Semiconductor technology and GNN
As described in ‘Application of AI to semiconductor design processes and semiconductor chips for AI applications’, current AI technologies are supported by semiconductor technologies. These include deep learning chips such as those from NVIDIA, high-performance DRAM (HBM) and processing-in-memory (PIM) technology.
GNN, also described in Graph Neural Networks, is a deep learning technology for handling graph data, which learns the characteristics of nodes and edges while taking into account the directed/undirected relationships in the graph structure represented by nodes (vertices) and edges (edges). This GNN technology is capable of capturing complex interdependencies between nodes and is being considered for application in various domains, making it a powerful machine learning method that can be applied to various aspects of semiconductor technology.
In this article, specific applications of GNNs to semiconductor technology are described.
1. device design and optimisation: as described in ‘Overview of GNN-based services for modelling material properties and structures, designing new materials and predicting their properties’, services for designing new materials and predicting their properties using GNNs are currently being investigated. These are mainly being considered for chemical or biological applications, but are also expected to optimise various parameters and conditions in the design process of semiconductor devices. Specific examples of possible applications include
- Material selection and property prediction: by modelling the properties of semiconductor materials and analysing the relationships between different materials using GNNs, the best material for a particular application can be selected. Nodes represent different materials and edges represent the relationships and property interactions between materials.
- Predicting device performance: device design parameters (e.g. dimensions, materials, structure) are treated as nodes and GNNs are used to predict performance (e.g. switching speed, power consumption, fault tolerance). This reduces the need for prototyping and shortens design time.
2. process optimisation: data analysis and optimisation in semiconductor manufacturing processes using GNNs is envisaged.
- Modelling manufacturing processes: each step in the manufacturing process can be represented as a node and the relationships between processes as edges, and process interactions and influences can be learnt using GNNs. This enables optimisation of manufacturing conditions and anomaly detection.
- Quality control and defective product detection: manufacturing data can be analysed using GNNs to identify the causes of defective products. Process parameters and product characteristics are represented graphically and models are built to detect anomalies.
3. simulation and analysis: the GNN can be used to simulate the operation and characteristics of semiconductor devices.
- Simulation of electrical characteristics: a GNN can be used to simulate the electrical characteristics of a device (e.g. current-voltage characteristics). Nodes represent device states and input signals, while edges represent interactions. This allows complex device behaviour to be analysed effectively.
- Thermal simulation: the thermal properties of semiconductor devices can be modelled using GNNs and optimised for thermal management and cooling. This leads to improved device reliability.
4. failure analysis and prediction: GNNs are also effective in the failure analysis and prediction of semiconductor devices.
- Failure mode identification: failure data of semiconductor devices can be represented as nodes and failure modes and their causes as edges, and failure modes can be identified using GNNs. This enables early detection of failures and more efficient maintenance.
- Lifetime prediction: using GNNs to analyse device usage conditions and historical data, a lifetime prediction model can be built, thereby reducing operating costs and enabling planned maintenance.
5. modelling complex systems: semiconductor technology is often a complex system with many interacting elements; GNNs are well suited to modelling these complex interactions.
- Whole-system optimisation: the interaction of multiple devices and circuits can be represented as a graph, and GNNs can be used to optimise the whole system. This can improve the overall performance of the system.
Specific examples of how GNNs capture correlations between multiple processes and parameters
This section details specific examples where GNNs capture correlations between multiple processes and parameters in semiconductor manufacturing processes.
Example 1: Analysis of data dependencies between manufacturing equipment
In semiconductor manufacturing, wafers are processed through multiple devices and the parameters of the processes (e.g. etching, deposition, lithography) performed by each device may affect the product quality.
Node configuration: each node corresponds to a different manufacturing device. For example, lithography and etching equipment are each one node. The operating conditions (parameters such as temperature, pressure, process time, etc.) for each piece of equipment are assigned to the node as a feature vector.
Setting edges: edges represent dependencies between equipment. For example, if the results of an etching device affect the next deposition process, an edge is set between those devices.
Role of GNNs: GNNs learn the operating parameters of each device (node characteristics) and their dependencies (edges) to predict how anomalous parameters of one device will affect other devices. For example, it learns how a temperature anomaly in the etching process affects uneven film thickness in the deposition process, so that signs of anomalies can be detected in advance.
Example 2: Relationship between process parameters and product quality
In a manufacturing process, product quality (e.g. defect rate, electrical properties, etc.) can be compromised if several parameters, such as temperature, pressure and material feed rate, are not optimised simultaneously.
Node configuration: nodes are assigned important parameters relevant to the manufacturing process. For example, wafer surface temperature, material feed rate, etch gas flow rate, etc. are represented as nodes.
Setting edges: the physical and chemical dependencies between each parameter are represented as edges. For example, the relationship between material feed rate influences temperature, temperature influences gas flow rate, etc. is set as an edge.
Role of GNNs: GNNs learn correlations between these multiple parameters and estimate how variations in one parameter (e.g. temperature) affect other parameters and final product quality. This helps to find out which parameters are likely to cause product defects or the optimum set of parameters for the process as a whole.
Example 3: Analysis of interactions between process steps:.
The semiconductor manufacturing process involves multiple steps, each of which influences the subsequent process steps. For example, the results of the lithographic process can have a significant influence on the results of the etching process.
Node configuration: each node represents a different step in the manufacturing process. For example, each process step such as lithography, etching and deposition is represented as a node.
Setting of edges: the interdependencies between each process (e.g. the impact of lithographic accuracy on the performance of the etching process) are represented as edges.
Role of GNNs: GNNs can be used to learn the impact of lithographic resolution and etching uniformity on final product characteristics (e.g. transistor operating speed and power consumption) and to find optimal manufacturing parameters and process sequences.
In this way, GNNs make it possible to efficiently learn, predict and optimise the complex correlations that exist between multiple processes and parameters of a semiconductor process. These include, specifically, the detection of abnormalities in manufacturing equipment, optimisation of parameters and causal analysis for improving product quality, and GNN is expected to be an effective tool throughout the entire semiconductor manufacturing process.
implementation example
The following section describes a typical implementation of a GNN to capture the correlation between multiple processes and parameters.
Implementation overview: based on a graph structure, the features (parameters) of each node are updated by exchanging information through edges (interactions between processes and parameters). This allows relationships and correlations between nodes to be learnt in the model.
Step 1: Preparation of graph data
First, graph data of nodes (representing processes and parameters) and edges (representing interactions and correlations between them) is prepared. This data can be represented using Python’s NetworkX library, for example as follows.
import networkx as nx
# Creating graphs
G = nx.Graph()
# Additional nodes (e.g. different processes or parameters)
G.add_nodes_from([
(0, {"feature": [0.5, 1.0]}),
(1, {"feature": [1.5, 2.0]}),
(2, {"feature": [2.5, 3.0]}),
])
# Add edges (representing relationships between parameters and processes).
G.add_edges_from([
(0, 1),
(1, 2)
])Step 2: Implement the GNN model
Next, implement the GNN model using PyTorch and PyTorch Geometric. In this section, a Graph Convolutional Network (GCN) is used as an example.
import torch
import torch.nn.functional as F
from torch_geometric.nn import GCNConv
from torch_geometric.data import Data
# Create feature matrices and edge lists for nodes
x = torch.tensor([[0.5, 1.0], [1.5, 2.0], [2.5, 3.0]], dtype=torch.float) # Node features.
edge_index = torch.tensor([[0, 1, 1, 2], [1, 0, 2, 1]], dtype=torch.long) # List of edges
# graphical data object
data = Data(x=x, edge_index=edge_index)
# Definition of the GCN model
class GCN(torch.nn.Module):
def __init__(self):
super(GCN, self).__init__()
self.conv1 = GCNConv(2, 4)
self.conv2 = GCNConv(4, 2)
def forward(self, data):
x, edge_index = data.x, data.edge_index
x = self.conv1(x, edge_index)
x = F.relu(x)
x = self.conv2(x, edge_index)
return x
# Model instantiation and forward paths.
model = GCN()
output = model(data)
print(output)Step 3: Capturing correlations
The GCN model described above is a mechanism whereby the features of each node are influenced and updated by the features of neighbouring nodes through edges. This allows interactions and correlations between nodes to be captured.
- Role of edges: edges define which nodes exchange information with each other. For example, if an edge shows a strong relationship, more information will flow through that edge.
- Node features: the feature vector of each node represents the characteristics of that node, and the representation of the node becomes richer by incorporating information from other nodes through edges.
Step 4: Learning process.
To train the model, a loss function is defined and an optimisation technique is used. Specifically, predictions are made using node features and the parameters are updated based on the error between the predictions and the correct labels.
optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
criterion = torch.nn.MSELoss()
# training loop
for epoch in range(100):
model.train()
optimizer.zero_grad()
output = model(data)
loss = criterion(output, torch.tensor([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0]], dtype=torch.float)) # 例としてのラベル
loss.backward()
optimizer.step()
print(f'Epoch {epoch}, Loss: {loss.item()}')reference book
Reference books are described below.
1. reference books on semiconductor technology
2. reference books on graph neural networks (GNNs)
Graph Neural Networks: Foundations, Frontiers, and Applications
3. applied books on the combination of semiconductor technology and GNNs
Machine Learning in VLSI Computer-Aided Design
EDA for IC Implementation, Circuit Design, and Process Technology
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