### 3.1.3 Mechanical, Thermal, and Other Properties

Mechanical Properties

| Silicon at room temperature is brittle - and that is about all there is to know.
| Well not quite. First of all, fracture of Si is quite an interesting topic to many people (searching for "fracture+silicon" produces about 20.000 hits in the Net)
|  | Second, there is brittle, and there is very brittle. What is the case for Si? While the microelectronics industry has learned not to break its wafers (that's the main reason why they are so thick), the crystalline Si (or Si-c) solar cell industry cannot afford to waste Si and keeps its "multi-crystalline" (10 × 10)cm2 slices as thin as possible (about 300 µm). As a result, breakage of the slices is becoming the major problem in industrial solar cell production. At present (2001) large research projects are started to find out more about fracture of (multicrystalline) Si.
|  | Fracture toughness, to give some numbers, has been reported to be 1.19 MPa · m½ for the {100} tensile surface and 1,05 MPa · m½ for the {111} tensile surface - there are certainly other numbers out there, too.
|  | If we compare that to, e.g., the fracture toughness of Steel (» 200 MPa · m½), Nylon (» 3 MPa · m½), or ceramics like Silicon nitride (Si3N4, Silicon carbide (SiC ) or Alumina (Al2O3) which are all » (3 - 5) MPa · m½, or common glass (» 0,8 MPa · m½), we see that Si is about as brittle as glass and "more" brittle than some of the tougher ceramics.
| Then we have the emerging "MEMS" industry, i.e Micro Electronic and Mechanical Systems. Obviously, the mechanical properties, especially the elastic coefficients and the elastic moduli are of prime interest (besides fracture, which simply must be avoided).
|  | Youngs modulus, is given as 131 GPa (or 107 GPa, or ...; it depends on the source), which again should be compared to that of diamond (1 000 GPa, the biggest there is), "hard" steels (» 200 GPa), ceramics (as above; » 400 GPa), Silver and gold (» 80 GPa), or Nylon (» 3 GPa).
|  | All in all, Silicons elastic properties are pretty good, but not breathtaking.

| But let's not forget that in most processes we heat up the Si to temperatures somewhere between 700 oC and 1200 oC, and at high temperatures Si is no longer brittle but ductile, i.e. it deforms plastically.
|  | Plastic deformation is always characterized by the yield stress ty which describes macroscopically the minimum shear stress needed to induce plastic deformation, and microscopically the minimum stress needed to induce dislocation movement.
|  | In a somewhat simple minded approach, we see that Si is brittle and fractures if the yield stress ty is larger than the stress needed for facture under the conditions used. Since the yield stress decreases with increasing temperature, we expect that plastic deformation takes over at some temperature.
|  | The figure below gives a compilation of t y data for Si (from a paper by J. Rabier and J.L. Demenet; phys stat sol (b) 222, 63 (2000)).
| In short, you must expect plastic deformation if the temperature is above, say 700 oC and you have some stress acting on your Si.
|  | If you started with a typical, completely dislocation free wafer, the initial ty might be somewhat larger because you first must generate some dislocations (which then can multiply).
|  | If some dislocations have been generated, however, its all over. You will experience plastic deformation and you will have introduced dislocations irreversibly into your material.
| Where do stresses come from? There are two major sources:
|  | 1. Running a batch of Si wafers (or slices, or whatever) into a piece of equipment that heats up the Si, the outside of the wafer will always tend to be hotter than the inside during heating up, and vice verse during cooling down. Thermal expansion will be different in different parts of the specimen, and that introduces stresses directly proportional to the temperature gradient in the sample. There is nothing you can do except keep the temperature gradients below the critical level. Typical tricks are to move into some oven s l o w l y , to have the equipment at some lower temperature and then go up slowly after the Si is inside, or to do both.
|  | 2. If there are any layers on the Si (or inside, e.g. heavily doped regions), differences in thermal expansion coefficients will generate stresses at sometimes very large levels. Again, while you cannot avoid the stress produced by the layer you need, you can use some tricks to minimize the over-all stresses: Keep the area small (provide holes in the layer where it is not needed); put the same kind of layer on the backside - the combined effects cancel to some degree, and be generally aware of what you have on the backside (many layers are automatically also deposited on the backside, and there are good and not so good times in a process sequence when you can take them off).
| If everything fails, you may want to try out some Si with a relatively high concentration of interstitial oxygen, Oi (say around 20 ppm).
|  | These impurity atoms make dislocation movement more difficult (and thus increase t y ) without degrading electronic properties too much (if you are lucky).
| Last not least we note that the exact process of dislocation generation and movement, with particular respect to the details of the dislocation fine structure, is of major interest to basic research, since ultra-perfect Si is an ideal proving ground for theories concerning deformation and dislocations in covalently bonded crystals.

| Thermal Properties
| The most important thermal properties of Silicon are:
|  | Thermal expansion coefficient aT,
|  | Thermal conductivity k, and, to a lesser extent
|  | Specific heat cp
| The thermal expansion coefficient is crucial whenever other materials are in contact with Si, or if temperature gradients are encountered. In both cases it is rather easy to destroy the device by building up large mechanical stresses leading to fracture or plastic deformation. Lets see why
|  | Si is in contact with other materials either during processing (when, e.g., a layer of SiO2 or Si3N4 or Al or ..., is deposited, often on the front and backside, or, as a finished device, when it is encapsulated in some housing, i.e. when it is packaged.
| If temperature changes for a Si / other material compound - because you use your cellular phone during skiing and in the summer, or because processing the wafer intrinsically needs high temperature - mechanical stress, being roughly proportional to the difference in thermal expansion coefficients and the amount of material present, is simply unavoidable.
|  | The art of processing and packaging thus includes to keep the stress levels always below the critical stresses required to induce plastic deformation or fracture. You may have to optimize the thermal expansion coefficient of materials in contact with Si - if you can.
|  | The black polymer compound, for example, that is universally used for cheap packaging, while still very different in thermal expansion, is matched as much as possible. Since this is still not good enough, the Si chips are usually ground down to a thickness far below the original wafer thickness.
| As we have seen above. if there is a temperature gradient in a piece of pure Si (e.g. a wafer), the hotter parts want to expand more then the cooler parts - again a mechanical stress is induced that is proportional to the temperature gradient and the thermal expansion coefficient.
|  | This is why you heat up the wafers s l o w l y, giving enough time for temperature equilibration. Otherwise, plastic deformation will occur, ruining your chips and leaving a wafer that is no longer flat - wafer warpage, one of the absolutely deadly wafer diseases, has occurred
| Here are data of the linear (as opposed to "volume") thermal expansion of Si and some comparison to other relevant materials
After Okada and Tokumaru, 1984
|  | At low temperatures, aT shows a pronounced minimum; an effect not easy to understand in cubic crystals, but nevertheless observed in most of the other cubic semiconductors, too. If we take the room temperature value of about 2,5 · 10–6 K–1, and compare it to the values of other materials important in Si technology, we have
Material | Si | Ge | GaAs | SiO2 | Si3N4 | Al | Polymers
aT [10–6 K–1] | 2,5 | 5,8 | 6,86 | 0,5 | 3,2 | 24 | ca. 50 ... 200

| The thermal conductivity k is important, because Si chips, like most semiconductor devices, are producing lots of heat in operation. It must transported out of the system and the resistance to heat flow is given by the thermal conductivity of the material.
|  | What do we have? Here is the Si value, again together with thermal conductivities of other relevant materials. Note that k is strongly temperature and structure dependend. For Si3N4, as an example, values may scatter from 0,2 - 1,2 W·cm–1 · K–1 .
Material | Si | Ge | GaAs | SiO2 | Si3N4 | SiC | Diamond | Cu; Ag
k [W · cm–1 · K–1] at room temperature | 1,5 1,4 | 0,6 | 0,46 0,54 | ca. 0,014 | ca. 0,2 | ca. 3.5 (3 - 5) | ca. 10 - 30 | 4
|  | Diamond, surprisingly, is the champion - and that is why thin diamond layers are sometimes used to transport the heat generated in some device to some heat sink as efficiently as possible.
| While it appears that you just must live with whatever thermal conductivity a material has - this is not entirely true. The thermal conductivity can be made substantially better, if the material is made from one isotope only!
|  | Here is a recent (may 2002) topic form the news ticker in the semiconductor business.
|  | Isonics Delivers Silicon-28 SOI Wafers Online staff -- 5/2/2002 Electronic News Isonics Corp. of Golden, Colo., today said that a major semiconductor manufacturer has taken delivery of Silicon-28 silicon-on-insulator (SOI) wafers for evaluation. Isotopically purified silicon-28 has 60 percent more thermal conductivity than natural silicon, Isonics said. This allows for reductions in the self heating of circuits made with natural SOI wafers. Incorporating Silicon-28 into SOI wafers made using either oxygen implantation or layer transfer technologies requires no change in the manufacturing processes developed for these wafers, the company said. "While SOI wafers are known to reduce power requirements for devices, heat has been a large concern for certain applications and is expected to become an even larger, more critical consideration as chip manufacturers continue to push for more performance," said Stephen J. Burden, Isonics VP of semiconductor materials, in a statement. "Semiconductor manufacturers, eager to design the optimum thermal/electrical solution for their specific device, are becoming aware of the outstanding performance offered by the marriage of our high thermal conductivity silicon-28 and the film SOI wafer technology. The wafers delivered to this customer were manufactured in cooperation with an existing thin-film SOI wafer supplier, Isonics said, instead of the company’s thick-film SOI facility. From "Semiconductor International 5-2002"

| The specific heat cp (of course for constant pressure) is not so important, but here are values anyway. In addition the Debye temperature Q is shown, too
Material | Si | Ge | GaAs | SiO2 | Si3N4 | Al
cp [J/g · K] at room temperature | 0,7 | 0,31 | 0,35 |  |  | 0,9
Q [K] | 645 | 374 | 362 |  |  |

| Other Properties
| Here is a table found in the Net with some more non-electrical data
|  | Some of the numbers deviate from the numbers given above; e.g. the thermal expansion coefficient.
|  | That is just the way it is - if you look up anything, you will find different numbers. Often just a little bit different (melting points, for example), but sometimes quite different (as in the thermal expansion coefficient here).
|  | Reasons for this might be: 1. The quantities compared are actually different. In the table above, the linear thermal expansion coefficient is given; in the table below it might be the expansion coefficient for the volume? 2. Watch out for units. Conversion can be tricky, especially for some quaint old British imperial units still much beloved by the Americans, too. 3. The samples might have been different. Giving the "conductivity" or "lifetime" for Si without some comments, obviously does not make much sense. How about other properties? 4. The number is simply wrong.
Si Properties
Refractive Index | 3.4179 @ 10 µm ; 3,45
Reflective Loss | 46.1 % @ 10 µm
Density | 2,3291 g/cm3
Melting Point | 1420 °C
Molecular Weight | 28.086
Thermal Conductivity | 1,63 W/(cm K); 1,4 W/(cm K)
Specific Heat | 0,703 J/(g K) @ 25 °C
Thermal Expansion | 4.05×10–6 / K @ 10...50 °C
Hardness (Knoop) | 1150 (Mohs 7)
Young’s Modulus | 131 GPa
Shear Modulus | 79.9 GPa
Bulk Modulus | 102 GPa
Rupture Modulus | 340 MPa
Elastic Coefficient | C11 = 167 / C12 = 65 / C44 = 80 GPa
Dielectric Constant | 13 @ f = 9.37 GHz

© H. Föll (Semiconductors - Script)