Sapphire thermal expansion coefficient

The invention of US-A-536S088 approaches the problem of stresses generated by the mismatch of the thermal expansion coefficients of HgCdTe and silicon by including a buffer layer of sapphire. The characteristic thermal expansivity of sapphire is more similar to the thermal expansivity of HgCdTe than that of silicon. 

The hybrid circuit 10 comprises a buffer structure 16 which is comprised of a material which accommodates the difference in thermal expansion coefficients of the HgCdTe detector array 12 and the silicon read-out chip 14. The buffer layer is made of sapphire which also has good thermal conductivity properties. The buffer structure has laser drilled vias 18 which are formed in registration with unit cells of the detector array and the read-out circuit. Each of the vias is provided with indium bumps 20 at opposing ends thereof. The buffer structure is interposed between the detector array and the read-out chip. Cold weld indium bump technology is employed to couple the bumps 20 to the buffer structure. The buffer structure is further... 

A large lattice mismatch between sapphire and nitrides (about 13% to AIN, 16% to GaN and 29% to InN) makes even very thin layers fully relaxed at the growth temperature. When the samples are cooled down after growth, a thermal strain is created. Such strain occurs for other materials, for example for GaAs on Si [14], and corresponds to a difference in thermal expansion between the layer and the substrate. Using thermal expansion coefficients for GaN and sapphire one can estimate that the compressive thermal strain Aa/a, which should be generated for MOCVD grown GaN on (00.1)... 

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. 

TABLE 6 Values of thermal expansion coefficient (TEC) for AIN, GaN and InN, together with the values for the most popular substrates sapphire, SiC and LiGaOi. 

Fig. 2. Certified values of thermal expansion coefficients for SRMs 731, 736, 737, and 739, along with tentative values for stainless steel, graphite, sapphire, and aluminum.

Taylor, C. T., Notcutt, M., Wong, E. K., Mann, A. G., and Blair, D. G., Measurement of the Thermal Expansion Coefficient of an All-Sapphire Optical Cavity, IEEE Trans. Instrum. Meas. 46, 183, 1977. [Sapphire]... 

The growth on foreign substrates typically leads to the presence of built-in strain in heteroepitaxial GaN layers owing to the difference in lattice parameters and thermal expansion coefficients between layers and substrates [19, 25-27]. Sapphire and SiC are among the most often used substrates, and typically growth is realized on the basal (0001) c-plane of sapphire and SiC. In such instances, nitride films grow along the polar [0001] direction. The sixfold symmetry of the basal planes of the wurtzite (nitrides, SiC) and rhombohedral (sapphire) crystal structures dictates their isotropy in the basal plane and hence, the thermal expansion coefficients, piezoelectric and elastic properties... 

The lattice parameters and thermal expansion coefficients at room temperature of GaN and sapphire are shown in Table 11.1 (on the basis of data given in Refs. 11 and 12). For the case of a-plane GaN grown on r-plane sapphire, the translational periods of the respective lattice planes [10] in [llOOjcaN direction is given by AjijoojGaN = V acaN for GaN and by A[oooi]a1203 = aAi.o, for the sapphire, and in the [0001]caN direction A[oooi]GaN = CcaN for GaN and... 

Table 11.1 Lattice parameters and thermal expansion coefficients at room temperature (perpendicular and parallel to the c-plane) for GaN and sapphire [11,12].

An important additional difference between the two materials lies in the thermal expansion coefficients. The room-temperature values for the linear thermal expansion coefficients perpendicular to and in the basal plane for GaN are about 25-30% higher for GaN compared with sapphire [12], which will lead to a stronger expansion of the GaN lattice with respect to the sapphire lattice during deposition, which in general takes place in the temperature regime of 600-1000 °C. 

Figure 2.8 Thermal expansion coefficient of sapphire on the c-plane (along the o-axis) and along the oaxis, and that of Si as a function of temperature. (After Ref [44].)...

The structure is bonded to a substrate 24 which is chosen to have a coefficient of thermal expansion that is selected for providing the resultant read-out chip assembly with an effective coefficient of thermal expansion that is approximately the same as an HgCdTe detector array 36. The substrate material may be GaAs (4.5-5.9 x 10"6 m/mK), CdTe, Ge (5.5-6.4 x 10"6 m/mK), and a-plane sapphire (3.5-7 5 x 10" m/mK) where the coefficients of thermal expansion are given in parentheses. The coefficients of thermal expansion for silicon, HgCdTe and epoxy are 1.2 x 10"6 m/mK, 3.8-4.5 x 1 O 6m/mK and 30-50 x 10"6 m/mK, respectively. Next, the substrate 16 is removed and aluminium pads 34a are formed. Indium bumps 34b are cold welded to corresponding indium bumps 36b. 

A cell constant close to 0.2 cm" was determined from measurements on aqueous KCl at 25 ""C and the cell constant change with temperature from the known coefficients of thermal expansion of sapphire and platinum was 0.4% over the entire temperature range (306 C-400°C). 

Adhesion to the film can be enhanced by surface treatment. The conventional method is corona discharge but more recently atmospheric pressure oxygen plasma treatments have been developed. The film can also be vacuum metallised to improve barrier performance, coated with copper for surface conductivity or with more advanced coatings such as sapphire. Mineral fillers can be used to provide higher modulus and to the control coefficient of thermal expansion in relation to particular coatings or specific applications. 

The measurement of Unear coefficients of thermal expansirm is made by dilatom-eters. There are differential and absolute dilatometers. A differential dilatometer measures the difference between the linear thermal expansimi of a well-known, high-temperature material and the tested samples. The standard materials are silica glass, polycrystaUine alumina, sapphire, and graphite. The temperature is measured in the middle of the sample by a thermocouple. The differential measurement of the linear coefficient of thermal expansion is made according to ASTM E831-14 [103] and ISO 2478 1987 [104]. The measurement of the thermal expansimi of heat insulation materials is made according to ISO 2477 1987 [105]. 

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