High-Frequency Characterization and Modeling of Integrated Circuit Interconnect Lines

Abstract

본 학위 논문은 칩투칩 혹은 모듈간 배선 설계에서 핵심적 역할을 하는 집적회로 전송선로의 고주파 특성화 및 모델링 방법에 대한 연구이다. 전송선로 관련 전기적 문제 및 기존의 해결 방법에 대한 조사하고, 현재까지 해결되지 않은 높은 손실의 유기 기판 상에 제작된 단일 및 결합 전송선로의 파라미터를 결정하는 새로운 실험적 특성화 및 모델링 방법을 제시한다. 더불어 혼합 유기 물질의 복소 유전율을 정확히 추출하는 방법에 대하여 논한다.

유기 물질 상에 제작된 단일 및 결합 전송선로는 주파수 종속 손실 및 공진 때문에 광대역 주파수에서 특성화 하기 어렵다. 따라서 제시하는 주파수의 함수와 실험 데이터를 결합하여 단일 전송선로의 직렬 임피던스 및 병렬 어드미턴스 파라미터를 광대역 주파수에서 모델링 한다. 결합 전송선로의 모델 파라미터의 경우, 단일 전송선로의 물리적 회로 모델과 결합 전송선로의 실험 데이터를 이용하여 기생 공진 현상들을 제거한다. 실험 데이터는 DC 저항 측정, 그리고 광학 프로필러 측정, 그리고 벡터 네트워크 분석기 및 마이크로파 프로브 팁을 이용하여 10 MHz부터 40 GHz까지 측정한 산란계수로 결정한다. 제시한 기술을 통해 전송선로를 고주파까지 안정적으로 특성화 하여 물리적 특성을 정확히 고찰할 수 있음을 보인다.

마이크로-스트립 전송선로에 주로 사용되는 혼합 유기 물질의 복소 유전율은 회로의 성능에 상당한 영향을 준다. 따라서 두 개의 서로 다른 유전 물질로 제작된 마이크로-스트립 전송선로의 실험 데이터와 단일 전송선로의 커패시턴스 및 컨덕턴스 모델을 결합하여 복소 유전율을 광대역 주파수에서 추출하는 방법을 제시한다. 제시한 방법의 물리적 타당성을 보이기 위해 전파 계수를 계산하고, 이를 공칭 값 및 측정 값과 기존의 방법으로 계산된 결과와 비교한다. 제시한 방법으로 특성화 된 복소 유전율은 고주파에서의 전송선로 손실을 정확하게 반영할 수 있다는 것을 보인다.

| This thesis is a study on the high-frequency characterization and modeling technique of integrated-circuit (IC) transmission lines (TLs) that play a key role in the design of interconnect lines between chips or modules. The transmission line-related electrical problems and existing solutions are investigated, and then new experimental characterization and modeling techniques are presented to accurately determine the parameters of single and coupled TLs fabricated on highly-lossy organic substrates that have been solved yet. Further, a technique of accurately extracting the complex permittivity of mixed organic materials is discussed.

Single and coupled TLs fabricated on organic materials are difficult to characterize over a broadband frequency due to the frequency-dependent loss and resonance. Therefore, series impedance parameters and parallel admittance parameters of a single TL are modeled over a broad frequency band by combining the proposed functions of frequency with experimental data. In the case of coupled TL parameters, parasitic resonance effects are eliminated by combining the physical circuit model of the single TL and the experimental data of the coupled TLs. Experimental data are determined by DC resistance measurement, optical profiler measurement, and the S-parameters measured from 10 MHz to 40 GHz using a vector network analyzer and microwave probe tips. It is shown that the single and coupled TLs on organic substrates can be reliably characterized up to high-frequencies, thus the physical characteristics can be accurately investigated.

The complex permittivity of the mixed organic materials used widely in micro-strip TLs has a significant effect on the performance of the circuit. Therefore, a technique of extracting complex permittivity at broadband frequencies by combining experimental data of two different dielectric materials with the capacitance and conductance models of the single TL models is presented. In order to show the physical validity of the determined complex permittivity of mixed organic materials, the wave propagation factor is calculated and compared with conventional methods’ nominal and measured value. The complex permittivity characterized by the proposed technique is shown to reflect accurately the loss of a TL at the high frequency.; This thesis is a study on the high-frequency characterization and modeling technique of integrated-circuit (IC) transmission lines (TLs) that play a key role in the design of interconnect lines between chips or modules. The transmission line-related electrical problems and existing solutions are investigated, and then new experimental characterization and modeling techniques are presented to accurately determine the parameters of single and coupled TLs fabricated on highly-lossy organic substrates that have been solved yet. Further, a technique of accurately extracting the complex permittivity of mixed organic materials is discussed.

Single and coupled TLs fabricated on organic materials are difficult to characterize over a broadband frequency due to the frequency-dependent loss and resonance. Therefore, series impedance parameters and parallel admittance parameters of a single TL are modeled over a broad frequency band by combining the proposed functions of frequency with experimental data. In the case of coupled TL parameters, parasitic resonance effects are eliminated by combining the physical circuit model of the single TL and the experimental data of the coupled TLs. Experimental data are determined by DC resistance measurement, optical profiler measurement, and the S-parameters measured from 10 MHz to 40 GHz using a vector network analyzer and microwave probe tips. It is shown that the single and coupled TLs on organic substrates can be reliably characterized up to high-frequencies, thus the physical characteristics can be accurately investigated.

The complex permittivity of the mixed organic materials used widely in micro-strip TLs has a significant effect on the performance of the circuit. Therefore, a technique of extracting complex permittivity at broadband frequencies by combining experimental data of two different dielectric materials with the capacitance and conductance models of the single TL models is presented. In order to show the physical validity of the determined complex permittivity of mixed organic materials, the wave propagation factor is calculated and compared with conventional methods’ nominal and measured value. The complex permittivity characterized by the proposed technique is shown to reflect accurately the loss of a TL at the high frequency.