1 Introduction

Temperature, one of the most significant factors owing to its close relationship with chemical, environmental, biological, physical and electronic systems [1]. Real-time, easily operable and precise monitoring of temperature in above mentioned systems demand a critical challenge [1]. In this context, a feasible and practical solution of temperature sensing is gathering a remarkable interest towards the field of automobiles, electronic skins in robots, defense, industry, food safety, human–machine interface and environmental temperature measurement [1, 2]. To develop an efficient temperature sensor, some physical parameters such as temperature coefficient of resistance (TCR), responsivity, thermal hysteresis and sensitivity are to be investigated.

Recently, numerous types of temperature sensors have been reported, comprising thermal-resistance temperature sensors, thermocouple sensors and thermal-responsive field-effect transistors [3, 4]. Rogers et al. developed a temperature sensor based on the serpentine gold and PIN diode using Si nanoribbons on elastomers [5]. Furthermore, Bao and colleagues introduced a Ni-polymer composite-based wireless temperature sensor, but it displays a small dynamic range (25–40 °C) [6]. However, so far reported sensors typically generate an insignificant thermal response thereby, a complex electronic circuitry is prerequisite to achieve accurate detection which is challenging for its integration [7]. Typically, temperature sensors are based on the detection of temperature by means of induced physical changes within material [8]. One of the most extensively applied type of detectors is the resistive temperature detector (RTD) which exhibits high accuracy, fast response and good stability [9]. In addition, the practice of thermal sensors, infrared temperature sensors and mercury thermometers are commonly prevalent. Nevertheless, the major drawback for the above mentioned sensors is the core materials which are typically metals, metal oxides, ceramics, etc. that fail to meet certain standards for a competent temperature sensor [10, 11]. Equally, they are limited by some of their own characteristics including their fragility, high-priced and bulkiness together with self-heating problems, non-linearity and limited configurations [12, 13]. Thus, growing demands of facile methodology for improved temperature measurements and miniaturization capabilities have prompted a search for employing novel materials in the field of temperature sensing applications. With the progress in nanotechnology, it has been observed that apart from the composition and organization of atoms within the materials, dimensionality also plays a pivotal role in determining their fundamental properties [14].

Graphene is at the cutting edge of condensed matter physics since 2004 and substantial research has been carried out owing to its striking properties which lacks in its counterpart [15]. The remarkable properties of graphene together with extremely small thickness, low mass, excellent electrical properties, low noise, high mobility, large surface area to volume ratio and high absorption coefficient make it principally suitable for sensing devices [16, 17]. Although there are several reports on the gas sensing properties of graphene based materials, but its temperature sensing properties have not been explored much.

A recent report has demonstrated wearable temperature sensor in the temperature range of 35–45 °C by utilizing reduced graphene oxide and graphene flakes [12, 13]. Another study features the application of cellular/rGO based composite films as a temperature sensor in the temperature range of 25–80 °C [18]. Also, there is a report underlining the use of CVD grown graphene monolayer as a thermistor [19]. Nonetheless, device fabrication steps in aforesaid graphene based temperature sensors are extremely complicated, and as a consequence there is a need to look for some alternative solutions that can provide easy fabrication tools.

In the light of foregoing discussions, the main objective of the present report is to overcome various shortcomings of the prior state of art which are outlined above. Herein, an effort has been made to address a simple, time-saving, scalable and eco-friendly approach by means of micro-wave assisted rapid exfoliation of graphene sheets for wide range temperature sensing applications.

2 Experimental

To start with, dispersion of graphite flakes (purchased from Sigma-Aldrich) in carbonated water has been prepared with initial concentration of 100 mg/100 mL. Subsequently, dispersion was sonicated by employing probe sonication (probe sonicator, PKS—750 F with working frequency of 20–25 kHz) for 5 min. The as sonicated suspension was subjected to liquid nitrogen (LN2) treatment in order to freeze the suspensions. Immediately, frozen suspension was exposed to microwave irradiation treatment at 800 W for 30 s. As a consequence, graphene flakes started assembling on the top of liquid surface. After discarding graphitic flakes which are settled at the bottom, we have obtained approximately 75% supernatant (upper phase) of total dispersed solution. Interestingly, the overall processing time of this proposed method is maximum 10 min which is comparatively lesser as per our previous report [20]. The schematic diagram of experimental process is illustrated in Fig. 1. For structural characterization, XRD patterns were recorded on X-ray diffractometer (D8 Focus, Bruker, Germany) in the 2θ range of 10–50° using Cu Kα radiation (λ ∼ 0.154 nm). The Raman spectra were recorded using an In Via Reflex micro-Raman spectrometer (Renishaw) with a 50× objective lens using argon laser excitation of 514.5 nm. The morphological investigations were carried out using Carl Zeiss SUPRA 55 apparatus operating at 15–30 kV under vacuum. TEM studies were implemented on a JEOL JEM 2100 microscope operated at 200 kV. For performing I–V studies (Keithley 2612-A), the collected graphene flakes were drop casted on an alumina substrate with gold electrical contacts.

Fig. 1
figure 1

Flowchart depicts the experimental process (dotted portion indicates assembling of graphene flakes)

Full size image

2.1 Sensor fabrication and testing methods

The as flocculated graphene flakes were carefully transferred onto alumina substrate (12 mm × 5 mm) having pre-deposited gold electrical contacts as depicted in inset of Fig. 2. For temperature sensing, the fabricated sensor was placed in a sample holder provided in the test chamber which is installed with temperature controlled oven. The change in real time voltage signal across a resistance (RL) connected in series with sensor was measured with Keithley Data Acquisition Module KUSB-3100 connected to a computer. Figure 2 depicts the current I flowing through the circuit which has been calculated using relation VO/RL, where VO is the output voltage across the load resistance RL. From the relation VS = I (RS + RL), sensor resistance RS was found, where VS is the input voltage. To test the performance of temperature sensor, the change in sensor resistance was measured throughout a change in temperature from 28 to 350 °C.

Fig. 2
figure 2

The diagram showing circuit of temperature sensing unit and inset displays fabricated graphene based temperature sensor

Full size image

2.2 Proposed mechanism for the synthesis of graphene flakes

In this proposed method, suspension of graphite flakes and carbonated water was treated with probe sonication. Throughout probe-sonication, dissolved CO2 molecules owing to their low viscosity, high diffusivity and comparable molecular size (~ 0.33 nm) intercalate between adjacent layers of graphite. After being subjected to liquid nitrogen treatment, intercalated CO2 molecules begin to freeze [20]. Upon immediate microwave irradiation treatment, the imbedded CO2 molecules gush out with an enormous pressure which induce expansion of graphitic lattice, thereby forcing the separation of the graphene flakes. This can be explained by the fact that when carbonated liquids are exposed to high temperatures, the solubility of dissolved gases gets decreased [21]. Consequently, gas tends to escape from liquid which leads to exfoliation of graphene sheets.

3 Results and discussions

3.1 XRD analysis

Figure 3 exhibits characteristic diffraction peak (002) of synthesized graphene nano-sheets. It is clear from figure that diffraction peak (002) seems to further de-convoluted into four sub-peaks. The latter has been confirmed by executing peak fitting of main peak (002) as shown in inset. Corresponding to sub peaks centered at 22.30°, 23.19°, 25.33° and 25.89°, d-spacing is found to be 0.398, 0.383, 0.351 and 0.344 nm respectively which has been calculated using Bragg’s diffraction law as follows [22].

Fig. 3
figure 3

XRD diffraction pattern of synthesized graphene flakes, graphs given in inset exhibit deconvolution of (002) diffraction peak and XRD pattern of parent graphite flakes

Full size image
$$2{\text{d}}\sin \uptheta ={\text{n}}\uplambda$$
(1)

where ‘d’ is interlayer spacing and λ is wavelength employed (~ 0.154 nm).

In accordance with sharp intense peak equivalent to (002) planes of graphite flakes, (shown in inset of Fig. 3) relatively lesser intense and broader (002) peak stamps the exfoliation of graphite flakes into graphene nanosheets [23, 24]. Furthermore, the average thickness (Lc) of stacked graphene layers (along ‘c’ axis) has been estimated by applying Scherer's equation to (002) diffraction peak as follows [24]:

$${\text{L}}_{{\text{c}}} = \frac{{0.94~ \times {\uplambda }}}{{\upbeta \cos ({\uptheta })}}$$
(2)

where λ is the X-ray wavelength ~ 0.154 nm; \({{\uptheta}}\) is diffraction angle and \({\upbeta}\) is FWHM (full width half maximum) determined from Lorentzian peak fitting.

In light of previous discussion, the obtained values of Lc lie between 1.30 and 2.61 nm which corresponds to formation of average 4–8 graphene layers. The above observation validates the formation of few layered graphenic material with ‘d’ spacing varying from 0.344 to 0.398 nm.

3.2 Morphological analysis

Transmission electron microscopy (TEM) is one of the most versatile method for the analysis of materials down to the atomic scale [25]. Figure 4(1–7) exhibits TEM images of graphene sheets comprising the existence of mono to few layer graphene sheets. Moreover, large sized graphene flakes of the order of micrometres have been achieved in a given sample. Additionally, layer count of attained graphene flakes has been determined from their relevant HR-TEM images which have been recorded corresponding to folding part of sheets [25] as indicated with dots in Fig. 4(3–4). Likewise, selected area electron diffraction (SAED) patterns of analogous graphene sheets have also been recorded to certify the crystallinity and layer count of graphene as given in Fig. 4(1–7). From SAED patterns, sixfold consistent hexagonal pattern with comparatively more intense and complete inner diffraction spots highlights the crystalline monolayer graphene character [26]. The foregoing observation has been confirmed from respective intensity profile diagram of indexed diffraction spots as presented in Fig. 4(5). From intensity profile diagram, intensity ratio I{1100}/I{2110} is found to be ~ 2.0, which points toward single layer graphene character [27]. It is evident from TEM images that quality of graphene nanosheets obtained with the present method is as good as in NMP and DMA solvents which being toxic degrade the overall quality of graphene sheets. In addition, above results also suggested that given sample contains mono to few layer graphene sheets which demonstrated the effective exfoliation of graphene sheets without degradation of original graphene structure.

Fig. 4
figure 4

1–7 demonstrate TEM, HR-TEM and SAED pattern of obtained graphene flakes

Full size image

Besides monolayer graphene flakes, we have also found few layer graphene flakes which are twisted and herein have been verified from their respective HR-TEM images and SAED patterns as mentioned earlier as displayed in Fig. 4(1–7). From SAED patterns, overlapping of 2–3 hexagonal patterns has been noticed which gives the idea about the misalignment between different graphene sheets [28]. The detailed study related to twisted graphene sheets has been discussed in our previous report [20].

Layered structure of graphene nanosheets has been confirmed from SEM images as displayed in Fig. 5.

Fig. 5
figure 5

SEM images of synthesized graphene flakes with morphology of graphite flakes shown in inset

Full size image

3.3 Raman analysis

Raman spectroscopy is a resourceful technique to probe the quality of produced graphene sheets in terms of layer count and degree of disorder [29]. The Raman spectrum of obtained graphene flakes is presented in Fig. 6. The distinguishing features of graphene lie in the range of 1000–3000 cm−1: with the noticeable D, G and 2D bands at around 1350, 1580 and 2700 cm−1 respectively [30]. The D mode is ascribed to the existence of defects in graphene and it is attributed to breathing modes of sp2 carbon atoms in aromatic rings [29, 30]. This band activates from transverse optical (TO) phonons around K point of Brillouin zone (BZ) and it discloses the atomic defects, stacking between neighbouring layers of graphene and edges in crystallite sites [31]. The band next to D band is graphitic G band which originate from in-plane vibration of sp2 carbon atoms and it is a doubly degenerate (TO and LO phonon mode: E2g symmetry) at centre of Brillouin zone [30]. Another noteworthy feature of graphene i.e. 2D band: the second order overtone of D band instigates from a two phonon double resonance Raman process is the notable band amongst graphenic materials after G band [29,30,31].

Fig. 6
figure 6figure 6

a–f Raman spectra of attained graphene flakes recorded at different focus area with their equivalent Raman micrograph shown in inset of each recorded spectra

Full size image

It is reported by Ferrari et al. [29] that the shape, intensity and 2D band position variations manifest about graphene layer count. Figure 6a–f demonstrates the manifestation of D, G and 2D band at 1352 cm−1, 1582 and 2779 cm−1 respectively. The existence of D band governs defects induced from both exfoliation and while transferring graphene flakes to substrates [20].

It has been reported by Ferrari et al. [30] that defect ratio ID/IG gives the evidence of degree of disorder in graphene sheets. Here, ID/IG ratio of synthesized few-layered graphenic material is found to lie in the range of 0.06–0.20 signifying trivial defects present in given sample which indicates the formation of highly ordered graphene layers. Since, we have recorded Raman spectra by changing focus area of sample under investigation with their corresponding Raman micrograph shown in inset, we have also observed single layer graphene signature as depicted in Fig. 6d.

Another remarkable factor is the intensity ratio of 2D and G band, I2D/IG which provides the information about graphene layer count [29,30,31]. It has been found that I2D/IG for the prepared sample fluctuates between 0.53 and 0.80 which highlights the idea of few layered graphene sheets together with I2D/IG ratio of 1.96 has been obtained which is well established signature of single layer graphene. In addition, de-convolution of Raman 2D band has been performed using Lorentzian peak fitting as shown in Fig. 6. This multi-peak structure of 2D band gives information about stacking of multiple graphene layers [30]. From figure, the number of components into which 2D band gets de-convoluted are 2 and 4 which gives idea about formation of bilayer to few layer graphene flakes.

3.4 UV–visible analysis

Figure 7(inset) represents UV–vis absorption spectra of obtained graphene flakes. The characteristic absorption peak centered at 265 nm has been observed, owing to π‒π* transitions relating to sp2 conjugation in hexagonal lattice of graphene [32]. In addition, the band gap of few layered graphene sheets has been estimated using Tauc’s relation as follows [24].

Fig. 7
figure 7

Tauc plot of obtained few layered graphene flakes and inset shows UV–visible absorption spectra of graphene flakes

Full size image
$${\left( {\upalpha\,\text{h}\, \upnu} \right)^{1/2}}=\left( {\text{h} \, \upnu - {{\text{E}}_{\text{g}}}} \right)$$
(3)

where α is absorption coefficient, hν is the photon energy and Eg is optical band gap.

By taking into account of indirect transitions, band gap from Tauc plot is found to be 1.25 eV as illustrated in Fig. 7. Chamoli et al. [21] and Sahoo et al. [27] had estimated the band gap for exfoliated few layered graphene nanosheets as 2.29 eV and 2.11–2.96 eV respectively. The relatively small band gap is obtained in the present work as compare to previous reports. This finite value of band gap in few layered graphene sheets has been attributed to interaction taking place between adjacent graphene planes which causes the splitting of π and π* electron bands. Besides, presence of disorders in form of twisted graphene layers and edge defects also contribute towards widening of band gap [29, 30].

3.5 Temperature sensing performance

Graphene based temperature sensor was fabricated using a resistor assembly whose schematic device structure is presented in Fig. 8.

Fig. 8
figure 8

The schematic representation of fabricated device structure

Full size image

To investigate the temperature sensing properties of graphene sensor, variation of its average electrical resistance values has been recorded as a function of temperature (28–250 °C) shown in Fig. 9a. From figure, it has been found that device resistance decreases exponentially with increasing temperature which indicates its ability of wide range temperature detection from 28 to 250 °C. Similar effects of temperature on sensor resistance have been recently observed by (1) Sahoo et al. [33] for filter deposited and chemically reduced GO sheets using hydrazine vapor (2) Zhuge et al. [34] with filter deposited and metal- diffused GO sheets and (3) Bartolomeo et al. [35] with multi-wall CNT based temperature sensors. It is noteworthy here, prior to each measurement a waiting period of 15 min was maintained at a target temperature to stabilize the device.

Fig. 9
figure 9

a Resistance versus temperature (R–T) variation of sensor in temperature range of 28–250 °C, inset shows R–T variation in 50–160 °C. b R–T variation in temperature range of 28–45 °C

Full size image

From Fig. 9a R–T curve was found to be well fitted with the single exponential equation 401.63 exp (− T/111.67) − 47.15. This curve is almost linear in temperature regime I (28–45 °C) and regime II (50–160 °C) as displayed in Fig. 9b and inset of Fig. 9a respectively. The latter suggests that fabricated sensors can not only be employed for monitoring the human body temperature range (35–38 °C), but can also be realized in high temperature applications where several processing parameters are required to be scrutinized at high temperature ranges such as in the fields of industry, defense, robotics and automotive.

In order to study the temperature sensitive properties of sensor, temperature coefficient of resistance or sensitivity (TCR, α), a characteristic parameter has been estimated by executing linear fitting to the R–T curve in the regime I (28–45 °C) and regime II (50–160 °C) and it is expressed as [8,9,10]

$$\upalpha =\frac{1}{{R\left( {T0} \right)}}\;\frac{{R\left( {T} \right)-{\text{R}}\left( {{\text{T}}0} \right)}}{{T - T0}}$$
(4)

where R(T) is resistance at a particular temperature T, R(T0) is a reference resistance corresponding to room temperature (28 °C). From Eq. 4, TCR of graphene sensor is found to be − 14.09 × 10−3 (°C)−1 and − 5.3 × 10−3 (°C)−1 for regime I (28–45 °C) and regime II (50–160 °C) respectively. It is clear from above mentioned values that graphene sensor is more sensitive in regime I (28–45 °C) which clearly points its ability to sense human body temperature with significant sensitivity. Interestingly, for regime I, TCR value of our graphene based temperature sensor is found to be 3 times higher that of reported standard commercial Pt temperature sensors [35]. In addition, TCR value is 4 and 20 times greater than that of reduced graphene oxide [33] and MWCNT based temperature sensors [36] respectively.

In perspective of temperature sensing, the sensor response (or sensor responsivity) is the change in resistance w.r.t initial sensor resistance with change in temperature and it is defined as follows [2]:

$${\text{S}}\% \;{\text{or}}\;\Delta {\text{R}}\% =\left| {\frac{{R - Ro}}{{Ro}}} \right| \times 100\%$$
(5)

where R and R0 are resistance values corresponding to particular temperature and room temperature (28 °C) respectively.

From Fig. 9b, a sensor responsivity of 25.80% has been obtained for temperature range (28–45 °C) which is approximately two and sixfold times higher than that of solar exfoliated rGO [13, 37] and commercially obtained graphene flakes [13] based temperature sensors respectively. By considering room temperature (28 °C) as a reference temperature, sensor responsivities for 60–270 °C are found to be 31.20–97.06% as depicted in Table 1 and Fig. 10(1a–f, 2a–b). The above calculated values clearly follows the linear fashion which is desirable for a particular temperature sensor as presented in Fig. 10(2c). Besides, the temperature sensitivity of graphene sensor has been extracted from the slope of linear fitted sensor responsivity-temperature curve and it is found to be 70% (°C)−1 in temperature range of 28–150 °C exhibited in Fig. 10(2c). The obtained sensor sensitivity in equivalent temperature range are higher than already reported temperature sensors based on PIN diodes [38]. Interestingly, the measurements were repeated four times and similar results were obtained for the device.

Table 1 The calculated values of Rav, <ve>, τe, τph, τ and sensor response (S%) at different temperatures
Full size table
Fig. 10
figure 10figure 10

1a–1f Shows variation of sensor resistance with time at different target temperature (2a, 2b) variation of sensor resistance with time in full temperature range of 28–350 °C. 2c Plot between sensor responsivity versus target temperature, inset shows magnified view of sensor responsivity in temperature range of 160–300 °C. 2d Plot between ln (R) versus 1000/T (Arrhenius plot)

Full size image

Graphene being peculiar material exhibits both semiconducting and metallic behavior while subjected to heat treatment. When graphene exhibits semiconducting properties, the dependence of resistance on temperature is determined by within generated thermally activated charge carriers [33]. With the effect of temperature, surplus thermally generated charge carriers jump from valence band (VB) to conduction band (CB) of graphene which leads to drop in resistance. In some literature reports, graphene displays metallic properties in which variation of its resistance with temperature is governed by charge-carrier scatterings which enhance with rising temperature effects [8, 11, 14].

The performance of our fabricated graphene based temperature sensor is consistent with the above theory which confirms its semiconducting properties. Based on this fact, the activation energy (Ea) of graphene sensor has been estimated from the slope of Arrhenius plot of ℓn (R) versus T−1 as shown in Fig. 10(2d). In this temperature regime, ℓn (R) versus T−1 plot was found to be best fitted to a straight line which emphasizes semiconducting Arrhenius like temperature dependence and value of activation energy is found to be 0.47 eV [8,9,10,11]. This type of R–T behavior indicates the governance of electron–phonon scattering in high temperature regime [39]. In addition to electron–phonon scatterings, there are other probable scatterings which take place at defects, impurities and edges of flakes [39, 40].

To further explore the temperature sensing performance of fabricated sensor, consecutive heating–cooling cyclic studies of graphene sensor had been performed at different temperature ranges. The graphs in Fig. 11a–d displays the variation of sensor resistance against time in temperature range of 28–350 °C. As the sensor heats up, its resistance continues to drop till saturated at target temperature. When sensor was allowed to cool from its hot-zone, its resistance starts increasing back to the level of baseline resistance corresponding to room temperature. Captivatingly after subjecting to repetitive heating–cooling cycles, sensor is able to recover its baseline resistance when heated up to 250 °C, beyond this temperature (< 250–350 °C) thermal hysteresis comes into picture (displayed in Figs. 10(1f) and 12a–c) which suggests the compositional breakdown in given sample at elevated temperatures [3]. In fact, thermal hysteresis controls the sensor recovery and it should be minimum for quick recovery of the sensor. In addition, the percentage of thermal hysteresis of sensor has been calculated by using following equation [32]:

Fig. 11
figure 11

a–d Heating–cooling cyclic variation of sensor resistance at different target temperatures

Full size image
$$\% \;{\text{Hysteresis}}=\left| {\frac{{{R_{mn}} - {R_{mp}}}}{{{R_{\text{max} }} - {R_{\text{min} }}}}} \right| \times 100\%$$
(6)

where Rmn (negative going) and Rmp (positive going) are the resistance values at the mean value of temperature range in each case (above 250 °C); Rmax and Rmin are the maximum and minimum values of the recorded resistance values at maximum and minimum temperature respectively.

The hysteresis results of sensor are shown in Fig. 12d.

Fig. 12
figure 12

a–c Resistance versus time graphs at temperature range of 290–350 °C (d) variation of thermal hysteresis with temperature, inset displays variation of sensor resistance during heating–cooling cycles in high temperature regime (270–350 °C)

Full size image

3.5.1 Repeatability test

Figure 13a–d demonstrates the repeatability test of fabricated sensor towards cyclic temperature variations. It has been noticed that sensor maintains its constant resistance variation even after repetitive cycles of temperature variation which validates its repeatable performance in various applications.

Fig. 13
figure 13

a–d Repeatability tests of synthesized temperature sensor on cyclic temperature variation

Full size image

3.5.2 Stability test

The long-term sensor stability is also one of the important parameter from the viewpoint of its practical application. To check the stability of sensor, the sensing response towards particular temperature has been recorded at different intervals for 50 days and results are illustrated in Fig. 14. It has been observed from figure that sensor exhibits satisfactory stability.

Fig. 14
figure 14

Long term stability curves of graphene temperature sensor

Full size image

3.5.3 Estimation of co-relation length for disorder scattering

It has been confirmed from graphs given in Figs. 10, 11 and 12 that there is a significant drop in sensor resistance as temperature exceeds RT. At this point we are in position to estimate co-relation length (ℓc) for disorder scattering in graphene flake and it is defined as [14]:

$${\ell_c}=\frac{{{\text{h}}}}{{2\pi \,T\,kB}}\,{{\text{v}}_{\text{f}}}$$
(7)

where h is Planck’s constant (6.63 × 10−34 J s−1), vf is fermi velocity of graphene (~ 108 cm/s), kB is Boltzmann constant (1.38 × 10− 23 J K−1) and T is temperature at which resistance subsiding sets up (~ 28–300 °C).

From above mathematical expression, ℓc is found to be 25.25–25.41 nm.

3.6 I–V measurement

The sensor response to change in temperature has also been examined by measuring the current–voltage (I–V) characteristics of device over a temperature range of 28–120 °C as shown in Fig. 15. From figure, it is obvious that current increases with increase in temperature validating negative temperature coefficient (NTC) of resistance as discussed earlier. The observed NTC behavior suggests the few-layered graphene sample functions as an intrinsic semiconductor with possibly thermally activated transfer of electrons takes place between graphene sheets [10, 11].

Fig. 15
figure 15

I–V studies of synthesized graphene flakes at different temperatures

Full size image

In context of temperature sensing mechanism, both phonon and free charge carriers are the key performers in the conducting channel (interlayer channel) medium and each contribute their own dynamics in conduction [40, 41]. In single layer graphene, valence band (VB) and conduction band (CB) overlap each other at the Dirac point i.e. charge neutrality point whereas in case of few to multilayer graphene owing to mutual interaction between adjacent graphene planes the splitting of π and π* electron bands takes place which induces gap between VB and CB as displayed in Fig. 16a, b. Under the action of an external stimulus, for instance temperature gradient the thermally generated charge carriers moving between interlayer channels jump across valence band (VB) to conduction band (CB) which lead to enhancement in conductivity [7,8,9,10].

Fig. 16
figure 16

a, b Energy band structure of single layer (SLG) and few layer graphene (FLG) with hexagonal unit cell of graphene (c) schematic sketch of electron scattering in interlayer channels

Full size image

Apart from contribution of charge carriers in conduction mechanism, phonons being principal heat carriers in graphene also play a significant role in heat transportation and their interaction with electrons plays a vital role in heat dissipation in graphene based devices [39,40,41]. Therefore, understanding of responsible phonons for heat transportation is prerequisite in light of above said facts.

Corresponding to two non-equivalent carbon atoms (A and B) in graphene hexagonal unit cell, there are six phonon branches in hexagonal lattice structure. The so-called phonon branches are the z-directional acoustic (ZA), transverse acoustic (TA), longitudinal acoustic (LA), z-directional optical (ZO), transverse optical (TO) and longitudinal optical (LO) branches. Out of three acoustic modes, LA and TA are the in plane acoustic modes which propagates along the basal plane with velocity of sound (~ 20 Km s−1) and these are the responsible phonons for carrier transport in 2D system [41,42,43]. By considering sp2 hybridization in flat hexagonal lattice of graphene, the un-hybridized π electrons freely move to yield a 2D electron gas system. Under the action of external electric field, these free e−s (π electrons) in interlayer channel are scattered by both phonons and thermally generated electrons [9]. The schematic representation is given in Fig. 16c.

According to carrier transport model in 2D electron gas system proposed by Fang et al. [9].

The scattering probability of electrons by phonons is given as:

$$\frac{1}{{{\tau_{ph}}}}={{\text{n}}_{{\text{as}}}}{{\text{d}}_{\text{a}}}<{\upnu_{\text{e}}}>$$
(8)

where nas is atomic concentration (38.17 nm−2), da is diameter of C atoms (0.142 nm) and <νe> is average velocity of thermal electrons which is defined as follows:

$$<{\upnu_{\text{e}}}>\;=\surd \frac{{\pi {K_B}T}}{{2m_{e}^{*}}}$$
(9)

The probability of e−–e− scattering is:

$$\frac{1}{{{\tau_e}}}=\frac{{\sqrt {2} {n_{es}}{e^{2}}}}{{4{\varepsilon _{0}}{\varepsilon _r}m_{{e}}^{*}<{\nu _e}>}}$$
(10)

where nes is e− concentration, \({\varepsilon_{\text{r}}}\) is relative permittivity, me is effective mass of e− and <νe> is average velocity of thermal e−s.

Since, electrons in interlayer channel are affected by both phonon and electronic scatterings.

Thus, from (8) and (10)

$$\frac{1}{\tau }=\frac{1}{{{\tau_{ph}}}}+\frac{1}{{{\tau_e}}}$$
(11)
$$\frac{1}{\tau }={\text{ }}{{\text{n}}_{{\text{as}}}}{{\text{d}}_{\text{a}}}<{\nu _{\text{e}}}>{\text{ }}+\frac{{\sqrt {2} {n_{es}}{e^{2}}}}{{4{\varepsilon _{0}}{\varepsilon _r}m_{{e}}^{*}<{\nu _{\text{e}}}>}}$$
(12)

From Eq. (12), it is clear that with rise in temperature electron- phonon scatterings dominate over e−–e− scattering effects. The calculated values are given in Table 1.

The corresponding e− mobility in interlayer channel is expressed as:

$${\upmu_{{\text{ic}}}}=\frac{{4\sqrt 2 \pi {e^{2}}{\varepsilon _{0}}{\varepsilon_{r}}m_{{e}}^{*}<{\nu_e}>{E_F}}}{{n_{{es}}^{2}e{h^{2}}\left( {{e^2}+2\sqrt 2 ~{\varepsilon _{0}}{\varepsilon_{r}}m_{{e}}^{*}<{\nu _e}>^{2}d} \right)}}$$
(13)

From Eq. (13), it is obvious that µic is direct function of <νe> which in turn depends upon temperature and hence e− mobility in interlayer channel increases and thereby conductivity in interlayer channel get enhanced with increasing temperature effects. The above discussed model is consistent with our experimental observations.

Another report features the theoretical and experimental predictions on carrier transport model in few layer graphene which is proposed by Zhu et al. [41].

According to model:

The density of states (D(EF)) in few layer graphene is constant i.e. \({\text{D}}\left( {{{\text{E}}_{\text{F}}}} \right){\text{ }}=\frac{{2{m^*}}}{{\pi {\hbar ^2}}}\); \({{\text{E}}_{\text{F}}} \propto {\text{n}}\), where m* is effective mass and n is charge density which is given as:

\({\text{n}} \propto \frac{{2{m^*}}}{{\pi {\hbar ^2}}}\;{{\text{k}}_{\text{B}}}{\text{T}}\), T is temperature.

Correspondingly, mobility is defined as µ = n (A + BT), where A and B are fitting parameters.

In nutshell for few layered graphene, enhancement in both carrier density and mobility takes place with temperature which has been attributed to screening effect of field of substrate surface phonons by interlayer channels that are formed due to additional graphene layers.

4 Conclusion

In conclusion, a simple structured temperature sensor based on pristine graphene sheets was developed by facile, rapid, cost-effective and environmental friendly microwave assisted exfoliation technique. The fabrication approach presented in this work allows direct production of graphene flakes using carbonated water without any role of surfactant and chemical solvents. Moreover, the overall processing time was significantly reduced to 10 min as compared to our previous report. The substantial sensor responsivities have been obtained with graphene flakes in wide temperature range of 28–250 °C which is relatively higher than that of conventional temperature sensors. The sensor considered in this work is adequate sensitive to monitor human body temperature which finds its applications in fields of flexible electronics, human health monitoring, electronic skins in robots and human–machine interface. The considerable “resistance quenching” in graphene resistors with rising temperature effects have also been noticed which could be implemented as thermal management systems in integrated circuits.