MITite: Designing Materials from First Principles

A novel class of semiconductors is introduced, based on computational design, to solve the long-standing problem of lattice and polarity mismatch in heteroepitaxial growth of III-V alloys on silicon substrates.

Ab initio total-energy calculations and quasi-particle GW calculations are used to investigate the physical properties of these new semiconductors. One particular configuration is designed to match lattice constant and polarity with the Si(100) surface and to possess a direct band gap of 1.59 µm, which is close to the canonical frequency used by the optoelectronics industry. These results could pave the way for eventual monolithic integration of optical materials on silicon.

In the optoelectronics industry, the canonical wavelength is 1.55 µm because of the efficiency of transmitting signals through fiberoptic cables at this wavelength. In order to design an optically-active (i.e. direct-gap) semiconductor near 1.55 µm, the industry has explored a large number of possible III-V alloys and II-VI alloys.

With the polarity-mismatch problem resolved, the next step is to identify candidates with lattice constants matching that of Si. Since the number of possible choices of atom types and Type I/II layered sequences is enormous, the effort to build and test the potential candidates experimentally would be formidable. In contrast, first-principle calculations on computers can go through many possibilities quickly. We proceed by searching the simple materials first and gradually increasing the complexity involved.

As a starting point, we use data on the tetrahedral-covalent radii of elements from Kittel and Shay to get the approximate lattice constants of various materials. (Detailed calculations later show that they could have an error as large as 4%.) Nonetheless, these estimated lattice constants are valuable in narrowing the search space. According to these estimates, there are 34 Type I and 41 Type II materials with lattice constants that fall within 10% of the Si lattice constant. We start by concentrating on a sampling of those within 3%, and use ab initio total energy methods to calculate more accurate lattice constants.

The total electronic energy within the local-density-approximation (LDA) is minimized using the preconditioned conjugate-gradient algorithm. The LDA calculations are performed with the Perdew-Zunger parameterized exchange-correlation energy and the Kleinman-Bylander separable form of optimized pseudopotentials. For Zn and Cd, nonlinear core corrections are used. The total energy is a function of the lattice constants as well as the basis vectors. The ions are relaxed according to the Hellman-Feynman forces for each given set of lattice vectors. The lattice constant is then located by finding the minimum of the total energy in the lattice vector space. The cutoff energy used in the calculations is E_c = 20 Ry except for materials involving first row elements, for which E_c = 40 Ry is used. The LDA method has been proven capable of predicting lattice constants to within 1% of the true values. Once materials with the correct lattice constants are found, their band structures are studied to see if they are direct band-gap materials with the desired gap size. Since LDA methods give poor band-gap results, a much more computationally intensive approach, involving the quasi-particle GW scheme, is used to obtain accurate band-gap information for the most promising candidates.

The formation enthalpies are calculated to investigate if these materials are stable against segregation into equilibrium phases of the elements. The formation enthalpies are positive, indicating the materials are stable. In the case of (ZnSi)_{1/2}As, it is 0.33 eV per atom. This is only half the value of that of the corresponding Chalcopyrite. Thus, our new material is only meta-stable. The convertion to Chalcopyrite, however, involves second-nearest-neighbor exchange and creation of interstitials. We expect the diffusion barrier to be very high and the process unlikely to occur.

We studied several alloys with different x values, and established the trend of lattice constant and band gap as x varies. In order to gauge how well the lattice constants continue to match as temperature increases, we can estimate the thermal expansion coefficients from the total energy surfaces for both the new material and Si. The difference in the percentage increase of the lattice constant (delta-a/a (T)) for the two materials is calculated to be less than 0.01% from 0K to 600K, and actually vanishes at 350K. This suggests that thermal expansion will not cause additional lattice mismatch.

Finally, the new alloy material that we have designed will possess a slight dipole moment, due to the difference in chemical properties of phosphorus and arsenic. However, this dipole moment can be eliminated if we invert every other cell in the growth direction, i.e. use a supercell twice as long in the growth direction.