Appendix C
Abstract
Modelling, Characterization and Optimization of InAlAs/InGaAs Heterojunction, InP based High Electron Mobility Transistor (HEMT) For Microwave and Millimetre Wave Frequency Applications
In order to optimize the operation of both classical HEMTs and of new structures, we must have an accurate understanding of their physical behaviour and have a deep knowledge of the various physical behaviour and physical phenomena occurring in these devices. In this connection, accurate analytical models are clearly needed in order to substitute inexpensive, fast, and accurate model prior to fabrication for very expensive systematically technological studies. The mandate of this research is, in broad terms, to advance the development, understanding and optimization of InAlAs/InGaAs heterostructure, InP based HEMTs.
Several groups have been pursuing their research to develop an accurate model for HEMT. The first breakthrough came with the model purposed by Daniel et al in 1982 that is reliable for describing the behaviour of AlGaAs/GaAs device. After that several models have been developed to predict the device characteristics assuming high band semiconductor to be fully depleted ignoring the effect of individual depletions by M-S contact and due to transfer of free carriers in the undepleted region to the quantum well. This also limits the model to predict characteristics before parallel conduction and require two different models to predict complete characteristics. A new analytical model has been developed in which HEMT can be viewed as two separate isolated structures brought in contact. The two structures when coupled, the depletion regions of the individual are overlapped and interpenetrate before parallel conduction starts thus increasing the potential (D) at the interface of the overlapped depletions and forming region I and region II as shown. For parallel conduction these regions are again separated as before, which resulted in zero potential (D = 0) i.e. conduction band crosses the Fermi level in InAlAs region giving rise to free carriers in this region, which are responsible for parallel conduction in InAlAs/InGaAs/InP HEMT. Considering this assumption parallel conduction can be included in one complete model. Furthermore, with this model, all effects arising from source, drain and gate electrodes can be considered as in MESFET and can be extended for two-dimensional analysis eliminating the complexity arising from boundary condition of normal electric field at the heterointerface. This model gives deep insight of how by creating a discontinuity in conduction band in MESFET structure leads to enhanced characteristics like enhancement of threshold voltage. The model is extended to predict sheet carrier density, the effect of parallel conduction through variation of depletion width, potential at the interface of depletions and DEc -Ef with gate voltage.
Another limiting feature of Daniel et al model was the Fermi level variation with electron density in the quantum well was neglected in order to get an analytical model. If it is accounted for, a few equations related to the model must be solved numerically. Several research works have been done to reduce the complexity of the model without neglecting the actual behaviour. Model proposed by Nandita et al in 1993 for calculating charge sheet equation for AlGaAs/GaAs system valid for the entire region has been recalculated for InAlAs/InGaAs system to formulate the Id~Vd characteristics and has been extended to obtain the expression for transconductance, output conductance and cut-off frequency of the device. These expression has been used to realize the effect of parasitic resistances through variation of drain current, transconductance and output conductance and cut-off frequency with drain and gate voltages and also with different gate lengths. The need for incorporating the effect of parasitic resistance at higher gate voltages, lower drain voltages and for submicron gate length device is emphasized through this chapter to accurately predict the device characteristics. Effect of lower gate length can be used to enhance the characteristics by increasing drain current, transconductance, output conductance and cut-off frequency of the device. This effect increases with the decrease in resistances. Using this model a maximum cut-off frequency of 83GHz and 175GHz were obtained for channel length of 0.25mm and 0.1mm respectively.
The developed expression has been used to discuss device improvement using delta doped structure by varying the device structure from uniformly doped structure to delta doped structure for identical threshold voltages and identical doping-thickness product through various contours of sheet carrier density, threshold voltage etc.. The device design procedure has been given to eliminate parallel conduction completely without affecting the device performance. The optimized value of Vc-Voff is then used to predict the transconductance and cut-off frequency of the device. From the analysis the maximum transconductance of 1.41 S/mm for channel depth of 200Å and a cut-off frequency of 627 GHz for channel depth of 300 Å can be achieved corresponding to gate length of 0.1mm with breakdown voltage of 14.8V. These enhancements have been further controlled and optimized using tri-step doped structure.
As the technology is switching from VLSI to ULSI technology by reducing the gate length. But reducing the gate length in comparison with channel depth give rise to short channel effects thereby limiting the 1-D analysis for correct estimation of results specially threshold voltage. There are two approaches to predict 2-D threshold voltage of the device. Either we solve Poisson equation considering mobile carriers and decreasing the gate voltage to achieve threshold. Other approach is to do analysis in subthreshold regime and increasing the gate voltage up to threshold voltage. The second approach sounds promising as it removes the complexity of solving Poisson equation coupled with continuity equation due to non-existence of free carriers in the region under consideration. Short-channel threshold voltage model has been developed for HEMT, following MESFET analysis considering fully depleted InAlAs region as two isolated depletions- one due to metal-semiconductor contact and other due to transfer of carriers from InAlAs region to the 2-DEG quantum well. This approach greatly reduces the complications which arise in the short-channel HEMT modelling. The two-dimensional Poisson’s equation has been solved both with Green’s function technique and the numerical technique (Finite difference). The solution obtained from the Green’s function technique is found to be in good agreement with the solution obtained from numerical method that proves the validity of our analytical model. The work has been further extended to model the behaviour of mobile charges to predict Id-Vd characteristics and conductances. The variations of channel potential, electric field and sheet carrier density for mobile charges along the channel have also been investigated in details to give a clear insight into device physics.