1.75 Балл Task 4
Is it possible to achieve velocity modulation and bunching of charged particles in semiconductor devices using the initial part of the field-velocity characteristic?
Estimate the speed at which an electron will travel through an interaction space of 0.1 μm with an applied voltage pulse of 0.6 [V]? The material is gallium arsenide. Is the pulse duration 6 ∙ 10-10 s and 6 ∙ 10-14 s? When answering, use the concepts of momentum and energy relaxation times.
Given:
Interaction space:
d = 0,1 μm
Voltage pulse:
Up = 0,6 V
Pulse duration:
t1 = 6 ∙ 10-10 s
t2 = 6 ∙ 10-14 s
Solving:
The analysis of carrier dynamics in semiconductors shows that velocity modulation and bunching are fundamentally limited by relaxation processes. On the initial (linear) part of the field–velocity characteristic, the electron drift velocity is proportional to the electric field, and all carriers respond almost identically to external excitation. As a result, although a certain velocity modulation can be introduced, the formation of electron bunches does not occur, since there is no mechanism for phase separation of carriers.
Calculation of the electron flight velocity:
where - μ mobility of charges; E - field strength.
Transform the expression for the mobility of charges:
Then:
For a pulse duration of 6∙10-14 s, we obtain the following electron velocity:
If we try to calculate the velocity for a pulse of length ..., we get a velocity greater than the speed of light - which is incorrect, meaning there must be reasons why the calculation is not suitable for this case: The duration is greater than the relaxation time of charge carriers, which is why the pulses cannot constantly maintain velocity.
Answer:
Velocity for pulse duration 6∙10-14 s:
0 Балл Task 5
It is known that frictional forces are electromagnetic in nature.
Explain the mechanism by which electromagnetic energy is generated through friction.
Answer:
The nature of frictional forces can be understood by considering the electromagnetic interaction between charged particles in solids. When two surfaces come into contact, their atoms interact through electron clouds, which are governed by Coulomb forces. As relative motion occurs, these charge distributions are continuously deformed, leading to time-varying electromagnetic fields.
From a microscopic point of view, friction is accompanied by the acceleration and deceleration of charges. According to classical electrodynamics, any accelerated charge emits electromagnetic energy. At the same time, part of the mechanical energy is transferred into internal degrees of freedom of the solid, primarily into lattice vibrations (phonons), as described in solid-state physics and in Physics of Semiconductor Devices.
As a result, the work done against friction is converted into a combination of thermal energy and electromagnetic fluctuations. These fluctuations manifest themselves as random currents and fields, which form the physical basis of thermal noise in electronic and microwave devices.
Thus, friction is fundamentally electromagnetic in origin, since it arises from interactions between charged particles, and the generation of electromagnetic energy during friction is a direct consequence of the acceleration of these charges and their interaction with the crystal lattice.
0.25 балл. Без квантовой теории не обойтись!!
Task 6
Determine the noise figure of an amplifier device in dB if its effective noise temperature is (100+ Nstudent*2.5)K.
Calculate the effective noise temperature of two such devices connected in cascade if the gain of each device is (10+ Ngroup *0.25) dB.
Analyze the result.
Given:
T0=300 K
Noise temperature:
Tn = 100 + 8*2,5 = 120 K
The gain of devices:
K = 10 + 6*0.25 = 13.6 dB
Solving:
The noise coefficient is calculated by the formula:
where NF - noise factor, calculated as:
Thus the noise factor is:
Hence, the noise coefficient of the amplifying device is:
Calculate the effective noise temperature of two such devices connected in cascade:
According
to the Friis formula, the noise factor of two devices connected in a
cascade is equal to:
Considering that in our case for each of the devices NF1 = NF2 = NF, then:
Calculate the gain of the device:
Then, according to the formula ():
The effective noise temperature of the cascade through the formula () is equal to:
Thus, the effective noise temperature of two cascaded devices is greater than the effective noise temperature of one device by (125,24 – 120) = 5,24 K
Analyzing the results obtained, we conclude that in the case of two devices connected in a cascade, the noise factor and the effective noise temperature increase, which can be considered as a negative phenomenon.
Answer:
Noise factor of the amplifying device:
Kn = 1,46 dB
Effective noise temperature of two devices connected in cascade:
Tn = 125,24 K