So for an NPN transistor to conduct the collector is always more positive with respect to both the base and the emitter. To have a good n+-p-n transistor, it is preferred that almost all the electrons injected by the emitter into the base are collected. With this requirement satisfied, an average electron injected at the emitter junction will diffuse to the depletion region of the base-collector junction without recombination in the base.
HETEROJUNCTION BIPOLAR TRANSISTOR
The InGaAs device physics
For a given fT, an InGaAs HBT would only require about a third of the collector current compared to a GaAs BJT [34]. By optimizing the In profile at the bottom of an InGaAs HBT, much higher Early voltage can be achieved than in BJTs. Canceling the base-emitter heterojunction capacitance improves the inter-modulation performance of HBT compared to MESFET and HEMT.
Applications of InGaAs HBT
Due to the advantages of InGaAs HBT, such as higher current gain, early voltage, breakdown voltage and pass frequency, reduced base resistance as well as better base transport properties, performance approaching GaAs technologies can be achieved. Therefore, InGaAs technology is a very good choice for high-frequency and high-temperature electronics at competitive costs. This translates into very good high-frequency operation (values in tens to hundreds of GHz) and low leakage currents.
THE EARLY VOLTAGE AND COMMON EMITTER CURRENT GAIN Depletion layer widths of bipolar junction transistor (BJT) and the quasi-neutral regions
Narrowing the collector has no significant effect, since the collector is much longer than the base. Both factors increase the collector or "output" current of the transistor by increasing the collector voltage. In the front active region, the Early effect changes the collector current (IC) and the front common emitter (F) as usually described by the following equations [1]-[2].
THE IMPORTANCE OF EARLY VOLTAGE AND CURRENT GAIN
REVIEW OF RECENT WORKS ON EARLY VOLTAGE AND CURRENT GAIN
Zareba derived a new VA model considering field-dependent diffusivity, velocity saturation, and bandgap narrowing effects for the doped Gaussian HBT basis[14]. This model was not in closed form and was made only for the triangular germanium profile in the base. A complete closed-form analytical model of VA and β for GaAs/InGaAs/GaAs HBT with different base doping profile (uniform and exponential) and base trapezoidal/triangular/indium box profile has not yet been reported where they are considered necessary effects.
SCOPE OF DISSERTAION
In chapter one, the importance of early voltage and current gain has been discussed and recent works on VA and β have been reviewed and the rationale for conducting the research has been given. In chapter three details mathematical analysis was given to derive closed form early voltage and common emitter current gai for uniform and. In chapter four graphical representation of early voltage, current gain, cutoff frequency, internal carrier wave.
Also, the results obtained by using our models were compared with the results available in the previous research works.
DERIVATION OF MAIN EQUATIONS
Derivation of collector current density (JCO) and common emitter current gain (β)
The electron current density Jn for an arbitrary base doping concentration NB(x) for InGaAs can be derived using general transport equation provided by Van Overstraeten [30]. Diffusion part depends on gradient of electron concentration and drift part depends on electric field. Where q is the charge of electron, DnInGaAs is the diffusion coefficient, µnInGaAs is the mobility, nonInGaAs is the effective intrinsic carrier concentration for InGaAs HBT.
It is assumed that the electric field at the base-collector junction is large enough to saturate the electron velocity. LW (WB) and nonInGaAs(WB) are doping concentration and effective intrinsic carrier concentration at base-collector junction, respectively.
Early voltage
Electric field
INTRODUCTION
An algebraic equation is used to express the trapezoidal/triangular/box indium profile.VA and depends on the effective intrinsic carrier concentration (nieInGaAs), field dependent diffusion coefficient (DnInGaAs) and electric field.
DERIVATION OF THE MODEL EQUATIONS
Normalized distance along the base ( x/WB )
- Model of early voltage and current gain
- CONCLUSION
- INTRODUCTION
- RESULT AND DISCUSSIONS
- Distribution of minority carrier within the base (n ieInGaAs )
The electric field that neglects recombination in the base and takes into account the narrowing effect of the band gap is [40] [43]. And ( ) is the peak base doping concentration at the base-emitter and base-collector junction, respectively. The subscript represents the low injection value of the corresponding parameter. From (3.7b) and (3.16), the electric field distribution across the base of an InGaAs HBT becomes [57].
The value for m for uniform and exponential will be 0 and mexp.y2.α for uniform and exponential base doping profile will be 0 and 1 respectively. For arbitrary base doped HBT with arbitrary Indium profile, the collector current density can be expressed as [54] [55]. Variations of internal concentration, diffusivity, electric field, early voltage, current gain with respect to various parameters are plotted separately for uniform and exponential profiles and then plotted again on the same graph to compare the variation of both profiles.
The effective intrinsic carrier concentration distribution (nieInGaAs) in the entire base region for uniform and exponential base doping is shown from Figures 4.1a to Figures 4.1c for a fixed value of yC and yE (yE remains 0.01 and yC is considered for two values of 0.01 and 0.5). For the same value of yC and yE, it can be seen in Figure 4.1a that the value of nieInGaAs does not change for a uniform basic doping profile in the base region, but increases exponentially towards the base-collector junction when yE and yC are not equal (for yE=0, 01 and yC=0.5). Again from Figure 4.1b it can be seen that for the exponential base doping profile, when yC and yE are equal, the nieInGaAs gradually decreases towards the base-collector junction, but when yC and yE are not equal (for yC=0.5 and yE=0 ,01) nieInGaAs. The relative variation for both profiles can be seen in Figure 4.1c. At exponential base doping for small values of yC (yC=.01) nieInGaAs is maximum at the base-emitter junction and then gradually decreases towards the base-collector junction, but at large values of yC (yC=0.5) nieInGaAs is minimum at the junction base-emitter and then increases exponentially towards the base-collector junction.
For uniform base doping for the same value of yC and yE, nieInGaAs remains constant, but for large values of yC (for yC=0.5) nieInGaAs increases gradually.
Base width(nm)Uniform at y
C =.01 and y E =.01
C =.5 and y E =.01
Base width(nm)Exponential at y
E =0.01 Exponential at y
Base width(nm)uniform at yC=.01 and yE =.01
From Figure 4.2c, it can be observed that nieInGaAs at the base-collector junction for uniform is much larger than exponential base-doping profile. Although BGN for uniform and exponential is the same at the base-collector junction for each yc, nieInGaAs is larger for uniform base-doping profile than exponential base-doping profile due to only difference in base-doping profile. Basedoping and BGN are both the same at the base-emitter junction for both profiles, so nieInGaAs is always the same in this junction.
Concentration at x=0 Uniform at x=W
B Exponential at x=W
Diffusivity profile
Diffusivity considering vS effect for uniform and exponential base doping profiles is shown from Figure 4.4a to Figure 4.4c.
Diffusivity(cm2/sec)
Exponential with vS
Early voltage profile
The base width, WB is 500 Å, the base-emitter junction doping peak is 1019 cm-3 and the base-collector junction doping minimum is 1017 cm-3 for exponential base doping profiles, 1019 cm-3 is considered a uniform doping profile. From equation (3.19b), it can be observed that if the effective intrinsic carrier concentration at the base-collector junction increases nieInGaAs(WB), the early voltage VA also increases. Here it is observed that with increasing yE, VA decreases exponentially for uniform and exponential base doping profiles.
As yE is increased, these results have no significant variation in nonInGaAs(WB), but it increases nonInGaAs throughout the base region. If nonInGaAs(WB) is fixed, but nonInGaAs increases in the base region while increasing yE, this decreases VA (3.19b).
Exponential doped base
Base width WB is 500 A, the peak doping at the base-emitter junction is 1019 cm-3 and the minimum doping at the base-collector junction is 1017 cm-3. Base width WB is 500Å, the peak doping at the base-emitter junction is 1019 cm-3 and the minimum doping at the base-collector junction is 1017 cm-3 for an exponential base profile and the base doping is considered to be 1019 cm-3 for a uniform base profile.
Exponential Uniform
The variation of VA with exponential coefficient mexp for the basic exponential doping profile is shown in Figure 4.7b. Doping concentration at base-collector junction for uniform doping NB (WB) =NB (0) and for exponential doping NB (WB) =NB (0)/100.
Exponential
Collector saturation current density (J CO ) and common emitter current gain ( )
Uniform with v S
Exponential with v S
Electron enters through emitter of an n-p-n transistor and due to electron-hole recombination, large fraction of electrons pass towards collector with negligible loss in the base region. When yC is small (~0.01) and yE (~0.2), the electron concentration is maximum near the base-emitter junction and gradually decreases towards the base-collector junction. While yC increases in the base-collector junction, causing JCO to increase.
After yC (~0.2), the electron concentration in the collector-base junction is greater than the base-emitter junction, causing a diffusion effect in the reverse direction of the normal electron flow from emitter to.
CONCLUSION
Here it can be observed that VA and β are highly observed in the In-mole fraction. It can be found that vS have significant influence on both JCO and diffusivity for uniform and exponential base doping profiles.
CONCLUSION
SUGGESION FOR FUTURE WORK
The HBT here was an InGaAs heterojunction bipolar transistor experiment to investigate the early voltage (VA) and current gain (β) using this model for InP, AlGaAs, etc. Sturm, “Current Gain-Early Voltage-Products in Heterojunction Bipolar Transistors with Non-uniform Base Bandgaps”, IEEE Electron Device Letters, Vol. Yuan and J. Song, "Early voltage of SiGe Heterojunction Bipolar Transistor", Electron Devices Meeting, IEEE Hong-kong, p.
Jakubowski, “Effect of Selected Material and Transport Parameters on Early Stress Modeling Accuracy in SiGe-Base HBT”, IEEE TransactionOnElectronDevices, Vol. 34; "RF-SoC": A Low-Power Single-Chip Radio Design Using Si/SiGe BiCMOS Technology," Proceedings of 3rd International Microwave and MillimeterWave Technology, pp. Harame, "Study of RF Linearity of SiGe HBT for Low-Power RFIC Design I, " Proceedings of the 3rd International Microwave and Millimeter Wave Technology, p.
Selvakumar, “Profile design considerations to minimize base transit time in SiGe HBTs for all levels of injection before the onset of the Kirk effect,” IEEE Trans. Basu, "Analytical modeling of base transit time for SiGe HBTs including effect of temperature," International Semiconductor Conference, CAS'08, vol. Lu, "Base transit time for graded-base Si/SiGe HBTs considering recombination lifetime and rate saturation, "Solid-State Electronics, vol.
Ziaur Rahman Khan, "Onset Voltage and Current Gain of Si1-yGey Heterojunction Bipolar Transistor".
