초저전력 듀얼 밴드 박막 리튬 니오베이트 변조기: 저유전율 언더필 적용 및 390Gbit/s PAM8 전송 위한 220GHz 대역폭 달성

Kernekoncepter

저유전율 언더필을 적용한 박막 리튬 니오베이트 변조기를 통해 C-band 및 O-band에서 낮은 구동 전압, 넓은 광대역폭 및 높은 변조 효율을 동시에 달성하여 차세대 광통신 시스템에 활용 가능성을 제시했습니다.

Resumé

고성능 듀얼 밴드 박막 리튬 니오베이트 변조기 연구 논문 요약

본 연구 논문에서는 저유전율 언더필을 적용한 고성능 듀얼 밴드 박막 리튬 니오베이트(TFLN) 변조기를 설계 및 구현하여 기존 변조기의 전압-대역폭 제한을 극복하고 전반적인 성능 향상을 이루었습니다.
TFLN 변조기의 배경 및 필요성

TFLN은 높은 포켈스 효과, 우수한 온도 안정성, 넓은 투명도 창, 컴팩트한 전극 레이아웃을 위한 강력한 광학적 감금 등 뛰어난 재료 특성을 지니고 있어 다용도 광학 플랫폼으로 주목받고 있습니다.
고속 TFLN 전기 광학(EO) 변조기는 미래의 대용량 데이터 센터, 통신 시스템 및 양자 광학에 필수적인 요소입니다.
기존의 동일 평면 도파관(CPW) 전극 기반 TFLN 변조기는 낮은 반파 전압과 넓은 변조 대역폭을 동시에 확보하기 어려웠습니다. 전극 간격을 줄이면 마이크로파 손실이 증가하기 때문입니다.
본 연구의 목표
본 연구에서는 저유전율 언더필을 사용하여 전압-대역폭 제한을 극복하고 높은 변조 효율을 유지하면서 넓은 EO 대역폭을 달성하는 고성능 TFLN 마하젠더 변조기(MZM)를 제안하고 시연하는 것을 목표로 합니다.

저유전율 언더필의 역할

낮은 유전율을 가진 BCB 언더필을 메인 CPW 전극 아래에 형성하여 유효 유전율을 감소시킵니다.
분포 커패시턴스를 줄여 더 넓은 신호 전극을 사용할 수 있도록 하여 전극 저항과 마이크로파 손실을 줄입니다.
BCB 언더필의 두께를 조정하여 유효 마이크로파 굴절률을 조정하여 속도 매칭을 실현합니다.
시뮬레이션 결과

2.7μm의 전극 간격에서 광학 흡수 손실은 0.5dB/cm 미만으로 유지하면서 변조 효율은 C-band(O-band)에서 VπL ~ 1.3V·cm(1.09V·cm)로 추정됩니다.
2μm 두께의 BCB 레이어와 85μm 너비의 신호 라인을 채택하여 마이크로파 손실을 줄였습니다.
7mm 길이의 CL-TWE를 통합한 TFLN 변조기에 대한 시뮬레이션 결과, 약 220GHz의 6.4dB 전기 대역폭과 -17dB 미만의 S11을 갖는 우수한 임피던스 매칭을 나타냈습니다.
C-band(O-band)에서 3dB EO 변조 대역폭은 약 240GHz(244GHz)로 추정됩니다.

Vigtigste indsigter udtrukket fra

Ultra-High-Efficiency Dual-Band Thin-Film Lithium Niobate Modulator Incorporating Low-k Underfill with 220 GHz Extrapolated Bandwidth for 390 Gbit/s PAM8 Transmission

by Hao Liu, Yut... kl. arxiv.org 11-25-2024

https://arxiv.org/pdf/2411.15037.pdf

Dybere Forespørgsler

저유전율 언더필 기술은 다른 종류의 광 변조기나 광 집적 회로 소자에도 적용 가능할까요?

네, 저유전율 언더필 기술은 TFLN 변조기뿐만 아니라 다른 종류의 광 변조기나 광 집적 회로 소자에도 적용 가능성이 높습니다.

다른 종류의 광 변조기: 저유전율 언더필 기술의 핵심은 전자기파와 광파의 속도 차이를 줄여주고, 마이크로파 손실을 줄여 광 변조기의 대역폭과 효율성을 향상하는 데 있습니다. 이는 TFLN 변조기뿐 아니라,

실리콘 기반 변조기 (Silicon Photonics modulator): 실리콘 포토닉스는 저렴한 비용과 CMOS 공정 호환성으로 주목받고 있지만, 실리콘 자체의 광 변조 효율이 낮다는 단점이 있습니다. 저유전율 언더필 기술을 활용하면 전극 구조를 변경하지 않고도 변조 효율을 향상시킬 수 있습니다.
III-V족 화합물 반도체 변조기: 높은 전자 이동도를 가진 III-V족 화합물 반도체는 고속 광 변조기에 적합하지만, 높은 마이크로파 손실이 제한 요소입니다. 저유전율 언더필 기술을 통해 마이크로파 손실을 줄여 성능을 향상할 수 있습니다.

광 집적 회로 소자: 광 집적 회로에서는 소자의 집밀도가 증가함에 따라 도파관 사이의 간섭, 신호 손실 등의 문제가 발생합니다. 저유전율 물질을 이용하면 빛의 가둠 현상을 향상시키고, 도파관 사이의 간섭을 줄여 집적도를 높일 수 있습니다.
결론적으로 저유전율 언더필 기술은 광 변조기 및 광 집적 회로 소자의 성능 향상에 핵심적인 역할을 할 수 있으며, 다양한 플랫폼 및 소자 구조에 적용될 가능성이 높습니다.

저유전율 언더필을 사용함으로써 발생할 수 있는 단점이나 제한 사항은 무엇이며, 이를 극복하기 위한 추가적인 연구 방향은 무엇일까요?

저유전율 언더필 기술은 분명 많은 장점을 제공하지만, 몇 가지 단점과 제한 사항 또한 존재합니다.
단점 및 제한 사항:

열 관리: 저유전율 물질은 일반적으로 열전도율이 낮아 소자 동작 중 발생하는 열을 효과적으로 방출하지 못할 수 있습니다. 이는 소자의 성능 저하 및 수명 단축으로 이어질 수 있습니다.
공정 복잡성: 저유전율 물질을 기존 반도체 공정에 통합하는 것은 공정 단계 추가 및 재료 호환성 문제 등의 어려움을 수반할 수 있습니다.
장기 신뢰성: 저유전율 물질의 장기적인 신뢰성에 대한 연구는 아직 충분하지 않습니다. 특히 고온 또는 고습 환경에서 시간 경과에 따른 성능 변화는 중요한 연구 주제입니다.

극복을 위한 추가 연구 방향:

열 관리 개선: 높은 열전도율을 가진 저유전율 물질 개발, 또는 저유전율 물질과 기존 열 방출 기술을 접목하는 등의 연구가 필요합니다.
공정 단순화 및 비용 절감: 저온 경화, 자기 정렬 (self-alignment) 등의 공정 기술을 개발하여 공정 단계를 줄이고, 대량 생산에 적합한 저비용 공정 기술 개발이 필요합니다.
신뢰성 향상 및 평가 기술 개발: 다양한 환경 조건에서 저유전율 물질의 장기 신뢰성을 평가하고, 신뢰성을 예측하고 향상시킬 수 있는 기술 개발이 필요합니다.

결론적으로 저유전율 언더필 기술의 단점 및 제한 사항을 극복하기 위한 지속적인 연구 개발을 통해, 차세대 광통신 및 광 집적 회로 기술 발전에 기여할 수 있을 것입니다.

광통신 기술의 발전이 인공지능, 클라우드 컴퓨팅, 메타버스 등 미래 기술 발전에 어떤 영향을 미칠 수 있을까요?

광통신 기술의 발전은 데이터 전송 속도와 용량을 획기적으로 증가시켜 인공지능, 클라우드 컴퓨팅, 메타버스 등 미래 기술 발전에 필수적인 기반을 마련할 것입니다.

인공지능 (AI):

대규모 데이터 처리: 인공지능 학습에는 방대한 양의 데이터 처리가 필수적인데, 고속, 대용량 데이터 전송이 가능한 광통신 기술은 인공지능 학습 시간 단축 및 성능 향상에 기여할 수 있습니다.
실시간 데이터 분석: 자율 주행, 스마트 팩토리 등 실시간 데이터 분석 및 처리가 중요한 분야에서 광통신 기술은 빠른 응답 속도를 제공하여 시스템 안정성 및 효율성을 높일 수 있습니다.

클라우드 컴퓨팅:

데이터센터 상호 연결: 클라우드 컴퓨팅 환경에서는 여러 데이터센터 간의 빠르고 안zawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzawzaw