Critical layer thickness

An even wider range of wavelength, toward the infrared, can be covered with quantum well lasers. In the Al Ga As system, compressively strained wells of Ga In As are used. This ternary system is indicated in Figure 6 by the line joining GaAs and In As. In most cases the A1 fraction is quite small, X < 0.2. Such wells are under compressive strain and their thickness must be carefully controlled in order not to exceed the critical layer thickness. Lasers prepared in this way are characterized by unusually low threshold current density, as low as ca 50 A/cm (l )-... 

It seems more likely, however, that the number of growing compound layers will decrease, not increase, with increasing time of interaction of initial substances A and B. This is due to the existence of critical layer thicknesses (see Sections 1.3.1 and 2.2). 

By applying similar equalities to equations (3.7 i)-(3.92), one obtains the expressions for the critical layer thicknesses ... 

By comparing equations (1.17), (1.22), (2.28 )-(2.292) and (3.30 )-(3.322), it is easy to understand that some of the critical layer thicknesses can be considered as practically the same in all three reacting systems A-ApBq-B, A-ApBq-ArB -B and A-ApBq-ArBs-AiBn-B, while the other are definitely different. Practically, not precisely, the same because the value of any critical thickness is dependent, though probably to a negligible extent, upon where the reacting atoms are diffusing from. 

Multiple dipping finally increases the maximum allowable thickness of the (calcined) crack-free membrane with respect to that obtainable in a single step [13,14,18]. At each given set of experimental conditions there is a certain critical layer thickness which should not be exceeded if cracking during drying and/or calcination is to be avoided. 

D. Leonard, K. Pond, P. M. Petroff Critical layer thickness for self-assembled InAs islands on GaAs, Phys. Rev. B 50,11687-11692 (1994)... 

Fig. 22. Schematic drawing of the principle of the thin layer mechanism (D, Dcrit, e, and ff stand for PS layer thickness, critical layer thickness, elongation at break, and load direction).

The Stranski-Krastanov (SK) mode (initially layer-by-layer growth, then two-dimensional islands), known as layer-plus-island growth, is an intermediate case. Initially, the process starts with two-dimensional growth, namely formation of the first monolayer, up to a few monolayers on the substrate. Then, at a critical layer thickness, the subsequent layer growth becomes unfavorable and three-dimensional islands are formed on top of this substrate. The growth continues through nucleation and coalescence of adsorbate islands (Scheme 18.1c). 

Fritz, I. J. (1987), Role of experimental resolution in measurements of critical layer thickness for strained-layer epitaxy. Applied Physics Letters 51, 1080-1082. 

JP Hirth, X Feng. Critical layer thickness for misfit dislocation stability in multilayer structures. J Appl Phys 67 3343-3349, 1990. 

Gurova and Kapustina were the first to describe ultrasonically induced bubble domains in large pitch nematic/cholesteric mixtures [17, 63]. It was found that relaxation of an ultrasound-induced perturbation at a critical layer thickness, which is com-... 

The transition from the two-dimensional layer-by-layer growth (Frank-van der Merwe mode) to the formation of three-dimensional islands on top of the flat layer (Stranski-Krastanov mode) takes place when tcrit = 0. This gives a critical layer thickness for the onset of surface roughening... 

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