Unification is the quest of science. This paper elucidates unified perspectives of the topics, namely, semiclassical carrier transport in the bulk of a semiconductor and the capacitance of a p-n junction, clarifying the unifying features of drift, diffusion, and thermoelectric currents in the former, and of the depletion and diffusion capacitances in the latter, to an extent not achieved in available books. The elucidation should be helpful in raising the comfort and retention levels and developing the theory building capacities of an average student studying the subject of semiconductor devices.

Shreepad Karmalkar

Department of Electrical Engineering

Carrier transport

Junction capacitance

Carrier mobility

Electric currents

Semiconductor devices

Semiconductor junctions

engineering education

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Simple unified elucidations of some semiconductor device phenomena

IEEE Transactions on Education

This paper presents a new approach to model the 2-DEG concentration (ns) versus gate voltage (VG) behavior and the equilibrium 2-DEG concentration (ns0) in a HEMT. The approach results in a model which is 'comprehensive' in the following sense. It is valid for both delta-doped and uniformly doped HEMT's. It captures all the three ns-VG nonlinearities (subthreshold, gradual pinchoff, and gradual saturation), and the effects of all the device parameters including temperature, in relation expressing ns as an explicit closed-form integrable function of VG having continuous first derivatives; thus, the function readily yields a device current-voltage/capacitance-voltage (I-V/C-V) model which can be incorporated in softwares meant for simulation of circuits, particularly of the analog variety. The simple model is shown to predict the results of complex numerical calculations and experiments. The closed-form ns0 expression of the model is the first of its kind reported for delta-doped HEMT's, and reveals an interesting feature unexposed by earlier ns0 models: the reciprocal of ns0 in both delta-doped and uniformly doped devices decreases linearly with reduction in spacer width, and saturates at low spacer widths in some delta-doped devices. It is shown that the measured ns0 in delta-doped devices is predicted correctly if the electrons in the V-shaped well are assumed to be trapped at the donor sites rather than to be filling the conduction subbands.

IEEE Transactions on Electron Devices

Simple yet comprehensive unified physical model of the 2-D electron gas in delta-doped and uniformly doped high electron mobility transistors

Appealing analogies are proposed to elucidate two important fundamental topics related to semiconductor devices, namely the carrier scattering in a crystal and the derivation of the diffusion capacitance of a p-n junction. The motion of an electron in a semiconductor crystal, according to Schrodinger's wave equation, is likened to that of a photon in a dielectric medium, such as glass, as per Maxwell's electromagnetic wave equations. A circuit analogy is given to clarify and contrast quasistatic and rigorous techniques of deriving the diffusion capacitance of a p-n junction. The analogies capture all aspects of these topics, highlight the important fundamental issues that may escape an average student's notice, and remove any confusion that may exist in the student's mind because of different and partial treatments of the topics in existing textbooks. Exposure to these and other analogies also plays a role in developing analogical reasoning among students who may pursue research.

Appealing analogies for aiding student's assimilation of some key physical concepts related to semiconductor devices

Homo- and hetero- grossly asymmetric junctions i.e. junctions between a heavily doped and a lightly doped layer are important building blocks of modern p+-i-n+ and n+-i-n+ diodes BJT's and MODFET's. We establish a hitherto unhighlighted aspect of the unity underlying the physics of these junctions based on a simple yet original deduction from available surface field-potential relations. We show that apart from pursuing the scientific quest for unification the deduction also leads to three new results of practical significance. Firstly simple expressions are obtained for important parameters of the space-charge layer of a general grossly asymmetric junction under equilibrium. These parameters include the width of the partially depleted region on the heavily doped side of the junction that could not be obtained from earlier analyses. Secondly applying this partial depletion width expression to the MODFET heterojunction a nonlinear MODFET 2-DEG charge versus gate voltage model is derived which is very useful for accurately simulating the effects of gradual saturation chargevoltage nonlinearity on dc and ac performance of analogue circuits. This charge-voltage model is expressed directly in terms of device parameters and temperature unlike earlier nonlinear charge-voltage models whose parameters were empirical and could be extracted only by fitting to experimental data or complex numerical calculations. Thirdly a new concept has emerged as per which the effects of electron confinement partial impurity ionization Fermi-Dirac statistics and small geometry in a grossly asymmetric junction can be treated simply as apparent band discontinuity narrowing phenomena and thus represented in an additive form by dimensionally identical parameters. The concept facilitates a comparison of different modulation doped heterojunction systems. We present calculations illustrating the above results. © 1998 IEEE.

A unified equilibrium treatment of modulation doped heterojunctions and grossly asymmetric homojunctions and its application to MODFET design

It is shown that, from the point of view of the behavior of the charge and position of the Two-Dimensional Electron Gas (2-DEG) as a function of gate-source and drain-source voltages, the complex High Electron Mobility Transistor (HEMT) can be regarded as a simple Buried-Channel (BC) MOSFET. Thus, the characteristics of a HEMT, namely channel charge and capacitance/transconductance as a function of gate voltage below and above threshold are akin those of a BC MOSFET. Hence, there are discrepancies in the conventional Surface Channel MOSFET-like approach to HEMT modeling. Existing simple BC MOSFET dc and ac models can be used for on-paper analysis and computer aided simulation of HEMT devices and circuits, if the HEMT is represented by an equivalent BC MOSFET as derived in this paper. The new representation can be useful for modeling of short-channel HEMT phenomena. © 1997 IEEE.

A new equivalent MOSFET representation of a hemt to analytically model non-linear charge control for simulation of hemt devices and circuits

It is shown that the equivalent box representation of implanted doping profiles, derived in terms of the process parameters by matching the charge-voltage relationships of the actual profile and the box profile, can be used for accurately simulating the electrical characteristics of surface-channel (SC) MOSFETs and MESFETs having implanted channels. © 1989 IEEE

Journal	IEEE Transactions on Education
ISSN	00189359
Open Access	No