The Research On Plasma Shock Waves Characteristics In Field-effect Transistors

In 1993,physicists Michel Dyakonov and Michel Shur demonstrated that fieldeffect transistors can produce plasma,which exists in the channel of field-effect transistors as plasma waves,meanwhile,these plasma waves have properties similar to "water waves".This theory is known as DS instability.Therefore,it produces a very important nonlinear coherent structure called "plasma shock waves" when the plasma waves propagate in the field-effect transistors.A great deal of research has been done based on the DS instability theory.However,there are still many problems must be solved.In short,previous studies are still confined to the linear characteristics of plasma waves propagation,and the nonlinear factors are rarely mentioned.The main factors leading to nonlinear plasma shock waves in field-effect transistors are friction and quantum effect.This paper focuses on the propagation characteristics of shock waves in the channel of the field-effect transistor.The main contents of this paper are as follows:(1)The propagation characteristics of shock waves with THz frequency in fieldeffect transistors is studied.Considering the viscosity caused by friction,the system of hydrodynamic equations with viscosity is established,and the Burgers equation is derived to describe the behavior of electronic fluids by using the reductive perturbation expansion.At the same time,the evolution law of this system is given by nonlinear dynamics analysis.The space-time distribution of plasma shock waves is simulated.The theoretical analysis shows that there are monotonic and oscillatory shock waves in the system;when the viscosity coefficient is small,the oscillation of the shock waves with THz frequency in field-effect transistor is significantly;the oscillation of the shock waves tends to plateau over time;there is a transform from oscillatory shock waves to monotonic shock waves in this system when the viscosity coefficient reaches a certain value.Furthermore,the oscillation of shock waves occurs at the drain because there is reflection of the plasma waves at the drain when the waves propagate from source to drain in the channel of field-effect transistor.(2)The propagation of nonlinear waves in field-effect transistors with quantum effects is researched.Nano-semiconductor devices have been used in the development and manufacture of various kinds of chips.At this time,the influence of quantum effects on device performance can’t be ignored.With the consideration of quantum effects,the quantum hydrodynamic equations describing the collective behavior of the electron gas in the channel of field-effect transistor are established.The Kd V-Burgers equation describing the propagation characteristics of nonlinear waves is obtained by using the reductive perturbation expansion.The dynamical method is used to study the phase trajectory of the system evolution,and the influence of quantum effects and viscosity on the nonlinear waves propagation characteristics is studied by numerical method.The results show that there are two different types of nonlinear waves,that is,shock waves and solitary waves,in the channel of field-effect transistors;The shock waves are formed when dissipation caused by viscosity and dispersion caused by quantum effects work together;And the shock waves changes into solitary waves when the dissipation disappears.The shock waves have oscillatory shock waves and monotonic shock waves.When viscosity coefficient reaches a certain value,the dissipation exceeds the dispersion eventually and the oscillatory shock waves changes into monotone shock waves.The shock waveforms break up over time due to quantum effects.Summing up the results,it can be concluded that the quantum effects enhance shock waves oscillation and solitary waves width.(3)Based on DS instability theory,the linear properties of THz plasma waves in graphene field-effect transistors with quantum effects is studied.The quantum hydrodynamic equations describing the motion characteristics of electron gas are linearized by means of simple normal mode analysis.To get the instability increment and oscillation frequency and the relationship between the quantum effect.The results show that: the quantum effects cause to the instability increment and frequency of THz oscillation change;the instability increment and oscillation frequency increase with sound velocity of the carrier fluid monotonically;when velocity of the carrier fluid is small,the influence of quantum effects on instability increment and oscillation frequency is obvious.Meanwhile,the reduction of channel length will lead to an increase in oscillation frequency and instability increment of THz plasma oscillation in graphene field-effect transistors.The instability window of terahertz plasma waves in graphene field-effect transistors is larger than those conventional materials.