# Hot Carriers in CVD-Grown Graphene Device with a Top h-BN Layer

Authors: C. Chuang; M. Mineharu; N. Matsumoto; M. Matsunaga; C.-W. Liu; B.-Y. Wu; Gil-Ho Kim; L.-H. Lin; Y. Ochiai; K. Watanabe; T. Taniguchi; C.-T. Liang; N. Aoki
Journal: Journal of Nanomaterials
 (2018)

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## Abstract

We investigate the energy relaxation of hot carriers in a CVD-grown graphene device with a toph-BN layer by driving the devices into the nonequilibrium regime. By using the magnetic field dependent conductance fluctuations of our graphene device as a self-thermometer, we can determine the effective carrier temperature T
e at various driving currents I while keeping the lattice temperature T
L fixed. Interestingly, it is found that T
e is proportional toI, indicating little electron-phonon scattering in our device. Furthermore the average rate of energy loss per carrier P
e is proportional to (T
e
2
-
T
L
2), suggesting the heat diffusion rather than acoustic phonon processes in our system. The long energy relaxation times due to the weak electron-phonon coupling in CVD graphene capped with h-BN layer as well as in exfoliated multilayer graphene can find applications in hot carrier graphene-based devices.


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## Body

## 1. Introduction

Recently, researchers in the graphene community are much interested in hot carriers in graphene-based systems since they determine the performance of high-power and high-frequency electronics, thermal management of electronic devices, optoelectronic devices, the quantum Hall metrology, and bolometric detectors [1–6]. Most of the hot carrier graphene devices in the high carrier density limit (the Bloch-Gruneisen temperature (T
BG) > the lattice temperature (T
L)) show the dominant cooling power from a weak coupling of carriers to acoustic phonon processes [7–10], which is represented by a heat flow power law equationP = Σ
(
T
e
δ
-
T
L
δ
) [11], where δ = 4 is a characteristic exponent, T
e is the carrier temperature, T
L is the lattice temperature, and Σ is the coupling constant. Furthermore, disordered-enhanced properties in hot carrier graphene devices revealed the supercollision cooling processes, where δ = 3 [12–14]. Recently, hexagonal Boron Nitride (h-BN) bottom substrate can be a great heat drained material for disordered graphene so as to extremely reduce the carrier-phonon scattering via Wiedemann-Franz law heat diffusion, which is δ = 2 [15–17]. However, the carriers of energy relaxation in such h-BN/disordered graphene systems with less substrate phonon interactions following the Wiedemann-Franz law heat diffusion are rarely studied. A key parameter for discussing the cooling process is the energy relaxation time (τ
ϵ), the characteristic time when the thermal energy is lost by the carriers [18–20].To date, CVD-grown graphene appears to be a good candidate for large-scale graphene-based applications. However, as such a system may not be air stable, it is highly desirable to cap the CVD graphene with an inert layer so as to experimentally realize stable, large-scale, and scalable devices. To this end, we have prepared CVD graphene with a top h-BN layer and studied the hot carrier effects in such a device. In this report, we studied the conductance fluctuations and hot carrier effects using a large measurement current (I) so as to raise the effective T
e above T
L on h-BN/CVD graphene and multilayer exfoliated graphene due to their disordered properties. Based on the self-thermometer linear properties between T
e and I due to Wiedemann-Franz law heat diffusion, we can investigate energy relaxation cooling processes under high carrier density limit (T
BG
>
T
L) between the h-BN/CVD graphene and multilayer exfoliated graphene for future graphene-based applications. By determining τ
ϵ from T
e and input power P
e, we can find that τ
ϵ of the CVD graphene with a top h-BN layer is almost two orders of magnitude longer than those in exfoliated pristine monolayer/bilayer graphene. Such a result may find applications in hot carrier graphene-based transistors as a result of the weak electron-phonon coupling.


## 2. Experimental Section

### 2.1. Preparation of the Samples

As shown in the schematic diagram in Figure1(a), we used the scotch tape method to mechanically exfoliate high purity and homogenous h-BN crystals synthesized by high pressure techniques [21] and transferred them by Gel-Pak polymer using the viscoelastic effect [22] on commercial chemical vapor deposition (CVD) graphene/285 nm SiO2/Si substrate [23]. The CVD graphene region outsideh-BN sheet was etched by oxygen plasma so as to confine to our CVD graphene region under theh-BN sheet. CF4 gas was used to etch h-BN sheet protected by photoresist for 8 terminals and Cr/Au metal depositions as shown in Figure 1(b).Figure 1
(a) Schematic fabrication diagram of a top h-BN/CVD graphene device. (b) The top h-BN/CVD graphene device (sample A) with a scale bar of 10μm.
(a)
(b)


### 2.2. Electrical Measurements

An ac driving current from lock-in amplifiers passed into the source and drain contacts through the graphene devices for Hall-bar measurements. The magnetoresistance was measured in a He3 cryostat equipped with a superconducting magnet.


## 2.1. Preparation of the Samples

As shown in the schematic diagram in Figure1(a), we used the scotch tape method to mechanically exfoliate high purity and homogenous h-BN crystals synthesized by high pressure techniques [21] and transferred them by Gel-Pak polymer using the viscoelastic effect [22] on commercial chemical vapor deposition (CVD) graphene/285 nm SiO2/Si substrate [23]. The CVD graphene region outsideh-BN sheet was etched by oxygen plasma so as to confine to our CVD graphene region under theh-BN sheet. CF4 gas was used to etch h-BN sheet protected by photoresist for 8 terminals and Cr/Au metal depositions as shown in Figure 1(b).Figure 1
(a) Schematic fabrication diagram of a top h-BN/CVD graphene device. (b) The top h-BN/CVD graphene device (sample A) with a scale bar of 10μm.
(a)
(b)


## 2.2. Electrical Measurements

An ac driving current from lock-in amplifiers passed into the source and drain contacts through the graphene devices for Hall-bar measurements. The magnetoresistance was measured in a He3 cryostat equipped with a superconducting magnet.


## 3. Results and Discussion

Figure2(a) shows the longitudinal resistivity ρ
x
x as a function of magnetic field with fixed currentI = 20 nA at different temperatures that are equivalent to T
L. The conductance fluctuations are observed, and they decrease as T
L increase from T
L = 0.32 to 50 K, which are typical properties in disordered mesoscopic graphene [24–27]. Figure 2(a) inset shows the corresponding Hall resistivity at T
L = 0.32 K, which can calculate the carrier density n
A = 3.5 ×
10
12 c
m
-
2 from the Hall slope and Hall mobility μ = 2092 cm2/Vs from carrier density and zero field resistivity. Figure 2(b) shows the results of ρ
x
x at various driving currents I fromI = 20 nA to 30000 nA at a fixed T
L of 0.32 K, which reveals similar conductance fluctuation characteristics by current heating in the nonequilibrium regime due to the hot carrier effects in disordered two-dimensional systems [18, 28–31].Figure 2
(a) Magnetoresistivityρ
x
x (B) at various T
L for sample A. The inset shows the Hall resistivity ρ
x
y (B) at T
L = 0.32 K. (b) Magnetoresistivity ρ
x
x (B) at various driving currents I at fixed T
L = 0.32 K for sample A.
(a)
(b)By using a conductance fluctuations-based thermometer betweenρ
x
x (I) and ρ
x
x (T), we are able to reveal the clear conductance variations for lattice temperature and current dependence betweenB = 0.5 and 3 T by subtracting a smooth background that avoids the zero field weak localization peak and high field Shubnikov-de Haas-like oscillations as shown in Figures 3(a) and 3(b) [13]. Hence, we determine the root mean square (RMS) conductance fluctuation (δ
g
rms, in units of e
2
/
h) for every δ
g
rms (T
L) and δ
g
rms (I) data set as a common graph (see Supporting Information (available here)) by averaging conductance fluctuations over the range of B so as to assign an effective T
e to the driving current as shown in Figure 4(a) [13, 18]. Interestingly, T
e shows a linear dependence on I. According to the seminal work done by Baker and coworkers about the energy transfer between carriers and the lattice [31], the following relation can be found:(1)
T
e
∝
I
α
,where α = 2/(p + 2) and p is the exponent for the inelastic scattering rate τ
in
-
1
∝
T
p. Therefore, Figure 4(a) shows that T
e (I) of our sample A follows (1) with p
≈
0 and α
≈
1, which suggested little carrier-phonon scattering in two-dimensional material heterostructure systems [26]. Furthermore, one would be interested in whether the heat dissipation was transferred by another mechanism rather than carrier-phonon scattering. Under the low-temperature limit (T
L
<
T
B
G), T
B
G
=
2
ℏ
s
k
F
/
k
B, where s is the sound velocity and k
F is the Fermi radius. For graphene systems (s = 2.1 × 104 ms−1), T
B
G ~ 54n
1/2 K≅ 93.4 K with the carrier density n
=
3.5 in units of 10
12
c
m
-
2 in sample A [13, 32]. The energy loss (P
e), the average rate of energy loss per carrier, is usually expressed to the carrier and lattice temperatures as (2)
P
e
=
A
T
e
β
-
T
L
β
,with a constant A and a characteristic exponent β. In general graphene systems, β
≈
3 suggests the supercollision cooling mechanism in disordered systems [13, 18, 33] and β
≈
4 suggests the two-dimensional acoustic phonon cooling processes in clean systems [34, 35]. Particularly, β
≈
2, the heat diffusion described by the Wiedemann-Franz law, was found in graphene on bottom h-BN substrate systems, where bottom h-BN substrate acts as a thermal conduction layer, effectively reducing the electron-phonon coupling [14–16]. Such interesting bottom h-BN substrate underneath graphene can change graphene heat transport mechanism from electron-phonon interactions (β
≈
3
~
4) to heat diffusion (β
≈
2). One might be interested in what heat transport mechanism will be in encapsulated graphene between bottom insulating SiO2 and toph-BN sheet as our sample A rather than traditional graphene on h-BN substrate [14–16]. Based on the work of Baker et al. [31], β =p+ 2, which suggested β in sample A should be close to 2 since the linear relation between T
e and I isp
≈ 0 (1 = α = 2/(p + 2)). Apparently, our results in sample A are highly consistent with this speculation for β
≈
2 as shown in Figure 4(b), where P
e = I
2
R
x
x
/
n
W
L (W and L are the width and length of our sample A, resp.). Interestingly, the heat transfer mechanism in our sample A with top h-BN sheet on graphene/SiO2 was dominated by heat diffusion (β
≈
2), which is the same as traditional graphene/h-BN substrate devices [14–16]. Such interesting results suggest that the top h-BN sheet coupled with graphene is strong heat transfer medium in comparison with other coupled materials, like SiO2 or air. Also, such structures in the top h-BN sheet on graphene not only protected graphene without air molecular adsorbing doping [2–36], but also screened graphene from electrostatic force [37, 38], a great advancement for graphene-based devices.Figure 3
(a) Conductance fluctuations in sample A as a function of magnetic field at various lattice temperatures with fixedI = 20 nA. (b) Conductance fluctuations in sample A as a function of magnetic field at various driving currents for T
L = 0.32 K.
(a)
(b)Figure 4
(a) EffectiveT
e versus driving current I in sample A. (b) P
e as a function of (T
e
2
-
T
L
2) for sample A and at T
L = 0.32 K.
(a)
(b)In order to further discuss the linear relation betweenT
e and I that indicates little carrier-phonon scattering in our sample A, we fabricate multilayer exfoliated graphene (sample B) that showed the same linear relation between T
e and I by zero field resistance as a thermometer and conductance fluctuations due to its disordered property as in our previous reports [23–26]. Again, we are able to measure the conductance fluctuations for temperature and current dependence as shown in Figure 5(a) and inset [13]. Consequently, we found the linear relation between T
e and I by utilizing δ
g
rms (T
L) and δ
g
rms (I) as a thermometer for determining T
e (see Supporting Information) [13] as shown in the inset of Figure 5(b), which suggestedp
≈ 0 and β
≈ 2. Under the low-temperature limit (T
L
<
T
BG), T
B
G
~
54
n
1
/
2 K≅ 188.6 K with the carrier density n
=
12.2 in units of 1012 c
m
-
2 in sample B [13, 32]. Consistently, P
e is proportional to (T
e
2
-
T
L
2) in sample B as shown in Figure 5(b), which belonged to Wiedemann-Franz law heat diffusion and corresponded to the transport situation for little carrier-phonon scattering for α
≈ 1 [7, 26]. Interestingly, the multilayer exfoliated graphene (sample B) has the same heat transfer mechanism (β
≈ 2) as the h-BN/graphene (sample A) systems [14–16].Figure 5
(a) Conductance fluctuations in sample B as a function of magnetic field at variousT
L with fixedI = 20 nA. The inset shows conductance fluctuations in sample B as a function of magnetic field with various driving currents at fixed T
L = 0.32 K. (b) P
e as a function of (T
e
2
-
T
L
2) for sample B and at T
L = 0.32 K. The inset shows effective T
e versus driving current I in sample B.
(a)
(b)Although the heat transfer mechanism of multilayer exfoliated graphene is the same as h-BN/CVD graphene for heat diffusion (β
≈ 2), the energy relaxation time can describe this cooling process about the typical time on which energy is lost from carriers [39, 40]. Therefore, the energy relaxation time can be expressed by (3)
P
e
=
k
B
T
e
-
T
L
τ
ϵ
.Figure 6 compares the energy relaxation time τ
ϵ between the h-BN/CVD graphene (sample A) and the multilayer exfoliated graphene (sample B). Interestingly, we could obviously find that τ
ϵ of h-BN/CVD graphene (sample A) is about two orders of magnitude faster than that of multilayer graphene (sample B). Both of these two samples are the samen-type of carrier density and far from the Dirac point, which cannot be ascribed to the fast energy relaxation of hot carriers near the Dirac point of graphene [18]. These results suggest that the carrier-phonon scattering is absent in the multilayer graphene and the h-BN/graphene. The extremely long energy relaxation times in both devices (at least two orders of magnitudes longer than those in pristine exfoliated graphene [27, 28] and graphene on SiC [30, 34]) can be advantageous for applications in graphene-based hot carrier transistors [41] since carriers can maintain their high kinetic energy (and hence the high effective temperature) with a relatively low driving current.Figure 6
(a) Comparison ofτ
ϵ (T
e) versus T
e on a log-log scale for sample A (h-BN/CVD graphene) and sample B (multilayer graphene).


## 4. Conclusion

We have studied conductance fluctuations and hot carrier effects caused by current heating on h-BN/CVD graphene and multilayer graphene as a self-thermometer. It has been shown thatT
e (P
e) is linearly proportional toI(T
e
2
-
T
L
2) in both of the disordered graphene devices, suggesting the little electron-phonon scattering and heat diffusion due to Wiedemann-Franz law. The extremely long energy relaxation time may find applications in graphene-based hot carrier devices. Such a result may be useful for other material systems [42, 43].



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*Source: 5174103-2018-05-14.xml*