**Tomasz Raszkowski \* and Mariusz Zubert**

Department of Microelectronics and Computer Science, Faculty of Electrical, Electronic, Computer and Control Engineering, Lodz University of Technology, 90-924 Lodz, Poland; mariuszz@dmcs.p.lodz.pl

**\*** Correspondence: traszk@dmcs.pl

Received: 18 April 2020; Accepted: 5 May 2020; Published: 9 May 2020

**Abstract:** This paper presents an analysis related to thermal simulation of the test structure dedicated to heat-diffusion investigation at the nanoscale. The test structure consists of thin platinum resistors mounted on wafer made of silicon dioxide. A bottom part of the structure contains the silicon layer. Simulations were carried out based on the thermal simulator prepared by the authors. Simulation results were compared with real measurement outputs yielded for the mentioned test structure. The authors also propose the Grünwald–Letnikov fractional space-derivative Dual-Phase-Lag heat transfer model as a more accurate model than the classical Fourier–Kirchhoff (F–K) heat transfer model. The approximation schema of proposed model is also proposed. The accuracy and computational properties of both numerical algorithms are presented in detail.

**Keywords:** Dual-Phase-Lag heat transfer model; thermal simulation algorithm; thermal measurements; Finite Difference Method scheme; Grünwald–Letnikov fractional derivative
