Colloidal semiconductor quantum dots (QDs) have been intensively investigated as a next-generation self-emission display element that forms a nanometer-sized semiconductor structure with excellent optical properties of high luminance efficiency, highly-tunable emission wavelength, and good color purity [[1], [2], [3], [4]]. Owing to these advantages, they are also attracting a huge attention in various applications such as image sensors [5] and solar cells [6]. In addition, colloidal QDs have been widely used as efficient color down-conversion phosphors, which absorb short-wavelength light and emit long-wavelength light [4]. Hence, both emission and absorption spectra are important optical properties of colloidal QDs. The optical absorption/emission properties of colloidal QDs are greatly affected by their structural parameters such as the layer thickness so that it takes a large amount of time and cost to obtain a desired optical property through a trial-and-error process of fabrication and measurement. Hence, prior to the synthesis of QDs, it is essential to predict the optical properties of QDs from their structural parameters based on the theoretical simulation models.

There have been several research efforts on the theoretical calculation of colloidal QDs such as the density functional theory [7], atomistic pseudopotential approach [8], and strain-modified effective mass approximation (EMA) [[9], [10], [11], [12], [13]]. Among them, the strain-modified EMA has been widely used to predict the emission/absorption spectrum depending on various structure parameters of colloidal QDs because it provides reliable calculation results without heavy mathematical and computational complexity [[9], [10], [11], [12], [13]]. However, the inverse design, finding an optimal structure of the QD to provide target optical properties, will be very challenging because it requires a huge number of numerical simulations even when traditional optimization methods such as the genetic algorithm [14] and particle swarm optimization [15] are applied. On the other hand, there have been a few research results to use machine learning (ML) models to predict the optical properties of colloidal QDs such as a forward prediction of the emission wavelength from their synthetic conditions or an inverse design of optimal synthetic conditions that provide specific optical properties [[16], [17], [18], [19]]. However, these ML-based approaches have the limitation of prediction accuracy due to the fact that synthetic conditions of colloidal QDs obtained by experimental data or published literatures are inconsistent and incomplete [[16], [17], [18], [19]].

The deep neural network (DNN) consists of several layers of artificial neurons together with input and output parameters. DNN-based forward prediction or inverse design between optical properties and structural parameters of analog materials has been intensively investigated [[20], [21], [22], [23]]. Currently, DNNs have been also applied to the forward prediction of optical properties based on forward neural networks (FNNs) as well as the inverse design of device structures through the inverse neural networks (INN) in various nanophotonic devices [[24], [25], [26]]. Especially, DNN-based forward predictions and inverse designs have been applied to multilayer thin-film photonic devices such as the scattering efficiency of multilayer nanoparticles [27], the transmission spectrum of multilayer thin films [28], and the light extraction efficiency of organic light-emitting diodes [29]. Because colloidal QDs are spherically-symmetric nanoparticles like multilayer thin-film photonic devices, DNNs can be also applied to the forward prediction and inverse design between the optical properties of the emission/absorption spectrum and the material structures such as the layer thickness. However, there has been no research effort to apply the DNN to the forward prediction and inverse design of colloidal QDs based on their structural parameters and emission/absorption spectrum.

In the case of nanophotonic devices, different structures of the multilayer thin-film photonic device can provide nearly the same optical property, which corresponds to a so-called non-uniqueness problem in the inverse design so that the INN has a problem of very slow convergence and low accuracy [28]. This non-uniqueness problem in the inverse design of the multilayer thin-film photonic device can be alleviated by means of the tandem neural network, which cascades an INN with a pre-trained FNN [[28], [29], [30]]. Because colloidal QDs are composed of spherically-symmetric multilayer thin-film materials, the non-uniqueness problem will also take place when structural features such as the layer thickness are used as input or output parameters for training datasets. However, this non-uniqueness problem in the inverse design of colloidal QDs has not yet been investigated. In addition, there is a growing interest in transfer learning because it significantly enables to improve the performance in the target task through the transfer of the learned knowledge from the source task [31]. When transfer learning is applied to the inverse design of QDs, the weights and biases of a source neural network, which is optimized to work for a certain material composition, can be transferred and tuned to work for a different set of material compositions with the enhanced performance. Nonetheless, transfer learning approach has never been used in the inverse design of colloidal QDs.

In this study, we propose, for the first time to the best of our knowledge, the forward prediction and inverse design of colloidal InP/ZnSe/ZnS QDs based on the DNN. The training datasets are generated by solving Schrödinger equation based on the strain-modified EMA, where the emission and absorption spectra are calculated with respect to the thicknesses of each core/shell/shell QD layer. Specifically, the emission spectrum has the ground-state peak wavelength between 450 and 680 nm. The absorption spectrum is calculated by considering all the QD confined states whose optical transitions are located in the visible wavelength region (430–700 nm). We identify the non-uniqueness problem, where nearly same optical emission spectra can be obtained at many different combinations of core/shell/shell thicknesses. In contrast, when both emission and absorption spectra are considered as input optical spectra, we can reduce the number of nearly degenerated input optical spectra at different combinations of core/shell/shell thicknesses. We demonstrate that applying a tandem DNN structure together with the simultaneous use of both emission and absorption spectra as input training datasets helps to alleviate the non-uniqueness problem in the inverse design of colloidal QDs. In addition, using our inverse design model, we can predict the most possible layer thicknesses of InP/ZnSe/ZnS QDs that resemble on-demand target optical emission/absorption spectra, which are enhanced at the specific blue wavelength region. In transfer learning approach, the pre-trained tandem DNN for InP/ZnSe/ZnS QDs is transferred and tuned to work for the inverse design of CdSe/ZnSe/ZnS QDs, where the amount of training data can be saved by a maximum of 71.4 %.