Science in China Series G: Physics, Mechanics & Astronomy © 2009

SCIENCE IN CHINA PRESS

www.scichina.com phys.scichina.com www.springerlink.com

Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy ZHOU QingLi1, SHI YuLei1†, LI Tong2, JIN Bin1, ZHAO DongMei1 & ZHANG CunLin1 1

Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Department of Physics, Capital Normal University, Beijing 100048, China; 2 Department of Electronics Engineering, Tianjin University of Technology and Education, Tianjin 300222, China

The carrier dynamics and terahertz photoconductivity in the n-type silicon (n-Si) as well as in the p-type Silicon (p-Si) have been investigated by using femtosecond pump-terahertz probe technique. The measurements show that the relative change of terahertz transmission of p-Si at low pump power is slightly smaller than that of n-Si, due to the lower carrier density induced by the recombination of original holes in the p-type material and the photogenerated electrons. At high pump power, the bigger change of terahertz transmission of p-Si originates from the greater mobility of the carriers compared to n-Si. The transient photoconductivities are calculated and fit well with the Drude-Smith model, showing that the mobility of the photogenerated carriers decreases with the increasing pump power. The obtained results indicate that femtosecond pump-terahertz probe technique is a promising method to investigate the carrier dynamics of semiconductors. semiconductor, terahertz, carrier dynamics

The transient transport dynamics of photoexcited carrier in semiconductors is important for advancing the physics of nonequilibrium phenomena and creation of optical and electronic devices. Femtosecond lasers have given rise to a wealth of information about ultrafast nonequilibrium dynamics. Compared to the conventional experimental techniques[1], the femtosecond pump-terahertz probe (FPTP) spectroscopy has a plethora of advantages that provide the ability to temporally resolve phenomena at the fundamental timescales of carrier motion[2]. The FPTP technique, as a noncontact method and being sensitive to carrier transport, can measure photoinduced changes in the photoconductivity, which con-

tains the information of carrier density and mobility, with a temporal resolution of sub-picosecond[3]. This could help us to further understand the material properties and find out the promising physical effect for application. In the past decade, although much work has been done by using FPTP techniques to investigate nonequi－ librium dynamics in photoexcited materials[2,4 9], few studies have been reported on photogenerated carrier dynamics in doped semiconductors. Here we use FPTP technique to investigate the carrier dynamics of n-Si and p-Si samples. The terahertz (THz) transmission has been measured at different pump powers irradiating on the two samples, respectively. Addi-

Received July 12, 2009; accepted August 31, 2009 doi: 10.1007/s11433-009-0308-6 † Corresponding author (email: [email protected]) Supported by the National Basic Research Program of China (Grant Nos. 2007CB310408 and 2006CB302901), the National Natural Science Foundation of China (Grant No. 10804077), Beijing Municipal Commission of Education (Grant No. KM200910028006), Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality, and the State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences

Citation: Zhou Q L, Shi Y L, LI T, et al. Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy. Sci China Ser G, 2009, 52(12): 1944-1948, doi: 10.1007/s11433-009-0308-6

tionally, we have calculated the transient photoconductivities in the terahertz range, and extracted the carrier mobilities at different pump powers by fitting the frequency-dependent photoconductivity data with the Drude-Smith model.

n- and p-Si, respectively. The difference in refraction indexes of those two samples corresponds to the 0.53 ps time delay of the waveforms in Figure 1.

1 Experiment The measurement is taken by using a Ti:sapphire regenerative amplifier delivering ultrashort optical pulses with a duration of 100 fs and a central wavelength of 800 nm at a repetition rate of 1 kHz. The source beam is split into three portions, corresponding to terahertz generation, probe, and pump beams, respectively. The terahertz wave generation is assigned to the four-wave mixing in the air plasma produced by a β-BaB2O4 (BBO) crystal[10]. The terahertz radiation is detected by free-space electro-optic sampling in a 1-mm-thick <110> ZnTe crystal[11]. The signal is collected by a lock-in amplifier with phase locked to an optical chopper. The path with terahertz radiation is enclosed and purged with dry nitrogen. The pump beam energy is variable. The spot size diameters of the pump laser and terahertz pulse are 5 and 2 mm, respectively, so that the terahertz could transmit a uniform region of photoexcitation. All experiments are performed at room temperature. In our experiment, the n-Si and p-Si samples are all 0.5-mmthick wafers. The Hall effect measurement shows the carrier densities of ~1013 cm−3 and ~1015 cm−3 for n- and p-Si, respectively.

Figure 1 The terahertz pulse of reference of free space and the signals through n- and p-Si wafers without pump, respectively.

2 Results and discussion The measured transmitted terahertz signals through the free space and samples without pump excitation are displayed in Figure 1. Compared to the reference signal, the terahertz waveforms transmitted through the samples exhibit a drop in amplitude and a delay in time. Furthermore, the signal of p-Si shows a time delay of about 0.53 ps relative to n-Si, suggesting that the refraction index of p-Si is larger than that of n-Si. From the transmitted terahertz waveforms, the complex refraction indexes of the two samples are calculated with real part n (refraction index) and imaginary part k (extinction coefficient) in the 0.4－1.6 THz region, respectively. As shown in Figure 2, the complex refraction index of p-Si is higher than that of n-Si. The average values of refraction indexes are about 3.13 and 3.45 for

Figure 2 The complex refraction index with (a) real part and (b) imaginary part for n- and p-Si samples in the 0.4－1.6 THz region.

The excitation intensity dependence of the relative change in transmission (ΔT/T0) is presented in Figure 3. For the two samples, it can be seen that when the terahertz pulse begins to encounter the pump pulse, the terahertz transmission decreases due to the photogenerated carriers and will be smaller under the higher pump powers due to more photogenerated carriers in the sample. As the delay time Δt between pump and terahertz pulses further increases, a process of carrier recombination occurs, which tends to be indistinct under the high

Zhou Q L et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1944-1948

1945

pump powers. This trend is expected for surface states or impurity levels filling, which may inhibit carrier recombination from changing carrier lifetime[12,13]. After excitation by the pump pulse, carriers could fill these states considerably and the carrier decay will then slow down.

rated electrons and original low-density holes can be ignored. Compared to the n-Si, the higher value of |ΔT/T0|max of p-Si might originate from the higher mobility of the photogenerated carriers.

Figure 4 The curves of the maximum |ΔT/T0| as the function of pump power for n- and p-Si samples.

In order to validate our conclusion, we calculate the transient frequency-dependent complex photoconductivity from the transmitted terahertz waveform with ( E pump ) and without ( E ) the optical excitation at a speFigure 3 Relative change in transmission of the peak of the terahertz pulse at the different pump power for (a) n-Si and (b) p-Si, respectively.

To further investigate the dynamics process, we plot the curves of the maximum of |ΔT/T0| (|ΔT/T0|max) as the function of pump power, as shown in Figure 4 for n- and p-Si samples. It is clear that when the pump power is lower than 50 mW, the |ΔT/T0|max of n-Si is larger than that of p-Si. However, when the pump power exceeds 50 mW, the |ΔT/T0|max of p-Si is larger than that of n-Si. It is known that the absorption of the terahertz radiation depends upon carrier density and mobility, exhibiting an increase in |ΔT/T0|max (i.e, absorption) with the increased carrier density and mobility[2]. Here, the motion of photogenerated holes is usually ignored because the effective mass of hole is much larger than that of electron. For the low pump power, the original holes in the p-Si will recombine some part of photogenerated electrons, leading to an obvious drop in the carrier density. Hence, |ΔT/T0|max of p-Si under this condition will be smaller than that of n-Si. On the other hand, at high pump power, the number of photogenerated carriers is sufficient and the influence of recombination between the photogene1946

without pump [14]

cific pump time delay . The ratio of Fourier transformation of these two waveforms is related to the complex conductivity σ (ω ) = σ 1 (ω ) + iσ 2 (ω ) through[15,16] E pump (ω ) n +1 (1) = ,  Ewithout pump (ω ) n + 1 + Z 0 dσ (ω )

where d is the thickness of the photoexcited layer (estimated to be 10 μm based on the penetration depth of the 800 nm pump in Si)[17], Z0 = 377 Ω is the impedance of free space[2], and n is the index of refraction in the terahertz range of the unexcited sample calculated from our experimental data (shown in Figure 2). Figure 5 shows the calculated photoconductivity with the real part σ1 and the imaginary part σ2 at the delay time of Δt = 133 ps under different pump excitation for (a) n-Si and (b) p-Si, respectively. For the same sample, it can be seen that the photoconductivity increases with the pump power. For the same pump excitation, the photoconductivity of p-Si is slightly larger than that of n-Si. Furthermore, we find that the calculated photoconductivities deviate from the Drude conductivity[18], showing that the real conductivity has a maximum at non-zero frequency and the imaginary part has some

Zhou Q L et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1944-1948

Figure 5 The complex photoconductivities for (a) n-Si and (b) p-Si under 50 and 180 mW pump powers, respectively. The solid lines are the fitting curves using Drude-Smith model.

negative values. Therefore we use the Drude-Smith model[19], which attributes the negative imaginary conductivity to the backward scattering of electrons as a result of the electron reflecting from surface, defects, or impurity, to fit the photoconductivity. Many studies indicate that the Drude-Smith model could provide a superior fit to both real and imaginary parts of conductivity for many materials[15,18,20]. The Drude-Smith model is given by[19]

σ (ω ) =

Ne 2τ / m* ⎡ c ⎤ 1+ , ⎢ 1 − iωτ ⎣ 1 − iωτ ⎥⎦

(2)

where the parameter c is a measure of persistence of velocity and its negative value implies a predominance of backscattering. N is the electron density, e is the elementary charge, m* is the electron effective mass, and τ is the characteristic scattering time. The effective mass of electron is 0.26m0 for Si material. The parameters of the fitting curves (solid lines in Figure 5) are (a) c = -0.83, N = 2.8×1018 cm−3, τ = 37 fs at 50 mW pump power, c = -0.84, N = 8.2×1018 cm−3, τ = 30 fs at 50 mW pump power for n-Si, and (b) c = -0.81, N = 2.8×1018 cm−3, τ = 45 fs at 180 mW pump power, c = -0.82, N = 8.2×1018 cm−3, τ = 42 fs at 180 mW pump power for p-Si, respectively. In the Drude-Smith model, the DC mobility is related to the Drude mobility μ = eτ/m* by μ(1+c). Hence, we have obtained the carrier DC mobility to be roughly 43 cm2·V−1·s−1 at 50 mW pump power,

33 cm2·V−1·s−1 at 180 mW pump power for n-Si, and 58 cm2·V−1·s−1 at 50 mW pump power, as well as 51 cm2·V−1·s−1 at 180 mW pump power for p-Si, respectively. The obtained results indicate that the extracted photogenerated carrier mobility of p-Si is larger than that of n-Si. Furthermore, the mobility decreases with the increasing pump power because the increased photoinduced carrier density results in the decreased interval of the collision time between the carriers. In Figure 5, the deviations of experimental data of the conductivity from the Drude-Smith model at high pump power originate from the decreased signal noise ratio of the system because the amplitude of the terahertz signal transmitting through the pump sample is greatly reduced by the photogenerated carrier absorption.

3 Conclusions In summary, we have used a direct noncontact method to measure photoexcited carrier dynamics in n-Si and p-Si wafers. It is found that the relative change in terahertz transmission of p-Si is different from that of n-Si, showing smaller change at low pump power as a result of the recombination between photoexcited electrons and original holes, and larger change at high pump power due to the greater mobility of carriers in p-type material. Furthermore, we have found that the extracted photogenerated carrier mobility by fitting the photoconductivity with Drude-Smith model decreases with the

Zhou Q L et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1944-1948

1947

increasing pump power. Our investigation suggests that the FPTP technique is a powerful method for detecting the ultrafast dynamics in those materials and could help 1

Averitt R D, Taylor A J. Ultrafast optical and far-infrared quasiparticle

us to reveal the material properties in the terahertz range and to find out the promising physical effect for application. 11

2

2002, 14: R1357－R1390 Beard M C, Turner G M, Schmuttenmaer C A. Transient photocon-

12

3

13

Prabhu S S, Ralph S E, Melloch M R, et al. Carrier dynamics of

4

eration in GaAs. Appl Phys Lett, 2006, 89: 232102 14

Liu K P H, Hegmann F A. Ultrafast carrier relaxation in radia-

5

terahertz spectroscopy. Appl Phys Lett, 2006, 89: 122103 15

Shi Y, Xu X, Yang Y, et al. Anomalous enhancement of terahertz ra-

6 7

self-assembled ErAs nanoislands embedded in GaAs measured by optical-pump terahertz-probe spectroscopy. Appl Phys Lett, 2005, 86:

Knoesel E, Bonn M, Shan J, et al. Charge transport and carrier dy-

201107 17

Lett, 2001, 86: 340－343 Abuabara S G, Cady C W, Baxter J B, et al. Ultrafast photooxidation 18

Phys Rev B, 1983, 27: 985－1009 Baxter J B, Schmuttenmaer C A. Conductivity of ZnO nanowires, nanoparticles, and thin films using time-resolved terahertz spectros-

19

copy. J Phys Chem B, 2006, 110: 25229－25239 Smith N V. Classical generalization of the Drude formula for the op-

20

Beard M C, Turner G M, Murphy J E, et al. Electronic coupling in InP

tical conductivity. Phys Rev B, 2001, 64: 155106

2001, 87: 017401 Xie X, Dai J, Zhang X-C. Coherent control of THz wave generation in ambient air. Phys Rev Lett, 2006, 96: 075005

1948

Aspnes D E, Studna A A. Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV.

nanoparticles. J Phys Chem C, 2007, 111: 11982－11990 Averitt R D, Lobad A I, Kwon C, et al. Ultrafast conductivity dynamics in colossal magnetoresistance manganites. Phys Rev Lett,

10

Prasankumar R P, Scopatz A, Hilton D J, et al. Carrier dynamics in

ductivity of GaAs nanowires. Nano Letters, 2007, 7: 2162－2165

of Mn(II)-Terpyridine complexes covalently attached to TiO2 9

B, 2007, 76: 125408 16

Parkinson P, Lloyd-Hughes J, Gao Q, et al. Transient terahertz con-

namics in liquids probed by THz time-domain spectroscopy. Phys Rev 8

Walther M, Cooke D G, Sherstan C, et al. Terahertz conductivity of thin gold films at the metal-insulator percolation transition. Phys Rev

diation from semi-insulating GaAs surfaces induced by optical pump. Appl Phys Lett, 2006, 89: 081129

Cooke D G, Hegmann F A, Young E C, et al. Electron mobility in dilute GaAs bismide and nitride alloys measured by time-resolved

tion-damaged silicon on sapphire studied by optical-pump-terahertzprobe experiments. Appl Phys Lett, 2001, 78: 3478－3480

1997, 70: 3245－3247 Lloyd-Hughes J, Merchant S K E, Fu L, et al. Influence of surface passivation on ultrafast carrier dynamics and terahertz radiation gen-

low-temperature-grown GaAs observed via THz spectroscopy. Appl Phys Lett, 1997, 70: 2419－2421

Sosnowski T S, Norris T B, Wang H H, et al. High-carrier-density electron dynamics in low-temperature-grown GaAs. Appl Phys Lett,

ductivity in GaAs as measured by time-resolved terahertz spectroscopy. Phys Rev B, 2000, 62: 15764－15777

Wu Q, Litz M, Zhang X-C. Broadband detection capability of ZnTe electro-optic field detectors. Appl Phys Lett, 1996, 68: 2924－2926

dynamics in correlated electron materials. J Phys-Condens Matter,

nanoparticle arrays. Nano Lett, 2003, 3: 1695－1699

Zhou Q L et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1944-1948