3.4 Diamond (c) usage trend

According to the combination of the most important parameters for electronic devices, diamond can be considered the most promising.

Diamond has a cubic crystal structure with strong covalent bonds of carbon atoms and with a record high atomic density of 1,76⋅10²³ cm^-3. This property determines many features of the diamond. With a band gap of 5,45 eV, the resistivity of an unalloyed diamond is 10¹³–10¹⁴ ⋅cm, the electron mobility is 2000 cm²/V⋅s. The breakdown field reaches 10⁷ V/cm. Diamond is extremely stable chemically, insoluble in hydrochloric, sulfuric and nitric acids. In the presence of oxygen, diamond is oxidized (etched) at temperatures above 600°С. However, the downside of the high inertia and hardness of diamond is serious problems associated with its processing [35].

Diamond has a record thermal conductivity among all known materials, namely: 2200 W/m⋅K at room temperature. This is due to its record-high Debye temperature Т_D = 1860 K, due to which the room temperature is «low» with respect to the dynamics of the diamond lattice. As a result, diamond can serve as an «ideal» heat-trapping dielectric substrate.

In addition, diamond is a radiation-resistant material. It is transparent in a wide range of the spectrum (from ultraviolet to radio wave), has a high hardness (81 – 100 GPa), a record high speed of sound propagation (18 km/s), low dielectric constant (ε = 5,5). Due to such unique properties, diamond is promising for use as heat-dissipating plates in microwave transistors and in semiconductor lasers [35].

Due to the uniquely high thermal conductivity (five times higher than that of copper), miniature heat-trapping substrates made of natural and technical single crystals of diamond have found application in avalanche-span diodes and laser diodes, allowing them to increase their power and reliability.

Also, theoretical calculations have shown that the power of MESFET transistors on diamond in the frequency range of 5-100 GHz should be 30 times higher than that of a GaAs transistor, and about four times higher than that of a silicon carbide transistor. However, despite many years of efforts to implement electronic devices on diamond, its potential as a material for the formation of active electronic devices is still not used enough. This is primarily due to the complexity of its alloying, especially with n-type impurities. The only reliable alloying impurity – boron, forms a deep acceptor level with an activation energy of Е_а = 0,37 eV. The donor nitrogen level – 1,7 eV, is even deeper and cannot be activated at room temperature [35].

4. Input and output volt-ampere characteristics of three SBGFET (Schottky Barrier Gate Field Effect Transistor) with the same size, doping level, but made of Si, GaN, GaAs. Justification of dependencies. Explanation of how the characteristics will change if the gate width is increased

4.1 Input and output volt-ampere characteristics of three sbgfet with the same size, doping level, but made of Si, GaN, GaAs

Picture 32 – Input voltage-ampere characteristic of SBGFET of different materials

With a negative voltage U_cut the drain current I_d  0, with a positive voltage of the order of _k a maximum is observed on the dependence. A further increase in voltage leads to a drop in the drain current caused by a branch of the source current to the gate. This corresponds to the phenomenon of current distribution in a triode when a positive potential is applied to the grid. In this case, the gate current occurs when the voltage _k and the voltage drop U_S are compensated on the «parasitic» resistive source-gate region: U_S  I_SR_S. At the same time, the depleted layer disappears at the extreme point of the gate closest to the source. As the positive voltage at the gate increases, the depletion region shifts towards the drain [27].

The cutoff voltage is defined by the following expression [36]:

U_cut = U_Schottky – U_K = U_Shot – (33)

where U_Schottky – Schottky barrier voltage; N_d – concentration of donor impurity; d_k – the depth of the impurity in the subcutaneous region; – dielectric constant of a semiconductor.

That is, we conclude that when comparing three SBGFETS with the same size, doping level, but made of Si, GaN and GaAs, the values of the cut-off voltage for each of the three materials is determined by the value of the dielectric constant: the lower the value of the dielectric constant of the material, the lower the value of the negative gate voltage must be applied before reaching the value of the drain current I_d = 0. So, Si has a permittivity value equal to = 11,7; GaN - = 10,4; GaAs - = 12,7.

Picture 33 – Output voltage-ampere characteristic of SBGFET of different materials

The linear region exists at low voltage values when the device has not yet reached saturation. The linear domain is characterized by a linear relationship between current and voltage, that is, Ohm's law is fulfilled. However, when the U_ds reaches the saturation voltage of U_dssat, the channel at the end of the gate on the drain side narrows, that is, it almost completely closes, so that no further increase in current occurs – the saturation area. That is, when the drain current increases, the voltage drop in the channel increases, which leads to a narrowing of the current channel and causes a decrease in current. With a further increase in the voltage at the U_ds drain, a breakdown of the transistor may occur, while the breakdown voltage directly depends on the value of the band gap width.

Let's write down the expression for the drain current on the linear section of the output volt-ampere characteristic of the transistor [37]:

(30)

where I₀ = Zµe²N_D²a³/6 L – channel cutoff current (µ - mobility of charge carriers).

That is, the slope of the initial section of the volt-ampere characteristic depends on the mobility of the charge carriers µ: for Si - µ = 1300 cm²/V s; for GaN - µ = 1500 cm²/V s; for GaAs - µ = 5000 cm²/V s. That is, the greatest slope of the initial section will be observed in GaAs, which is depicted on the output of volt-ampere characteristic the transistor (picture 33).

At the same time, the value of the breakdown voltage is calculated according to the following formula [37]:

= (34)

where – width of the bandgap; N – impurity concentration.

Hence, we conclude that the magnitude of the breakdown voltage depends on the value of the bandgap width: for Si - =1,12 eV; for GaN - = 3,4 eV; for GaAs - = 1,42 eV. Thus, the greatest breakdown voltage will be observed at GaN.