CUENTAS DEL CORREDOR VIAL 1. CUENTA DE PAGO TPD

Most QD/barrier material combination calculated and fabricated so far are endowed with a positive or type-I VBO, i.e. the energy of the QD material VB is higher than the barrier material VB. The possibility of manufacturing QD-IBSCs with a negative or type-

(a) (b)

Figure 4.6: Study of the electronic characteristics of the InAs1-yNy/GaxAs1-xP QD material particularized

for the stoichiometry that provides an optimum QD-IBSC material (x=0.37 and y=0.1). (a) Band diagram of the InAs0.9N0.1/Ga0.37As0.63P heterojunction. The lattice mismatch (∆alc) between barrier and QD

materials is also indicated. (b) Energy diagram of the CBO with all the confined levels arising within the CBO up to 7.5 nm. The optimum radius is indicated.

II VBO has been identified [Tomi´c et al., 2011]. The idea of this type-II VBO is to extend the wavefunction of the holes in the VB so that the Auger interband relaxation can be inhibited. This Auger mechanism could be partly responsible for favoring the electronic thermalization between confined states in the CB, which ultimately blocks the phonon- bottleneck effect. In this respect, the InAs/AlxGa1-xAsySb1-y heterojunction is identified

as a candidate material for type-II QDs.

The AlxGa1-xAsySb1-y quaternary covers a very large area in the bandgap/lattice con-

stant (EG(alc)) graph, as it is represented in Fig. 4.7. Most of the III-V binary compounds

are represented in the graph as well as the ternaries produced by the alloys formed by each two of these binaries. The solid lines represent the direct bandgap ternaries and the dashed lines represent the indirect bandgap ternaries. The four binaries that form the AlxGa1-xAsySb1-y quaternary (Al, Ga, As and Sb) are highlighted in the graph with a red

circle and the binary forming the QDs is represented with a green circle. The area of the quaternary is delimited by the contour delimited by the ternary compounds connecting the four binaries: AlxGa1-xAs, AlAsxSb1-x, AlxGa1-xSb and GaAsxSb1-x. The stripped region

inside this area approximately corresponds to the AlxGa1-xAsySb1-y quaternary alloy of

indirect bandgap. The indirect bandgap region is preferred in our calculation because it is associated to values of the barrier material bandgap closer to the optimum. This indirect region has been defined from the direct-indirect crosspoint of the AlxGa1-xAs ternary to

intermediate value between the bowing parameter of both ternaries has been selected to delimit this indirect bandgap region.

Figure 4.7: EG(alc) graph representing most of the III-V semiconductors. The indirect bandgap

AlxGa1-xAsySb1-y quaternary alloys are represented with blue stripped area and the valid solutions for

the desired host material of the type-II QD system are represented with a solid rectangle.

The definition of the indirect bandgap region is important in order to carry out the calculation of the band alignment of the alloyed heterostructure with our HEBAM. Once this region has been identified, the constraints of our QD system have to be set. The first of them is of course the negative VBO, for which the condition 0 meV>VBO(InAs/AlGaAsSb)>- 100 meV is defined (a very negative VBO is not desired). A second constraint determines the lattice mismatch between the quaternary and the substrate on top of which it is grown. The only commercially available substrate far enough (in the EG(alc) graph) from

the AlxGa1-xAs alloy (that always produces type-I VBOs) seems to be InP. Actually, in this

region of the graph, only GaAs and InAs are alternative substrate candidates, but unfortu- nately the AlxGa1-xAsySb1-yalloys which are reasonably lattice matched to each of the are

not suitable. In the first case (GaAs) the reason is that these AlxGa1-xAsySb1-y alloys are

far from producing the desired type-II VBOs and in the second case (InAs) the problem is that very little mismatch would be produce between the barrier and the QD materials so as to produce the nucleation of the dots by S-K growth mode. As this ∆alc(AlGaAsSb/InP)

cannot be large if a relatively thick high quality solar cell is to be grown, we impose the following condition: ∆alc(AlGaAsSb/InP)<0.5%. Only the solutions with alc > alc(InP)

are selected so that a higher ∆alc(InAs/AlGaAsSb) is obtained and thus a better nucle-

determines the solutions of the problem, which are located within the blue solid rectangle shown in the figure. A third condition is established: |CBO|< EG-100 meV. It is meant

to prevent the possible carrier tunneling between the confined states in the CBO and the barrier material VB. However, no alloy is disregarded with this last constraint, although the CBOs of these heterojunctions are large (in the range of 1.3-1.5 eV, as it is represented in Table 4.4).

Table 4.4: Valid solutions for the quaternary alloys with their respective stoichiometries, bandgaps, VBO, CBO, effective masses and lattice mismatch for the InAs/AlxGa1-xAsySb1-ytype-II heterojunction.

Al[%] Ga[%] As[%] Sb[%] VBO CBO EG,barrier m*e,barrier m * e,QD ∆alc 0.64 0.36 0.54 0.46 -0.0976 -1.290 1.601 0.266 0.0254 0.0318 0.65 0.35 0.54 0.46 -0.095 -1.295 1.608 0.266 0.0254 0.0318 0.66 0.34 0.54 0.46 -0.0928 -1.299 1.614 0.265 0.0254 0.0317 0.67 0.33 0.54 0.46 -0.0905 -1.303 1.621 0.264 0.0254 0.0317 0.68 0.32 0.53 0.47 -0.0996 -1.314 1.621 0.263 0.0253 0.0308 0.68 0.32 0.54 0.46 -0.0881 -1.307 1.628 0.264 0.0254 0.0317 0.69 0.31 0.53 0.47 -0.0973 -1.318 1.627 0.262 0.0253 0.0308 0.69 0.31 0.54 0.46 -0.0857 -1.312 1.634 0.263 0.0254 0.0316 0.7 0.3 0.53 0.47 -0.0950 -1.322 1.634 0.261 0.0253 0.0308 0.7 0.3 0.54 0.46 -0.0834 -1.316 1.641 0.262 0.0254 0.0316 0.71 0.29 0.53 0.47 -0.0927 -1.327 1.641 0.261 0.025 0.0307 0.71 0.29 0.54 0.46 -0.0811 -1.320 1.647 0.26 0.0254 0.0315 0.72 0.28 0.53 0.47 -0.0904 -1.331 1.647 0.260 0.0253 0.0307 0.72 0.28 0.54 0.46 -0.0788 -1.325 1.654 0.261 0.025 0.0315 0.73 0.27 0.52 0.48 -0.0994 -1.342 1.648 0.258 0.0252 0.0298 ... ... ... ... ... ... ... ... ... ... 0.98 0.02 0.55 0.45 -0.00895 -1.435 1.834 0.243 0.0254 0.0313 0.99 0.01 0.5 0.5 -0.0671 -1.479 1.812 0.237 0.024 0.0271 0.99 0.01 0.51 0.49 -0.0557 -1.472 1.818 0.238 0.0250 0.0279 0.99 0.01 0.52 0.48 -0.0440 -1.464 1.823 0.239 0.0251 0.0288 0.99 0.01 0.53 0.47 -0.0319 -1.456 1.8295 0.240 0.0252 0.0296 0.99 0.01 0.54 0.46 -0.0195 -1.448 1.835 0.241 0.0253 0.0304 0.99 0.01 0.55 0.45 -0.00684 -1.440 1.840 0.243 0.0254 0.031 1. 0. 0.5 0.5 -0.0652 -1.484 1.819 0.236 0.0249 0.0271 1. 0. 0.51 0.49 -0.0537 -1.477 1.825 0.237 0.0250 0.0279 1. 0. 0.52 0.48 -0.0420 -1.469 1.830 0.238 0.0251 0.0287 1. 0. 0.53 0.47 -0.0299 -1.461 1.83 0.240 0.0252 0.0296 1. 0. 0.54 0.46 -0.0175 -1.453 1.842 0.241 0.0253 0.030 1. 0. 0.55 0.45 -0.00474 -1.445 1.848 0.242 0.0254 0.0312

A reduced sample of the results produced by the HEBAM applied to the InAs/AlxGa1-xAsySb1-y

VBO and CBO, and bandgaps and effective masses of both the barrier and the QD ma- terials as a function of the stoichiometry of such materials. The lattice mismatch is also given in the table. The model produces a very large list of results and not all of them are shown in the table. Actually, a line filled with points separates the beginning and the end of the list of valid results.

The AlAs0.55Sb0.45 quaternary alloy is taken as an example for the calculation of the

limiting efficiency as QD-IBSC. Its parameters are necessary to calculate the energy of the confined electron levels (the confined holes are not necessary in these type-II struc- tures). They can be obtained from the table: EG, barrier = 1.848 eV, CBO = 1.445 eV,

m*_e,barrier=0.242 and m*_e,QD=0.0254084. Thanks to these data, the confined levels in the CBO can be calculated. These confined levels are shown in Fig. 4.8(a). A graphical repre- sentation of the mathematical verification of the Schr¨odinger equation inside and outside the potential well is also shown in Fig. 4.8(b).

(a) (b)

Figure 4.8: (a) Confined electron levels as a function of the QD radius in an InAs/AlxGa1-xAsySb1-y

QD system assuming the approximation of spherical dots. (b) Graphical expression of the mathematical verification of the Schr¨odinger equation inside and outside the potential well that represents the QD surrounded by the barrier material.

The optimum QD radius [Linares et al., 2011] is again defined as in section 4.2.2 (in this case, it is only 1.89 nm large). The bandgap distribution (EGand EL) is deduced from

the previous analysis and the limiting efficiency is calculated for maximum concentration. An ηmax≈63% is obtained with this configuration.