HIGH PURITY SILICON FOR OPTICAL APPLICATIONS

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Silicon is the second most abundant element in the Earth’s crust, making up 25% of the crust by mass. By virtue of its remarkable electrical and optical characteristics, silicon is used in countless industrial, consumer, optical, computer, and power generation applications. Solar cells, electronics, infrared optics, thin film coatings, and laser mirrors are some examples of applications for high purity silicon. The solar and semiconductor industries consume approximately 95% of the high-purity silicon supply, with solar at about 55% and semiconductor at about 40%. The remaining 5% of the market is made up by all other applications, including optics for transmissive and reflective applications. Si transmits very well from 2 to 6µm, is light weight, strong and thermally stable, non-toxic, inert to most chemicals, has a high index (3.4), is readily available, and is inexpensive relative to other IR materials. The market for infrared optical imaging systems has grown tremendously over the last two decades, driven by the desire for secure borders and factories, and sophisticated military hardware to give the good guys the greatest advantage possible. As is often the case, the technology developed for these uses has found a wide range of applications in the every-day world – you can now buy a car with a thermal imaging camera to help you see deer on the side of the road at night. This paper discusses the application of high-purity silicon for transmissive optics, the properties that make silicon a desirable optical material, and how those properties are adjusted in order to meet the application requirements.

MAKING SILICON FOR INFRARED OPTICS The same 99.9999999% pure feedstock, called virgin polysilicon, is used whether growing semiconductor ingots or optical ingots. The Czochralski (Cz) growth method is a relatively fast crystal pulling technique that begins by melting polysilicon in a quartz crucible and then dipping a seed crystal into the melt. The molten silicon is held at the freezing (same as melting) point temperature, and the crystal growth process is basically one of melting and then re-freezing the material, in an orientation determined by the seed. The physical characteristics of the ingot are determined by carefully controlling the melt temperature, the seed rotation rate, and the rate at which the seed is pulled vertically out of the melt. When thermal equilibrium is maintained at the seed-melt interface, the atoms solidify in a perfect crystalline lattice that matches the orientation of the seed crystal. The growth rate is 1-2mm per minute, and the largest Czgrown ingots are about 400mm diameter. The transmission and electrical characteristics are controlled by adding dopant to the pure silicon feedstock. High amounts of doping result in lower transmission and resistivity, One side effect of the Cz method is that the quartz (SiO2) crucible breaks down during the process, which results in oxygen atoms migrating into the ingot. The oxygen has a minimal impact on transmission for mid-wave infrared applications, but causes a strong absorption band at about 9um. The floztaone (Fz) crystal growth method starts with either a Cz-grown ingot or a polysilicon feed rod, which is placed in a vacuum chamber and encircled by an RF heater coil. The energized coil is moved along the rod to create a melted zone. Since impurities are more soluble in the molten silicon than the solid, impurities are migrated along the rod in the molten zone, and eventually solidified in the end of the ingot which is later cut off and recycled. Float zone growth results in higher purity than Cz, with correspondingly higher transmission and resistivity (particularly around 9µm), but the growth technique is expensive and the maximum diameter is limited to 150mm to 200mm.

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Figure 1 illustrates the transmission curves for the two different types of high-purity silicon, Cz and Fz. These transmission curves are based on actual data taken on uncoated samples. After anti-reflection (AR) coating, the transmission of silicon is typically ~98% from 2.5 – 5.0µm.

OPTICAL GRADE SILICON FLOATZONE SILICON

Transmission VS. Wavelength 60 50 40 %T 30 20 Cz

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Sample thickness: 0.2"

Figure 1 Transmission Curves Uncoated Czochralski and floatzone silicon Silicon’s transmission characteristics in these wavelength ranges makes it a good choice for infrared imaging systems. The wavelength of infrared energy emission is easily calculated using Wein’s Displacement Law, and these four common items fall within silicon’s transmission range:  Common mammals = 100°F = 9.3µm  Car Engine = 190°F = 8.0µm  Jet Exhaust = 1050°F = 4.1µm  Rocket/Missile Exhaust = 1300°F = 3.0µm Keep in mind these are the peak transmission wavelengths. If the peak transmission wavelength for car a engine is 8µm it actually transmits across a wide band from about 6 to 10µm, which means silicon is a good choice for optical systems designed to look for automobiles, tanks, troop carriers, and other objects with internal combustion engines. There is a clear difference between Cz and Fz silicon around 9µm. The absorption band in Cz-grown silicon is caused by the presence of oxygen in the lattice, which is caused by the quartz crucible breaking down during the growth process. Floatzone silicon is grown without a crucible and is thus almost completely oxygen-free, so absorption at 9.3 microns is much less pronounced. Manufacturers of optical systems designed to look for objects about 100°F often times specify floatzone silicon for just this reason.

SPECIFICATIONS FOR OPTICAL SILICON Since silicon is such a versatile material, different industries will have different primary characteristics they require for their applications. Some of these specifications are common across applications, but there are specifications that don’t necessarily apply to particular applications. Table 1 is a list of the most commonly specified characteristics and their relevance by application.

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Table 1 Relevance of Common Silicon Specifications, by Application

Transmission Resistivity Type Orientation Carrier Lifetime Index Purity

Electronics

Power Generation

X X X X

X X Secondary X

X

X

Transmissive Optics X Secondary * Secondary * Secondary

Reflective Optics

Secondary

X X

* Resistivity is critical for optical applications when the window substrate itself is used as a heater element for frost prevention, or for applications where the window must dissipate static or RF energy.

TRANSMISSION For all but a few optical applications the primary specification of concern is the absorption/transmission of light through the bulk material. At Lattice Materials, we understand how critical the transmission characteristics are in an optical system, and we test transmission on every ingot before it is issued to the production floor. Our standard minimum transmission specification is >52% through a polished, uncoated 0.2” thick sample from 2.5um to 5.0um. (Recall that AR coating will take the transmission to about 98%.) Transmission witness samples are retained for each optical ingot that Lattice Materials uses. All ingot data is permanently stored electronically, and we’ll provide the transmission data for the ingots used for your order if you request it. Ingots with transmission >52% are classified as optical-grade ingots, and ingots with lower transmission are segregated for other applications. The highest transmission we typically experience for Cz-grown silicon is about 53.3%. If transmission >53.3% is required we will normally recommend floatzone silicon, especially if the sample thickness required is thicker than the standard 0.2”.

RESISTIVITY Resistivity is an electrical property of silicon that is directly related to the amount of dopant added to the bulk material, and is an indirect indicator of purity. The resistivity is highest at the top of the ingot, which is the first part pulled from the melt. The dopant tends to concentrate in the melt as the ingot is pulled, so the dopant concentration is lowest at the top of the ingot. In the majority of optical grade silicon applications, the transmission of the material is a greater concern than the resistivity and should be the primary specification requirement. But there are a few applications where the resistivity is also important:   

to dissipate static electricity build-up to reduce radar signature by conducting incident RF energy to the surrounding structure to facilitate heating of the window to eliminate frost formation

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In the early days of silicon optics it was understood that "if the resistivity is N>10 or P>30 Ohm cm, then the transmission will be good enough for IR optics," although the relationship between resistivity and transmission wasn’t’ very well understood. Having tested thousands of ingots at Lattice Materials, we’ve learned that our standard resistivity specification of N>1 or P>10 Ohm cm results in transmission characteristics that exceed the specification requirements for most systems. Adding the N>10 / P>30 specification will add cost and may delay the manufacturing process by restricting our ability to select optimum sized ingots. This higher resistivity should only be specified for the most demanding high transmission applications. If you require a particular transmission specification for your application, the best way to guarantee that you receive suitable silicon is to specify the transmission, not the resistivity. And in cases where the resistivity specification is fixed we will do our best to use the highest yielding ingots in order to help control costs.

TRANSMISSION AND RESISTIVITY Transmission and resistivity are directly related, though not linearly. Higher dopant concentration lowers the resistivity, and also the lowers the transmission. Figure 2 shows the relationship based on empirical data from our own qualification tests. Although the correlation is quite loose, it is clear that above a particular resistivity value the transmission performance does not necessarily improve. It is equally clear that specifying a resistivity value does not guarantee a transmission level. Some specifications call for a low resistivity and high transmission, which presents quite a conundrum: if the silicon is doped to achieve the resistivity spec, the transmission will be lower than required. In such cases it is critical to consider the practical reason for the resistivity requirement, and relax or remove the specification if at all possible. If the resistivity specification can’t be widened, the transmission specification may have be reduced by a fraction of a percent.

Transmission @ 3.0um Through uncoated polished 0.2" thick sample

54

Transmission (%)

53.5

53

52.5

The transmission range lines are a graphical approximation of the material properties of optical-grade silicon based on empirical data. These lines do not constitute a specification or guarantee our ability to meet a particular transmission vs resistivity specification.

52

51.5 0

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Resistivity (Ohm cm)

Figure 2 Transmission vs. Resistivity © 2015 Lattice Materials LLC • 516 E Tamarack St., Bozeman, MT 59718 • (406) 586‐2122 • www.LatticeMaterals.com 

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EMI/RF DISSIPATION AND HEATED-SUBSTRATE APPLICATIONS In some optical applications the resistivity is critical and must be coupled with good optical performance. When the window is electrically contacted and used as heater to prevent frost, or when the window must conduct electricity to prevent static charge build-up, the resistivity plays a key role in the overall performance. The low- and tight resistivity specification associated with these applications imposes limitations on the transmission performance that can be expected. For the lowest resistivity range used in these applications, typically 7 Ohm cm or lower, a typical transmission value will be in the range of 52.4% through a 0.2” thick sample. Note that this requires N-type silicon, because P-type will typically not transmit at resistivity lower than 10 Ohm cm. Lattice Materials has developed robust ingot growth recipes that maximize the optical transmission in the 3 – 5 um range for these demanding low-resistivity applications.

ELECTRICAL TYPE The electrical type of the silicon is determined by the dopant that is used to control the resistivity. Lattice Materials dopes with phosphorous for N-type silicon, and for P-type boron is used. Other ingot growers may use different dopants for N-type, including arsenic and antimony. N-type and P-type silicon behave differently with respect to doping and transmission: a sample of N-type silicon at 10 Ohm cm will have a higher transmission than a sample of P-type silicon at 10 Ohm cm. That’s why our standard specification is N>1 or P>10 Ohm cm. The different dopant atoms affect transmission at different wavelengths, as well. This is a physical property of the material based on atomic physics. Figure 3 illustrates a difference in transmission profiles between N-type and P-type silicon. Both of these ingots were qualified for use under our standard specifications from 2.5 – 5.0 µm (>52%), and both passed our standard resistivity specification of N>1 and P>10 Ohm cm.

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Transmission, N- & P-Type Through uncoated polished 0.2" thick sample

53.4 53.2

Transmission (%)

53.0 52.8 52.6 52.4 N-type, 5.3 Ohm cm

52.2

P-type, 11 Ohm cm

52.0 2.0

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5.0

Wavelength (um)

Figure 3 Transmission of N- and P-type Silicon

ORIENTATION The orientation of the crystal lattice in the ingot is determined by the seed crystal used to grow the ingot. The most common crystalline orientations of Cz grown silicon for optical applications are and , though polycrystalline silicon is also sometimes specified. When it comes to machining silicon for optical applications, there is no apparent difference in mechanical characteristics between , , and polycrystalline silicon. It’s all equally hard and dense, and none are any more prone to breaking or fracturing than any other. It is generally true that polishing material takes longer than material, however. Polycrystalline silicon may be more difficult to polish to a very fine finish, especially if using a chemicalmechanical polish method. Considering that each grain of the polycrystalline material is oriented randomly and differently than its neighbors, each grain will polish at a different rate. With conventional pitch-mounted optical fine polishing techniques polycrystalline silicon can be polished to the same finish as monocrystalline silicon. Lattice Materials offers a number of orientation options for optical- and mirror-grade silicon: 

Slip free silicon—or single crystal silicon—the crystal lattice is perfectly aligned, with no dislocations in the crystallographic planes. Semiconductors used in electronic applications require slip free silicon; optical applications typically do not require slip free silicon. Slip-free can be more costly, due to selection and yield reasons. Slip can be detected by slight changes in the facet lines (lines where crystal planes meet) on the outer edge of the crystal. As a rule of thumb, if an ingot is cut at least the length of 2 of its diameters above where the changes occur, the crystal above that point can be reliably considered to be slip free.



Monocrystalline silicon is single crystal silicon that has a “slip” in the lattice. There is still only one crystal orientation, but the crystal lattice has slipped uniformly by atomic distances along one of

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the crystal planes. Monocrystalline material can be finished to the same quality as slip-free silicon, and there is no way to discern the difference visually once a part has been machined. 

Polycrystalline silicon will have grains, or small sections, of crystal with random orientations. There are two types of polycrystalline silicon: standard and fine-grained. o

Standard polycrystalline silicon will some have visible grain structure, although sometimes only a single visible grain line will show. Very small parts taken from the polycrystalline portion of an ingot may be classified as polycrystalline, even if they do not have any visible grain lines.

o

Fine-grained polycrystalline silicon will have visible grain structure across essentially the entire surface of the part. There will be grains of many different sizes; no single grain will dominate the appearance of the surface of the part.

It used to be true that polycrystalline silicon was less expensive because it was the cast-offs from semiconductor ingot factories, but that’s really no longer the case. The growth process is well enough controlled that ingots rarely “go poly”, so if an application requires polycrystalline material the ingot most likely will be custom grown. Monocrystalline material is the most readily available, most cost effective, and suitable for nearly any application unless there is a known reason for specifying polycrystalline.

CARRIER LIFETIME The carrier lifetime refers to the ability of electrical charge carriers (electrons or holes) to move through the silicon, and it is a property that is of primary concern for solar cell and electronic device manufacturers, but is of no concern to the optics industry. If carrier lifetime specifications appear on a part specification for an optical application, it may be that a silicon electrical properties table was copied from a technical reference onto the part print.

INDEX OF REFRACTION Lattice Materials does not measure the index of refraction of our silicon because it is expensive and a somewhat imprecise measurement. For example, various published sources provide index values that differ in the third decimal place, even though index is often specified to four decimal places. Table 2 shows the values we provide. Table 2 Silicon Index of Refraction WAVELENGTH (µm) 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00

n 3.4307 3.4288 3.4272 3.4255 3.4238 3.4226 3.4219 3.4211 3.4203

Source: H.W. Icenogle, B.C. Platt, W.L. Wolfe, "Refractive Indexes and Temperature Coefficients of Silicon and Germanium," Appl. Opt. Vol 15, No. 10, Oct 1976, pp2348-2351.

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Different references will almost always report different index values in the third or fourth decimal place.

PURITY The purity of silicon is critically important to electronic manufacturers, since even parts-per-billion levels of unwanted impurities may render their electronic circuits useless. Lattice Materials’ standard purity specification is 5N pure (99.999%), which is suitable for all but the most demanding research and development optics applications. In any case, specifying the actual transmission requirement is the most effective guarantee that the right material is delivered, and will necessarily mean that the appropriate high purity silicon is used for the part. When silicon is used for mirror applications the purity specification may come into play again. A purity specification of 5N in this case may help avoid problems inherent in low quality silicon alloys. The relatively high concentration of impurities in 3N or 4N pure silicon can significantly alter the physical properties of the mirror substrate, such as stiffness or thermal conductivity, and some of the desirable characteristics of silicon may be lost.

PHYSICAL PROPERTIES From time to time physical characteristics of silicon are specified on drawings, such as Mohs hardness, coefficient of thermal expansion, density, or modulus of rupture. These and other examples of the intrinsic physical properties of silicon are listed in the Appendix, and apply to high purity silicon. These properties are not tested or certified simply because they are intrinsic to the material and it is an unnecessary expense to measure or characterize them.

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Physical Properties Symbol Atomic Number Atomic Weight Crystal Structure Density (g/cm3) @ 25°C Atomic density (atoms/ cm3) @ 20°C Lattice Constant (nm) @ 23°C Dielectric Constant Surface Tension (mN/m, dyne/cm), liquid @ melting point Modulus of Rupture (MPa) Modulus of Rupture (PSI) Mohs Hardness Hardness, knoops (kg/mm2) Bulk Modulus (GPa) Young's Modulus (GPa) Poisson’s Ratio (125K-375K)

Si 14 28.086 Diamond Cubic 2.329 5.00 x 1022 0.543089 11.8 736 125 1.8 x 104 7 964 ; 948 102 131 ; 187 0.279

Elastic Constants (cm2/dyne)

S11 = 7.68 x 10-13, S12 = -2.14 x 10-13, S44 = 12.56 x 10-13

Elastic Coefficients (dynes/cm2)

C11 = 16.57 x 1011, C12 = 6.39 x 1011, C44 = 7.96 x 1011 Electronic Properties 2.4 x 105 1500 600 1.14 1.17 1.22 x 1010

Intrinsic Resistivity (Ω cm) Intrinsic Electron Drift Mobility (cm2/(V*s)) Intrinsic Hole Drift Mobility (cm2/(V*s)) Band Gap Minimum (eV) @ 25°C Band Gap Minimum (eV) @ 0 K Number of Intrinsic Electrons (cm-3)

Thermal Properties Melting Point ( C) Boiling Point ( C) Heat Capacity (cal/(mol*K)), Solid Heat Capacity (cal/(mol*K)), Liquid @ melting point Heat of fusion (cal/g) Coefficient of Linear Expansion (10-6/K) Thermal Conductivity (W/(m*K))

1412 2878 4.78 6.755 264 233 @ 25 °C, for other temperatures see attached graph 163 @ 25 °C, for other temperatures see attached graph

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180

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Thermal Conductivity (W/(m K))

Thermal Expansion (EE-6/K)

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Temperature - C CONDUCTIVITY

EXPANSION

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