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표면파 측정법을 이용한 구리 박막의 특성 평가

김태형1,2, 김윤영1,#orcid

Characterization of a Copper Thin Film Using the Surface Acoustic Wave Measurement Technique

Taehyung Kim1,2, Yun Young Kim1,#orcid
Journal of the Korean Society for Precision Engineering 2024;41(3):183-189.
Published online: March 1, 2024

1 충남대학교 기계공학과

2 한국산업기술기획평가원

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#E-mail: y.kim@cnu.ac.kr, TEL: +82-42-821-6648
• Received: October 19, 2023   • Revised: December 25, 2023   • Accepted: January 2, 2024

Copyright © The Korean Society for Precision Engineering

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  • The elastic property of a copper (Cu) thin film was investigated using the surface acoustic wave (SAW) measurement technique. The Cu film was deposited on a quartz substrate using a direct current magnetron sputter and its surface morphology was inspected using atomic force microscopy. Time-domain waveforms of the SAW on the film were acquired at different propagation distances to estimate the Young’s modulus of Cu such that the experimentally-obtained dispersion curve can be compared to the analytical result calculated using the Transfer Matrix method for curve-fitting. Results showed that the film’s elastic property value decreased by 18.5% compared to that of the bulk state, and the scale effect was not significant in the thickness range of 150–300 nm, showing good agreement with those by the nanoindentation technique. The property, however, increased by 15.5% with the grain coarsening.
  • KEYWORDS: Copper, Thin film, Mechanical property, Surface acoustic wave, Laser measurement
  • KEYWORDS: 구리, 박막, 기계적 물성, 표면파, 레이저 측정

A

Amplitude

c

Wave Velocity

D

Field Matrix

E

Young’s Modulus

f

Frequency

k

Wavenumber

t

Time

u

Displacement

w

Angular Frequency

α

Longitudinal Wave Velocity

β

Transverse Wave Velocity

λ

The 1st Lamé’s Constant

μ

The 2nd Lamé’s Constant

υ

Possion’s Ratio

ρ

Density

σ

Stress

φ

Scalar Function

ψ

Vector Function
메모리 반도체, 애플리케이션 프로세서, 디스플레이 등의 전자제품 제조업에서 반도체 칩을 제작하기 위하여 박막증착, 노광, 식각 등의 공정을 활용한다. 이때, 수 마이크로미터에서 나노미터 단위의 두께를 갖는 박막은 벌크상태의 동일 재료와 비교할 때에 물성의 변화를 보이는 경우가 많은데, 이는 부피 대비 높은 표면적과 그에 따라 증대되는 미세구조의 영향성에 기인한다. 따라서, 반도체 공정을 통하여 생산되는 제품의 불량을 줄이고 수율을 높이기 위해서는 박막의 물성에 대한 정보를 정확히 파악하고 있어야 한다. 그중 탄성계수는 변형에 대한 재료 강성도를 나타내며, 제품설계 및 공정에 고려되어야 할 핵심요소이다.
박막의 탄성계수를 측정하는 방법에는 여러 가지가 있는데, 레이저 초음파를 활용한 비파괴 검사법은 레이저로 시험편에 유도 초음파를 발생시키고, 그 전파특성을 분석하여 물성을 측정하는 방법이다. 이는 매질의 밀도, 탄성계수, 푸아송비 등 재료 물성에 따라 초음파의 전파거동이 달라지는 원리를 활용한다. 이와 관련한 선행연구로는 Cai 등[1]이 박막의 두께 효과를 확인하기 위해 레이저 초음파를 활용하여 23-225 μm 두께의 구리가 갖는 탄성계수를 측정하였다. Grünwald 등[2]은 695 nm 두께의 텅스텐 박막에 펄스 레이저광을 조사하고 유도 초음파를 검출하여 탄성계수를 측정하였다. Sherman 등[3]은 기판과 200 nm 구리박막 사이의 잔류응력 측정을 위해 표면파를 측정하고 유한요소 모델과 비교분석 하였다. Kudělka 등[4]은 실리콘 기판 위에 증착된 34-156 nm 두께의 석영 박막을 나노압입시험법과 표면파 측정법을 사용하여 탄성계수를 측정하였고, 두께가 작을수록 실험결과 간 오차가 증가함을 확인하였다.
그 외 다양한 선행연구[5-7]에도 불구하고 나노스케일 박막의 물성 평가에 관한 연구는 여전히 충분하지 않다. 특히, 나노압입 시험법 등 기존의 측정법으로는 신뢰도 높은 물성 평가가 어려운 300 nm 이하 두께의 박막에 대해서 더 많은 연구가 필요하다. 따라서, 본 연구에서는 나노스케일에서도 높은 정확도를 갖는 표면파 측정법을 사용하여 구리 박막의 탄성계수를 평가하였다. 구리는 타 금속과 비교하여 높은 전기전도도를 가지고 있기 때문에 알루미늄을 대체할 반도체 금속배선 소재로 각광받고 있다. 다만, 박막 공정의 미세화 추세로 야기되는 구리 결정립 감소는 전기적 저항을 증가시키므로 이를 보완하기 위해 열처리를 통해 결정립의 크기를 증가시키는 연구[8-10]가 있었다. 하지만, 열처리 후 기계적 특성의 변화에 관한 연구는 미흡하므로 본 연구에서 그 효과를 살펴보았다.
본 연구에서 이론해를 구하기 위하여 Lowe의 전달 행렬법[11]을 사용하였다. 그 내용을 간략히 정리하면 다음과 같다: 3차원 직교좌표계 상의 등방성 무한 탄성체에서 벡터 형식의 파동방정식은 다음과 같다:
(1)
ρ∂2u∂t2=λ+μ+∇∇⋅u+μ∇2u=0
여기서 ρ는 밀도를, u는 변위를, t는 시간을, 그리고 λ와 μ는 각각 라메의 제1 계수와 제2 계수를 뜻한다. Helmholz의 분산정리[12]에 따르면, 닫힌 표면적에서의 경계조건이 정해진 벡터함수는 스칼라 함수(ϕ)와 벡터 함수(Ψ)에 의해 표현될 수 있으며, 이를 응용하면 파동의 종파(L)를 스칼라 함수(ϕ), 횡파(S)를 벡터 함수(Ψ)로 하여 아래와 같이 나타낸다:
(2)
u=uL+uS=∇ϕ+∇×Ψ
(3)
ϕ=ALeik⋅x-wt=ALeik1x1+k2x2+k3x3-wt
(4)
Ψ=ASeik⋅x-wt=ASeik1x1+k2x2+k3x3-wt
여기서 k는 파수를, 그리고 w는 각주파수를 뜻한다. 식(2)의 해를 구하기 위해 종파변위(uL)와 횡파변위(us)를 각각 대입할 경우, 아래의 식을 얻을 수 있다:
(5)
ρ∂2uL∂t2=λ+2μ∇2uL=0
(6)
ρ∂2uS∂t2=μ∇2uS=0
식(5), 식(6)을 종파속도(cL)와 횡파속도(cs)에 관하여 표현하면 다음과 같다:
(7)
λ+2μρ=∂2uL∂t2∇2uL=∂2∇ϕ∂t2∇3ϕ=w2ϕk2ϕ=cL2
(8)
μρ=∂2uS∂t2∇2uS=∂2∇×Ψ∂t2∇2∇×Ψ=w2Ψk2Ψ=cS2
라메상수(λ, μ)는 탄성계수(E)와 푸아송비(υ)로 표현할 수 있으므로 종파속도와 횡파속도는 다음과 같이 정리된다:
(9)
cL=wk=λ+2μρ=E1-vρ1+v1-2v=α
(10)
cS=wk=μρ=E2ρ1+v=β
그리고 탄성체를 구성하는 층간 파동전파를 표현하기 위해 식(2)의 종파변위와 횡파변위를 행렬식으로 표현하면 식(11), 식(12)로 나타낼 수 있으며, 이는 Fig. 1의 반무한매질 기판 위 단층 박막을 모델로 한다. 이때, 두께 방향(x3)의 변화는 없는 것으로 가정한다.
(11)
uL=∇ϕ=k1k20ALeik⋅x-wt
(12)
uS=∇×Ψ=k2-k10ASeik⋅x-wt
Fig. 1

A layer of thin film on a semi-infinite half space

KSPE_2024_v41n3_183_f001.jpg
층별 파동 전파는 층간 경계에서 반사 또는 굴절되며 파동의 주파수와 파수는 Snell 법칙에 의하여 x1 방향으로 동일하다. 즉, 같은 층에서 변위와 응력은 같은 주파수와 파수(k1)에 의해 영향을 받는다고 볼 수 있으므로 아래의 공통변수로 나타낸다:
(13)
F=eik1x1-wt
그리고 각층에 대한 k2는 식(9), 식(10)을 통해 k1에 관한 식으로 표현한다:
(14)
k2L±=±w2α2-k12
(15)
k2S±=±w2β2-k12
식(11)부터 식(15)를 행렬식의 형태로 정리하면 다음과 같이 된다:
(16)
u1u2σ22σ21=DAL+AL-AS+AS-
여기서 [D]는 변위/응력과 파동의 진폭 간 관계를 나타내는 4×4 행렬이다[11]. 파동의 분산곡선을 구하기 위해 진폭에 관한 식으로 변환하면 아래와 같이 나타낸다:
(17)
AL+AL-AS+AS-subst =Dsubst,top-1u1u2σ22σ21subst,top =Dsubst,top-1Lfilmu1u2σ22σ21film,top =Su1u2σ22σ21film,top 
여기서 하첨자 subst는 기판을, film은 박막을 나타내며, top은 각 층의 윗면을, bottom은 아랫면을 나타낸다. 경계조건으로부터 박막의 윗면은 자유표면으로 무응력상태(σ12 = 0, σ22 = 0)이며, 기판은 반무한매질이므로 기판의 바닥면으로부터 반사되는 파동 성분이 없기 때문에 AL-과 AS-또한 0이 된다. 따라서 이는 다음과 같이 정리된다:
(18)
AL+0AS+0subst =Su1u200film,top 
(19)
00=S21    S22S41    S42u1u2=S'u1u2
최종적으로 det[S’] = 0인 해의 조합을 찾으면 분산곡선을 얻을 수 있다.
3.1 시험편 및 표면분석
10 nm 두께의 TaN 확산방지막이 증착된 2인치 석영 웨이퍼에 DC 스퍼터링(ENDURA-5500 by Applied Materials)으로 150 nm와 300 nm두께의 구리박막을 성장시켰다. 박막의 두께는 2D Profiler (Dektak-8 by Veeco Instruements)로 단차를 10회 측정 후 평균하여 확인하였다. 결정립 성장이 탄성계수에 미치는 효과를 확인하기 위하여 400ºC에서 15초간 급속 열처리(AW610 by Allwin21)을 하였으며, 질소 분위기에서 10ºC/s의 율로 가열 및 냉각을 하였다. 결정립의 크기 변화를 관찰하기 위하여 열처리 전후로 원자힘현미경(XE-100 by Park Systems)을 사용하여 1 × 1 μm2의 면적을 스캔하였고, NanoScope Analysis 소프트웨어 프로그램을 사용하여 그 크기를 정량화하였다. 표면파 측정결과의 타당성을 검증하기 위하여 300 nm 시험편에 대하여 연속강성측정이 가능한 나노압입시험(INano by KLA-Tencor)을 9회 실시 후 결과를 평균하였다. 측정조건은 최대압입하중 35 mN, 최대압입깊이 300 nm, 진동수 100 Hz, 최대하중유지시간 1 초로 설정하였다.
3.2 표면파 측정 실험
1,030 nm 파장, 1.5 ns 펄스폭, 1 kHz 반복률, 500 μJ 펄스 에너지의 레이저(Flare NX by Coherent)로 표면파를 생성하였으며, 532 nm 파장, 100 mW 파워의 연속파 레이저(Sapphire SF by Coherent) 기반의 마이켈슨 간섭계를 사용하여 파형을 검출하였다. 1 GHz 대역폭의 오실로스코프(WaveSurfer 510 by Teledyne LeCroy)를 사용하여 파형을 30,000번 평균하여 수집하였으며, 두 지점 이상에서 측정한 시간영역의 파형 함수 Φ(t)를 고속 푸리에 변환하여 주파수영역의 함수 Φ(f)를 구하였다. 그러면 아래의 식을 통해 위상속도(v)와 주파수 (f)에 관한 함수를 도출할 수 있다[13]:
(20)
vf=x2-x12πfΦ2f-Φ1f
이와 같이 실험으로부터 얻은 분산선도를 식(19)의 이론해와 곡선맞춤 하여 탄성계수를 추정하였으며, Fig. 2에 시행착오법에 관한 절차를 순서도 형식으로 나타내었다.
Fig. 2

The optimization process between experimental and theoretical data

KSPE_2024_v41n3_183_f002.jpg
4.1 300 nm 시험편 측정 및 검증
상대적으로 두꺼운 300 nm 시험편에 대하여 표면파 측정 실험과 나노압입시험을 병행하여 결과의 타당성을 비교 검증하였다. 먼저, 오실로스코프로 획득한 시간영역 파형을 Fig. 3에 나타내었으며, 파동의 전파거리가 길어질수록 고주파수 성분의 파동의 도달 시간이 늦어지는 전파 거동을 확인할 수 있다. Fig. 4는 식(20)을 사용하여 두 개의 파형으로부터 얻은 분산곡선을 보여주며, 이론해와 곡선맞춤한 결과 106±2 GPa의 탄성계수 값을 얻었다. 이때, ρCu = 8,900 kg/m3, ρquartz = 2,202 kg/m3, Equartz = 72 GPa, υCu = 0.35, υquartz = 0.18의 값을 적용하였다.
Fig. 3

Time-domain waveforms of the surface acoustic wave on the 300 nm-thick film: (a) at the reference position, (b) at a propagation distance of 5.0 mm

KSPE_2024_v41n3_183_f003.jpg
Fig. 4

The dispersion curve of the 300 nm-thick film and the curve-fitting result. Dashed lines are the error bounds (±2 GPa in terms of the Young’s modulus)

KSPE_2024_v41n3_183_f004.jpg
다음으로, 나노압입시험결과를 Fig. 5에 나타내었다. 참고로, 나노압입시험에서 모재효과를 배제하기 위하여 시료 두께의 10% 미만으로 압입깊이를 설정하는 것이 일반적인데, 30 nm 이하로 압입깊이가 줄어들면 압입하중-변위곡선이 왜곡되고 오차가 증가하여 신뢰도 있는 결과를 얻기 어렵다. 따라서, 본 연구에서는 압입깊이가 시험편 두께의 10%인 지점에서의 탄성계수를 대표 값으로 하였다. 또한, 압입깊이의 증가에 따라 모재효과로 탄성계수가 감소하는 것을 볼 수 있으며, 박막 두께의 1/10 지점에서의 값은 100±5 GPa인 것을 볼 때에, 본 실험결과와 상대오차 5.7% 범위 내에서 잘 일치하는 것을 확인하였다. 이로부터 14-33 nm 압입깊이 범위의 나노압입시험결과가 본 측정결과와 ±5% 오차범위 내에서 신뢰성 있는 구간으로 간주한다. 한편, 실리콘 기판 위에 스퍼터로 증착된 300 nm 두께의 구리 박막에 대하여 나노압입시험을 실시한 Cao 등[5]의 실험과 비교하면 약 2.8%의 상대오차를 확인하여 거의 유사한 결과를 보였다. 구리의 경우 거시재료의 물성이 130 GPa 내외로 알려져 있으며[6,7], Grünwald 등[2]의 실험에서 1 μm 두께의 구리박막이 갖는 탄성계수는 132 GPa로 나타난 점을 볼 때, 본 실험결과로부터 박막상태에서 탄성계수가 약 18.5% 감소하는 것이 확인된다.
Fig. 5

The nanoindentation testing result on the 300 nm-thick film

KSPE_2024_v41n3_183_f005.jpg
4.2 150 nm 시험편 측정 및 결정립 성장 효과 연구
150 nm 두께의 구리 박막에 대하여 동일한 실험절차를 반복하여 탄성계수를 구하였다. Fig. 6은 실험으로부터 얻은 분산선도와 이론해를 곡선맞춤한 결과를 보여준다. Ecu = 103±3 GPa의 결과를 얻어 300 nm 시험편과 유사한 값을 확인하였으며, 본 시험편의 두께 범위에서는 크기효과가 나타나지 않는 것을 알 수 있었다.
Fig. 6

The dispersion curve of the 150 nm-thick film and the curve-fitting result. Dashed lines are the error bounds (±3 GPa in terms of the Young’s modulus)

KSPE_2024_v41n3_183_f006.jpg
결정립 성장에 따른 물성 변화를 살펴보기 위하여 급속 열처리를 실시한 시험편을 측정한 결과 119±3 GPa의 값을 얻어 탄성계수가 약 15.5% 증가한 것을 확인하였다. Fig. 7은 열처리한 시험편에 대한 분산선도 결과를 보여준다. 원자힘현미경으로 표면을 관찰한 결과 Fig. 8에 나타난 것과 같이 결정립의 성장이 확인되었으며 평균 크기가 85.6 nm에서 192.2 nm로 약 2.2배 성장하였다. 이처럼 결정립의 성장에 따라 탄성계수가 증가하는 경향은 수치해석 및 분자동역학 시뮬레이션 연구에서 보고된 바 있는데, Zhu 등[14]은 결정립 표면의 경계 에너지와 결정립 경계의 비 국소적 상호작용에 의한 나노결정 재료의 탄성계수 변화를 살펴보았으며, 100 nm 미만의 결정립 크기 변화 구간에 대하여 유효 탄성계수가 증가하는 경향을 얻었다. Phillpot 등[15]과 Schiøz 등[16]은 분자동역학 연구를 통해 나노결정 구리에서 결정립 크기의 감소에 따라 탄성계수 또한 감소하는 경향을 보고하였다. Kim 등[17] 또한 30-60 nm 크기 범위의 구리결정립에 대하여 탄성계수가 4.6% 증가하는 해석결과를 확인하였다.
Fig. 7

The dispersion curve of the 150-nm thick film after heat treatment and the curve-fitting result. Dashed lines are the error bounds (±3 GPa in terms of the Young’s modulus)

KSPE_2024_v41n3_183_f007.jpg
Fig. 8

Atomic force microscopy images of the 150 nm films: (a) as-deposited, (b) heat-treated. Note that the scan area was 1 × 1 μm for both samples

KSPE_2024_v41n3_183_f008.jpg
본 연구에서 사용된 표면파 측정법을 다른 재료의 특성 평가에 적용하기 위해서는 박막이 펄스파를 흡수할 수 있도록 해당 파장에서 충분한 광침투깊이를 가져야 하며, 그와 동시에 표면변위 측정을 위해 간섭계의 레이저광을 반사할 수 있어야 한다. 금속박막의 경우 레이저 초음파의 생성과 검출에 큰 어려움이 없는 반면, 질화규소나 산화실리콘처럼 광투과도가 높은 재료의 경우 표면에 금속층을 추가로 증착할 필요가 있으며, 그에 따라 해석 모델도 단층박막에서 이층박막으로 확장되어야 한다. 이러한 한계를 극복하기 위하여 추가적인 연구가 필요하다.
본 연구에서는 표면파 측정법을 사용하여 나노스케일 구리박막의 탄성계수를 평가하고, 결정립 성장 효과를 분석하였다. 300 nm 시험편의 탄성계수를 측정한 결과 106±2 GPa의 값을 얻었으며, 나노압입시험과 비교 검증한 결과 5.7%의 상대오차를 확인하였다. 150 nm 시험편의 탄성계수 역시 103±3 GPa로 측정되어 크기효과는 나타나지 않는 것을 확인하였다. 한편, 박막을 급속 열처리한 경우 탄성계수가 15.5% 증가하여 결정립 성장이 기계적 물성에 미치는 영향을 확인하였다. 본 연구는 나노스케일 구리 박막의 특성을 규명함으로써 차세대 반도체 배선재 연구, 나노소자 안정성 설계 등 다양한 응용분야에 기여할 것으로 기대된다.
본 연구는 충남대학교 학술연구비에 의해 지원되었음. 스퍼터 증착과 2D profiler, 나노압입시험은 나노종합기술원의 연구장비를 사용하였음. 급속 열처리와 원자힘현미경 측정은 울산과학기술원 연구지원본부의 연구장비를 사용하였음.
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Taehyung Kim
KSPE_2024_v41n3_183_bf001.jpg
Assistant researcher in the Program Planning Team at Korea Planning & Evaluation Institute of Industrial Technology. His research interest is technology evaluation.
Yun Young Kim
KSPE_2024_v41n3_183_bf002.jpg
Associate Professor in the Department of Mechanical Engineering, Chungnam National University. His research interest is laser ultrasonics and materials characterization.

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Characterization of a Copper Thin Film Using the Surface Acoustic Wave Measurement Technique
J. Korean Soc. Precis. Eng.. 2024;41(3):183-189.   Published online March 1, 2024
DOI: https://doi.org/10.7736/JKSPE.023.125
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Characterization of a Copper Thin Film Using the Surface Acoustic Wave Measurement Technique
J. Korean Soc. Precis. Eng.. 2024;41(3):183-189.   Published online March 1, 2024
DOI: https://doi.org/10.7736/JKSPE.023.125
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Characterization of a Copper Thin Film Using the Surface Acoustic Wave Measurement Technique
Image Image Image Image Image Image Image Image
Fig. 1 A layer of thin film on a semi-infinite half space
Fig. 2 The optimization process between experimental and theoretical data
Fig. 3 Time-domain waveforms of the surface acoustic wave on the 300 nm-thick film: (a) at the reference position, (b) at a propagation distance of 5.0 mm
Fig. 4 The dispersion curve of the 300 nm-thick film and the curve-fitting result. Dashed lines are the error bounds (±2 GPa in terms of the Young’s modulus)
Fig. 5 The nanoindentation testing result on the 300 nm-thick film
Fig. 6 The dispersion curve of the 150 nm-thick film and the curve-fitting result. Dashed lines are the error bounds (±3 GPa in terms of the Young’s modulus)
Fig. 7 The dispersion curve of the 150-nm thick film after heat treatment and the curve-fitting result. Dashed lines are the error bounds (±3 GPa in terms of the Young’s modulus)
Fig. 8 Atomic force microscopy images of the 150 nm films: (a) as-deposited, (b) heat-treated. Note that the scan area was 1 × 1 μm for both samples

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Characterization of a Copper Thin Film Using the Surface Acoustic Wave Measurement Technique
JKSPE : Journal of the Korean Society for Precision Engineering

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