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.     

New challenges to the modelling and electrical characterisation of ohmic contacts for ULSI devices

Continuing developments in semiconductor process and materials technology have enabled significant reductions to be achieved in the contact resistance R_c of devices. This reduction is commonly assessed in terms of the specific contact resistance (SCR) parameter ρ_c (Ω cm²) of the metal–semiconductor interface. Such a reduction in SCR is essential, for as device dimensions decrease, then so also must ρ_c and the corresponding contact resistance in order not to compromise the down-scaled ULSI device performance. Thus the ability to accurately model contacts and measure ρ_c is essential to ohmic contact development. The cross kelvin resistor (CKR) test structure is commonly used to experimentally measure the Kelvin resistance of an ohmic contact and obtain the specific contact resistance ρ_c. The error correction curves generated from computer modelling of the CKR test structure are used to compensate for the semiconductor parasitic resistance, thus giving the SCR value. In this paper the increased difficulty in measuring lower ρ_c values, due to trends in technology, is discussed. The challenges presented by the presence of two interfaces in silicided contacts (metal-silicide–silicon) is also discussed. Experimental values of the SCR of an aluminium–titanium silicide interface is determined using multiple CKR test structures.     

The effect of die attach voiding on the thermal resistance of chip level packages

The presence of voids in the die bond region is known to adversely affect the thermal resistance of the packaged chip-level device. Unfortunately, such voids are easily formed in the solder layer during manufacturing, and are found to nucleate, grow and coalesce with thermal cycling. Although the relationship between package thermal resistance and voids has been examined extensively, little data exist concerning the precise effects of void size, configuration and position. The present study allows the experimental investigation of these effects through application of an innovative experimental technique that carefully controls void geometry and distribution. The results show that for small, random voids, the thermal resistance, θ_jc, increases linearly with void volume percentage, V_%, according to the equation θ_jc = 0.007V + 1.4987, and for large, contiguous voids the increase follows the exponential relationship, θ_jc = 1.427e^0.015V. At 73% voiding, θ_jc was found to increase 30% and 200% for random and contiguous voids, respectively.     

Features of the Behavior of the Figure of Merit for <Emphasis Type="Italic">p</Emphasis>-Type Solid Solutions Based on Bismuth and Antimony Chalcogenides

Thermoelectric and galvanomagnetic properties of p-type solid solutions based on bismuth and antimony chalcogenides (Bi,Sb)₂(Te,Se)₃ have been studied to analyze the features of the figure of merit Z. The increase of Z and ZT for the p-Bi_2−x Sb _x Te₃ composition at x = 1.6 in the temperature interval of 370 K to 550 K was shown to be defined by the increase of the density-of-states effective mass, the slope of the temperature dependence of the carrier mobility, and the reduction of the lattice thermal conductivity for optimal charge carrier concentration. High carrier mobility and low lattice thermal conductivity provide the increase of Z and ZT in the p-Bi_2−x Sb _x Te_3−y Se _y (x = 1.3, y = 0.06) solid solution in the interval from 300 K to 370 K. The growth of Z in these compositions is determined by the increase of the compression of the constant-energy ellipsoids along binary and bisector directions, and by the change of the tilt angle Θ between the principal axes of the ellipsoids and the crystallographic axes.     

Study of electrically active defects in n-GaN layer

Deep level defects in both p⁺/n junctions and n-type Schottky GaN diodes are studied using the Fourier transform deep level transient spectroscopy. An electron trap level was detected in the range of energies at E_c−E_t=0.23–0.27 eV with a capture cross-section of the order of 10⁻¹⁹–10⁻¹⁶ cm² for both the p⁺/n and n-type Schottky GaN diodes. For one set of p⁺/n diodes with a structure of Au/Pt/p⁺–GaN/n–GaN/n⁺–GaN/Ti/Al/Pd/Au and the n-type Schottky diodes, two other common electron traps are found at energy positions, E_c−E_t=0.53–0.56 eV and 0.79–0.82 eV. In addition, an electron trap level with energy position at E_c−E_t=1.07 eV and a capture cross-section of σ_n=1.6×10⁻¹³ cm² are detected for the n-type Schottky diodes. This trap level has not been previously reported in the literature. For the other set of p⁺/n diodes with a structure of Au/Ni/p⁺–GaN/n–GaN/n⁺–GaN/Ti/Al/Pd/Au, a prominent minority carrier (hole) trap level was also identified with an energy position at E_t−E_v=0.85 eV and a capture cross-section of σ_n=8.1×10⁻¹⁴ cm². The 0.56 eV electron trap level observed in n-type Schottky diode and the 0.23 eV electron trap level detected in the p⁺/n diode with Ni/Au contact are attributed to the extended defects based on the observation of logarithmic capture kinetics.     

Numerical analysis of a SWEAT structure with an improved one dimensional nonlinear model

An improved one dimensional (1 − D) nonlinear model of the thermal response of the Standard Wafer-level Electromigration Accelerated Test (SWEAT) structure is described. The major improvement in this model are accurate predictions of the critical current density j_o; according to older models j_o is inversely proportional to the “power” I²R/R(T_s), while our model shows a different (increasing) trend and is confirmed by measurements. The ratio of the maximum temperature increase to the average temperature increase (γ) for the investigated structure depends on the relative change of the resistance and normalized current , and can be calculated within 1% from basic material and structure parameters. The model includes the edge correction factor α depending on the geometry of the structure (W_n/t_i), material parameters and stress current I. Using the corrected values for the edge correction factor, the maximum temperature increase in the SWEAT test structure can be calculated within less than 5°C.     

Estimation of series system reliability for exponentially distributed component life times

The reliability of a series system with P components which have exponential life times is estimated using Type II censored samples. The series system reliability is a function of , where λ_j is the hazard rate constant for the j^th component, j=1,2,…P. An estimator of μ( ) which dominates the MLE in terms of the risk is derived. This improved estimator of μ( ) is used for estimating the series system reliability. Monte Carlo simulation is used to estimate the risks of the proposed estimators, and comparisons with the ML estimators are made.     

Electro-ultrasonic spectroscopy of polymer-based thick film layers

We have studied the properties of polymer-based thick film layers by electro-ultrasonic spectroscopy. Electro-ultrasonic spectroscopy method is based on the interaction between ultrasonic vibrations and electrical conductivity of solids. The ultrasonic vibrations of frequency f_U change the contact area between conducting grains in the thick film structure and then the resistance is modulated by the frequency of ultrasonic excitation. An intermodulation voltage is created on this structure. It depends on the value of AC current varying with frequency f_E and on the ultrasonic excited resistance change ΔR varying with frequency f_U. We have measured the intermodulation voltage U_m for a set of polymer-based thick film resistors made by different resistive pastes. It was found that for given sample the intermodulation component of frequency f_m = f_E − f_U increases linearly with electric excitation for the constant ultrasonic excitation. We have normalized the intermodulation voltage U_m by the electric current I_E and this quantity is proportional to the ultrasonic excited resistance change ΔR. The relative resistance change ΔR/R_X is of the order of 10⁻⁷–10⁻⁴. From the comparison of the results measured for the samples made by the same resistive pastes it follows, that relative resistance change ΔR/R_X can be used as an indicator of sample quality.     

Development of a standard for transient measurement of junction-to-case thermal resistance

The paper summarizes the development of a standard method to measure the thermal resistance “junction-to-case” θ_JC of semiconductor devices with heat flow through a single path. Power switches or amplifiers are typical examples. θ_JC is a key performance metric to decide whether a device can be used in thermally critical applications. Hence an accurate and reproducible method to measure θ_JC is required. This is not easy, especially for low θ_JC, which is reflected by the fact that no JEDEC industry standard existed then to measure θ_JC. During the last 4 years we have evaluated approaches and developed a new method called Transient Dual Interface (TDI) method. It uses two measurements of the thermal impedance Zth or more specific Z_θJC(t) of the device with different cooling conditions at the interface of device case and a heat sink. To evaluate these measurements two methods are applied. Method 1 determines θ_JC directly from the separation of Zth-curves. θ_JC is the thermal impedance Z_θJC(t_s) at the time t_s where the two Z_θJC(t)-curves separate. Method 2 first calculates cumulative structure functions and uses their separation point to determine θ_JC. Both data evaluation methods complement each other, because method 1 is most accurate for low θ_JC in the range of 1 K/W or below, while method 2 is more accurate for higher θ_JC > 1 K/W. The TDI method allows to measure θ_JC with higher accuracy and better reproducibility than the steady state method used in industrial practice up to now. The TDI method was published as JEDEC standard JESD51-14 in November 2010. Problems of the traditional steady state measurement and main steps of the development of the TDI method are discussed.     

Investigation of Au/Ti/Al ohmic contact to N-type 4H–SiC

In this study, investigation on Au/Ti/Al ohmic contact to n-type 4H–SiC and its thermal stability are reported. Specific contact resistances (SCRs) in the range of 10⁻⁴–10⁻⁶ Ω cm², and the best SCR as low as 2.8 × 10⁻⁶ Ω cm² has been generally achieved after rapid thermal annealing in Ar for 5 min at 800 °C and above. About 1–2 order(s) of magnitude improvement in SCR as compared to those Al/Ti series ohmic systems in n-SiC reported in literature is obtained. XRD analysis shows that the low resistance contact would be attributed to the formation of titanium silicides (TiSi₂ and TiSi) and Ti₃SiC₂ at the metal/n-SiC interface after thermal annealing. The Au/Ti/Al ohmic contact is thermally stable during thermal aging treatment in Ar at temperature in the 100–500 °C range for 20 h.     

Nonstandard Harman Response for Separate Measurements of the Stages of Multicascade Thermoelectric Modules

We investigated the Harman response R = f(t) (electric resistance R versus time t) from separate stages of two-stage thermoelectric modules with various numbers of elementary thermocouples in a stage. Some special cases were considered when the thermal flow in stages was either coincident or opposed. It was shown that the Harman response from the first stage of modules, and sometimes from modules in general, can have an unusual appearance because of the thermal influence of the second stage. It was found that, by connecting one-stage modules in pairs “head to head,” one can reduce thermal losses from their working joints during measurements in air. It is shown that this effect can be used to increase the accuracy of Harman figure of merit Z _H measurements in air when sampling one-stage modules during mass production.     

High breakdown voltage Schottky rectifier fabricated on bulk n-GaN substrate

Vertical Schottky rectifiers have been fabricated on a free-standing n-GaN substrate. Circular Pt Schottky contacts with different diameters (50 μm, 150 μm and 300 μm) were prepared on the Ga-face and full backside ohmic contact was prepared on the N-face by using Ti/Al. The electron concentration of the substrate was as low as 7 × 10¹⁵ cm⁻³. Without epitaxial layer and edge termination scheme, the reverse breakdown voltages (V_B) as high as 630 V and 600 V were achieved for 50 μm and 150 μm diameter rectifiers, respectively. For larger diameter (300 μm) rectifiers, V_B dropped to 260 V. The forward turn-on voltage (V_F) for the 50 μm diameter rectifiers was 1.2 V at the current density of 100 A/cm², and the on-state resistance (R_on) was 2.2 mΩ cm², producing a figure-of-merit (V_B)²/R_on of 180 MW cm⁻². At 10 V bias, forward currents of 0.5 A and 0.8 A were obtained for 150 μm and 300 μm diameter rectifiers, respectively. The devices exhibited an ultrafast reverse recovery characteristics, with the reverse recovery time shorter than 20 ns.     

Bit error rate experiments in ring-shaped RSFQ circuits

Ring-shaped rapid single flux quantum (RSFQ) circuits composed of segments of Josephson transmission lines (JTLs) and other RSFQ circuits enable permanent SFQ pulse circulation. New ring structures of different designs have been realized which comprise T-flipflop (TFF) and multiplier (MULT) circuits. Reliability in circuit operation has been proven experimentally by a bit error rate BER≅10⁻¹⁶. The fabrication process has been optimized by using PTB-4 μm Nb/Al₂O₃–Al/Nb trilayer technology with externally shunted tunnel junctions of critical current densities of j_c=≅1 kA/cm². Characteristic voltage is V_c=250 μV and Steward–McCumber parameter β_c≤1. A linear dependence of pulse circulation frequency on JTL bias currents has been measured within a bias current interval of 20%.     

Power Factor Anisotropy of <Emphasis Type="Italic">p</Emphasis>-Type and <Emphasis Type="Italic">n</Emphasis>-Type Conductive Thermoelectric Bi-Sb-Te Thin Films

The best films for thermoelectric applications near room temperature are based on the compounds Bi₂Te₃, Sb₂Te₃, and Bi₂Se₃, which as single crystals have distinct anisotropy in their electrical conductivity σ regarding the trigonal c-axis, whereas the Seebeck coefficient S is nearly isotropic. For p- and n-type alloys, P _⊥c > P _||c, and the power factors P _⊥c of single crystals are always higher compared with polycrystalline films, where the power factor is defined as P = S ² σ, ⊥c and ||c are the direction perpendicular and parallel to the c-axis, respectively. For the first time in sputter-deposited p-type (Bi_0.15Sb_0.85)₂Te₃ and n-type Bi₂(Te_0.9Se_0.1)₃ thin films, the anisotropy of the electrical conductivity has been measured directly as it depends on the angle φ between the electrical current and the preferential orientation of the polycrystals (texture) using a standard four-probe method. The graphs of σ(φ) show the expected behavior, which can be described by a weighted mixture of σ _⊥c and σ _||c contributions. Because (σ _⊥c/σ _||c) _p  < (σ _⊥c/σ _||c) _n , the n-type films have stronger anisotropy than the p-type films. For this reason, the angular weighted contributions of P _||c lead to a larger drop in the power factor of polycrystalline n-type films compared with p-type films.     

Transient dual interface measurement of junction-to-case thermal resistance in AlGaN/GaN HEMT utilizing an improved infrared microscope

The junction-to-case thermal resistance (R_θJC) of a GaN/AlGaN HEMT is measured by Transient Dual Interface Method (TDIM). Different from other works about TDIM, an improved transient infrared microscope is used to measure the cooling curves, other than the traditional electrical method. Z_th curves are used to determine the R_θJC following the procedure of JESD51-14. The results demonstrate that the R_θJC at 40 W power dissipation are about 0.791 K/W. In order to validate the method, measurements following MIL Std 833 have been done, and the results are consistent with the existing papers.     

High temperature transport kinetics in heteroepitaxial LaFeO3 thin films

Heteroepitaxial LaFeO₃(1 1 0) thin films with a thickness of 150 nm were grown on LaAlO₃(0 0 1) by reactive sputtering in an inverted cylindrical magnetron geometry. Equilibrium conductivity was measured as a function of partial pressure of oxygen at T=1000 °C, and logσ plotted vs. logP(O₂) showed a minimum in conductivity for P(O₂)=10⁻¹¹ atm and a linear response between 10⁻¹⁰ and 1 atm. This linear response makes thin films of LaFeO₃ a promising material for oxygen sensor applications. We have also measured the time response of the film conductivity upon an abrupt change in the partial pressure of ambient oxygen from 10⁻² to 10⁻³ atm, which was determined at 60 s for T=700 °C and <3.5 s at T=1000 °C.     

Evaluation of SiGe:C HBT intrinsic reliability using conventional and step stress methodologies

The reliability of SiGe:C HBT devices fabricated using the Freescale’s 0.35-μm RF-BICMOS process was evaluated using both conventional and step stress methodologies. This device technology was assessed to determine its capability for various power amplifier applications (e.g., WLAN, Bluetooth, and cellular phone), which are more demanding than conventional circuit designs. The step stress method was developed to allow a rapid evaluation of product reliability, as well as, a quick method to monitor product reliability. For all tests the collector current I_C and collector voltage V_C were kept constant throughout the test, and the current gain β (I_C/I_B) was continuously monitored. The nominal bias condition was V_C = 3.5-V and J_C = 50-kA/cm² (or 0.5-mA/μm²). The “failure criterion” for all reliability evaluations was −10% degradation in β from the initial value at the start of each stress test or interval. The median time to failure (MTTF) at a junction temperature (T_JCN) of 150 °C for the conventional stress test was 1.86E6-h, and the thermal activation energy was 1.33-eV. In contrast for the temperature step stress tests the combined results gave an MTTF at T_JCN = 150 °C of 5.2E6-h and a thermal activation energy of 1.44-eV. Considering the differences in the two test methods, these results are quite close to one another. The intrinsic reliability of this device at the nominal bias condition and T_JCN = 150 °C is more than adequate for a 5-year system life.     

Determination of the exciton energy from electron beam excited luminescence in direct gap semiconductors

The exciton radiative recombination spectra of CuCl, ZnSe, CuGaS₂ and AgGaSe₂ have been investigated at 300 K. The sample was excited by electron beams of different energies. The reabsorption is determined by the ratio η of the spectra obtained for different electron beam energies such as 5 and 40 kV. This ratio is independant of hv when the absorption coefficient α is small (< 10³cm⁻¹). It increases when α becomes larger than the inverse of the penetration depth ( 3 μ) of the 40 kV electron beam. In this case, η is approximately proportional to the absorption coefficient. In particular, its maxima give the excitonic energies E_ex. We find the following values, in agreement with previous reflectivity and absorption measurements: for CuCl, E_ex(Z₃) = 3.26 eV and E_ex(Z₁₂) = 3.33 eV: for ZnSe, E_ex = 2.70 eV; for CuGaS₂, E_ex(A) = 2.46 eV and E_ex(B) = 2.59 eV. In the case of AgGaSe₂, there is no peak in the η spectrum and we have fitted our data to a broadened exciton model. We obtain E_ex(A) = 1.80 eV.     

Exact fiducial bounds for the reliability of series systems with components having exponential time to failure distributions

Series systems with dissimilar components which have exponential times to failure, with parameters α_j, are considered. The fiducial distribution of the system parameter, φ = Σ α_j, is derived. This distribution is used to construct fiducial bounds for φ and for the reliability of the system R. Illustrative examples are given and the results are compared with three approximate fiducial bounds.     

Characterization of ohmic contacts in polymer organic field-effect transistors

It is well known that contact resistance R_c limits the performance of organic field-effect transistors (OFETs) that have high field-effect mobilities (μ_FET ≳ 0.3 cm² V⁻¹ s⁻¹) and short channel lengths (L_ch ≲ 30 μm). The usual transfer-line method (TLM) to analyze R_c calls for extrapolation of total resistance to zero L_ch at constant drain and gate voltages. This requires an unrealistic assumption that R_c does not vary with source−drain current I_sd (nor with channel carrier density σ). Here we describe a self-consistent TLM analysis that instead imposes the condition of constant I_sd and σ. The results explicitly reveal the dependence of R_c on I_sd and σ. We further describe how this R_c(I_sd, σ) surface can be modelled to yield the specific contact resistivity ρ_c of the metal/organic semiconductor (OSC) interface, a key parameter that has so far been neglected in OFETs. We illustrate the application of these analyses to high-performance staggered top-gate bottom-contact poly(2,5-bis(alkyl)-1,4-dioxopyrrolo [3,4-c]pyrrole-3,6-diyl-terthiophene-2,5″-diyl) (DPPT2-T) OFETs fabricated on bottom Au source–drain electrode arrays, with high contact-corrected μ_FET of 0.5 cm² V⁻¹ s⁻¹. We show that when these electrodes are modified to impose weak, and then strong hole-doping of the DPPT2-T interface, R_c diminishes and its dispersion, i.e. dependence on I_sd and σ, weakens. The ultimate ρ_c attained for the strongly hole-doped contact is ca. 1 Ω cm², broadly independent of I_sd and σ, which we propose is a hallmark of a true metal/OSC ohmic contact. For comparison, the bare Au/DPPT2-T contact gives ρ_c of the order of 10 Ω cm² with a marked σ dependence. The lowest ρ_c reached here shortens the current transfer length down to ca. 5 μm, enabling short electrode lengths to be advantageously employed in technology.