Compact Models of Spreading Resistances for Electrical/Thermal Design of Devices and ICs

Building upon our recent work (IEEE Electron Device Lett., vol. 26, pp. 909-912, Dec, 2005), we present simple and continuous closed-form models for several rectangular and circular spreading resistance geometries encountered in electrical/thermal design of devices and integrated circuits. The resistance geometries considered involve current/heat flow between parallel contacts of rectangular or circular shape and concentric or eccentric nature, between a horizontal and a vertical stripe, and between a horizontal circular contact and a surrounding vertical cylindrical contact. The modeling procedure involves normalization of the spreading resistance with respect to its value under 1D flow conditions, followed by a curve-fit of the variation of this normalized resistance with contact area in terms of physical parameters. The resistance models may also be used to estimate the reciprocal of capacitance of similar insulator-electrode geometries, by replacing the resistivity by the reciprocal of the insulator permittivity.     

A process-parameter-based circuit simulation model forion-implanted MOSFETs and MESFETs

It is shown that the correct-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 electric characteristics of surface-channel MOSFETs and MESFETs having implanted channels. Because the correct box representation is known directly in terms of the doping profile parameters, which can be obtained from process simulation, the need for experimental determination of the box is obviated. The application of the model can substantially reduce the number of experimental trial-and-error iterations involved in the development of devices and circuits. The correct box is also applicable to the CCDs whose physics of operation is similar to that of MOSFETs     

Enhancement of breakdown voltage in AlGaN/GaN high electronmobility transistors using a field plate

We investigate the breakdown (V_br) enhancement potential of the field plate (FP) technique in the context of AlGaN/GaN power HEMTs. A comprehensive account of the critical geometrical and material variables controlling the field distribution under the FP is provided. A systematic procedure is given for designing a FP device, using two-dimensional (2-D) simulation, to obtain the maximum V_br , with minimum degradation in on-resistance and frequency response. It is found that significantly higher V_br can be achieved by raising the dielectric constant (ε_i) of the insulator beneath the FP. Simulation gave the following estimates. The FP can improve the V_br by a factor of 2.8-5.1, depending on the 2-DEG concentration (n_s) and ε_i. For n _s=1×10¹³/cm², the V_br can be raised from 123 V to 630 V, using a 2.2 μm FP on a 0.8 μm silicon nitride, and 4.7 μm gate-drain separation. The methodology of this paper can be extended to the design of FP structures in other lateral FETs, such as MESFETs and LD-MOSFETs     

A unified compact model of electrical and thermal 3-D spreading resistance between eccentric rectangular and circular contacts

The spreading resistance between two parallel contacts, the smaller of which is located arbitrarily over the area of the larger, is of wide interest in electrical/thermal design of devices and ICs. We propose a simple, continuous, and asymptotically correct closed-form expression to predict the accurate but involved calculations of this resistance for all contact conditions. The contacts may be rectangular or circular, and the boundary condition on these may either be equipotential/isothermal or uniform current density/uniform heat flux. The validity of the model is established by comparisons with accurate numerical calculations of spreading resistances having aspect ratios in the range zero to 1000 and with experimental observations.     

Introducing the Device Modeling Procedure to Electrical Engineering Students

This paper presents the contents of a lecture for enhancing the interest of electrical engineering students in semiconductor device modeling and providing a deep appreciation of the conflicting requirements for an ideal model, of the sequence and interconnectivity of steps in the modeling procedure, and of the types of models existing in modern times. The lecture can be included in courses on semiconductor devices or device modeling. The lecture uses a resistor with 3-D effects and much simpler physics than a p-n junction for illustration, and coins mnemonics for key aspects. Objective assessment data confirm the need and efficacy of the proposed lecture. The work of this paper shows how proper introduction of a topic with carefully chosen illustrations and mnemonics can improve the teaching/learning process and how such improvements can be assessed     

A unified equilibrium treatment of modulation doped heterojunctionsand grossly asymmetric homojunctions, and its application to MODFETdesign

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, BJTs and MODFETs. 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 charge-voltage 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     

Effects of Oxide-Fixed Charge on the Breakdown Voltage of Superjunction Devices

Superjunction devices may employ oxide layers for termination and for isolating adjacent pillars. Fixed charges present in these oxide layers are shown to have the following influence on the device breakdown voltage V_br. The effect of a positive fixed charge is equivalent to an increase in the n-pillar charge. The resulting charge imbalance degrades V_br, and can be compensated either by increasing the p-pillar doping or by decreasing the n-pillar doping by an amount ap(1.2N_fT+4N_fI)/(pillarwidth), where N _fT and N_fI are the fixed charges in the termination and isolation oxides, respectively. Contrary to expectation, the V_br of such compensated devices can be significantly higher than that of a balanced superjunction of the same doping level without fixed charge, due to the uniform lateral depletion effect of the fixed charge     

Edge Effects on Gate Tunneling Current in HEMTs

We elucidate five considerations for accurate estimation of electron tunneling from the gate edges of high-electron mobility transistors (HEMTs). These considerations are listed as follows: 1) edge roughness; 2) net charge at the AlGaN/passivation interface; 3) dielectric constant of the medium above the HEMT surface; 4) nontriangular potential barrier; and 5) negligible angular tunneling from the gate edge. Using these considerations, we calculate the reverse gate current I_G of AlGaN/GaN HEMTs based on thermionic trap-assisted tunneling (TTT) and direct tunneling (DT) mechanisms. These calculations establish that the observed rise in I_G for a gate voltage beyond the threshold is due to tunneling from the gate edges. The calculations also show that the TTT mechanism can predict the measured I_G of AlGaN/GaN HEMTs over a wide range of gate voltages and temperatures and point to the possibility of a rapid rise in I_G at high gate voltages due to the DT mechanism.     

A simple yet comprehensive unified physical model of the 2Delectron gas in delta-doped and uniformly doped high electron mobilitytransistors

This paper presents a new approach to model the 2DEG concentration (n_s) versus gate voltage (V_G) behavior and the equilibrium 2DEG concentration (n_s0) 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 HEMTs. It captures all the three n_s-V_G nonlinearities (subthreshold, gradual pinchoff, and gradual saturation), and the effects of all the device parameters including temperature, in relation expressing n_s as an explicit closed-form integrable function of V_G 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 software 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 n_s0 expression of the model is the first of its kind reported for delta-doped HEMT's, and reveals an interesting feature unexposed by earlier n_s0 models: the reciprocal of n_s0 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 n_s0 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