Thermal management of AlGaN-GaN HFETs on sapphire using flip-chip bonding with epoxy underfill

Self-heating imposes the major limitation on the output power of GaN-based HFETs on sapphire or SiC. SiC substrates allow for a simple device thermal management scheme; however, they are about a factor 20-100 higher in cost than sapphire. Sapphire substrates of diameters exceeding 4 in are easily available but the heat removal through the substrate is inefficient due to its low thermal conductivity. The authors demonstrate that the thermal impedance of GaN based HFETs over sapphire substrates can be significantly reduced by implementing flip-chip bonding with thermal conductive epoxy underfill. They also show that in sapphire-based flip-chip mounted devices the heat spread from the active region under the gate along the GaN buffer and the substrate is the key contributor to the overall thermal impedance.     

Influence of substrate thickness on thermal impedance of microelectronic structures

The thermal impedance Z_th(jω) has been calculated numerically, using the boundary element method, for a silicon substrate with a uniform heat source on top. The key feature is that the dynamic thermal behaviour is calculated directly in the frequency domain. The calculations were performed for a wide range of values for the thickness of the substrate. By representing the thermal impedance in a Nyquist plot (i.e. Im[Z_th(jω)] vs. Re[Z_th(jω)] with ω as parameter), mainly two circular arcs are observed. For the lower frequency arc, the impedance values as well as the frequency scale are found to be largely influenced by the substrate thickness. The arc corresponding to high frequencies on the other hand remains unchanged under thickness variations.Further analysis revealed an almost perfectly linear relationship between the thermal resistance R_th = Z_th(jω = 0) and the substrate thickness, even when the heat source is not centred on the substrate. Both the slope and intersection value obtained from the curve fitting can be explained by a simple geometrical model including the fixed-angle heat spreading approximation, used since many years in the literature.     

Impedance matching considerations for ferrite Faraday rotators

When a linearly polarized plane wave propagates from a dielectric medium into a medium with Faraday rotation, a reflected wave will always occur at the interface. This reflection is necessary because the normal-mode wave impedances in the medium with Faraday rotation are nondegenerate, while the equivalent normal-mode wave impedances for the dielectric medium are degenerate. Therefore it is not possible to match both normal modes simultaneously at the interface. This paper investigates the peculiar reflected wave associated with impedance matching of Faraday rotators, and shows that it should have minimal impact on practical devices.     

Simple derivation of the expression for the synchronous field in circular cylindrical cavity gyrotrons

It is shown that the expression for the synchronous field at any point in a circular cylindrical cavity can be easily obtained using Graf's formula. The result is applied to the calculation of cavity-beam coupling impedances. Results for the ratio of coupling impedances in tubes using magnetron injection guns and tubes in which the guiding centre of the electron beam is on the cavity axis are given. For operation at half the cyclotron magnetic field, the coupling impedance is much higher for tubes of the second type.     

Heat spreading in a thin longitudinal fin

In view of the trend towards higher power densities in ever shrinking geometries, understanding heat spreading fundamentals is gaining importance. In this paper heat spreading in thin longitudinal geometries is considered. This geometry is of practical interest in one-dimensional Cartesian geometries. A characteristic length is derived and it is shown that this has physical significance for the distance that heat spreads, and for the total amount of heat cooled away. Furthermore, it is investigated when “thin” is a viable assumption. The use of the characteristic length is illustrated for the case of a line source cooling to a plate and for the case of the fins of a plate heatsink. The results are compared to numerical simulations. The work is an extension of the authors' earlier work on heat spreading in infinite longitudinal geometries and heat spreading in infinite and finite circular geometries.     

Radiation characteristics of a source in a thin substrate mountedover a dielectric medium

The radiation pattern of a line source is calculated for the case in which the source is lying on the top or the bottom surface of a lossless dielectric substrate that is mounted on the top of semi-infinite dielectric medium. It is found that in both cases the pattern along the interfaces has a null; that the pattern in the upper semi-infinite medium has a single lobe; and that the pattern in the lower semi-infinite medium has many lobes, the number of which varies with the substrate thickness. In both cases, the power radiated into the lower medium is more than that radiated into the upper medium. Applications of this calculation to remote sensing, microstrip antenna technology, and antenna arrays are discussed     

正负折射率的一维圆形受限光子晶体特性研究

对正负折射率材料构成的一维光子晶体,在横向圆形受限的条件下,推出了光波在其中传播时模式所满足的条件,并利用特征矩阵法研究了正负折射率绝对值相同时,光波在不同模式和不同介质厚度可见光能实现透射波和零反射。正负折射率绝对值不等时,得出介质厚度为半波长时透射波出现在中心波长处;随着模式数即入射角增大,透射波曲线向短波方向移动;介质折射率差的绝对值越大、周期数增加都使透射波谱宽度变窄。     

An accurate analysis of noise in rectangular bipolar transistors including current crowding

An accurate analysis of noise in rectangular bipolar transistors is developed from a distributed model using a collective approach and the transport noise theory. In this model, emitter current crowding effect are taken into account and noise behaviour at intermediate and low values of source impedance is precisely described. The structure of teh equivalent lumped circuit is established, and the analytical relationships characterizing its elements in an extended range of current and frequency are given. It is shown that; (a) the active base region must be represented by a nonlinear impedance with a generalized thermal noise source; (b) for low source impedances the equivalent input voltage shot noise generator is higher than predicted by low injection theories. Furthermore it is found that emitter crowding induces a uniform and important decrease in (a) base impedance (b) thermal noise and (c) the correlation between shot noise generators of the equivalent lumped circuit. Finally it appears that classical low injection theories are valid when crowding occurs in transistors biased with high source impedances.     

Mechanism of heat loss from ferrite storage cores in still air

The thermal equivalent circuit of a core in a coincident current-storage plane depends only on the dimensions of the core and the wires. The circuit thermal impedances for a 0.050 in core are given. Temperature rises of different-sized cores of similar shape are compared, and thermal time constants are discussed.     

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.     

Thermal resistance analysis by induced transient (TRAIT) method forpower electronic devices thermal characterization. II. Practice andexperiments

For pt.I see ibid., vol.13, no.6, p.1208-19 (1998). The TRAIT method for thermal characterization of electronic devices, whose theory was exposed in part I for one-dimensional (1-D) structures, was here applied to systems having heat fluxes with three-dimensional (3-D) dependence in order to demonstrate that the spatial resolution of the thermal resistance analysis is still qualitatively maintained in this type of structure too. The analytical procedure was first applied to simulated structures whose temperature transients and steady-state fields were obtained by means of a finite-element thermal simulation program. In these cases, the knowledge of the steady-state temperature distribution allowed identifying the thermal physical domains which correspond to the cells of the calculated equivalent thermal circuit composed by resistances and capacitances. Furthermore, some experiments on real electronic devices with purposely designed assembling structures were exposed and discussed. The samples were power-integrated circuits with plastic packages mounted on various substrates and Schottky diodes in TO-3 packages. The experiments on both simulated and real devices demonstrated that TRAIT analysis, being able to recognize the localization of some induced defects, maintains its spatial resolution character, despite the large distortion of the thermal domains occurring when the defects are close to the heat source     

A directional coupler of a vertically installed planar circuitstructure

A 3-dB directional coupler is described which is fabricated by installing a vertical second printed circuit board on a main printed circuit board. The added vertical substrate significantly increases the freedom of design parameters. Coupling parameters are easily controlled by changing either the dielectric constants or the thicknesses of the substrates. This makes almost any coupling constant available along with good isolation and a suitable input impedance. The three-dimensional structure also makes a good use of space, resulting in a compact circuit structure. Experimental results agree well with a numerical calculation based on the boundary-element method and show the relaxed tolerances possible in fabrication. Effective permittivities and characteristic impedances for both even and odd modes were obtained and were substituted into the scattering matrix to obtain the parameters for a symmetrical directional coupler. A simplified design chart is also provided showing the dependence of characteristic impedances for odd and even modes on substrate thicknesses used     

Analytical-Numerical Calculation of Diffraction Coefficients for a Circular Impedance Cone

An analytical-numerical computation of diffraction coefficients is described for a semi-infinite impedance cone of circular cross section illuminated by an electromagnetic plane wave. To enable an incomplete separation of variables, both the incident and scattered fields are expressed in terms of the Kontorovich-Lebedev (KL) integrals; an inversion of the Leontovich condition on the cone's surface yields equations for the spectra, whose Fourier coefficients satisfy certain functional difference equations of the second order; the latter are then converted to integral equations of the second kind which are solved numerically; using the so obtained spectra in the KL-integrals for the scattered field and evaluating the integrals in far field leads to diffraction coefficients. Numerical results are included both for verification purposes and for displaying the diffraction behavior for different incident and diffraction angles, as well as for several cone impedances.     

Analysis and synthesis of coplanar coupled lines on substrates offinite thicknesses

This paper presents two sets of newly developed CAD-oriented formulas for the evaluation of the quasi-static even and odd-mode characteristics of coplanar coupled lines on substrates of finite thicknesses. The first set of expressions is derived based on the conformal mapping method. Numerical results show that both the even- and odd-mode characteristic impedances and effective dielectric constants computed by these expressions are in good agreement with the results generated by the spectral domain method. The second set of formulas is derived based on a seminumerical approach and can be used to calculate the geometrical parameters of coplanar coupled lines directly from the given electrical parameters, without using an iterative approach. These seminumerical formulas give maximum error in impedance calculation of about 2.0% (c/h<2), over a wide range of impedance and dielectric constant values     

Heat Flow Pattern and Thermal Resistance Modeling of Anisotropic Heat Spreaders

To ensure safe operating temperatures of the ever smaller heat generating electronic devices, drastic measures should be taken. Heat spreaders are used to increase surface area, by spreading the heat without necessarily transferring it to the ambient in the first place. The heat flow pattern is investigated in heat spreaders and the fundamental differences regarding how heat conducts in different materials is addressed. Isotropic materials are compared with anisotropic ones having a specifically higher in-plane thermal conductivity than through plane direction. Thermal resistance models are proposed for anisotropic and isotropic heat spreaders in compliance with the order of magnitude of dimensions used in electronics packaging. After establishing thermal resistance models for both the isotropic and anisotropic cases, numerical results are used to find a correlation for predicting thermal resistance in anisotropic heat spreaders with high anisotropy ratios.     

Thermal impedance plots of micro-scaled devices

The complex thermal impedance Z_th of a microelectronic heat source on the surface of a silicon wafer has been calculated semi-analytically as a function of the frequency. By representing the results in a Nyquist plot, almost perfect circular curves are obtained. This result is analogous to complex loci of the dielectric constant obtained for some materials.     

Input filter design for multiple-module DC power systems

When multiple DC/DC power converters are operated from a DC bus with a nonzero source impedance, undesirable interactions can occur between an individual regulator and the input impedance of the other regulators on the bus. Consequently, criteria for input filter design in the presence of a significant source impedance are developed, which, when used in conjunction with already-known input filter criteria, permit the input filter to be designed so that each regulator operates reliably. Proper filter design tends to decouple the negative regulator impedances from the bus, leaving only the passive input filter impedances to affect the other converters. These filter impedances appear in parallel with the source impedance and reduce the overall source impedance. Hence, the use of multiple modules on the same bus actually improves the performance of the individual regulators. An example, the buck current mode controlled power converter, is examined in detail. Extensive experimental evidence is presented to verify the analytical results     

Temperature profile and thermal-spreading resistance for a semi-infinite type-IIa-diamond heat sink

The steady-state temperature profile and thermal-spreading resistance for a uniform heat source on a semi-infinite type IIa-diamond heat sink are calculated. The inverse temperature dependence of the diamond thermal conductivity is taken into account.     

Thermal properties of very fast transistors

Recent predictions that thermal effects will limit future transistor speed improvement motivated an interest in predicting and measuring these effects. A mathematical model of the three-dimensional transient heat flow problem is presented which takes into account the physical structure of the device and the actual region of power dissipation. At any point within the device, the model predicts the time-dependent temperature response to a change in power dissipation. A new method of measuring the local time-dependent thermal behavior of small bipolar transistors is described and used to verify the model. It was found that the thermal spreading resistance becomes important in silicon transistors when the emitter stripe dimensions approach 1 µ. Furthermore, the thermal response is much slower than the electrical response. Also, it was confirmed that adjacent devices in integrated circuits are essentially thermally isolated as far as thermal spreading resistance is concerned.     

An Insulated Coaxial Probe for EM Local Heating

An insulated miniature coaxial probe with a modified geometry has been developed for EM local heating of a biological (or conducting) medium. This probe is basically a lossy coaxial cavity, and its input impedance, current distribution, and power dissipation pattern can be controlled by the selection of terminal impedances, insulating sheath, and the dimensions of the probe. An approximate theory and an experimental study on the probe are presented.