size during epitaxy of the cap epilayer .
we assume that by using step - cooling lpe , the growth of the cap epilayer from the strongly cooled liquid phase will address this problem .
thus , we have presented an example of the inassbp quaternary qds , pits and dots  pits cooperative structures growth on the inas(100 ) substrates by lpe . the interaction and surface morphology of the dots  pits combinations were investigated .
lifshits  slezov - like distribution for the amount and surface density of  small  qds , and pits versus their average diameter was experimentally detected .
application of the inassbp and other similar quaternary materials opens up interesting physical and technological prospects for the dirigible growth of qds , pits and dots  pits cooperative systems . by the corresponding and independent variations of the v - group elements concentrations ,
the results of our study can be also used for producing controlled arrays of strain - induced qds , which is very important for the fabrication of wide - band photodiodes , thermo - photovoltaic cells and other inas - based mid - infrared devices .
this work was carried out in the frame of armenian national governmental program for nano - electronics and istc grant a1232 .
this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .
this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .
 an example of inassbp quaternary quantum dots ( qds ) , pits and dots  pits cooperative structures growth on inas(100 ) substrates by liquid phase epitaxy ( lpe ) is reported . 
 the interaction and surface morphology of the dots  pits combinations are investigated by the high - resolution scanning electron microscope . 
 bimodal growth mechanism for the both qds and pits nucleation is observed . 
 cooperative structures consist of the qds banded by pits , as well as the  large  pits banded by the quantum wires are detected . 
 the composition of the islands and the pits edges is found to be quaternary , enriched by antimony and phosphorus , respectively . 
 this repartition is caused by dissociation of the wetting layer , followed by migration ( surface diffusion ) of the sb and p atoms in opposite directions . the  small  qds average density ranges from 0.8 to 2  109 cm2 , with heights and widths dimensions from 2 to 20 nm and 5 to 45 nm , respectively . 
 the average density of the  small  pits is equal to ( 610 )  109 cm2 with dimensions of 540 nm in width and depth . lifshits  slezov - like distribution for the amount and surface density of both  
 small  qds and pits versus their average diameter is experimentally detected . 
 a displacement of the absorption edge toward the long wavelength region and enlargement toward the short wavelength region is detected by the fourier transform infrared spectrometry . 