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== Abstract ==<br>
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[[Category:Projects]]
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* Members: Jiayue Liang, Zicong Wen<br>
+
[[Category:Final Year Projects]]
−
* Supervisor: Prf. Nelson Tansu<br>
+
[[Category:2021s1|13482]]
 +
In telecommunications, 6G is the 6th generation standard for telecommunication that is currently under research and development for wireless communication technologies for supporting cellular data networks. It is the successor of the 5G network and will be significantly faster. The development of 6G communication technologies requires new devices that will access into Terahertz spectral range.
 +
 
 +
== Introduction ==
 +
Compared to 5G, the most outstanding difference between 5G and 6G is that 6G communication technology will access into Terahertz(THz) spectral range. To access the terahertz frequency spectral, we need electronic devices that can operate in the terahertz frequency environment. Some high-speed electronic devices such as High Electron Mobility Transistor (HEMT) has already been used at the top edge of the communication devices, and the result is successful. However, other high-speed electronic devices such as Heterogeneous Bipolar Transistors (HBTs), Resonance Tunneling Diodes (RTDs) have even better high-frequency performance.
 +
 
 +
=== Project team ===
 +
==== Project students ====
 +
* Zicong Wen - responsible for HBT
 +
* Jiayue Liang - responsible for RTD
 +
 
 +
==== Supervisors ====
 +
* Professor Nelson Tansu
 +
 
 +
=== Objectives ===
 +
This project aims to research electronic devices that can support the 6G wireless telecommunication technology standard and analyse the frequency performance of the researched devices. Two devices were researched in this project, Heterogeneous Bipolar Transistor and Resonance Tunnelling Diode
 +
 
 +
== Background ==
 +
=== 6G Requirements ===
 +
As 5G initiated, many organizations have already defined the 6G system in various ways. A difference that distinguishes 6G telecommunication technology from its predecessors is that 6G technology can access into Terahertz frequency range. The development of 6G technology does not only mean the revolution of telecommunication technology, it also means the speed of wireless data transmission technology will be progressed significantly. The following table shows the comparison of 4G, 5G and 6G network systems [1].
 +
{| class="wikitable"
 +
|+ Key requirements of 5G, beyond 5G and 6G network systems
 +
|-
 +
! '''KPI''' !! 5G !! Beyond 5G !! 6G
 +
|-
 +
| Operating frequency bandwidth || Sub-6 GHz Mm-Wave for fixed access  || Sub-6 GHz Mm-Wave for fixed access || Sub-6 GHz Mm-Wave for mobile access
 +
Exploration for higher frequency and THz bands
 +
|-
 +
| Rate requirements || 1Gb/s || 100Gb/s || 1Tb/s
 +
|}
 +
 
 +
==== Heterostructures ====
 +
[[File:Heterojunctions.png|thumb|Three types of semiconductor heterojunctions. Type (a), straddling heterojunction, type (b) staggered heterojunction, and type (c) broken-gap heterojunction.Page text.<ref>T. Ihn, "ch. 5.1 Band engineering". Semiconductor Nanostructures Quantum States and Electronic Transport. United States of America: Oxford University Press, 2010.</ref>]]
 +
Different semiconductors have distinctive band structures, the interface between dissimilar semiconductors layers with unequal band gaps build a heterojunction. And a heterostructure is the combination of multiple heterojunctions.
 +
Due to its unique characteristic, the heterostructure is used widely in specialized applications. Two of the applications are focused on, Heterogeneous Bipolar Transistor and Resonant Tunneling Diode.
 +
 
 +
== Method ==
 +
===Resonant Tunneling Diode (RTD)===
 +
RTD is one type of diode based on the quantum mechanical phenomenon, resonant tunnelling. The electrons can flow through the energy barriers with some probability, which is impossible in classical physics. And the tunnelling can happen in an instant. Its IV graph also indicates its negative resistance characteristic. Due to these features, RTD can operate over the THz theoretically.
 +
[[File:RTD_structure.png|100px|thumb]]
 +
<br>
 +
====Structures and Materials====
 +
Resonant tunnelling diode is one of the applications based on the resonant tunnelling phenomenon. The figure is the case of a typical double-barriers structure RTD. The undoped materials sandwich the middle undoped layer to form a quantum well. The barriers are in the same material and different from the well. undoped. The conducting layers are in the same materials as the quantum well, but heavily n-type doped.
 +
The combinations of the semiconductor materials that were used in the project are in the table below.
 +
{| class="wikitable"
 +
|-
 +
! Barriers !! Well !! Potential height (eV) !! Effective mass (Barrier)(kg) !! Effective mass (Well)(kg) !! Density of state (cm<sup>-3</sup>)
 +
|-
 +
| Ga<small>0.47</small>In<sub>0.53</sub>As || InAs || 0.27 || 0.041•m<sub>0</sub> || 0.023•m<sub>0</sub> || 8.7×10<sup>16</sup>
 +
|-
 +
| Al<small>0.3</small>Ga<sub>0.7</sub>As || GaAs || 0.297 || 0.0879•m<sub>0</sub> || 0.063•m<sub>0</sub> || 4.7×10<big>17</big>
 +
|-
 +
| Al<small>0.72</small>Ga<sub>0.28</sub>N || GaN || 1.3 || 0.258•m<sub>0</sub> || 0.15•m<sub>0</sub> || 1.2×10<sup>18</sup>
 +
|}
 +
 
 +
[[File:Matrix formulation.png|thumb|The matrix formulation describes a wave function that travels through a double-barrier structure.]]
 +
 
 +
====Transmission Coefficient====
 +
The quantum levels in the quantum well where if the incident electrons have the energy level close to them, the tunnelling probability can approach unity. In order to analyse the tunnelling properties, the matrix formulation is taken in this project which is cited from the book written by Prof. Nelson Tansu.<ref>N. Tansu, "Ch.7: Numerical Formulation of Schrodinger's Wave Equation". Applied Quantum Mechanics for Engineers.</ref> This method treats the potentials to be discrete potential functions and assign them into regions. And the 1-D Schrödinger wave equations are used to find the numerical solution. This method is feasible also for the double barriers with a bias voltage applied.
 +
 
 +
====Current Charactoristic====
 +
If there is no voltage applied on each side of RTD, the electrons are incident both from left and right due to the symmetrical structure. When a small voltage is applied, the electrons from the left can tunnel through the first resonant quantum level and a current occurs. The Fermi level of the left side is equal to the quantum level and the tunnelling probability reaches a maximum, which corresponds to a peak current J<sub>P</sub> in the I-V figure. When a larger voltage is applied, the energy band of the left is higher than the resonant quantum level, and the current flows have a significant drop as the b-c interval. The negative differential resistance (NDR) happens as the current drops along the voltage is increasing. The current drop will reach a minimum spot when the coming energy band is located in middle between the quantum levels, which is the current valley J<sub>V</sub>. And as the bias voltage applied raises, the energy band will approach the second quantum level, the current increase again. This process repeats if there are more quantum levels in the quantum well.
 +
 
 +
===Heterogeneous Bipolar Transistors (HBT)===
 +
Bipolar Junction Transistor (BJT) has dominated the electronic world for a very long time. It is a good, effective semiconductor that is widely used in many applications. However, with the rapid development of the 6G technology, BJT is no longer fulfilling the demand for extremely high transmitting speed. Hence, introducing HBT can enable devices to work in the terahertz environment so that the speed of the device is improved.
 +
====Material used====
 +
The following table shows the key material parameters for the heterojunction in the project.
 +
{| class="wikitable"
 +
|+ style="text-align: center;" | Key material parameters for the Heterojunction
 +
|-
 +
! '''Device''' !! '''Bandgap difference (ᐃE<sub>g</sub>)''' !!'''Base material'''!! '''Electron mobility in base region (cm^2*V^-1*s^-1)'''
 +
|-
 +
| '''Si/SiGe HBT''' || 0.08 eV|| SiGe|| ≤700
 +
|-
 +
| '''AlGaAs/GaAs HBT''' || 0.374 eV|| GaAs|| ≈8500
 +
|-
 +
| '''InGaAs/InP HBT''' || 0.604 eV|| InGaAs|| ≤1200
 +
|-
 +
| '''InGaAs/InSb HBT''' || 0.74 eV|| InSb|| ≤77000
 +
|-
 +
|}
 +
 
 +
====Current Components====
 +
[[File:Current component of an NPN transistor.jpg|thumb|Figure 1: Current components of an NPN transistor [1]]]
 +
Figure 1 [1] is a model of the current components of an NPN transistor, it is applicable for either BJT and HBT. The description of these components is given as the following:
 +
* I<sub>nE</sub>: Electron diffusion current injected at the EB junction
 +
* I<sub>pE</sub>: Hole diffusion current injected at the EB junction
 +
* I<sub>B</sub>: Base current
 +
* I<sub>C</sub>: Collector current
 +
* I<sub>E</sub> = I<sub>nE</sub> + I<sub>pE</sub>
 +
* I<sub>E</sub> = I<sub>B</sub> + I<sub>C</sub>
 +
<br>
 +
Therefore, the DC parameters of HBT can be calculated using these relationships.<br>
 +
 
 +
====Transistor parameters====
 +
The following parameters are essential to study and evaluate the characteristics of a transistor.
 +
# Emitter Injection Efficiency: Emitter injection efficiency defines the efficiency of the majority carrier injects from base to emitter. It is the quotient of the I<sub>C</sub> and I<sub>nE</sub>.
 +
# Base transpose factor: The base transpose factor is defined as the base current that requires transferring the emitter current to the collector current. It is the quotient of the I<sub>nE</sub> and I<sub>E</sub>.
 +
# Current transpose factor: Current transpose factor represents the emitter-to-collector current amplification, it is also known as the common-base current gain. It is the product of the emitter injection efficiency and the base transpose factor.
 +
# Amplification factor: The Amplification factor is defined as the ratio of the collector current to the base current. It is also known as common-emitter current gain. It is the quotient of the I<sub>C</sub> and I<sub>B</sub>.
 +
 
 +
====Frequency Response====
 +
Frequency response is an important parameter that demonstrates the performance of the device in the frequency environment. The cut-off frequency is an indicator in a frequency response diagram at which the power of the system begins to be reduced. It usually corresponds to the frequency that is 3 dB less than the initial gain, which is -3 dB in this case. The reason why choosing -3 dB as the standard for cut-off frequency is that reaching 3 dB means the output current is two times less than the input current.
 +
 
 +
== Results & Discussion ==
 +
 
 +
===Resonance Tunneling Diode===
 +
<br>
 +
<br>
 +
<br>
 +
 
 +
===Heterogeneous Bipolar Transistor===
 +
The result of the HBT simulation will be demonstrated in two parts. The first part demonstrates the DC characteristics and frequency performance of BJT and HBTs. The second part demonstrates how the size of the base width of the devices affects the frequency performance.
 +
 
 +
====DC characteristics and frequency performance of BJT and HBTs====
 +
 
 +
{| class="wikitable"
 +
|+ style="text-align: center;" | Simulation results of the BJT and HBT (Base Width = 1 micormetre)
 +
|-
 +
! '''Device''' !! '''Emitter injection efficiency''' !! '''Base transpose factor''' !! '''Current transpose factor''' !! '''Amplification factor''' !! '''Cut-off frequency'''
 +
|-
 +
| '''BJT''' || 0.99123 || 0.9958 || 0.99119|| 112.48|| 248.75 MHz
 +
|-
 +
| '''Si/SiGe HBT''' || 1|| 0.99307|| 0.99307|| 142.32|| 437.33 MHz
 +
|-
 +
| '''AlGaAs/GaAs HBT''' || 1|| 0.99984 || 0.99984 || 6209.1|| 2.3471 GHz
 +
|-
 +
| '''InGaAs/InP HBT''' || 1|| 0.99995|| 0.99995|| 19989|| 3.2977 GHz
 +
|-
 +
| '''InGaAs/InSb HBT''' || 1|| 0.99998|| 0.99998|| 44025|| 10.582 GHz
 +
|-
 +
|}
 +
<br>
 +
It is obvious that introducing the heterojunction to transistors improves the emitter injection efficiency and the base transpose factor. Moreover, when the energy bandgap between the two semiconductors is getting bigger, the base transpose factor is getting closer to 1. This also leads to the current transpose factor equal to the base transpose factor due to the current transpose factor being the product of the emitter injection efficiency and the base transpose factor. The current amplification factors of the HBT simulations are generally higher than BJT
 +
 
 +
====Size of the base region====
 +
{| class="wikitable"
 +
|+ style="text-align: center;" | Frequency performance of the HBT with different base width
 +
|-
 +
! '''Device''' !! '''1 micrometre base width''' !! 45 nanometre base width
 +
|-
 +
| '''Si/SiGe HBT''' || 437.33 MHz|| 67.532 GHz
 +
|-
 +
|  '''AlGaAs/GaAs HBT'''  || 2.3471 GHz|| 1.1535 THz
 +
|-
 +
| '''InGaAs/InP HBT'''  || 3.2977 GHz|| 1.6285 THz
 +
|-
 +
| '''InGaAs/InSb HBT'''|| 10.582 GHz|| 5.2247 THz
 +
|-
 +
|}
 +
 
 +
When the base width is 1 micrometre, the devices are not able to work under a terahertz frequency environment. However, when the base width of the device is decreased to 45 nanometres, InGaAs/InP and InGaAs/InSb HBTs can work under terahertz frequency. The frequency simulation of the InGaAs/InSb HBT indicates it is even feasible to work under 5-terahertz environments. Therefore, as the width of the base decreases, the devices have a higher cut-off frequency, which means they can operate in a higher frequency environment.
 +
 
 +
====Overall comparison====
 +
The following table shows the comparison of the bandgap difference between Emitter and base versus the amplification factor, and the base electron mobility versus the cut-off frequency.
 +
 
 +
{| class="wikitable"
 +
|+ style="text-align: center;" | Bandgap difference VS Amplification factor and Base electron mobility VS cut-off frequency
 +
|-
 +
! '''Device''' !! '''Bandgap difference (ᐃE<sub>g</sub>)'''!!'''Amplification factor''' !!'''Base material'''!! '''Electron mobility in base region (cm^2*V^-1*s^-1)'''!!'''Cut-off frequency (Base width = 1 micrometre)'''
 +
|-
 +
| '''Si/SiGe HBT''' || 0.08 eV||143.32|| SiGe|| ≤700 ||  437.44 MHz
 +
|-
 +
| '''AlGaAs/GaAs HBT''' || 0.374 eV||6209.1|| GaAs|| ≈8500 || 2.3471 GHz
 +
|-
 +
| '''InGaAs/InP HBT''' || 0.604 eV||19989|| InGaAs|| ≤1200 || 3.2977 GHz
 +
|-
 +
| '''InGaAs/InSb HBT''' || 0.74 eV||44025|| InSb|| ≤77000 || 10.582 GHz
 +
|-
 +
|}
 +
According to this table, as the energy bandgap difference increases, the current amplification factors increases exponentially. Also, the cut-off frequency is proportional to the mobility of the electron in the base region.
 +
 
 +
== References ==
 +
[1] W. Saad, M. Bennis and M. Chen, "A Vision of 6G Wireless Systems: Applications, Trends, Technologies, and Open Research Problems," in IEEE Network, vol. 34, no. 3, pp. 134-142, May/June 2020, doi: 10.1109/MNET.001.190028
 +
 
 +
[2] ...

Latest revision as of 17:13, 25 October 2021

In telecommunications, 6G is the 6th generation standard for telecommunication that is currently under research and development for wireless communication technologies for supporting cellular data networks. It is the successor of the 5G network and will be significantly faster. The development of 6G communication technologies requires new devices that will access into Terahertz spectral range.

Introduction

Compared to 5G, the most outstanding difference between 5G and 6G is that 6G communication technology will access into Terahertz(THz) spectral range. To access the terahertz frequency spectral, we need electronic devices that can operate in the terahertz frequency environment. Some high-speed electronic devices such as High Electron Mobility Transistor (HEMT) has already been used at the top edge of the communication devices, and the result is successful. However, other high-speed electronic devices such as Heterogeneous Bipolar Transistors (HBTs), Resonance Tunneling Diodes (RTDs) have even better high-frequency performance.

Project team

Project students

  • Zicong Wen - responsible for HBT
  • Jiayue Liang - responsible for RTD

Supervisors

  • Professor Nelson Tansu

Objectives

This project aims to research electronic devices that can support the 6G wireless telecommunication technology standard and analyse the frequency performance of the researched devices. Two devices were researched in this project, Heterogeneous Bipolar Transistor and Resonance Tunnelling Diode

Background

6G Requirements

As 5G initiated, many organizations have already defined the 6G system in various ways. A difference that distinguishes 6G telecommunication technology from its predecessors is that 6G technology can access into Terahertz frequency range. The development of 6G technology does not only mean the revolution of telecommunication technology, it also means the speed of wireless data transmission technology will be progressed significantly. The following table shows the comparison of 4G, 5G and 6G network systems [1].

Key requirements of 5G, beyond 5G and 6G network systems
KPI 5G Beyond 5G 6G
Operating frequency bandwidth Sub-6 GHz Mm-Wave for fixed access Sub-6 GHz Mm-Wave for fixed access Sub-6 GHz Mm-Wave for mobile access

Exploration for higher frequency and THz bands

Rate requirements 1Gb/s 100Gb/s 1Tb/s

Heterostructures

Three types of semiconductor heterojunctions. Type (a), straddling heterojunction, type (b) staggered heterojunction, and type (c) broken-gap heterojunction.Page text.[1]

Different semiconductors have distinctive band structures, the interface between dissimilar semiconductors layers with unequal band gaps build a heterojunction. And a heterostructure is the combination of multiple heterojunctions. Due to its unique characteristic, the heterostructure is used widely in specialized applications. Two of the applications are focused on, Heterogeneous Bipolar Transistor and Resonant Tunneling Diode.

Method

Resonant Tunneling Diode (RTD)

RTD is one type of diode based on the quantum mechanical phenomenon, resonant tunnelling. The electrons can flow through the energy barriers with some probability, which is impossible in classical physics. And the tunnelling can happen in an instant. Its IV graph also indicates its negative resistance characteristic. Due to these features, RTD can operate over the THz theoretically.

RTD structure.png


Structures and Materials

Resonant tunnelling diode is one of the applications based on the resonant tunnelling phenomenon. The figure is the case of a typical double-barriers structure RTD. The undoped materials sandwich the middle undoped layer to form a quantum well. The barriers are in the same material and different from the well. undoped. The conducting layers are in the same materials as the quantum well, but heavily n-type doped. The combinations of the semiconductor materials that were used in the project are in the table below.

Barriers Well Potential height (eV) Effective mass (Barrier)(kg) Effective mass (Well)(kg) Density of state (cm-3)
Ga0.47In0.53As InAs 0.27 0.041•m0 0.023•m0 8.7×1016
Al0.3Ga0.7As GaAs 0.297 0.0879•m0 0.063•m0 4.7×1017
Al0.72Ga0.28N GaN 1.3 0.258•m0 0.15•m0 1.2×1018
The matrix formulation describes a wave function that travels through a double-barrier structure.

Transmission Coefficient

The quantum levels in the quantum well where if the incident electrons have the energy level close to them, the tunnelling probability can approach unity. In order to analyse the tunnelling properties, the matrix formulation is taken in this project which is cited from the book written by Prof. Nelson Tansu.[2] This method treats the potentials to be discrete potential functions and assign them into regions. And the 1-D Schrödinger wave equations are used to find the numerical solution. This method is feasible also for the double barriers with a bias voltage applied.

Current Charactoristic

If there is no voltage applied on each side of RTD, the electrons are incident both from left and right due to the symmetrical structure. When a small voltage is applied, the electrons from the left can tunnel through the first resonant quantum level and a current occurs. The Fermi level of the left side is equal to the quantum level and the tunnelling probability reaches a maximum, which corresponds to a peak current JP in the I-V figure. When a larger voltage is applied, the energy band of the left is higher than the resonant quantum level, and the current flows have a significant drop as the b-c interval. The negative differential resistance (NDR) happens as the current drops along the voltage is increasing. The current drop will reach a minimum spot when the coming energy band is located in middle between the quantum levels, which is the current valley JV. And as the bias voltage applied raises, the energy band will approach the second quantum level, the current increase again. This process repeats if there are more quantum levels in the quantum well.

Heterogeneous Bipolar Transistors (HBT)

Bipolar Junction Transistor (BJT) has dominated the electronic world for a very long time. It is a good, effective semiconductor that is widely used in many applications. However, with the rapid development of the 6G technology, BJT is no longer fulfilling the demand for extremely high transmitting speed. Hence, introducing HBT can enable devices to work in the terahertz environment so that the speed of the device is improved.

Material used

The following table shows the key material parameters for the heterojunction in the project.

Key material parameters for the Heterojunction
Device Bandgap difference (ᐃEg) Base material Electron mobility in base region (cm^2*V^-1*s^-1)
Si/SiGe HBT 0.08 eV SiGe ≤700
AlGaAs/GaAs HBT 0.374 eV GaAs ≈8500
InGaAs/InP HBT 0.604 eV InGaAs ≤1200
InGaAs/InSb HBT 0.74 eV InSb ≤77000

Current Components

Figure 1: Current components of an NPN transistor [1]

Figure 1 [1] is a model of the current components of an NPN transistor, it is applicable for either BJT and HBT. The description of these components is given as the following:

  • InE: Electron diffusion current injected at the EB junction
  • IpE: Hole diffusion current injected at the EB junction
  • IB: Base current
  • IC: Collector current
  • IE = InE + IpE
  • IE = IB + IC


Therefore, the DC parameters of HBT can be calculated using these relationships.

Transistor parameters

The following parameters are essential to study and evaluate the characteristics of a transistor.

  1. Emitter Injection Efficiency: Emitter injection efficiency defines the efficiency of the majority carrier injects from base to emitter. It is the quotient of the IC and InE.
  2. Base transpose factor: The base transpose factor is defined as the base current that requires transferring the emitter current to the collector current. It is the quotient of the InE and IE.
  3. Current transpose factor: Current transpose factor represents the emitter-to-collector current amplification, it is also known as the common-base current gain. It is the product of the emitter injection efficiency and the base transpose factor.
  4. Amplification factor: The Amplification factor is defined as the ratio of the collector current to the base current. It is also known as common-emitter current gain. It is the quotient of the IC and IB.

Frequency Response

Frequency response is an important parameter that demonstrates the performance of the device in the frequency environment. The cut-off frequency is an indicator in a frequency response diagram at which the power of the system begins to be reduced. It usually corresponds to the frequency that is 3 dB less than the initial gain, which is -3 dB in this case. The reason why choosing -3 dB as the standard for cut-off frequency is that reaching 3 dB means the output current is two times less than the input current.

Results & Discussion

Resonance Tunneling Diode




Heterogeneous Bipolar Transistor

The result of the HBT simulation will be demonstrated in two parts. The first part demonstrates the DC characteristics and frequency performance of BJT and HBTs. The second part demonstrates how the size of the base width of the devices affects the frequency performance.

DC characteristics and frequency performance of BJT and HBTs

Simulation results of the BJT and HBT (Base Width = 1 micormetre)
Device Emitter injection efficiency Base transpose factor Current transpose factor Amplification factor Cut-off frequency
BJT 0.99123 0.9958 0.99119 112.48 248.75 MHz
Si/SiGe HBT 1 0.99307 0.99307 142.32 437.33 MHz
AlGaAs/GaAs HBT 1 0.99984 0.99984 6209.1 2.3471 GHz
InGaAs/InP HBT 1 0.99995 0.99995 19989 3.2977 GHz
InGaAs/InSb HBT 1 0.99998 0.99998 44025 10.582 GHz


It is obvious that introducing the heterojunction to transistors improves the emitter injection efficiency and the base transpose factor. Moreover, when the energy bandgap between the two semiconductors is getting bigger, the base transpose factor is getting closer to 1. This also leads to the current transpose factor equal to the base transpose factor due to the current transpose factor being the product of the emitter injection efficiency and the base transpose factor. The current amplification factors of the HBT simulations are generally higher than BJT

Size of the base region

Frequency performance of the HBT with different base width
Device 1 micrometre base width 45 nanometre base width
Si/SiGe HBT 437.33 MHz 67.532 GHz
AlGaAs/GaAs HBT 2.3471 GHz 1.1535 THz
InGaAs/InP HBT 3.2977 GHz 1.6285 THz
InGaAs/InSb HBT 10.582 GHz 5.2247 THz

When the base width is 1 micrometre, the devices are not able to work under a terahertz frequency environment. However, when the base width of the device is decreased to 45 nanometres, InGaAs/InP and InGaAs/InSb HBTs can work under terahertz frequency. The frequency simulation of the InGaAs/InSb HBT indicates it is even feasible to work under 5-terahertz environments. Therefore, as the width of the base decreases, the devices have a higher cut-off frequency, which means they can operate in a higher frequency environment.

Overall comparison

The following table shows the comparison of the bandgap difference between Emitter and base versus the amplification factor, and the base electron mobility versus the cut-off frequency.

Bandgap difference VS Amplification factor and Base electron mobility VS cut-off frequency
Device Bandgap difference (ᐃEg) Amplification factor Base material Electron mobility in base region (cm^2*V^-1*s^-1) Cut-off frequency (Base width = 1 micrometre)
Si/SiGe HBT 0.08 eV 143.32 SiGe ≤700 437.44 MHz
AlGaAs/GaAs HBT 0.374 eV 6209.1 GaAs ≈8500 2.3471 GHz
InGaAs/InP HBT 0.604 eV 19989 InGaAs ≤1200 3.2977 GHz
InGaAs/InSb HBT 0.74 eV 44025 InSb ≤77000 10.582 GHz

According to this table, as the energy bandgap difference increases, the current amplification factors increases exponentially. Also, the cut-off frequency is proportional to the mobility of the electron in the base region.

References

[1] W. Saad, M. Bennis and M. Chen, "A Vision of 6G Wireless Systems: Applications, Trends, Technologies, and Open Research Problems," in IEEE Network, vol. 34, no. 3, pp. 134-142, May/June 2020, doi: 10.1109/MNET.001.190028

[2] ...

  1. ↑ T. Ihn, "ch. 5.1 Band engineering". Semiconductor Nanostructures Quantum States and Electronic Transport. United States of America: Oxford University Press, 2010.
  2. ↑ N. Tansu, "Ch.7: Numerical Formulation of Schrodinger's Wave Equation". Applied Quantum Mechanics for Engineers.
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