7. Assessment and Calculation

7.1 Silicon Die Coefficient

The manufacturing emissions of a silicon die depend on its area and the process node it is fabricated on. Greenpixie holds one coefficient for each process node, giving the manufacturing emissions of a unit of die area fabricated on that node. One table of those coefficients covers processor and accelerator dies alike. Each coefficient is calculated with the model published by Gupta, U. et al. from five quantities, being the energy a fabrication plant consumes per unit of wafer area, the carbon intensity of the electricity supplying that plant, the process gas emissions of the node, the materials footprint of the wafer, and the fabrication yield.

Fabrication energy and process gas emissions per unit area are both higher on newer process nodes. A die fabricated on a current leading node carries roughly twice the emissions per square millimetre of one fabricated at 28 nm. The coefficients account for wafer losses during die production. The coefficient is multiplied by the die area as published.

Where a die is fabricated on a node Greenpixie holds no coefficient for, the emissions are calculated at the coefficient for the nearest node in the table.

7.2 Processor Emissions

The manufacture of every die in a processor package is in scope, being the compute chiplets and the input and output die together. Their total die area is multiplied by the coefficient for the process node of the compute chiplets, described in Section 7.1.

A fixed value is then added for the package itself, covering the substrate, the integrated heat spreader, and inbound transport, adapted from the life cycle inventory of Gröger, J. et al. A server built with two populated sockets holds two processors. The emissions of each processor are calculated separately.

Several of the processors the cloud providers design for their own fleets have no published die area. Greenpixie estimates the die area of each such processor from its process node and its hardware thread count, using the average die area per thread observed across processors at that node. Section 11.3 states the uncertainty a figure produced this way carries.

7.3 Accelerator Emissions

The emissions of an accelerator are the sum of four terms, being the silicon die at the coefficient described in Section 7.1, the high bandwidth or graphics double data rate memory at a rate for each gigabyte of capacity, a fixed value for the board and the components carried on it, and a value for the cooling solution that scales with the thermal design power of the part.

Greenpixie derives the memory rate and the cooling solution value from the memory and thermal shares of the product carbon footprint summaries NVIDIA publishes for its HGX baseboards. Subtracting the die, the memory, and the cooling solution from each published total gives the board value.

The figure for one accelerator is multiplied by the number of accelerators attached to the instance. An instance size sold with a partition of an accelerator, or billed in fractional accelerator time, takes the corresponding fraction of that figure.

7.4 Memory Emissions

Memory emissions are calculated by converting capacity into die area and applying a coefficient to the result. The capacity of a module is divided by the die density held for its generation, giving the die area of the module. That area is then multiplied by the emissions of manufacturing a unit of memory die area, adapted from the life cycle inventory of Gröger, J. et al.

A fixed value is added for each module, covering the board, the connector, and inbound transport. The memory allocated to an instance is divided evenly across the module slots the host is modelled as carrying. A given capacity delivered by many small modules therefore carries more module assemblies than the same capacity delivered by few large ones. Memory carried on the processor package is counted as part of that package and takes no separate module value.

7.5 Drive Emissions

The emissions of a solid state drive are calculated the same way as memory. Its capacity is divided by the die density held for its NAND flash generation, giving die area. That area is then multiplied by the emissions of manufacturing a unit of NAND flash die area, which rise with the number of layers stacked on the die and so differ by generation. A fixed value is then added for each drive, covering the controller, the board, the casing, and assembly.

A mechanical hard disk drive takes a single fixed value for each drive, independent of capacity.

Where a cloud provider divides one physical drive across several instances, each instance takes its share of that drive.

7.6 Fixed Server Component Emissions

The power supplies, the steel chassis, the fans, the motherboard, and the expansion cards of a server each take a fixed value, adapted from the cradle-to-grave life cycle assessments Dell publishes for its PowerEdge rack servers. A further fixed value covers the electricity consumed in assembling the server, adapted from the life cycle inventory of Gröger, J. et al.

The power supply value counts once for each unit fitted.

7.7 Transport and End-of-Life Allowances

Greenpixie calculates the allowances for transport to the data centre and for end-of-life processing as a percentage of the component manufacturing total of the hardware they relate to, at rates set for each type of hardware, being servers, drives, accelerators, and network devices. The rates differ by type as the mass of the hardware, its value for a given mass, and the way it is freighted all differ. Upstream transport of parts to the point of manufacture is accounted for within the manufacturing figures.

End-of-life emissions follow the recycled content method of the GHG Protocol Product Life Cycle Accounting and Reporting Standard, so the calculation takes no credit for material recovered when the hardware is withdrawn from service.

An allowance for the data centre shell, covering the share of the building attributable to the unit of cloud usage, is added to the figure Section 7.8 produces.

7.8 Amortisation and Apportionment

The component emissions of a whole server, with their transport and end-of-life allowances, are divided by the operating hours of the lifetime the hardware is assumed to have, described in Section 5.7, giving the emissions attributable to one hour of its operation.

That hourly figure is then split across the capacity the server presents. The part of that hourly figure apportioned by processor capacity is divided by the hardware thread count of the server, giving a rate for each vCPU for each hour. Memory emissions are divided by the memory capacity populated on the host, giving a rate for each gigabyte for each hour. An accelerator is amortised individually over the same lifetime, giving a rate for each accelerator for each hour.

An instance takes its vCPU count at the first of those rates, its memory allocation at the second, and its accelerator count at the third, for the duration it is billed for. The result is converted into the usage unit the SKU is billed in and expressed in tonnes CO₂e.