A novel machine learning workflow to optimize cooling devices grounded in solid-state physics

Abstract

Cooling devices grounded in solid-state physics are promising candidates for integrated-chip nanocooling applications. These devices are modeled by coupling the quantum non-equilibirum Green's function for electrons with the heat equation (NEGF+H), which allows to accurately describe the energetic and thermal properties. We propose a novel machine learning (ML) workflow to accelerate the design optimization process of these cooling devices, alleviating the high computational demands of NEGF+H. This methodology, trained with NEGF+H data, obtains the optimum heterostructure designs that provide the best trade-off between the cooling power of the lattice (CP) and the electron temperature ([Formula: see text]). Using a vast search space of [Formula: see text] different device configurations, we obtained a set of optimum devices with prediction relative errors lower than [Formula: see text] for CP and [Formula: see text] for T_e. The ML workflow reduces the computational resources needed, from two days for a single NEGF+H simulation to 10 s to find the optimum designs.

Fig. 1

Potential profile of the double-barrier heterostructure based on AlGaAs. , , and , are the lengths of the b1, QW, and the b2, respectively. The height of the first barrier () is determined from the band offset between AlAs and the emitter, and the height of the second barrier () is proportional to , which is the fraction of aluminium in the alloy. V is the bias between the Fermi energy of the emitter and the Fermi level of the collector (), is the energy interval between the (E₀) and . The is the energy interval between E₀ and the conduction band edge of the b2 (.

Fig. 2

Machine learning procedure. From the combination of the design parameters () and the material energy gaps, the first solution of the potential profile () is constructed, and its features are reduced by applying the principal component analysis (PCA(PP₀)) to obtain the principal components (). The combined with the V are the inputs of the first multi-layer perceptron (MLP1), which gives the difference between potential profile (PP) and (PP-PP₀) as the output. The PP of the device is obtained by applying the inverse principal component analysis (PCA) ((PP-PP₀) and adding the PP₀. The inputs of the second multi-layer perceptron (MLP2) are the PP obtained from the application of PCA(PP) to the PP. Finally, the MLP2 provides, as output the information about the cooling properties (CP, ) and the device activation energies (, ).

Fig. 3

The correlation for each point of the PP, denoted as E, between the NEGF+H simulations and MLP1 predictions is depicted in the top figures for the training (a) and test (b). The Pearson’s coefficient (CC) equal to 1 shows the perfect correlation line between prediction and simulation. An example of the reconstructed PP of MLP1 predictions in comparison to NEGF+H simulations, for randomly selected profiles, is illustrated in the bottom figures from both the training subset (c) and the test subset (d). The variable x is the distance from the start of the emitter contact.

Fig. 4

Performance of MLP2 on training (left) and test (right) subsets for the output variables CP (a–b), (c–d), (e–f), and (g–h). The black line (CC=1) is the line of perfect correlation, and y-axis error bars correspond to the root-mean-square error (RMSE).

Fig. 5

dependence with design parameters and a. Diagram of the main mechanisms for electron tunnel injection in the QW b.

Fig. 6

dependence with design parameters and a. Diagram of the main electron mechanisms for thermionic emission from the QW b.

Fig. 7

Colour maps for CP a and b as a function of the activation energies and . The red contour serves as a benchmark criterion for the highest performance devices. The hatched area delimits the region where falls below the .