1.2 Calculation of the gate length of a field-effect transistor
Calculate the gate length of a field-effect transistor using the following formula [23]:
Lg
= vs
= 
(26)
where – drift time under the gate; vs = 105 m/s – saturation rate.
Using formula (25), for we also get:
= = = 1,989 10-11 s
Using the formula (26), we calculate the maximum possible length of the gate:
Lg = vs = 105 1,989 10-11 = 1,989 10-6 m = 1,989 µm
1.3 Analysis of the obtained results of calculating the thickness of the bipolar transistor base and the gate length of the field effect transistor
Analyzing
the results obtained, we conclude that the thickness of the base of
the bipolar transistor (Wb
= 0,446 µm) is significantly less than the gate length of the
field-effect transistor (Lg
= 1,989 µm), namely: the thickness of the base of the bipolar
transistor is 1,989/0,446
5 times less than the gate length of the field-effect transistor.
This is due to the fact that the rate of carrier diffusion through the base of a bipolar transistor is significantly less than the rate of carrier drift under the gate of a field-effect transistor.
1.4 Calculation of the angle of flight of a bipolar transistor
The angle of flight of a bipolar transistor is calculated by the following formula [23]:
=
(27)
where – the diffusion time of charge carriers through the base of a bipolar transistor.
The diffusion time of charge carriers through the base can be represented as follows, using the formula (27):
=
=
(28)
Using the formula for the thickness of the base (24):
Wb
=
=
Hence, the formula for the angle of flight of a bipolar transistor:
=
=
= 0,9998 rad
1 rad
1.5 Calculation of the angle of flight of a field-effect transistor
Let 's estimate the angle of flight of a field - effect transistor using the following formula [23]:
=
=
=
(29)
where L – gate length; vS = 105 m/s - saturation rate.
From here, we calculate the angle of flight of the field-effect transistor by the formula (29):
=
=
=
0,9998 rad
1 rad
2. Let's compare the advantages and disadvantages of using HEMT devices and transistors with ballistic transport in the microwave range. Calculate the thickness of the high-alloyed HEMT region. Let's estimate the distance by which an electron can shift from the equilibrium position in this layer at T = 300 K
2.1 Advantages and disadvantages of hemt (High Electron Mobility Transistor)
Picture 29 – HEMT structure
Picture 29 shows the HEMT structure in cross section. An unalloyed GaAs buffer layer is grown on a semi-insulating gallium arsenide (GaAs) substrate. A thin semiconductor layer with a different band gap (InGaAs) is built up on this layer, such that a region of two-dimensional electron gas is formed. The top layer is protected by a thin spacer based on aluminum-gallium arsenide (AlGaAs). The silicon-doped layer of n-AlGaAs and the heavily doped layer of n+-GaAs under the contact pads of the drain and source follow above. The gate contact is close to the region of a two-dimensional electron gas [24].
Describing the principle of operation of HEMT, we can say that HEMT uses the properties of a heterojunction formed by thin single-crystal layers of two semiconductor materials with a similar crystal structure, but different band gap width. There are quite a few analogues of GaAs semiconductor materials that have a crystal lattice step close to GaAs. This makes it possible to use GaAs as a basis for creating a wide class of heterostructural transistors with their own unique characteristics.
In HEMT, the GaAs – AlXGa1-XAs heterojunction is most often used as a heterojunction. At the same time, the value of x shows the relative content of Al. With the growth of x, the width of the forbidden zone ∆E increases smoothly [24].
Picture 30 – Equilibrium energy diagram of the heterojunction
Note that alloying impurities are used to create conductivity in semiconductors. However, the resulting conduction electrons experience collisions with impurity cores, which negatively affects the mobility of carriers and the speed of the device. In HEMT, this is avoided due to the fact that electrons with high mobility are generated at a heterojunction in the contact area of a high-alloyed N-type donor layer with a wide band gap (AlGaAs) and an unalloyed channel layer with a narrow band gap without any alloying impurities (GaAs).
The electrons formed in the thin N-type layer completely move into the GaAs layer, impoverishing the AlGaAs layer. Depletion occurs due to the bending of the potential barrier in the heterojunction, that is, a quantum well is formed between semiconductors with different band gap widths. Thus, the electrons are able to move quickly without collisions with impurities in the unalloyed GaAs layer. A very thin layer is formed with a large concentration of high mobility electrons having the properties of a two-dimensional electron gas. The resistance of the channel is very low, and the mobility of carriers in it is high.
Due to the good correspondence of GaAs and AlGaAs crystal lattices, a low density of surface states and defects is ensured in the heterojunction. For these reasons, for electrons accumulated in the region of a two-dimensional electron gas, a very high mobility is achieved in weak electric fields, close to the bulk mobility for unalloyed GaAs (approximately 8·103 cm2/V·s at Т = 300 K). Moreover, this mobility increases sharply with a decrease in temperature, since scattering on the lattice prevails in undoped GaAs [24].
Thus, an important advantage of HEMT, in comparison with the structure of metal-semiconductor transistors, is the lower density of surface states at the boundary between AlGaAs and the dielectric, and the greater height of the Schottky barrier (about 1 V). Due to the lower density of surface states, the negative surface charge and the thickness of depleted regions in the source — gate and gate — drain intervals decrease. This makes it possible to obtain less parasitic resistances of depleted areas. Due to the higher height of the Schottky barrier, a higher (up to 0,8 V) forward voltage Ugs is possible for HEMT devices, which is especially important for normally closed transistors, the operating voltages at the gates of which can vary only in a narrow range limited from above by the voltage of the metal —semiconductor control junction. Also, HEMT is characterized by a low noise level at high frequencies [24].
At the same time, the disadvantages of GaAs transistors include low breakdown voltage, low power density, low permissible operating temperature. The latter drawback is extremely significant, since it requires a very careful design of the heat sink system, which often becomes a critical factor for high-power amplifiers.
However, these disadvantages are devoid of GaN HEMT, and today GaN HEMT have serious competition with GaAs due to a more compact design and light weight, low power consumption, extended temperature range, high reliability and the highest linearity in the industry [25].
Picture 31 – HEMT structure on GaN
Devices on GaN are capable of operating in a wider frequency range, at higher temperatures, as well as with higher output power compared to devices on Si, GaAs, SiC.
The advantages of HEMT on GaN also include [25]:
1. Record specific density of output power (at f = 2 GHz POUT =170 W; at f = 10 GHz POUT = 14 W).
2. High operating temperature (theoretically ~ 600 °C, in reality up to 400°C);
3. Low noise level in the frequency range 1 – 25 GHz;
4. The possibility of creating hybrid and monolithic chips on GaN transistors.
5. High performance of GaN transistors at low frequencies.