Study of terahertz radiation from InAs and InSb

JOURNAL OF APPLIED PHYSICS VOLUME 91, NUMBER 9 1 MAY 2002 Study of terahertz radiation from InAs and InSb Ping Gu, a) Masahiko Tani, Shunsuke Kono, b) and Kiyomi Sakai Kansai Advanced Research Center, Communications Research Laboratory 588-2 Iwaoka, Kobe 651-2492, Jaan X.-C. Zhang Deartment of Physics, Alied Physics and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York, 12180-3590 Received 24 Setember 2001; acceted for ublication 6 February 2002 Terahertz radiation from InSb and InAS, which are tyical narrow band-ga semiconductors, was investigated using time-resolved THz emission measurements. When we comared between the olarity of the THz waveforms of these narrow band-ga semiconductors with that of InP, which is a wide bandga semiconductor, we concluded that the ultrafast buildu of the hoto-dember field is the main mechanism for the emission of THz radiation in both InAs and InSb. The emission efficiency of InSb is aroximately one-hundredth of that of InAs, although the electron mobility in InSb is higher than in InAs. Wavelength-deendent measurements imlied that the anomalously low THz emission efficiency of InSb might be due to a reduction in transient mobility resulting from the scattering of electrons into the low-mobility L valley. 2002 American Institute of Physics. DOI: 10.1063/1.1465507 I. INTRODUCTION Narrow ga semiconductors have attracted much attention as emitters of THz radiation uon irradiation with femtosecond laser ulses because InAs, a tyical narrow bandga semiconductor, has been found to have the highest emission efficiency of the bulk semiconductors investigated to date and to show a strong enhancement of emission efficiency under a magnetic field. 1 However, the THz emission mechanism in such narrow band-ga semiconductors is not yet fully understood. Narrow band-ga semiconductors tend to have high electron mobilities, which are thought to be one of the reasons for their high THz emission efficiency. For examle, InAs has a mobility of 30 000 cm 2 /V/s band-ga E g 0.36 ev. InSb, another tyical narrow band-ga semiconductor, has a higher mobility of 76 000 cm 2 /V/s (E g 0.1 ev. Therefore, we would exect InSb to be as efficient as InAs in emitting THz radiation. In fact, however, InSb is not as efficient as InAs, as we reorted in a revious aer: 2 the THz ower observed from InSb was a mere onehundredth of that observed for InAs without a magnetic field bias. The urose of this work was to investigate the anomalously low emission efficiency of InSb as well as to investigate the emission mechanisms in these narrow bandga semiconductors. The THz emission mechanisms in bulk semiconductors are categorized into nonlinear and linear rocesses: the nonlinear rocess is exlained as the otical rectification of ultrafast laser ulses in semiconductors, 3 and the linear rocess is exlained by the current-surge model on the semiconductor surface induced by hotoexcitation. The current surge is a Present address: Deartment of Physics, Faculty of Education, Wakayama University, 930 Sakaedani, Wakayama City, Wakayama 640-8510, Jaan; electronic mail: guing@center.wakayama-u.ac.j b Present address: Fundamental Research Laboratories, NEC Cororation, 34 Miyukigaoka, Tukuba 305-8501, Jaan. thought to have two origins: 1 the acceleration of hotoexcited carriers by the surface deletion field, and 2 the hoto-dember effect originating from the difference between the diffusion velocities of the electrons and holes electrons gain much faster velocity due to their higher mobility comared to holes. In semiconductors with a wide band ga, such as GaAs (E g 1.43 ev or InP (E g 1.34 ev, we would exect the contribution of the hoto-dember effect to be negligible because the absortion deth is relatively long the hoto-dember field is roortional to the carrier-density gradient and the deletion field is generally strong. 4 For narrow band-ga semiconductors, on the other hand, the deletion field is generally weaker because of the small band-ga energy. In the excitation with near-infrared light (h 15 ev of a narrow band-ga semiconductor, the absortion deth is very short 100 nm, 5 and the hotoexcited electrons gain much kinetic energy from the large amount of excess energy in the excitation. These conditions, as well as high electron mobility, enhance the hoto-dember effect in narrow band-ga semiconductors. Consequently, the ultrafast buildu and relaxation of the hoto-dember field may be an efficient mechanism for generating THz radiation in narrow band-ga semiconductors. In this work, we reared n and tyes of InSb and InAs and observed the THz radiation emitted from these samles using a time-resolved detection system. First, we measured the azimuthal angle deendence of the THz radiation amlitude to investigate the contribution from the nonlinear rocess to THz emission. We then checked the olarity of the waveforms for the n- and -tye samles, from which we were able to judge which surge-current mechanism was dominant. If the hoto-dember effect is dominant, the olarity of the waveform will remain the same for n- and -tye samles because the direction of carrier diffusion will not change with the tye of doing, while the olarity will fli deending on the tye of doing because the deletion-field 0021-8979/2002/91(9)/5533/5/$19.00 5533 2002 American Institute of Physics

5534 J. Al. Phys., Vol. 91, No. 9, 1 May 2002 Gu et al. direction flis according to doing tye. Lastly, we investigated the excitation wavelength deendence. The results of the wavelength-deendent measurements indicated that intervalley scattering, which may considerably reduce transient mobility, is imortant and may thus be the reason for the low THz emission efficiency in InSb. II. EXPERIMENT In our exeriment, a mode-locked Ti:sahire laser ulse with a 40 fs ulse width, a 76 MHz reetition rate, and a central wavelength of 800 nm was used as the um laser to excite the samles and to gate a hotoconductive PC antenna detector. The angle of incidence of the um laser beam on the samle was 45, and the radiation emitted in the direction of otical reflection was collected and focused onto the PC antenna detector using a air of arabolic mirrors. The um beam was olarized and the maximum averaged ower at the samle surface was about 80 mw. The PC detector consisted of a 30- m-long diole antenna with a 5 m hotoconductive ga, colanar transmission lines couled to the antenna, and a hotoconductive substrate layer beneath the antenna electrodes. The hotoconductive substrate was an annealed low-temerature-grown GaAs film grown on a 0.4-mm-thick semi-insulating GaAs substrate. The timeresolved wave forms of the radiation were obtained from the DC hotocurrent in the antenna detector by varying the delay time between the uming and gating ulses. The samles used are listed in Table I: an n-tye and -tye InSb 100 with a carrier concentration of n 10 16 cm 3, and n-tye InAs 111 and -InAs 100 with a carrier concentration of n 10 18 cm 3, and an n-tye and -tye of InP 100 with a residual carrier concentration of n 10 18 cm 3. The InP samles were also used as the reference. The band-ga energies at room temerature, as well as the mobilities, are also listed in the table. All measurements were carried out at room temerature. III. RESULTS AND DISCUSSION A. Azimuthal angle deendence Taking the surface normal as the x axis and the reflection lane as the x- y lane, the electronic olarization P induced in a zinc-blende semiconductor due to otical rectification for the 111 and 100 surfaces is exressed by Eqs. 1 and 2, resectively: 2,6 P x z y d 14 0 E 2 1 3 cos2 2 3 sin2 2 6 cos2 cos 3 2 cos sin 3 2 6 cos2 sin 3 1 P 2 cos2 sin 2 x y 14 0 E sin 2 sin z d sin 2 cos 2. Here, is the angle between the surface normal and the excitation laser beam refracted inside the samle, and is the azimuthal angle of the samle orientation around the x axis. E is the electric field amlitude of the um laser, and d 14 ( 0) is the nonlinear suscetibility coefficient for otical rectification. As THz radiation was detected in the reflection geometry for olarization, the observed THz field amlitude is exected to be roortional to x sin THz y cos THz, 3a where THz is the refraction angle of THz radiation at the interface between the samle surface and air. The refraction angles for the otical and THz beam were determined by the generalized Snell s law as sin 45 n ot sin n THz sin THz, 3b where n ot and n THz are the refractive index for the um laser and THz radiation, resectively. For the um-laser wavelength of 800 nm, is 10.9, 9.0, and 11.8 for InAs, InSb, and InP, resectively. For THz radiation, THz is estimated to be 10.9, 21.5, and 11.9 for InAs, InSb, and InP, resectively. Using these values, the azimuthal angle deendence of the radiation amlitude due to otical rectification can be written as follows: 2 E 0.773 cos 3 0.153 d 14 for 111 InAs, 4a E 0.182 sin 2 d 14 for 100 InAs, 4b E 0.069 sin 2 d 14 for 100 InSb, 4c E 0.199 sin 2 d 14 for 100 InP. 4d In our exerimental configuration, the nonlinear contribution was roortional to the azimuthal angular modulation of cos 3 with a small dc offset for 111 -oriented crystals, and sin 2 for 100 -oriented crystals. The constants before the cos 3 or sin 2 function in Eqs. 4a 4d reresent the geometrical factors of the nonlinear contribution for the 45 um-incidence on the samles. Although nonlinear otical rectification coefficients, d 14 ( 0), for InSb, InAs and InP are not known, the second harmonic generation coefficients, d 14 (2 ), may be helful in indicating the relative magnitude of d 14 ( 0) among the samles: d 14 (2 ) at 1.06 m is 520 47, 364 47, and 167.0 m/v for InSb, InAs, and InP, resectively. 7 Figure 1 a shows the azimuthal angle deendence measured for the 111 InAs samle. A ronounced angle deendence is observed solid squares, which agrees well with the 3 -deendence described by Eq. 4a solid line. From the angle-deendent art of the THz radiation, we can estimate the ratio of the nonlinear contribution to the total radiation amlitude. In the case of the 111 InAs samle, the nonlinear contribution to the total radiation amlitude with estimated to be 40%. The azimuthal angle deendence for the 100 -oriented n-insb samle is shown in Fig. 1 b by the solid circles. There is also a small angle deendence, which

J. Al. Phys., Vol. 91, No. 9, 1 May 2002 Gu et al. 5535 FIG. 1. Azimuth angle deendence of THz radiation amlitude from semiconductors with a n-inas 111 solid squares and b n-insb 100 solid circles surfaces at a 45 incident angle of the excitation light on the samle. The solid lines are the sin 3 or sin 2 angle deendence fitted to the data. agrees well with the 2 -deendence described by Eq. 4b solid line. The ratio of the nonlinear contribution to the total radiation amlitude is estimated to be 6% from the magnitude of the angle-deendence comonent solid line. It should be noted that the small nonlinear contribution arises from the off-normal incidence of the um-laser beam 45 in this case, because the nonlinear electro-otic effect is always zero for the normal incidence of the excitation laser beam for 100 -oriented zinc-blende crystals. The azimuthal angle deendences for the other 100 -oriented samles were as weak as the deendence observed for the 100 -oriented n-insb samle. From the results of the azimuthal angle deendence, we can conclude that the nonlinear contribution to THz radiation was not very significant for 100 -oriented samles, although for 111 -oriented samles we have to take the nonlinear contribution into consideration. The contribution of the surge-current alone to THz emission can be investigated by comletely suressing the nonlinear contribution by choosing the aroriate azimuthal angle deending on the crystal orientation. That is, when we use an azimuthal angle of 26 for 111 InAs and 90 for all 100 -oriented samles, the nonlinear contribution is effectively zero Eqs. 4a 4d equal zero. In the following measurements of THz waveforms, we emloyed such angles to reduce the nonlinear contributions. B. Polarity of waveforms The time-domain wave forms for both tyes of InSb and InAs samles are shown in Figs. 2 a and 2 b, resectively. The THz-radiation waveforms of n- and -InP are shown in Fig. 2 c for comarison. The azimuthal angle of crystal orientation was set near 26 for the n-inas 111 samle and 90 for the other 100 -oriented samles to suress the contribution from the otical rectification effect. It is known that FIG. 2. Time-domain waveforms of THz radiation from n- and - a InSb, b InAs and c InP. The azimuthal angle of crystal orientation was 26 for n-inas 111, and 90 for other 100 -oriented samles so that the contribution from the otical rectification effect was suressed. the generation of THz radiation from InP originates mostly from the ultrafast screening of the surface deletion field by the hotoexcited carriers. 4 THz radiation due to screening of the surface deletion field flis its olarity for the oosite tye of doing due to the reversal of the direction of the surface deletion field, as is clearly shown in Fig. 2 c. However, when THz radiation is emitted by the hoto-dember effect, which originates from the different diffusion coefficients of electrons and holes, the olarity of the THz radiation remains the same for n-tye and -tye semiconductors because the diffusion coefficient of electrons is always bigger than that of holes, irresective of the doing tye of the semiconductor. The THz waveforms of n-tye and -tye samles have the same olarity, as shown in Figs. 2 a and 2 b, for both InSb and InAs. In addition, their olarity is the same as that of the n-inp the direction of the surface deletion field of the n-inp is exected to be the same as that of the hoto-dember field. These results suggest that the rincial excitation mechanism of THz radiation in InSb and InAs is an ultrafast buildu and relaxation of the hoto- Dember field. Deeer insight into the mechanism of THz emission can be obtained by considering the electronic roerties of narrow band-ga semiconductors. The surface deletion fields of InAs and InSb should be much smaller than that of InP due to their low band-ga energy. For 800 nm light, the enetration deth d for InSb and InAs is calculated to be 94 nm and 142 nm, resectively, while that of InP is 304 nm. Electron mobility ( e ) and excess energy ( E) in InSb ( e 76 000 cm 2 /V/sec, E 1.38 ev and InAs ( e 30 000 cm 2 /V/sec, E 1.18 ev with 800 nm light excitation 1.55 ev are much higher than those of InP ( e 4000 cm 2 /V/sec, E 1.21 ev because of their narrow band gas see Table I. All these conditions suggest the existence of a large hoto-dember field for InSb and InAs under 800 nm otical excitation. Thus, we conclude the main

5536 J. Al. Phys., Vol. 91, No. 9, 1 May 2002 Gu et al. TABLE I. List of samles. Tye Carrier concentration (cm 3 ) Crystal orientation Electronic bandga at 300 K ev Mobilities e / (cm 2 /V/sec) InSb n 10 16 100 0.17 76 000/800 10 16 100 (b 95) InAs n 10 18 111 0.36 30 000/240 10 18 100 (b 125) InP n 10 18 100 1.34 4000/650 10 18 100 (b 6) source of THz radiation for InAs and InSb is the hoto- Dember field, not the screening of the surface deletion field. The radiation amlitude of the n-tye InAs and n-tye InSb is a little bigger than that of their -tye counterarts. This suggests that there might be an enhancement of THz radiation due to the surface deletion field because the direction of the surface deletion and hoto-dember fields is the same in n-tye semiconductors. C. Wavelength deendence Steady-state hoto-dember voltage (V D ) is described by the following equation: 8 V D k BT b 1. 5 e b 1 ln 1 b 1 n n 0 b 0 Here, b e / is the mobility ratio of the electrons ( e ) and holes ( h ), and n 0, 0, and T are the initial density of the electrons and holes, and the temerature of hotoexcited electrons and holes, resectively. This equation tells us that the hoto-dember effect is enhanced by higher levels of electron mobility ( e b) and electron excess energy ( E T e ). Narrow band-ga semiconductors ossess conditions that favor the creation of a large hoto-dember field, that is, the high levels of electron mobilities and excess carrier energies. Moreover, the hoto-dember field (V D /d, d: absortion layer deth in narrow band-ga semiconductors is further enhanced by the thin absortion deth. On the other hand, we would exect the surface deletion field to be small because of the small band-ga energy, in contrast to that in wide-ga semiconductors. It is noteworthy that, according to Eq. 5, a lower residual electron and hole concentration (n 0 and 0 ) are referable, and that the um intensity (I n) deendence of hoto-dember voltage is exected to be linear at a low intensity regime ( to I) and roortional to ln( n) ln(i) ata high intensity regime ( n n 0, 0 ). It is also known from Eq. 5 that the hoto-dember voltage does not deend strongly on arameter b the ratio of the electron and hole mobilities when b is large enough ( 10), which is the case for InSb (b 95) and InAs (b 125). Because of the short enetration deth of InSb 92 nm, the hoto-dember field (E V D /d) in InSb should be almost twice as big as that of InAs 142 nm for 800 nm light excitation. In addition, the electron mobility of InSb is about twice as great as that of InAs. Because the emitted THz-radiation-field amlitude is FIG. 3. Time-domain waveforms of n-inas 111 excited by a 780 nm and b 1.55 m light. roortional to the acceleration field and electron mobility surge current i e e E), we would exect the THz emission efficiency of InSb to be about four times greater in amlitude and therefore 16 times greater in ower than that of InAs. However, the exerimental results did not suort this simle theoretical rediction. The unexectedly low THz emission of InSb might be exlained by reduction of the transient mobility due to intervalley scattering of electrons to the L valley, where we would exect electron mobility to be considerably lower. Because the energy of the L valley from the to of the valence-band edge the oint is 1.03 ev corresonding to 1.2 m in InSb, the electrons are easily scattered into the L valley by 800 nm light excitation (h 1.55 ev. On the other hand, as the energy of the L valley is 1.53 ev the energy barrier is higher than this value in InAs, we would exect the scattering of electrons to the L valley to be not so efficient and most of electrons to remain in the valley under the same 800 nm light excitation. Since the rate of intervalley scattering strongly deends on the excitation wavelength, the wavelength deendence of THz radiation rovides imortant information on the suggested mechanism. Figure 3 shows the THz radiation wave forms of n-inas 111 at 780 nm excitation for a ower of 3.3 mw solid curve and at 1.55 m excitation for a ower of 9.0 mw dotted curve. When the amlitude signal was normalized with the resective um and robe-beam ower, the THz emission efficiency at 1.55 m was estimated to be almost one order of magnitude lower than that at 780 nm. The long enetration deth (d 590 nm and smaller amount of excess energy ( E 0.44 ev at a 1.55 m excitation should give about one-sixth the hoto-dember field of that exected at a 780 nm excitation (d 140 nm, E 1.23 ev if the simle theory of the hoto-dember effect is valid note that the hoton number for 1.55 m light was doubled with the same ower for 780 nm light. Thus, the hoto-dember field model agrees reasonably well with the exerimental results at different wavelengths for InAs. In contrast to the case of InAs, Howells et al. 9 reorted that the emission efficiency of THz radiation from InSb increases by about six times in amlitude normalized by the hoton numbers at 1.9 m excitation comared to that at 800 nm. This observation is inconsistent with the hoto- Dember model, which redicts a considerable decrease in THz emission efficiency at 1.9 m comared to that at 800

J. Al. Phys., Vol. 91, No. 9, 1 May 2002 Gu et al. 5537 nm because of the long enetration deth for 1.9 m light. However, this result can be exlained if we assume a significant reduction in transient mobility due to the L-valley scattering of electrons, as Howells et al. also suggested in their aer. In fact, Nuss et al. 10 reorted a significant dro in mobility due to intervalley scattering in GaAs. Although further exerimental studies are needed to come to a definite conclusion, we believe that intervalley scattering lays an imortant role in the THz emission mechanism of the semiconductors and exlains the low THz emission efficiency observed for InSb with 800-nm excitation. IV. CONCLUSIONS In conclusion, we studied the emission roerties of THz radiation from tyical narrow band-ga semiconductors, InSb and InAs, by measuring the azimuthal angle deendence and time-domain wave forms using a time-resolved detection system. By comaring the olarity of the THz radiation from n- and -tye samles, we concluded that the main mechanism for the emission of THz radiation from InSb and InAs is the ultrafast buildu and relaxation of the hoto-dember field. The hoto-dember model can exlain the result of the THz emission efficiency observed at 1.55 m and 780 nm excitation for InAs, however, it disagrees with the result of the wavelength deendence reorted for InSb. We susect that the low emission efficiency of InSb at shorter wavelengths is due to a significant reduction in transient mobility caused by electron scattering to the lowmobility L valley in InSb. ACKNOWLEDGMENTS One of the authors P.G. acknowledges the suort of the Jaan Science and Technology Agency through a Domestic Research Fellowshi and the research budget associated with it. 1 N. Sarukura, H. Ohtake, S. Izumida, and Z. Liu, Al. Phys. Lett. 84, 654 1998. 2 S. Kono, P. Gu, M. Tani, and K. Sakai, Al. Phys. B: Lasers Ot. 901 2000. 3 For review aer, see, for examle, S. L. Chuang, S. Schmitt-Rank, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 1992 ;A. Rice, Y. Jin, X. F. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, Al. Phys. Lett. 64, 1324 1994 ; A. Bonvalet, M. Joffre, J. L. Martin, and A. Migus, ibid. 67, 2907 1995. 4 X.-C. Zhang and D. Auston, J. Al. Phys. 71, 326 1992. 5 T. Dekorsy, H. Auer, H. J. Bakker, H. G. Roskos, and H. Kurz, Phys. Rev. B 53, 4005 1996. 6 Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, J. Ot. Soc. Am. B 18, 823 2001. 7 S. Singh, in Handbook of Lasers, edited by R. J. Pressley, CRC Press, Cleveland, 1971. 8 Winfried Mönch, Semiconductor Surfaces and Interface: Surfaces Sciences Sringer, Berlin, 1993,.68. 9 S. C. Howells, S. D. Herrera, and L. A. Schlie, Al. Phys. Lett. 65, 2946 1994. 10 M. C. Nuss, D. H. Auston, and F. Caasso, Phys. Rev. Lett. 58, 2355 1987.