Embodied carbon footprint modeling has become an area of growing interest due to its significant contribution to carbon emissions in computing. However, the deterministic nature of the existing models fail to account for the spatial and temporal variability in the semiconductor supply chain. The absence of uncertainty modeling limits system designers' ability to make informed, carbon-aware decisions. We introduce CarbonClarity, a probabilistic framework designed to model embodied carbon footprints through distributions that reflect uncertainties in energy-per-area, gas-per-area, yield, and carbon intensity across different technology nodes. Our framework enables a deeper understanding of how design choices, such as chiplet architectures and new vs. old technology node selection, impact emissions and their associated uncertainties. For example, we show that the gap between the mean and 95th percentile of embodied carbon per cm$^2$ can reach up to 1.6X for the 7nm technology node. Additionally, we demonstrate through case studies that: (i) CarbonClarity is a valuable resource for device provisioning, help maintaining performance under a tight carbon budget; and (ii) chiplet technology and mature nodes not only reduce embodied carbon but also significantly lower its associated uncertainty, achieving an 18% reduction in the 95th percentile compared to monolithic designs for the mobile application.

翻译：隐含碳足迹建模因其对计算领域碳排放的重要贡献而日益受到关注。然而，现有模型的确定性本质未能考虑半导体供应链中的空间和时间变异性。不确定性建模的缺失限制了系统设计者做出明智的、具备碳感知的决策的能力。我们提出了CarbonClarity，这是一个概率框架，旨在通过反映不同技术节点在单位面积能耗、单位面积气体消耗、良率和碳强度等方面不确定性的分布来建模隐含碳足迹。我们的框架能够更深入地理解设计选择（如芯粒架构和新旧技术节点选择）如何影响排放及其相关不确定性。例如，我们表明对于7nm技术节点，每平方厘米隐含碳的均值与第95百分位数之间的差距可达1.6倍。此外，我们通过案例研究证明：(i) CarbonClarity是设备配置的宝贵资源，有助于在严格的碳预算下保持性能；(ii) 芯粒技术和成熟节点不仅能减少隐含碳，还能显著降低其相关不确定性，在移动应用场景中，与单片设计相比，其第95百分位数实现了18%的降低。