Research ArticleMATERIALS SCIENCE

Leverage electron properties to predict phonon properties via transfer learning for semiconductors

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Science Advances  04 Nov 2020:
Vol. 6, no. 45, eabd1356
DOI: 10.1126/sciadv.abd1356
  • Fig. 1 Schematic of TL from electron property to phonon properties.

    A total of 1245 electronic bandgap data of semiconductors that have phonon information in the MP database are used as the proxy property in the source task, while the constrain on semiconductor to have a phonon bandgap [e.g., boron arsenide (BAs) dispersion in the inset] reduces the data for the target property down to 124. A DNN is pretrained on the electronic bandgap, and its architecture and parameters are transferred to the target task, where the DNN is further fine-tuned using the small phonon bandgap data.

  • Fig. 2 Classification model performance evaluated on the testing data.

    (A) The confusion matrix illustrating the number of true positive, false positive, false negative, and true negative. (B) The ROC curve. (C) The precision-recall curve (PRC). (D) The top four most important descriptors identified from the random forest model. HFsum, the sum of the heat of fusion of the compound elements; ENmax, the maximum value of electronegativity of the compound elements; Bandgapsum, the sum of the ground state bandgap of the compound elements; SVmin, the minimum value of the sound velocity of the compound elements.

  • Fig. 3 DNN model for proxy property.

    (A) The MLP DNN architecture of the best-performing model for electronic bandgap. In the parentheses are the numbers of neurons in each layer. (B) DNN-predicted electronic bandgap versus DFT-calculated bandgap (ground truth) for this model.

  • Fig. 4 TL model for phonon bandgap.

    Predicted phonon bandgap versus DFPT calculation using (A) the non-TL and (B) the TL model with the same DNN architecture. (C) MAE and (D) R2 on 15 different random testing datasets for non-TL and TL models. (E) Box plot comparison of MAE for the cases where no pretrained parameters on electronic bandgap are used for phonon bandgap model (“non-TL”), TL model takes pretrained parameters from all three hidden layers (full TL), TL model receiving only the first hidden layer parameters from pretrained model (1st layer TL), and TL model receiving pretrained parameters for the second layer only (2nd layer TL). Insets show transferred layers in blue and nontransferred in orange. (F) Box plot of MAE for different TL fine-tune experiments: “No fine-tune,” all parameters in the three hidden layers are imported from the pretrained model but are not allowed to be fine-tuned in retraining; “3rd layer,” the first two hidden layers are frozen, and only the third layer is fine-tuned; “2nd + 3rd layer,” only the second and third hidden layers are fine-tuned, while the first layer remains unchanged; and full TL, normal TL that all hidden layers are allowed to be fine-tuned. Insets show fine-tuned layers in blue and not fine-tuned layers in black.

  • Fig. 5 TL model performance for speed of sound and heat capacity.

    Box plots of MAE and R2 for (A and B) speed of sound and (C and D) heat capacity with and without TL.

  • Table 1 Model performance for phonon bandgap, speed of sound, and heat capacity.

    Phonon
    bandgap
    (cm−1)
    Speed of
    sound (km/s)
    Heat capacity
    (J mol−1 K−1)
    Non-TL modelMAE: 23.847MAE: 0.501MAE: 6.002
    R2: 0.764R2: 0.763R2: 0.883
    TL modelMAE: 8.458MAE: 0.433MAE: 2.739
    R2: 0.960R2: 0.838R2: 0.985
    Learning from
    full data
    MAE: 0.455MAE: 2.390
    R2: 0.870R2: 0.989
  • Table 2 TL-predicted phonon properties and reference values for some III-V semiconductors not included in the original database.

    Does it have phonon bandgap?Phonon bandgap (cm−1)Heat capacity (J mol−1 K−1)Speed of sound (km/s)
    PredictedReferencePredictedReferencePredictedReferencePredictedReference
    InN (mp-22205)YesYes (54)208.382 ± 3.524215.0 (54)37.483 ± 1.73341.73 (55)4.029 ± 0.1553.80 (55)
    GaSb (mp-1156)YesYes (61)9.129 ± 4.26223.3 (61)45.67 ± 2.77547.87 (62)3.141 ± 0.1463.17 (62)
    InAs (mp-20305)YesYes (61)12.405 ± 4.50915.8 (61)45.886 ± 2.20847.43 (55)3.127 ± 0.1023.03 (55)
    InSb (mp-20012)NoNo (61)45.663 ± 3.09047.32 (62)2.667 ± 0.1312.66 (62)

Supplementary Materials

  • Supplementary Materials

    Leverage electron properties to predict phonon properties via transfer learning for semiconductors

    Zeyu Liu, Meng Jiang, Tengfei Luo

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    • Sections S1 to S4
    • Table S1
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