Expansion coefficient semiconductors

Because of the high functional values that polyimides can provide, a small-scale custom synthesis by users or toU producers is often economically viable despite high cost, especially for aerospace and microelectronic appHcations. For the majority of iudustrial appHcations, the yellow color generally associated with polyimides is quite acceptable. However, transparency or low absorbance is an essential requirement iu some appHcations such as multilayer thermal iusulation blankets for satellites and protective coatings for solar cells and other space components (93). For iutedayer dielectric appHcations iu semiconductor devices, polyimides having low and controlled thermal expansion coefficients are required to match those of substrate materials such as metals, ceramics, and semiconductors usediu those devices (94). 

The thermal conductivity of diamond at 300 K is higher than that of any other material, and its thermal expansion coefficient at 300 K is 0.8 x 10". lower than that of Invar (an Fe-Ni alloy). Diamond is a very widc-band gap semiconductor Eg = 5.5 eV), has a high breakdown voltage (I07V cm-1), and its saturation velocity of 2.7 x I01 cm s-1 is considerably greater than that of silicon, gallium arsenide, or indium phosphide. 

Thermal expansion of a semiconductor depends on its microstructure, i.e. stoichiometry, presence of extended defects, ffee-carrier concentration. For GaAs [24] it was shown that for samples of free-electron concentrations of about 1019 cm"3, the thermal expansion coefficient (TEC) is bigger by about 10% with respect to the semi-insulating samples. Different microstructures of samples examined in various laboratories result in a large scatter of published data even for such well known semiconductors as GaP or GaAs. For group III nitrides, compounds which have been much less examined, the situation is most probably similar, and therefore the TECs shown below should not be treated as universal values for all kinds of nitride samples. It is especially important for interpretation of thermal strains (see Datareview A 1.2) for heteroepitaxial GaN layers on sapphire and SiC. 

Certain semiconductor device fabrication methods require the formation of a single-crystal deposit of the semiconductor on an insulating substrate. In epitaxial methods, the semiconductor is deposited on a single-crystal piece of substrate chosen, in part, on the basis of the match of the lattice parameters, thermal expansion coefficients and chemical compatibihty of the substrate and deposit. Singlecrystal substrates include those of AI2O3, MgAl204, Q -quartz andZrSi04. ... 

Similar to the case of semiconductor thin films and quantum well structures, there is a need to deposit buffer layers prior to deposition of the superconducting thin-film, see Fig. 14.6. The role of a buffer layer is to prevent detrimental interactions between the film and substrate and to diminish the effect of surface defects on the film growth. In addition, there are examples of film/substrate combinations where the mismatch in thermal expansion coefficients is severe enough to cause cracking in the thin films [14.16, 14.17]. A suitably chosen intermediate buffer layer can reduce the stress caused by such a mismatch. 

The number of circuits which can be placed on one silicon "chip" is restricted by the difficulty of keeping the wafer of silicon bonded to its ceramic substrate as it heats up. At present, the most frequently used packaging material is alumina which has a thermal expansion coefficient, nearly twice that of silicon. Differential expansion between the silicon and its substrate is containable in current packages but the manufacturers want to move to larger circuits, for faster computers and to reduce size and cost of the overall equipment, so differences in expansion set a limit on how large the circuits can be. The semiconductor companies have a real need for a substrate material with thermal expansion similar to that of silicon. (Table 3)... 

The Debye characteristic temperature of isotropic bodies is directly associated with the bulk modulus and therefore with all the other properties of matter dependent, to a certain degree, on the atomization energy, the surface energy u, the elasticity moduli, the expansion coefficients, the width of the forbidden band in semiconductors, etc. 

There are, however, several sources of degradation that are dependent on environmental, packaging, or radiation conditions. For example, low-temperature operation may result in excessive stress due to the difference in thermal coefficients of expansion between the package and the semiconductor. This stress may lead to defects in the semiconductor that will reduce the life of the LED. As a result, new packaging materials that match the low-temperature properties or thermal expansion coefficient of the semiconductor materials have been developed. 

I tested the GAP models on a range of simple materials, based on data obtained from Density Functional Theory. I built interatomic potentials for the diamond lattices of the group IV semiconductors and I performed rigorous tests to evaluate the accuracy of the potential energy surface. These tests showed that the GAP models reproduce the quantum mechanical results in the harmonic regime, i.e. phonon spectra, elastic properties very well. In the case of diamond, I calculated properties which are determined by the anharmonic nature of the PES, such as the temperature dependence of the optical phonon frequency at the F point and the temperature dependence of the thermal expansion coefficient. Our GAP potential reproduced the values given by Density Functional Theory and experiments. 

Table 4.1-7 Linear thermal expansion coefficient a of Group IV semiconductors and IV-IV compounds and its temperature dependence...

Kerns et al. have described results obtained with a newly developed composite of copper and micrometer-size Type I diamond powder called Dymalloy. Although the thermal conductivity is considerably lower than that of CVD diamond substrates—420 compared to 1200 W/(m K)— its thermal expansion coefficient can be tailored to match that of a semiconductor die mounted on it. 

---