Supporting Information
Significant thermal conductivity reduction of silicon nanowire arrays through discrete surface doping of germanium
Ying Pan, Guo Hong, Shyamprasad N. Raja, Severin Zimmermann, Manish K. Tiwari, Dimos
Poulikakos a)
1. Silicon nanowire fabrication
P-type, (100) oriented silicon (Si) chips (resistivity of ca. 10–30 Ohmcm) were used in the experiments. The surfaces of the Si chips were made hydrophilic as follows. First, the Si substrate was rinsed in acetone and isopropyl alcohol (IPA) at room temperature for 10 minutes to remove any organic contamination. Subsequently, the Si chip was rinsed in piranha solution (3:1 (v/v) H
2
SO
4
/H
2
O
2
), buffered hydrofluoric (HF) acid solution and another fresh
Piranha solution for 30 minutes. Finally, the silicon chip was rinsed with deionized (DI) water several times and was dried in nitrogen.
Polystyrene (PS) spheres with diameter of 300 nm were purchased from Bangslab Company.
The PS sphere solution (10%) was mixed with DI water and surfactant (4:4:3 by volume) before assembly of the monolayer arrays. The surfactant used for dispersing the polystyrene beads is sodium dodecyl sulfate (SDS) mixed with DI water (1.2345:100 by weight). The monolayer of PS beads was generated with a standard spin-coating method. The Si chip was mounted onto the spinner and a drop of 80 µl diluted PS beads solution was applied to the chip. The spinning program was 1300 rpm for 120 s and 1500 rpm for 30 s. A large area of close-packed monolayer of PS beads was thus formed on the Si chip.
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The size of the PS beads was reduced slowly by reactive ion etching (RIE). The flow of gases in the RIE (Oxford Instrument Plasma lab 80) treatment were oxygen and argon at a flow rate of 9.1 sccm and 90.9 sccm, respectively, and a pressure of 53 μbar, and the applied radio frequency (RF) power was 50 W. The diameter of the PS beads can be reduced to the desired value by varying the etching time. The thermal deposition of the gold film was conducted in a vacuum evaporator (Evaporation Plassys II) at a pressure of 1×10
-7
Pa with deposition rate of
0.1 nm/s. The thickness of the gold film was 12 nm for all the samples discussed in this work.
For the metal assisted etching process, an etching mixture consisting of DI water, HF and
H
2
O
2
(88.5:10:1.5 by volume) was used at room temperature. The concentrations of HF and
H
2
O
2
were 48% and 30%, respectively. The etching time was varied from 30 to 60 min depending on the required length of the nanowires. After etching, the substrate was immersed in potassium iodide solution for 1 minute to remove the gold film. The PS beads were removed by immersion in toluene for 2 hours in a sonication bath. Subsequently, the sample was rinsed in isopropyl alcohol and DI water for 10 min. Finally, critical point drying was used to dry the nanowire samples. .
After drying, upstanding SiNW arrays with uniform length and diameter were formed. The deposition of the germanium (Ge) nanoparticles was also conducted in the vacuum evaporator as shown in Fig. S3. The thickness was set to be 3 nm. Due to the intrinsic shadow effect of the nanowire forest, Ge nanoparticles form evenly and randomly on the Si nanowire surfaces.
Ge-particle doped SiNWs were annealed in rapid thermal annealing (RTA) oven at 800 o
C for
10 minutes.
The Ge-doped SiNWs were detached from the substrate by probe sonication and collected in ethanol. The wires were suspended in ethanol and transferred to a carbon-copper grid for
TEM characterization.
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X-ray Photoelectron spectra were acquired with Sigma Probe (Thermo Electron Cooperation).
The X-ray source was a non-monochromatic Al Kα (1486.6 eV) twin anode run at 20 mA and
10 kV.
2. Sources of Measurement Errors
One prominent error source of the measurements is the contact thermal resistance R c
. To decrease R c
, a liquid metal paste (GaIn) was applied between the sample and the copper piston, followed by 1 bar pressure applied on the upper piston. A comparative method based on measuring two samples with the same diameter but different lengths was used to quantify the contact thermal resistance R s
and subtract its contribution from the total resistance measurement, obtaining the thermal resistance of the nanowire forest. The samples were fabricated in the same batch with different HF etch time, yielding different length but similar surface conditions.
Another error source in the measurement is the heat transfer losses from the four sidewalls of the nanowire arrays. For a 10 mm×10 mm chip, it was calculated that only 0.012% of the nanowires was located at the sidewalls of the nanowire arrays. Under such circumstance, the heat transfer loss induced by these sidewall nanowires does not introduce noticeable errors in our measurements.
3. Error Analysis-Thermal resistance
The individual contributions to the measurement errors are listed in Table S1. The temperature measurement error is defined as the double standard deviation of the individual measurements. The needle type sensor positioning with an outer diameter of 0.5mm
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(HTMQSS-IM050U-45) is estimated to be around ±0.06mm. The liquid metal and copper thermal properties are based on handbook values.
1
To derive the overall thermal resistance δR tot
error, Gaussian error propagation is used in equation S2, where γ i
denotes the i-th contribution parameter.
𝑅 𝑡𝑜𝑡
=
𝑇 𝑠,𝑢
−𝑇 𝑠,𝑙
(S1)
𝑄 𝛿𝑅 𝑡𝑜𝑡
𝜕𝑅 𝑡𝑜𝑡
𝜕𝛾 𝑖 𝛿𝛾 𝑖
)
2
𝛾 𝑖 𝜖[𝑇 𝑠,𝑢
, 𝑇 𝑠,𝑙
, 𝑄, 𝐴, 𝑘
𝐶𝑢
] (S2)
In order to keep the derivation simple and clear, the error propagation is divided into multiple error propagations.
Cu piston end temperature is
𝑇 𝑠,𝑢
= 𝑏𝑧 𝑠,𝑢
+ 𝑐 (S3) where Z s,u
is the piston end position, b and c are determined by linear regression. Slope b is defined as the average of the slopes from the temperature regression lines for the upper and lower piston.
𝜕𝑏
𝜕𝑧 𝑖 𝛿𝑧 𝑖
) 2
𝜕𝑏
+ (
𝜕𝑇 𝑖 𝛿𝑇 𝑖
) 2 ] (S4)
The derivation for the lower piston end temperature T s,l
is approximately the same, except that care must be taken regarding the indices.
𝑇 𝑠
= 𝑇 𝑠,𝑢
− 𝑇 𝑠,𝑙
(S5) 𝛿𝑇 𝑠
= √(𝑧 𝑠,𝑢
− 𝑧 𝑠,𝑙
)𝛿𝑏 2 + 𝑏 2 (𝛿𝑧 2 𝑠,𝑢
+ 𝛿𝑧 2 𝑠,𝑙
𝜕𝑐
𝜕𝑧 𝑖 𝛿𝑧 𝑖
) 2 + (
𝜕𝑐
𝜕𝑇 𝑖 𝛿𝑇 𝑖
) 2 ]
2
(S6)
Heat flux,
𝑄 = −𝑏𝑘 𝑐𝑢
𝐴 (S7)
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𝛿𝑄 = √(𝛿𝑏𝑘
𝐶𝑢
𝐴) 2 + (𝑏𝛿𝑘
𝐶𝑢
𝐴) 2 + (𝑏𝑘
𝐶𝑢 𝛿𝐴) 2
(S8)
Thermal conductance, 𝛿𝑅 𝑡𝑜𝑡
= √( 𝛿𝑇 𝑠
𝑄
𝐴)
2
+ (
𝑇 𝑠
𝑄 𝛿𝐴)
2
+ (
𝑇 𝑠
𝑄 2 𝛿𝑄)
2
(S9)
Hence, the average thermal resistance uncertainty of the sample from eq. (S9) is close to 4% for 3μm nanowires (upper bound of uncertainty is close to 9%).
4. Error Analysis-Thermal conductivity
In addition to the thermal resistance errors above, one needs to characterize the uncertainties of length, diameter and nanowire coverage coefficient of the sample. The thermal conductivity uncertainty can be obtained from: 𝛿𝑘 𝑘
= √( 𝛿𝑅
𝑅
)
2
+ ( 𝛿𝑙 𝑙
)
2
+ 2 ( 𝛿𝑑 𝑑
)
2
+ ( 𝛿(𝑛𝐴 𝑛𝐴 𝑠 𝑠
)
)
2
(S10)
The length and diameters of the nanowires can be measured using an SEM with an uncertainty of 5 to 10nm. To obtain the individual nanowires, the sample was immersed in
IPA aqueous solution. After short, low energy ultrasonic treatment for 2minutes, the nanowires disperse into the solution and practically none remains on the growth substrate. For a 3μm (or 6μm) long nanowires, δ(l)
/ l =6.7% (or 3.3%). The uncertainty of the diameter measurement (from SEM images) was about 5nm, this introduces an uncertainty δ(d) / d =5% to the calculated thermal conductivity. Moreover, the PS bead spin coating defect leads to
δ(nA s
) / nA s
=10% nanowire coverage uncertainty. Taking into account the above partial errors, the uncertainties of thermal conductivities are 14.3% (SiNW 3 μm), 14.4% (Si/Ge NW 3 μm), and 14.3% (Si/Ge NW annealing 3 μm), respectively, based on eq. (S10).
1 C. L. Yaws, Handbook of thermal conductivity, Volume 4 Inorganic compounds and
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elements (Gulf Professional publishing, Houston, 1997).
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Table S1. Magnitude of the measurement errors
Description
Temperature Measurement error
Sensor Placement Error
Manufacturing Tolerance
Liquid Metal Thermal Properties
Copper Thermal Properties
Symbol Unit
δT i
[K]
δz i
δz s,u/l
δR th, LM
δk
Cu
[mm]
[mm]
[Kmm
2
/W]
[W m
-1
K
-1
]
Error
±0.1
±0.06
±0.05
1.7±0.4
403±2
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FIG. S1. (a) Photograph of the thermal tester. (b) Schematic of the bulk thermal tester. Two copper pistons were used as top and bottom contacts to the sample. A resistance heater was mounted on top of the upper piston. The lower piston was placed on a cold plate with a water cooler and served as a heat sink. A liquid metal paste (GaIn) was applied between the copper piston and the sample. Twelve thermocouples were used to measure the temperature distribution along the copper piston.
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FIG. S2. Overall thermal resistance of different samples including upper and lower contact resistances.
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FIG. S3. Deposition of the germanium (Ge) nanoparticles on SiNWs in vacuum chamber
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