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Recently, the two dimensional complex MA$_2$Z$_4$ structures have beensuggested as suitable replacements for silicon channels in field-effecttransistors (FETs). Specifically, two materials of MoSi$_2$N$_4$ andWSi$_2$N$_4$ due to their very desirable electrical and thermal properties arenoticed. On the other hand, the reliability of transistors, which is determinedby the maximum temperature they obtain during the performance, specifies theusefulness of the newly proposed channels for thermal management solution. Inthis work, the FETs, including MoSi$_2$N$_4$ and WSi$_2$N$_4$ channels, areinvestigated using Monte Carlo simulation of the phonon Boltzmann equation. Inparticular, the phonon analysis has been carried out to investigate the peaktemperature rise. Our calculations confirm that MoSi$_2$N$_4$ and WSi$_2$N$_4$present lower maximum temperature than the previously suggested candidate, theblue phosphorene (BP) which itself reaches a shallow temperature. Concretely,the phonon exploration shows that the competition between the dominant heatcarrier velocity, and its related frequency settles the maximum temperaturevalue. The material WSi$_2$N$_4$ with much more phonons in TA mode, with almosthigh velocity and relatively low-frequency, shows adequate thermal condition,and its peak temperature is very low, say 110 K, less than that of BP. Thematerial MoSi$_2$N$_4$ attains the maximum temperature of only 10 K less thanBP peak temperature. This behavior attributes to the dominant LA phonons whichare fast but also have high frequency and consequently make the temperature getlarger than that of the WSi$_2$N$_4$. In summary, WSi$_2$N$_4$, with very lowpeak temperature, and in the next step MoSi$_2$N$_4$, both with beneficialelectrical/thermal properties, are suggested as very suitable candidates forproducing more reliable FETs, fulfilling the thermal management.

An investigation into the reliability of newly proposed MoSi$_2$N$_4$/WSi$_2$N$_4$ field-effect transistors: A monte carlo study