Making Tokens, Pt. 2: Pulling the Crystal

Part two of the Making Tokens series. In Part 1 we turned quartzite into 9N polysilicon. Now we have to turn that polysilicon into wafers, which means we have to coax a single perfect crystal of silicon out of a melt. For the silicon logic chips in this series, the starting point is a single-crystal wafer. Other semiconductor materials and growth routes exist.

The constraint: every atom in the same place

A transistor only works if the electrons flow through silicon whose atomic lattice is undisturbed. Polycrystalline silicon (the kind that comes out of a Siemens reactor) is full of grain boundaries: places where one crystallographic orientation meets another. Carrier mobility tanks across those boundaries. So before you can build a chip, you have to convert poly-Si into a monocrystalline ingot, where every atom sits in the same regular lattice from one end to the other.

There are a couple of ways to do this. The dominant one, by an enormous margin, is the Czochralski process (CZ), invented in 1916 by the Polish metallurgist Jan Czochralski more or less by accident. He dipped a pen into what he thought was an inkwell and pulled out a wire of crystallized molten tin. The semiconductor industry has been pulling crystals out of melts the same way ever since.

The mechanics

Inside a CZ puller you have:

• A quartz crucible holding ~200-300 kg of polysilicon chunks
• A graphite susceptor wrapped around the crucible, heated above 1414 °C, silicon's melting point
• An argon atmosphere to keep the melt clean
• A small seed crystal of monocrystalline silicon, with a precisely defined orientation, mounted on a wire that can be raised, lowered, and rotated independently of the crucible

The procedure is unsentimental and slow. The crucible heats up. The poly melts into a clear, near-mercury-colored pool. The seed is lowered until it just kisses the surface. The melt freezes onto the seed, atom by atom, in the same crystallographic orientation. Then you start pulling. Slowly.

The seed and crucible rotate as the crystal is pulled upward. Growth rate, diameter, and thermal conditions have to stay coordinated. SUMCO describes the CZ process and magnetic-field-assisted and float-zone alternatives. There is no single ingot size or cycle time that describes all of them.

The result is a large single crystal. That sounds simple until you try to hold its geometry and impurity profile steady throughout the pull.

Why this is hard

The CZ process looks deceptively simple, but it is governed by some of the more annoying coupled physics in industrial chemistry.

Heat transfer. You're balancing the heat input from the susceptor against the heat removed by conduction up the growing ingot and by radiation from the melt surface. Get the balance wrong and you get either constitutional supercooling (the melt freezes faster than the seed can guide the crystal structure) or a runaway shape change. Modeling the thermal field is a serious CFD exercise.

Mass transport. As the crystal grows, impurities segregate. Some elements (like boron) prefer to stay in the melt; others (like oxygen, dissolved from the quartz crucible) get pulled into the crystal at a known rate. This is what gives you the doping profile along the length of the ingot. The first wafers sliced from the top of an ingot are often a slightly different doping concentration than the wafers from the tail.

Vibration and convection. The melt has internal Marangoni convection (driven by surface tension gradients) and buoyancy-driven flow. These need to be controlled, often with a static magnetic field, to keep the growth front flat. "Magnetic CZ" (MCZ) is the standard for the highest-quality wafers used in leading-edge logic.

Crucible erosion. The quartz crucible dissolves slowly into the melt at 1414 °C. The resulting oxygen incorporation in the crystal is actually useful at controlled concentrations (it helps getter metallic impurities), but uncontrolled, it ruins the wafer.

Equipment throughput depends on diameter, recipe, maintenance, and how much of the ingot passes inspection. Those details matter more than a generic annual count of pulls.

From ingot to wafer

What comes out of the puller is one giant rod of single-crystal silicon. The next stage is purely mechanical and pretty brutal.

Cropping: the ends of the ingot are sawn off and recycled. The seed end has the seed cone, the tail end has the segregated impurities.

Grinding: the ingot is ground to a precise outer diameter (300 mm) and a flat or notch is ground along one side to mark crystallographic orientation.

Slicing: an inner-diameter or wire saw cuts the ingot into wafers. The cut removes material, and later finishing removes more. Kerf and finishing losses depend on the process; 30% is an assumption for the example below, not a universal specification.

Lapping and grinding: the wafer surfaces are flattened mechanically.

Etching: a quick chemical etch removes any subsurface damage from the mechanical steps.

Polishing: chemical-mechanical polishing (CMP) brings one side of the wafer to an atomic-scale smoothness. The mirror finish you see in promo photos is the polished front-side. The back is rougher.

Cleaning: cleaning and inspection remove contamination and catch defects before the wafer goes to a fab.

What ships to the fab is a polished single-crystal wafer. For a geometry example, take a 300 mm diameter and a finished thickness of 775 micrometers. At a silicon density of about 2.33 g/cm³, that wafer weighs approximately 128 grams. Prices depend on specification and contract; bare-wafer prices should not be confused with processed-wafer or accelerator prices.

Keep the mass balance honest

Here is an illustrative calculation, not a production recipe:

• Start with 200 kg of polysilicon.
• Assume 180 kg remains after cropping and other losses.
• Assume 30% of that is lost during slicing and finishing, leaving 126 kg.
• Divide by 0.128 kg per finished wafer: approximately 980 wafers.

A full 300 mm diameter cylinder two meters long would weigh about 329 kg before any cropping. It cannot also be the 180 kg ingot in this example. Geometry and mass have to describe the same object.

Die count introduces a second problem. A wafer's total circular area is not all usable: rectangular dies have to fit around the edge, with room for scribe lanes and edge exclusion. Defect yield comes after that geometric loss. You cannot get a defensible count of working accelerators by dividing the circle's area by die area alone.

The suppliers

Major silicon-wafer suppliers include Shin-Etsu, SUMCO, GlobalWafers, Siltronic, and SK siltron. The market is concentrated, but "four companies make every wafer" leaves out an important supplier and overstates the point. Siltronic's product overview shows the range of wafer types and applications behind the category.

Sources and calculation notes

• SUMCO: production processes, for the manufacturing sequence.
• Siltronic: products, for wafer types and applications.
• Wafer mass: π × (15 cm)² × 0.0775 cm × 2.33 g/cm³ ≈ 128 g.
• Ingot cylinder mass: π × (15 cm)² × 200 cm × 2.33 g/cm³ ≈ 329 kg. The example losses above are explicit assumptions.

What's next

By the end of this stage, we have a clean, polished, single-crystal silicon wafer. In photolithography, deposition, patterning, etching, and many other operations turn it into circuits. The bare wafer, the processed wafer, the packaged die, and the complete accelerator are different products with different costs.

Photolithography is where this stops being chemistry and starts being something else.