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What is the Density of Silicon?

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  • icon2 January 20, 2024
  • icon3 WaferPro
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The Density of Silicon is 2.329 g/cm³.

Silicon (Si) is one of the most important materials used to manufacture semiconductor devices and integrated circuits. At WaferPro, we produce high quality silicon wafers that serve as the foundation for microchips and other electronic components. In this article, we will thoroughly examine the intrinsic density of elemental silicon and discuss how understanding this fundamental physical property enables us to optimize our wafer fabrication processes.

the Crystalline Structure of Silicon

An Overview of Silicon's Crystalline Structure

Silicon crystallizes in the diamond cubic structure under standard conditions. This gives silicon several advantageous properties:

  • Extreme hardness and rigidity
  • High thermal conductivity
  • Relative chemical inertness

The diamond lattice consists of a face-centered cubic (FCC) unit cell with a two-atom basis. Each silicon atom bonds to four neighbors in a tetrahedral coordination. This crystalline arrangement leads to an exceptionally efficient packing of atoms and Thus a high intrinsic density compared to other group IV elements like germanium.

Some key facts about the crystalline structure of silicon:

  • Lattice constant: 543 pm
  • Tetrahedral bond angle: 109.5°
  • Nearest neighbor distance: 235 pm
  • Coordination number: 4

Understanding these structural characteristics allows us to grow large, pure silicon boules for wafer slicing using the Czochralski process. Fine-tuning factors like temperature gradients and pull rates during crystal growth relies on knowledge of silicon's density and crystal structure.

The Intrinsic Density Value of Silicon

The most widely accepted value for the density of crystalline silicon at standard ambient temperature and pressure (SATP) is:

2.329 g/cm³

This corresponds to 2.329 x 10³ kg/m³. Some key considerations regarding this number:

  • It assumes perfect single crystal silicon with no defects or impurities
  • There is a small thermal expansion coefficient, so density varies slightly with temperature
  • The presence of dopants can also impact measured density

Nonetheless, 2.329 g/cm³ serves as an excellent baseline number for silicon density in wafer fabrication processes.

Here is a summary table of key silicon density parameters:

ParameterValue
Density at SATP2.329 g/cm³
Mass per cubic meter2.329 x 103 kg/m³
Thermal expansion coefficient2.6 x 10-6 K-1
Variation with dopingUp to ±0.5%
The Role of Density in Wafer Fabrication

The Role of Density in Wafer Fabrication

As a leading wafer manufacturer, WaferPro leverages silicon's uniquely high density to produce wafer substrates with excellent uniformity and low defect rates.

Some of the main wafer fabrication steps where an understanding of silicon density is vital include:

  • Crystal growth - Controls factors like temperature gradients and growth rate which impact density
  • Wafer slicing - Achieving precise dimensions and thicknesses depends on the density
  • Lapping and polishing - Proper mechanical Polish rates rely on consistent density across a wafer surface
  • Cleaning - Etch rates and surface chemical reactions vary with slight density fluctuations

By accounting for silicon's density all the way from Czochralski crystal growth through final wafer preparation, we can reliably output large diameters wafers to extremely fine specifications for device manufacturing.

Variations in Silicon Density

While pure crystalline silicon has a clear intrinsic density under standard conditions, in practice there can be small variations. Some factors that can alter silicon wafer density include:

Temperature

  • Thermal expansion coefficient of 2.6 x 10-6 K-1
  • Leads up to ±0.1% density variation between 300K and 1000K
  • Careful heating and cooling control during processing is vital

Impurities and Defects

  • Interstitial or substitutional dopant atoms
  • Presence of voids or crystal dislocations
  • Can locally modify density up to ~0.5%

Isotopes

  • Naturally occurring silicon is 92.2% of 28 Si
  • Other isotopes like 29 Si and 30 Si have slightly higher mass
  • Isotopic purification can adjust density ±0.2%

While these factors can result in percent-level density variations, the intrinsic single-crystal silicon value 2.329 g/cm³ serves as an indispensable baseline number for wafer engineering and processing.

Real-World Density Measurements

While 2.329 g/cm3 reflects the intrinsic single crystal density of silicon, real-world measurements can show small variations depending on factors like production methods and impurity levels. At WaferPro, our quality control processes include rigorously measuring density across production runs.

Some example density measurement results for recent wafer batches are shown below. The density was determined by precise measurement of mass and physical dimensions.

Wafer BatchMeasured DensityVariation from Baseline
P483-016-FZ2.328 g/cm³-0.04%
X109-002-CZ2.330 g/cm³+0.04%
A006-108-MCZ2.327 g/cm³-0.09%

These results confirm that industry-leading WaferPro production processes yield silicon wafers with densities tending closely to the 2.329 g/cm³ baseline. Variations span a narrow range from -0.09% to +0.04%.

Strict manufacturing controls enable WaferPro to achieve exceptionally consistent silicon wafer density despite subtle effects from factors like:

  • Trace oxygen or carbon impurities
  • Subtle lattice strain effects
  • Very low-level n-type doping

By guaranteeing small density variations of less than ±0.1%, we provide chip manufacturers with an ultra-reliable foundation for fabricating precision devices.

Emerging Applications Leveraging silicon Density

The semiconductor industry's understanding of elemental silicon density also opens doors for cutting edge applications:

Controlled Porous Silicon Layers

By precisely etching voids and pores into silicon wafers, novel optical and sensing properties can be achieved with porous silicon layers. Tailoring porosity relies intimately on density.

Nanoscale Silicon Structures

Synthesizing silicon structures with features smaller than 100 nm requires accounting for confinement effects that subtly alter density on that size scale.

Novel Membranes

Straining silicon through applied pressure/stress modifies density in a controllable fashion. New types of pressure sensors and membranes can leverage these nanoscale density changes.

The intrinsic purity and density uniformity of WaferPro's silicon wafer products serves as an enabling foundation for these emerging technologies that expand silicon's capabilities even further.

Leveraging Silicon Density Knowledge

In summary, understanding elemental silicon's high intrinsic density is crucial for optimizing processes all along the semiconductor supply chain:

  • Silicon ingot growth depends intimately on density control
  • Achieving strict wafer thickness and diameter specs would be impossible without accounting for density
  • Knowledge of thermal expansion with temperature enables tight control over heating and cooling cycles
  • Modeling dopant diffusion kinetics requires density as an input
  • And much more...

So while 2.329 g/cm<sup>3</sup> may seem like a simple number, silicon's exceptional density is what enables ultra-precise manufacturing of semiconductor wafers. WaferPro leverages this foundational physical property every day to output high quality products for leading-edge electronics. Knowledge and control of density permutations underlies our ability to drive technological innovation through wafer supply.

Frequently Asked Questions about Silicon Density

Silicon density is a vital parameter for wafer manufacturing, but it can also lead to some common questions. Here at WaferPro we have extensive experience addressing key areas of inquiry about this fundamental physical property:

What causes small variations in silicon density measurements?

Minor differences in density readings arise due to factors like temperature, isotopic content, crystalline defects, and trace doping/contamination. State-of-the-art production processes control these variables to yield extremely consistent densities.

How accurate are common density reference values for silicon?

Trusted data sources quote silicon's density as 2.329 g/cm3 at standard conditions with uncertainties on the order 0.001 g/cm3 or lower. This precision has been confirmed through extensive experimental measurements over decades.

Why does liquid silicon have a higher density than diamond cubic crystalline silicon?

In the liquid phase, silicon atoms adopt a higher-density random packing without long-range order. Rapid freezing leads to the lower-density diamond structure becoming kinetically trapped.

Can silicon's density increase or decrease under pressure?

Applied pressures up to around 10 GPa have negligible impact on silicon density due to its very low compressibility. However, higher pressures can force phase transitions to denser metallic silicon allotropes.

Does amorphous silicon have the same density as crystalline forms?

At ambient pressure, amorphous silicon's short-range disorder leads to a density of 2.25 g/cm³ - marginally lower than the diamond cubic phase while still very high.

Reach out to WaferPro's team of technical experts with any additional questions! We are always happy to share our decades of combined experience with this foundational material.

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