Characteristics of THz carrier dynamics in GaN thin film and ZnO nanowires by temperature dependent terahertz time domain spectroscopy measurement

Seongsin Kim

doi:10.1016/J.SSE.2012.05.050

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Characteristics of THz carrier dynamics in GaN thin film and ZnO nanowires by temperature dependent terahertz time domain spectroscopy measurement

Seongsin Kim

2012, Solid-State Electronics

https://doi.org/10.1016/J.SSE.2012.05.050

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7 pages

Abstract

We present a comprehensive study of the characteristics of carrier dynamics using temperature dependent terahertz time domain spectroscopy. By utilizing this technique in combination with numerical calculations, the complex refractive index, dielectric function, and conductivity of n-GaN, undoped ZnO NWs, and Al-doped ZnO NWs were obtained. The unique temperature dependent behaviors of major material parameters were studied at THz frequencies, including plasma frequency, relaxation time, carrier concentration and mobility. Frequency and temperature dependent carrier dynamics were subsequently analyzed in these materials through the use of the Drude and the Drude-Smith models.

Key takeaways
AI

The study investigates temperature-dependent carrier dynamics in n-GaN and ZnO nanowires using THz time domain spectroscopy.
Key material properties include complex refractive index, dielectric function, conductivity, and plasma frequency.
THz-TDS measurements reveal that carrier concentration decreases with increasing temperature in n-GaN.
For Al-doped ZnO nanowires, conductivity decreases with temperature, differing from behavior observed in n-GaN.
Drude and Drude-Smith models effectively describe frequency-dependent carrier dynamics across studied materials.

Characteristics of THz carrier dynamics in GaN thin ﬁlm and ZnO nanowires by temperature dependent terahertz time domain spectroscopy measurement Soner Balci, William Baughman, David S. Wilbert, Gang Shen, Patrick Kung, Seongsin Margaret Kim ⇑ Department of Electrical and Computer Engineering, The University of Alabama, Tuscaloosa, AL 35487, USA article info Article history: Available online 30 June 2012 The review of this paper was arranged by Prof. A. Zaslavsky Keywords: Terahertz time domain spectroscopy Carrier dynamics Complex conductivity Drude–Smith model GaN ZnO abstract We present a comprehensive study of the characteristics of carrier dynamics using temperature depen- dent terahertz time domain spectroscopy. By utilizing this technique in combination with numerical cal- culations, the complex refractive index, dielectric function, and conductivity of n-GaN, undoped ZnO NWs, and Al-doped ZnO NWs were obtained. The unique temperature dependent behaviors of major material parameters were studied at THz frequencies, including plasma frequency, relaxation time, car- rier concentration and mobility. Frequency and temperature dependent carrier dynamics were subse- quently analyzed in these materials through the use of the Drude and the Drude–Smith models. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Terahertz time domain spectroscopy (THz-TDS) has been widely investigated for many applications in sensing and imaging technologies over the past two decades. Terahertz wave, with a fre- quency between 300 GHz and 10 THz, is especially attractive for various applications including security monitoring, biomedical imaging, high speed electronics and communications, and chemi- cal and biological sensing. There is also an increasing interest for nondestructive testing using the THz waves because they have un- ique properties of propagation through certain media and cover a number of important frequencies. For such applications, THz-TDS has become a powerful tool and measurement technique that en- ables carrier dynamics at high frequencies to be characterized, and thus may lead to a better understand of the characteristics of high frequency optoelectronics and many other fundamental prop- erties of materials. [1–5] Using THz-TDS, one can determine frequency dependent basic properties of materials, including their complex dielectric constant, refractive index and electrical conductivity. Unlike conventional Fourier-Transform spectroscopy, THz-TDS is sensitive to both the amplitude and the phase, thereby allowing for a direct approach to determining complex values of material parameters with the advantage of high signal to noise ratio and coherent detection [6]. In addition, it is possible to carry out THz-TDS experiments without any electrical contact to the sample probed, which signiﬁcantly simpliﬁes electrical measurements of any type of nanostructures and nanomaterials. There have been a number of reports of dielectric properties of various materials probed by THz-TDS [7–9]. Among them, wide bandgap GaN and ZnO nano- structures are the most interesting materials to pursue because of their extensive applications in optoelectronic devices, photovol- taics, and high power electronic devices [10–14]. The high mobility and saturation drift velocity of GaN makes it one of potential mate- rials for high power electronics that can operate beyond the giga- hertz and reach to the terahertz frequency range [15–17]. ZnO nanowires (NWs) have been intensively used for many different types of sensors and recently for base structure for nanowire based photovoltaics [18]. For solar cell applications, it is critical to know the electrical properties of such nanowires as they would transport photogenerated carriers. THz-TDS measurement can be the most convenient and suitable method to determine such characteristics since electrical contacting to nanowires is almost not possible. Although many studies have been published on the electrical prop- erties of GaN thin ﬁlm and ZnO NW measured by THz-TDS, and only a few have investigated the temperature dependent THz- TDS measurements on bulk ZnO [19], there is no temperature dependent THz-TDS study of GaN or ZnO NWs. Since temperature is an important factor in the operating con- ditions of any device, understanding its effect on carrier dynamics in constituent materials is a critical step in the optimization of high-frequency devices. In this work, we present a study of the temperature dependent carrier dynamics in GaN thin ﬁlms and 0038-1101/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.sse.2012.05.050 ⇑ Corresponding author. Tel.: +1 205 348 5755; fax: +1 205 348 6959. E-mail address: seongsin@eng.ua.edu (S.M. Kim). Solid-State Electronics 78 (2012) 68–74 Contents lists available at SciVerse ScienceDirect Solid-State Electronics journal homepage: www.elsevier.com/locate/sse

ZnO NWs obtained from THz-TDS measurements and extract important material properties in the THz. 2. Theoretical background The theoretical approach and calculations have been discussed elsewhere [20]. Brieﬂy, the THz wave propagation through the interface between two media and the relative ﬁeld strength de- pend on both the complex reﬂection coefﬁcient, r 12 =(n 1  n 2 )/ (n 1 + n 2 ), and complex transmission coefﬁcient, t 12 =2n 1 /(n 1 + n 2 ), at that interface. Let S o (x) be the complex amplitude of an incident THz wave propagating through a medium (e.g. air) indexed as 1. A reference conﬁguration in our experiments consists of a THz wave passing through a substrate medium, indexed as 3, and whose amplitude is therefore given by: S ref (x)= t 13  S o (x)exp(i x d/c), where d is the thickness of the substrate medium, c is the speed of light. In a three medium conﬁguration, when a thin ﬁlm (indexed as 2) is between medium 1 and the substrate, by consid- ering multiple reﬂections within the ﬁlm, the amplitude of the THz wave can be represented by: S sample ðxÞ¼ t 12  t 23  S o ðxÞ  expðix~ nd=cÞ=½1  r 21 r 23 ði 2 ~ nxd=cÞ: The complex spectral representation, S(x), as a function of fre- quency can be obtained by Fast Fourier Transform (FFT) for each transmitted THz electric ﬁelds. The complex transmission coefﬁ- cient T(x), deﬁned as the ratio of the transmitted signal S sample (x) through the sample (medium of interest) to reference signal S ref (x) (with only the substrate), can be written as: T ðxÞ¼ S sample ðxÞ S ref ðxÞ ¼ 2~ n s ð~ n r þ 1Þ expðixð~ n s  1Þd=cÞ ð1 þ ~ n s Þð~ n s þ ~ n r Þþð~ n s  1Þð~ n r  ~ n s Þ expð2ix~ n s d=cÞ ð1Þ (a) (b) Fig. 1. SEM images of the Cross section of (a) GaN epilayer on sapphire substrate and (b) vertically aligned ZnO NWs. Fig. 2. Terahertz time domain spectrometer based on Ti:Sapp ultrafast laser at 790 nm. ZnTe is used for the detection and LT-GaAs photoconductive switch is used for emitter. -4 -2 0 2 4 6 8 Amplitude (a.u.) Time Delay (ps) Al2O3 GaN 6.80 6.85 6.90 6.95 7.00 7.05 7.10 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Time Delay (ps) 105 ° ° ° ° ° ° ° ° ° C 95 C 85 C 75 C 65 C 55 C 45 C 35 C 25 C 6 7 8 9 4 6 8 10 12 -1 0 1 2 3 THz Amplitude (a.u.) Time Delay (ps) (a) (b) Fig. 3. (a) Measured THz responses transmitted through both the GaN thin ﬁlm grown on sapphire substrate and the bare sapphire substrate for comparison and (b) temperature dependent measurement of GaN thin ﬁlm with peak intensity changes with temperatures (inset). S. Balci et al. / Solid-State Electronics 78 (2012) 68–74 69

where ~ n S and ~ n r are the complex refractive indices of the thin ﬁlm of interest and the reference substrate, respectively. Through numeri- cal simulation of experimental measurement of T (x), the complex refractive index of the sample thin ﬁlm, ~ n S (for example, GaN ﬁlm or ZnO NW ensemble) can be determined. Once this complex refrac- tive index is obtained, the material complex conductivity and dielectric function can be determined through: ~ eðxÞ¼ e dc þ i ~ rðxÞ xe 0 ¼ ~ n 2 S ð2Þ where e 0 is the free-space permittivity, e dc is low frequency dielec- tric constant (e dc = 9.4 for GaN, and e dc = 7.46 for ZnO), and ~ eðxÞ; ~ rðxÞ, and ~ n S are the frequency dependent complex dielectric function, electrical conductivity, and index of refraction, respectively. 3. Experiments The GaN thin ﬁlm used in this study is 4.8 lm thick, n-type doped (n = 10 18 m 3 ) and grown on a sapphire (Al 2 O 3 ) substrate by metalorganic vapor phase epitaxy. The details of the growth condition were reported elsewhere [21]. The growth of ZnO nano- wires on sapphire substrates was carried out in a three-zone tube furnace at a temperature of 900 °C. A ﬁne powder mixture of ZnO and graphite in a 1:2 M ratio was used as the source material and placed in a quartz boat in the tube furnace. Undoped ZnO NWs was grown using the ZnO seeds realized on the substrates following a wet chemistry process as reported earlier [22]. To enhance the n-type electrical conductivity of the nanowires, aluminum was used as a dopant by introducing Al in the powder mixture and car- rying out the growth at low pressure. Both undoped and n-type (ZnO:Al) ZnO NWs were vertically aligned and the length of NWs can range from 5 to 20 lm depending on the growth duration, as shown in Fig. 1. Terahertz measurements of the samples were carried out using the time-domain transmission spectrometer shown in Fig. 2. A 790 nm mode-locked laser with 120 fs pulses is used to pump the spectrometer. Broadband terahertz radiation (0.2–3.5 THz) is generated by photo excitation of a photoconductive antenna based on LT-GaAs with an applied voltage bias of 130 V at 15 kHz. Detection of the terahertz electric ﬁeld is obtained using a ZnTe electro-optic crystal and balanced photodiodes. The sample is mounted on a three-axis, motion controlled stage perpendicular to the incident wave. Two polyethylene lenses are used to focus the collimated radiation to a diameter of 0.5 mm on the sample and re-collimate the radiation into the detection array. The motion controlled stage allows for precise positioning of the sample in the path of propagation. Measurements are performed under a nitro- gen blanket to minimize absorption of the terahertz radiation by water vapor. For the temperature dependent measurements, a mount with embedded resistance heating was used and the samples were placed in thermal contact with between two heated ceramic plates with concentric 2 mm apertures. The temperature of the mount was measured by an embedded thermocouple and controlled using 0 0.5 1 1.5 2 0 50 100 150 0 2 4 6 8 10 12 14 Frequency (THz) Temperature ( ° C) Real Refractive Index (T,f) 0 0.5 1 1.5 2 0 50 100 150 0 2 4 6 8 10 12 14 Frequency (THz) Temperature ( ° C) Imaginary Refractive Index (T,f) 0.0 0.5 1.0 1.5 2.0 2 4 6 8 10 (a) (b) 12 Real Imaginary Refractive Index Frequency (THz) Fig. 4. Refractive index measured by THz-TDS. (a) Real and imaginary parts of refractive index at 25 °C vs frequencies and (b) Real and imaginary parts of refractive indices vs temperatures and frequency. 70 S. Balci et al. / Solid-State Electronics 78 (2012) 68–74

a basic feedback loop. The actual sample temperature was cali- brated using an external thermocouple in contact with the sample surface as a function of heating time and the embedded thermo- couple. Careful assessment of temperature and thermal stabilities were made for each step of increases and decreases of the temperatures. 4. Results and discussions 4.1. GaN thin ﬁlm Fig. 3a compares the measured THz responses transmitted through both the GaN thin ﬁlm grown on sapphire substrate (‘‘sample’’) and the bare sapphire substrate (‘‘reference’’). Due to absorption from the GaN epilayer, the peak amplitude of the THz electric ﬁeld transmitted through the sample is about 30% that of the THz wave transmitted through the reference alone. We also ob- served minor oscillations due to residual moisture and echoes of the reﬂections in the sample with a slight delay of the peak. For simplicity, we did not take into account wave reﬂections in the sample and oscillations after the main THz pulse. The complex fre- quency dependent THz ﬁeld is then obtained through Fast Fourier Transform (FFT), which is generated automatically by the in-house software we developed. Fig. 3b shows changes in the THz response for increasing temperatures, with a magniﬁed view of the peak shown in the inset. The peak amplitude increases with tempera- ture, which means the absorption actually decreases. At 105 °C, the peak intensity increases by 12% from the value at 25 °C, while it stays almost the same with no change for sapphire with increas- ing temperature. The complex refractive index (~ n) of the GaN epilayer material is determined from Eq. (1) through numerical iteration as a function of temperature and frequency. Fig. 4a shows that both the real refractive index and extinction coefﬁcient decrease with increasing frequency at room temperature. This frequency dependent behav- ior remains at elevated temperatures. It is noticed that water vapor absorption at 1.2 and 1.6 THz led to the kinks in the calculation -5 0 5 10 15 20 25 30 35 40 Conductivity (Ωcm) -1 Real Imaginary Frequency (THz) 0.5 1.0 1.5 2.0 20 40 60 80 100 15 20 25 30 Real Conductivity (Ω- cm) -1 Temperature ( o C) 0.5 THz 1.0 THz 1.5 THz 2.0 THz (a) (b) Fig. 5. (a) Real and imaginary part of conductivity at 25 °C vs frequencies and (b) real conductivity vs temperature at selective frequencies. 0.0 0.5 1.0 1.5 2.0 16 20 24 28 T = 25 o C T = 55 o C T = 105 o C Fitted curve Real Conductivity (Ω- cm) -1 Frequency (THz) Fig. 6. Measured real part of conductivity vs. frequency at three selected temper- atures and ﬁtted using the simple Drude model (Eq. (3)). 35 40 45 50 55 60 65 70 75 80 ω p -plasma frequency ω p (THz-rad) Temperature ( o C) (a) 4 5 6 7 8 τ 0 -relaxation time τ 0 (s)x10 -14 20 40 60 80 100 120 20 40 60 80 100 120 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 N ( 1/cm 3 )x10 18 Temperature ( ° C) N-carrier concentration μ ( cm 2 /Vs ) 300 350 400 450 500 550 600 μ-mobility (b) Fig. 7. Summary of the temperature dependent characteristics of carrier dynamics of n-GaN including plasma frequency, relaxation time, carrier concentration, and mobility obtained from Drude model at THz frequencies. S. Balci et al. / Solid-State Electronics 78 (2012) 68–74 71

results due to lower experimental signal-to-noise ratio at those two frequencies. Fig. 4b summarizes the temperature and fre- quency dependence of the complex refractive index of GaN as mea- sured by THz-TDS. As shown in this plot, the real and imaginary parts change more rapidly with frequency while they slowly de- crease when the temperature is increased. The complex electrical conductivity can be extracted from the measured complex refractive index by using Eq. (2), and its real and imaginary parts are plotted in Fig. 5a as a function of fre- quency. Again, both parts vary monotonously with frequency, but their trends are different. The real conductivity-which is the con- ventional conductivity- decreases with frequency. There are a few reports describing a similar behavior. By contrast, the imagi- nary conductivity increases with frequency. The complex conduc- tivity was also calculated as a function of temperature from 25 °C to 105 °C. For all temperatures, the frequency dependency of both real and imaginary parts followed a trend similar to the one shown in Fig. 5a. Fig. 5b illustrates this for the temperature dependent real conductivity at a few selected THz frequencies. The real electrical conductivity decreases as temperature increases: from 25 (X-cm) 1 at 25 °C down to 22 (X-cm) 1 at 105 °C (0.5 THz), and from 20.5 (X-cm) 1 at 25 °C down to 17 (X-cm) 1 at 105 °C (1.5 THz). The frequency dependent complex conductivity was ﬁtted using the Drude model [23] to further analyze carrier dynamics and extract important material parameters, including the plasma frequency x p and the carrier relaxation time s 0 . In the General Drude model, these are related to the complex conductivity arising from free carriers following the relation: rðxÞ¼ e 0 x 2 p s 0 =½1 ðixs 0 Þ a  c ð3Þ In the case the exponents are such that a = 1 and c = 1, the model becomes a simple Drude model, which is used here to ﬁt the mea- sured values of conductivity obtained for n-GaN. By ﬁtting to the expression of frequency dependent conductivity using Eq. (3) for the simple Drude model for each given temperature, the plasma frequency and relaxation time can be extracted for that chosen temperature. Fig. 6 plots the resulting curve ﬁts at three different temperatures. The extracted values for x p and s 0 can be used -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Amplitude (a.u) Delay Time (ps) Al 2 O 3 Undoped ZnO Al-doped ZnO 5 6 7 8 9 20 40 60 80 100 120 5.2 5.6 6.0 6.4 6.8 Peak Amplitude (mV) Temperature ( o C) Undoped ZnONWs Al-doped ZnONWs (a) (b) Fig. 8. (a) Measured THz signal transmitted through both undoped and Al-doped ZnO NWs and their comparison with a reference signal and (b) Comparison of peak amplitude vs. temperatures for undoped and Al-doped ZnO NWs. 1 2 3 4 5 Refractive Index_Real Frequency (THz) T=40 o C T=60 o C T=80 o C T=90 o C T=95 o C 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 1 2 3 4 5 Real Refractive Index Frequency (THz) T=25 o C T=45 o C T=65 o C T=85 o C T=105 o C T=115 o C (a) (b) Fig. 9. Real part of refractive index vs. frequency and temperature for (a) Al-doped NWs and (b) undoped NWs. 0.4 0.8 1.2 1.6 2.0 0 2 4 6 8 10 12 Real Conductivity (Ω- cm) -1 Frequency (THz) Al-doped NW Undoped NW Fig. 10. Calculated frequency dependent real conductivities of both undoped NWs and Al-doped NWs at 25 °C. 72 S. Balci et al. / Solid-State Electronics 78 (2012) 68–74

further relate to the material properties. For example, the plasma frequency is related to the carrier concentration (N) through x p =[Ne 2 /e 0 m  ] 1/2 and relaxation time is related to the carrier mobil- ity (l) through s 0= lm  /e, where m  is the effective electron mass and is 0.22m e . These two parameters are plotted as a function of temperature in Fig. 7, which shows characteristics of the carrier dynamics when temperature is varied. The plasma frequency we obtained shows a clear dependency on temperature and was found to be decreasing with temperature, which translates into a corre- sponding reduction of the carrier concentration. By contrast, the relaxation time slightly increased with temperature, which results in a slightly increasing mobility. The values of mobility obtained are very close to that obtained from Hall measurement. 4.2. ZnO nanowires Both undoped and Al-doped ZnO NW were realized and com- pared in terms of their temperature dependent carrier dynamics at THz frequencies. Both NWs were very well vertically aligned and were grown under the same conditions such as temperature and gas ﬂows, except that Al was added in a separate boat during the Al doped ZnO NW growth. The resulting density of the NWs was also similar for both types. The transmitted THz electric ﬁeld through the ZnO NWs did not change too much for undoped ZnO NW as shown in Fig. 8a. The peak amplitude was about 90% that of the THz wave transmitted through the bare sapphire substrate (‘‘reference’’). However, the peak amplitude in the case of the Al- doped ZnO NW ended up being 60% of the reference peak, which is consistent with the behavior of n-GaN where a stronger THz absorption is expected from the higher free carrier concentration arising from doping. Fig. 8b compares the THz transmitted wave peak amplitudes as a function of temperature for both undoped and Al-doped NWs. The peak intensities of both NWs decrease as temperature increases. It is noted that this behavior is different from what we observed in the case of n-GaN in the previous sec- tion. We tentatively attribute this observation as an indirect conse- quence of the already high doping level in the n-GaN, since the ZnO NWs were either only lightly doped or undoped and exhibited a different behavior in THz transmission. However, the amount of decrease is small at the same time. Since the wavelength of the light used in this study is much lar- ger than the diameter of ZnO NWs, the refractive index of ZnO NW cannot simply be subtracted out from the refractive index of the ZnO NW/air composite. Therefore, effective medium theory should be taken into account [24]. This theory is mostly used to calculate the permittivity of a composite material while the permittivity and volume fraction of each of the individual components. One of the most commonly used effective medium theories is the Bruggeman effective medium approximation (EMA) [25] given by f ðe p  eÞ=ðe p þ KeÞ À Á þð1  f Þððe m  eÞ=ðe m þ KeÞÞ ¼ 0 ð4Þ where f is the volume fraction of NWs from the density of NWs, e is the permittivity of the composite (ZnO NW/air), e m is the matrix permittivity which is 1 (air) in this study, e p is the particle permit- tivity (ZnO NWs), and K is a geometric factor which is 1 for an array of cylinders with its axis collinear with the incident radiation and 2 for spherical nanoparticles. The Bruggeman EMA can be used in re- verse to calculate the permittivity of one component (ZnO NWs) while those of both the other component (air) and the composite (ZnO NW/air) are known. Rearranging Eq. (4) to solve e p , with e m = 1, and K = 1, one gets: e p ¼ e f ð1 þ eÞþðf  1Þð1  eÞ ½  f ð1 þ eÞðf  1Þð1  eÞ ð5Þ By using the relation between the complex refractive index and per- mittivity (Eq. (2)), the complex refractive index of ZnO NW was ex- tracted from the composite (ZnO NW/air). The same process was applied in the case of all temperatures in order to yield a tempera- ture dependent (real) refractive index as a function of frequency for Al-doped and undoped NWs, as shown in Fig. 9a and b, respectively. Fig. 9a shows that the refractive index smoothly decreases both as the frequency increases and as the temperature increases. At higher temperature, the decrease with frequency becomes more pro- nounced. In addition, the temperature dependency shows a distinct 6 8 10 12 14 T=40 o C T=80 o C T=90 o C fitted by Drude-Smith model Real Conductivity (Ω- cm) -1 Frequency (THz) 0.4 0.8 1.2 1.6 2.0 0.3 0.6 0.9 1.2 1.5 1.8 0 2 4 6 Real Conductivity (Ω- cm) -1 Frequency (THz) T=25 o C T=65 o C T=85 o C fit for T=25 o C (a) (b) Fig. 11. Real conductivity and curve ﬁts using the Drude–Smith model for (a) Al- doped NWs and (b) undoped NWs at different temperatures. Table 1 Summary of parameters obtained from Drude–Smith model by ﬁtting the frequency dependent conductivity for undoped ZnO NWs and Al-doped ZnO NWs. T °C x p (THz-rad) s 0 (s)  10 14 N(1/cm 3 )  10 18 l(cm 2/Vs ) c Undoped ZnO NW 25 27.29 9.84 0.06 721.12 0.85 Al-doped ZnO NW 25 54.42 7.29 0.22 534.43 0.67 40 74.18 5.17 0.42 379.01 0.74 80 57.29 6.68 0.25 489.27 0.68 90 50.85 7.45 0.20 545.76 0.61 S. Balci et al. / Solid-State Electronics 78 (2012) 68–74 73

feature. Indeed, there were only minimal changes in the refractive index with temperature at lower frequencies (below 0.6 THz), while the changes were more discernible as both temperature and fre- quency increase (above 0.6 THz). In the case of undoped ZnO NWs, as shown in Fig. 9b, a more dynamic change in the refractive index. Although the refractive index seems to decrease with tem- perature and frequency above 0.6 THz, similar to the Al-doped NW case, there seems to be multiple stages involved in the fre- quency dependent behavior. The complex conductivities were obtained using the same method as discussed in the previous section and the real parts of the conductivities are plotted in Fig. 10 for both undoped NWs and Al-doped ZnO NWs at 25 °C. Both types show an increase in conductivity as frequency increases. It is also clearly visible that the electrical conductivity increases by a factor of 3 at THz frequencies due to the incorporation of Al into the ZnO NWs. It should be emphasized that the THz-TDS method is unique and easy to obtain the conductivity changes in materials without having to make metal contacts, which still remains a technologically chal- lenging task to perform in the case of NW. Fig. 11 shows the calculated conductivity as a function of fre- quency for both undoped NWs and Al-doped NWs at selected tem- peratures. In the case of Al-doped NWs (Fig. 11a), the conductivity decreases with temperature, which is similar to what was observed in n-GaN in the previous section. However, there is a fundamental difference with n-GaN when one considers the frequency depen- dence. In the case of GaN, the conductivity varied by approximately the same amount for all frequencies when the temperature is changed. In the case of Al-doped ZnO NWs, the amount of change depended on the frequency regime. Below 0.6 THz, the conductiv- ity did not change much as the temperature increases whereas, above 0.6 THz, it decreases as temperature increases. The calcu- lated conductivity for undoped NWs is shown in Fig. 11b. At 25 °C, the frequency dependent behavior of the conductivity is similar to the one observed in Al-doped NWs. But at elevated tem- peratures, it shows the multiple stages of frequency dependence similar to the frequency dependent refractive indices. We observed that at lower frequencies the conductivity increases, while it de- creases at elevated temperatures and higher frequencies. To ﬁt the calculated conductivity in ZnO NWS, we had to use the Drude–Smith model, which is described by the following expression, rðxÞ¼ e 0 x 2 p s 0 ð1  ixs 0 Þ 1 þ X 1 n¼1 c n ð1  ixs 0 Þ " # ð6Þ The Drude–Smith model is a relatively simple classical model that describes systems in which the memory effects in scattering process is incorporated. Negative Im[r] was well explained with this model [7]. It assumes that persistence of velocity is retained for only one collision. This includes important parameter C, which varies from 1 (back scattering only) to 0 (Drude scattering only, i.e. simple Drude model case). It is expected that back scattering becomes an important contribution to the conductivity behavior of nanostructures since carriers are more closely conﬁned within and strong localization can appear in the structure [7]. The ﬁtted frequency dependent conductivities are included in Fig. 11. Table 1 summarizes the characteristics of carrier dynamics ob- served in ZnO NWs based on the parameters obtained from the Drude–Smith model. 5. Conclusion We have presented a comprehensive study of the temperature dependent carrier dynamics of n-GaN and ZnO NWs based on THz-Time Domain Spectroscopy measurements. Combining exper- imental measurements and numerical calculations, the complex refractive index, dielectric function, and conductivity of n-GaN, undoped ZnO NWs, and Al-doped ZnO NWs were obtained. The unique temperature dependent behaviors of these material parameters were studied at THz frequencies. Further analysis of temperature dependent carrier dynamics were obtained consider- ing both the Drude and the Drude–Smith models in order to extract the plasma frequency, relaxation time, carrier concentration and mobility. Acknowledgements This work was supported by NSF EECS 0824452 and NSF CA- REER award. S.B. acknowledges a fellowship from the Turkish Min- istry of National Education. References [1] Cheung KP, Auston DH. Infrared Phys 1986;26:23. [2] Grischkowsky D, Keiding S, van Exter M, Fattinger Ch. J Opt Soc Am B 1990;7:2006. [3] Ferguson B, Zhang X-C. Nature Mater 2002;1:26. [4] Zhang XH, Guo H, Yong AM, Ye JD, Tan A, Sun XW. J Appl Phys 2010;107:033101. [5] Van Exter M, Grischkowsky D. Phys Rev B 1990;41:12140–9. [6] Schmuttenmaer CharlesA. Chem Rev 2004;104:1759–79. [7] Baxter JB, Schmuttenmaer CA. J Phys Chem B 2006;110:25229. [8] Tsai Tsong-Ru, Chen Shi-Jie, Chang Chih-Fu, Hsu Sheng-Hsien, Lin Tai-Yuan, Chi Cheng-Chung. Opt Express 2006;14:4898–907. [9] Han Jiaguang, Azad Abul K, Zhang Weili. J Nanoelectronics Optoelectronics 2007;2:222–33. [10] Nakamura S, Mukai T, Senoh M. Appl Phys Lett 1994;64:1687–9. [11] Ramaiah KS, Su YK, Chang SJ, Kerr B, Liu HP, Chen IG. Appl Phys Lett 2004;84:3307–9. [12] Nakamura S, Senoh M, Nagahama S, Iwasa N, Yamada T, Matsushita T, et al. Jpn J Appl Phys Part 2 1996;35:L74–6. [13] Ponce FA, Bour DP. Nature 1997;386:351–9. [14] Özgür Ü, Alivov YI, Liu C, Teke A, Reshchikov MA, Dog ˘an S, et al. J Appl Phys 2005;98:041301. [15] Gaska R, Yang JW, Osinsky A, Chen Q, Khan MA, Orlov AO, et al. Appl Phys Lett 1998;72:707–9. [16] Pearton SJ, Zolper JC, Shul RJ, Ren F. GaN: processing, defects, and devices. J Appl Phys 1999;86:1–78. [17] Morkoc H, Strite S, Gao GB, Lin ME, Sverdlov B, Burns M. J Appl Phys 1994;76:1363–98. [18] Wan Q, Li QH, Chen YJ, Wang TH, He XL, Li JP, et al. Appl Phys Lett 2004;84:3654. [19] Baxter J, Schmuttenmaer CA. Phys Rev B 2009;80:235206. [20] Duvillaret L, Garet F, Coutaz JL. IEEE J Sel Topic Quant Elect 1996;2:739. [21] Dawahre N, Shen G, Balci S, Baughman W, Wilbert DS, Harris N, et al. J Electron Mater 2011. http://dx.doi.org/10.1007/s11664-011-1803-x . [22] Gayen RN, Bhar R, Pal AK. Indian J Pure Appl Phys June 2010;48:385–93. [23] Smith NV. Phys Rev B 2001;64:155106. [24] Choy TC. Effective medium theory: principles and applications. Oxford, UK: Clarendon Press; 1999. [25] Bruggeman DAG. Ann Phys 1935;24:636. 74 S. Balci et al. / Solid-State Electronics 78 (2012) 68–74

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References (25)

Cheung KP, Auston DH. Infrared Phys 1986;26:23.
Grischkowsky D, Keiding S, van Exter M, Fattinger Ch. J Opt Soc Am B 1990;7:2006.
Ferguson B, Zhang X-C. Nature Mater 2002;1:26.
Zhang XH, Guo H, Yong AM, Ye JD, Tan A, Sun XW. J Appl Phys 2010;107:033101.
Van Exter M, Grischkowsky D. Phys Rev B 1990;41:12140-9.
Schmuttenmaer CharlesA. Chem Rev 2004;104:1759-79.
Baxter JB, Schmuttenmaer CA. J Phys Chem B 2006;110:25229.
Tsai Tsong-Ru, Chen Shi-Jie, Chang Chih-Fu, Hsu Sheng-Hsien, Lin Tai-Yuan, Chi Cheng-Chung. Opt Express 2006;14:4898-907.
Han Jiaguang, Azad Abul K, Zhang Weili. J Nanoelectronics Optoelectronics 2007;2:222-33.
Nakamura S, Mukai T, Senoh M. Appl Phys Lett 1994;64:1687-9.
Ramaiah KS, Su YK, Chang SJ, Kerr B, Liu HP, Chen IG. Appl Phys Lett 2004;84:3307-9.
Nakamura S, Senoh M, Nagahama S, Iwasa N, Yamada T, Matsushita T, et al. Jpn J Appl Phys Part 2 1996;35:L74-6.
Ponce FA, Bour DP. Nature 1997;386:351-9.
Özgür Ü, Alivov YI, Liu C, Teke A, Reshchikov MA, Dog ˘an S, et al. J Appl Phys 2005;98:041301.
Gaska R, Yang JW, Osinsky A, Chen Q, Khan MA, Orlov AO, et al. Appl Phys Lett 1998;72:707-9.
Pearton SJ, Zolper JC, Shul RJ, Ren F. GaN: processing, defects, and devices. J Appl Phys 1999;86:1-78.
Morkoc H, Strite S, Gao GB, Lin ME, Sverdlov B, Burns M. J Appl Phys 1994;76:1363-98.
Wan Q, Li QH, Chen YJ, Wang TH, He XL, Li JP, et al. Appl Phys Lett 2004;84:3654.
Baxter J, Schmuttenmaer CA. Phys Rev B 2009;80:235206.
Duvillaret L, Garet F, Coutaz JL. IEEE J Sel Topic Quant Elect 1996;2:739.
Dawahre N, Shen G, Balci S, Baughman W, Wilbert DS, Harris N, et al. J Electron Mater 2011. http://dx.doi.org/10.1007/s11664-011-1803-x.
Gayen RN, Bhar R, Pal AK. Indian J Pure Appl Phys June 2010;48:385-93.
Smith NV. Phys Rev B 2001;64:155106.
Choy TC. Effective medium theory: principles and applications. Oxford, UK: Clarendon Press; 1999.
Bruggeman DAG. Ann Phys 1935;24:636.

FAQs

What unique behaviors were observed in GaN thin films at elevated temperatures?add

The study reveals that the peak THz intensity in GaN increases by 12% from 25 °C to 105 °C, indicating decreasing absorption. Both the real refractive index and extinction coefficient decrease with increasing frequency, even at elevated temperatures.

How does n-type doping affect the dielectric properties of ZnO nanowires?add

Al-doped ZnO NWs exhibited a peak amplitude of THz transmission at 60% of the reference, compared to 90% for undoped NWs. This suggests higher free carrier concentration in Al-doped NWs, correlating with stronger THz absorption.

What methodologies were used to analyze temperature dependent conductivity?add

The research utilized both the Drude and Drude-Smith models to analyze the temperature dependent complex conductivity. The Drude-Smith model accounts for memory effects in scattering processes, resulting in distinct behavior for n-GaN and ZnO NWs.

When examining carrier dynamics, how were plasma frequency and relaxation time affected by temperature variations?add

The plasma frequency decreased with temperature, while the relaxation time slightly increased, indicating varying carrier mobility. These relationships allow for a deeper understanding of material behavior in high-frequency applications.

What implications do THz-TDS findings have for high-frequency electronics?add

The findings demonstrate that temperature influences carrier dynamics in GaN and ZnO, essential for optimizing high-frequency device performance. Understanding these properties can improve design and efficiency in optoelectronics and related technologies.

Characteristics of THz carrier dynamics in GaN thin film and ZnO nanowires by temperature dependent terahertz time domain spectroscopy measurement

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