Kuan Chen

Electron beam lithography in nanoscale fabrication: recent development

Miniaturization is the central theme in modern fabrication technology. Many of the components used in modern products are getting smaller and smaller. In this paper, the recent development of the electron beam lithography technique is reviewed with an emphasis on fabricating devices at the nanometer scale. Because of its very short wavelength and reasonable energy density characteristics, e-beam lithography has the ability to fabricate patterns having nanometer feature sizes. As a result, many nanoscale devices have been successfully fabricated by this technique. Following an introduction of this technique, recent developments in processing, tooling, resist, and pattern controlling are separately examined and discussed. Examples of nanodevices made by several different e-beam lithographic schemes are given, to illustrate the versatility and advancement of the e-beam lithography technique. Finally, future trends in this technique are discussed.

Natural convection in an air layer enclosed within rectangular cavities

Natural convection in an air layer contained in a rectangular cavity having side walls of different temperatures has been investigated experimentally for various aspect ratios ranging from 4.9 to 78.7. Measured temperature profiles are analyzed with the flow regimes. Two Nusselt-Grashof correlations are presented for the measured heat-transfer data, fitting the data with an average deviation of less than 7.8%. The Grashof number based on layer thickness ranged from 1.5 × 103 to 7.0 × 106.

A practical extension of the 3ω method to multilayer structures

An improved data reduction method is used to extend the popular 3ω method to general layered geometries. This approach utilizes an unapproximated analytical solution, cast in terms of thermal impedance, to simultaneously measure thermal conductivity, thermal capacity, conductivity anisotropy, and interlayer contact resistance in multilayer planar structures. This method places no restrictions on the number or thickness of individual material layers, and it allows experimental measurements to be taken over a much wider range of frequencies than was previously possible. The search algorithm associated with the model is straightforward, robust, and requires no specialized software to compose. Experimental results are presented for a two-layer borosilicate glass/zeolite structure as well as a Si∕SiO2 structure. In both instances, the algorithm was able to simultaneously extract thermal conductivity and thermal diffusivity values using a single series of 3ω measurements.

Thermal analysis and simulation of the microchannel flow in miniature thermal conductivity detectors

The microchannel flow in miniature TCDs (thermal conductivity detectors) was investigated analytically and numerically. Effects of channel size, inlet and boundary conditions, as well as changes in gas properties on the heat transfer rate were examined in detail. Without preheating the gas stream, the distance for a miniature TCD to reach the conduction-dominant region was found to be approximately four times the thermal entry length for pipe flows of constant properties and uniform boundary conditions. If the gas temperature at the channel inlet is in the neighborhood of the mean gas temperature in the conduction-dominant region, the entrance region is much shorter. Another important finding of the present study is that the change in heat transfer rate in the entrance region is proportional to the square roots of the changes in gas density, specific heat, and thermal conductivity, but depends primarily on the thermal conductivity change in the conduction-dominant region.

An analysis of the heat transfer rate and efficiency of TE (thermoelectric) cooling systems

The heat transfer rate and efficiency of TE (thermoelectric) cooling systems were investigated. The emphasis of the present study is focused on the use of large-scale TE refrigerators for air conditioning applications. A one-dimensional heat transfer analysis was performed to determine the cooling power and electricity consumption of the TE elements. The constant-property results are in good agreement with the variable-property solutions for TE materials and temperatures typical for air conditioning applications. A heat transfer analysis was also carried out for TE refrigerators equipped with a heat exchanger. Both parallel- and counter-flow heat exchangers were considered. Fluid temperature variations of these two flow arrangements were found to be quite different, but the efficiencies and cold fluid exit temperatures differed only slightly when a uniform current was used for all TE elements. If the length of the heat exchanger exceeds an optimal value, the cold fluid temperature begins to rise and the efficiency drops for both parallel- and counter-flow arrangements. The second law of thermodynamics was applied to the optimization of TE refrigerators operating between two constant-temperature reservoirs and between two flowing fluids. It was found that if a TE cooling system incorporates a heat exchanger, a nonuniform current distribution should be used to achieve the maximum efficiency and the lowest cold fluid temperature. The optimization results for TE refrigerators operating between two constant-temperature reservoirs are not applicable to TE cooling systems between two flowing fluids. The most energy-efficient current distribution for the parallel-flow arrangement is the one which increase in the direction of the cold fluid.

Fabrication and characterization of thermal conductivity detectors (TCDs) of different flow channel and heater designs

Different flow channel designs and heaters made from different materials were tested for improving the performances of silicon-based thermal conductivity detectors. One of the designs involved an electric heater sandwiched between two identical flow channels for high heat transfer rates. The heater of the other design was suspended over a slot to reduce heat losses. The flow channels were etched in silicon wafers and nickel heating elements were deposited on Pyrex glass, polyimide, and silicon nitride membranes. The transient behaviors of the heaters and the wafer temperatures were measured and analyzed for different voltages. The effects of flow channel design and membrane material on the heat transfer characteristics and sensitivities of the detectors were examined. Simple heat transfer models were developed to aid in understanding and diagnosing detector behaviors and performances. The polyimide heater had the best signal conditions. The warm-up times of the TCDs were found to be primarily dependent upon the package dimensions and properties. The double-channel TCD exhibited 20% higher heat transfer rate compared to the single-channel design, but the sensitivities of these two designs differed only slightly.

An analytical study of the Chemical Vapor Deposition (CVD) processes in a rotating pedestal reactor

Abstract The epitaxial growth and fluid dynamics characteristics of pedestal Chemical Vapor Deposition (CVD) reactors were studied analytically, with emphasis on the effects of susceptor rotation and thermal diffusion on the epitaxial growth rate. The coupled transport equations were solved by numerical integration and a multiple shooting technique. The pressure, velocity, temperature and concentration distributions were calculated and studied for various rotation speeds and operating conditions. The ranges of the process parameters in actual CVD reactors were estimated. It is found that different combinations of the external forced flow and the susceptor rotation have similar temperature and concentration distributions for the Schmidt number around unity when the results are presented in terms of a properly normalized vertical coordinate. The changes in susceptor rotation and external forced flow have nearly identical effects on the epitaxial growth rate for the Schmidt numbers greater than unity. At small Schmidt numbers, the epitaxial growth rate can be enhanced by increasing the forced flow velocity.

A two-dimensional mesh generator for variable order triangular and rectangular elements

Abstract An improved method is presented for generating variable order elements by superelement generation. This method is simple to apply and requires less execution time in comparison with other variable order mesh generators. Depending on geometrical complexity and material variation, the superelements are manually determined to be refined into high or low order elements. Different mesh generation subroutines are employed to generate elements of different orders. The refined elements of different orders are finally patched to form a hybrid mesh. A FORTRAN program is given to generate finite element meshes of linear and quadratic triangular and rectangular elements automatically.

Heat and mass transfer in horizontal vapor phase epitaxy reactors

Heat and mass transfer processes were studied in a horizontal vapor epitaxy reactor with simultaneously developing velocity, temperature and concentration distributions. The susceptor placed in the reactor was either horizontal or slightly titled. An analytical solution was obtained using previous heat transfer results in entry length and fully developed duct flow, and the heat-mass transfer analogy for growth rate calculations. The mean concentration distributions along the susceptor are presented in dimensionless forms based on constant properties and laminar flow. The influences of axial temperature variation and wall cooling on the epitaxial growth rate distribution are examined in this study. Results of experimental studies of silicon growth from SiH4 in hydrogen agree well with the analysis.

Supersonic flow in miniature nozzles of planar configuration

Supersonic flow of nitrogen gas through miniature nozzles of planar configuration was investigated experimentally and compared with numerical simulations to assess the applicability and accuracy of the various viscous-flow models. The design Mach number of the nozzles is 3, and the inlet pressures range from 0 to 10 atm (gauge). The measured thrust of the meso nozzle with a throat area of 0.773 mm2 agreed well with the numerical solution (96%). The agreement of the micro nozzle, with a throat area of 0.0625 mm2, decreased to 80% for pressure differences beyond the design flow condition. At low-pressure differences, separated flow occurred after the shock in the nozzle, causing unstable and asymmetric velocity distributions on the nozzle exit plane. Thrust was found to be not only a function of pressure difference but also a function of the flow history. The numerical simulation was successful in modeling these effects, but at different pressures.