Journal of Luminescence 8 (1974) 462—470. © North-Holland Publishing Company TWO-PHOTON ABSORPTION IN CdS BY LOW POWER CW LASER F. CORNOLTI, G. FORNACA, A. GIULIETTI and M. VASELLI Laboratorio di Fisica Ato mica e Molecolare, C.N.R., Pisa, Italy Received 1 June 1973 Revised manuscript received 16 July 1973 Our aim is to study the two-photon induced luminescence in CdS crystals by using a low power CW laser (5 mW). We discuss briefly the possibility given by the electron-pulse-counting technique to detect weak optical signals. This technique enables us to investigate the luminescence spectra (which show two bands at 2.4 and 2.0 eV) and the dependence of the luminescence intensity on the laser power. The discussion of the experimental results makes it clear that the level re2 s. sponsible for the red emission is partially saturated at a laser intensity of 1023 photon/cm 1. Introduction The study of the two-photon induced luminescence in crystals is generally performed by using high power pulsed lasers. However, intensities of ‘S-’ 106 W/cm2 typical for this kind of experiments are enough to produce collateral effects (such as shock-waves, photoemission, heating and so on) [1] which considerably complicate the analysis of the results. To avoid these problems we have evaluated the possibility of a two-photon absorption experiment in CdS by a low power CW laser. Preliminary measurements of the two-photon cross-section a(2) of this process at room temperature have been carried out, by using an Nd pulsed laser and an He—Ne laser. We employed the double beam technique to perform the measurements, a technique well known (see for example ref. [21) and we found for u(2) the value ~ = 1.5 X l0~~cm4 s, which is very near to the value of ref. [3]. With this value we can calculate the two-photon absorption rate for a 5 mW He—Ne laser. If the beam is focused into a region of ~-‘ l0~ cm2 (far from the diffraction limit [4]), a flux of 1.5 X 1023 photon/cm2 s is obtained; so we have an absorption of 3 X 1 ~ photon/s in the volume of 3 X 10~l cm3. The experimental set-up described in the next section enables us to study luminescence induced by this weak absorption at 300°K. 462 F. Cornolti eta!., Two-photon absorption 463 Cd S He-Nt laser LIi~ Fig. 1. Experimental set-up. 2. Experiment The experimental set-up is shown in fig. 1. The laser output (He—Ne Spectra. Physics mod, 120 S mW) is filtered by a 2-61 Corning filter F1, whose transmis— sion for X <6100 A is less than 1%, then focused by a microscope objective on the CdS crystal whose c-axis is parallel to the laser beam. Our CdS single crystals, supplied by Harshaw Chemical, have purity SN (Cu impurity especially does not exceed 0.3 ppm). The fluorescence light is collected at 900 by a Bausch and Lomb 500 mm monochromator M, having 16.5 A/mm linear dispersion. Before the entrance slit we put a Baizers LS 694 filter F2, whose transmission is iO~~ for laser light, 80% in the visible region and the cut-off is between 6100 and 6200 A. A photomultiplier (Philips XP 1110) follows. Due to the very low intensity, a direct measurement of photocurrent is not possible. Indeed, it is well known that a photocurrent consists of a d.c. component and an a.c. component of unipolar sharp pulses. For low intensities there is more power in the a.c. portion than in the d.c. portion [5]. Moreover, it has been shown experimentally (6] and tested by ourselves, that the pulse rate is proportional to the light intensity if the optical power involved is less than 10—12 w. Therefore, we have performed pulse-counting, after choosing the discrimination level for the best S/N ratio. The background is found when the slits of the monochromator are closed, and is 25 ±1.6 counts per second. If we consider the minimum detectable signal for which S/N = 1, we can detect, with 10 s counting, 2 events/s corresponding to an rms current of 1.5 x 10—12 A for our phototube (see also refs. 15] and [6]). 3. Results The luminescence spectra obtained from two different CdS crystals are shown in figs. 2 and 3. These spectra are obtained with the entrance and exit slits 2 mm large. The uncertainty in the F2 transmission near 6200 A involves errors in this region. Both crystals show very weak luminescence at 5200 A and stronger one near 6100 A. 464 F. Cornolti eta!., Two-photon absorption 4 3 2 .62 .61 .60 .59 .58 .57 Fig. 2. Luminescence spectra between 0.62 and 0.55 jim: 100— o .56 .55 sample no. 1. ~ sample no. 2. —____ 50 .0 0 £ ‘ .57 .56 £ .55 .55 .55 .52 £ .51 A(,um) Fig. 3. Luminescence spectra between 0.57 and 0.50 pm: cjsample no. 1, ~ sample no. 2. F. Cornolti eta!., Two-photon absorption 465 The luminescence spectra of the two crystals are very similar but crystal no. 1 is more efficient at 5200 A by a factor 3. We have verified that, for X < 6200 A, there is no contribution from scattered laser light. The same experimental apparatus has been employed in studying the dependence of luminescence intensity ‘F on the excitation intensity ‘L~The luminescence intensity induced by laser flux from 1023 to 1021 photon/cm2 s is plotted in figs. 4 and 5. The two crystals show again similar behaviour. Variation of ‘L is obtained by laser beam attenuation using neutral density filters. At strong attenuations the error in the determination of filter transmission and the low counting rates cause remarkable errors. In these measurements the monochromator slits are 10 mm large (~X= 165 A) and the center of the band is at 5200 and 6100 A respectively. In the studied range ‘F increases with the laser power ‘L as I~where n = 0.92 ±0.03 at 6100 A and 1.45 ±0.04 at 5200 A. The dependence of the 6100 A luminescence band on the excitation is not reported in the literature to our knowledge. The luminescence at 5200 A has a different dependence on ‘L in different 100 I 1. 0.5 II Ii.. II~ liii,,, (photofl~rn2sec~..b~ Fig. 4. Dependence of fluorescence intensity on excitation intensity for the sample no. 1: .6100 A band, 0 5200 A band. 466 F. Cornolti etal., Two-photon absorption 100 . . - —S I C U ‘I __________- . - _____________ IL. ~phOtoflS,km2 sec; .rb unit.) Fig. 5. Dependence of fluorescence intensity on excitation intensity for the sample no. 2: .6100 A band, a 5200 A band. samples, as quoted in refs. [7] and [8]: the exponent runs from 1.0 to 1.6 and for same crystals, in particular conditions of excitation, higher values have been found. Including detection efficiency, we can evaluate a full-solid angle emission of about 2 X l0~photon/s (sample 1) at 5200 ±80 A and 108 photon/s at 6100 ±80 A for ‘L 1023 photon/cm2 s. 4. Discussion The measured value of a(2) (see section 1) allows us to evaluate the two-photon transition rate from valence to conduction band, induced by low power laser radiation as described in section 2. The order of magnitude of the transition rate is 1020 cm3 s~.Assuming for the electrons in the conduction band a mean life of about 2 X i0~ s [9], we conclude that there is a conduction band population of nearly 1011 electron cm~3.Following this assumption, we try to interpret some spectral properties, especially ‘F versus ‘L dependence. Two emission bands (6100 and 5200 A) in nominally pure CdS crystals have F. Cornolti eta!., Two-photon absorption 467 been recently reported, although with different experimental conditions [10,111. In these papers the authors ascribe them to a decay through unspecified crystaldefect levels, whose density is evaluated as nearly 1014 cm3 [10—131. Figure 6 is a diagram of the levels (see also refs. [10] and [11]). The 6100 A band is ascribed to 2—I level decay and the 5200 A band to 3—1 decay. The mean life is r 2 10—2 s for level 2 and r3 l0~ s for level 3. We will show that this scheme can explain the luminescence versus laser intensity dependence of both bands after suitable assumptions on capture probabilities of traps 2 and 3 (see diagram). We will callN the total electron state density, while n and p are the electron. occupied and electron-unoccupied state density (so ii +p N); subscripts 1, 2 and 3 refers to levels 1, 2 and 3 respectively. ‘L is the excitation laser light;12 and 13 are the intensities of the 6100 and 5200 A luminescence band respectively. We have 12Pl (1) ‘—‘ ‘ 12 ~~ 13 ~fl3Pl (2) , where n 2, n3, p1 depend on 1L’ (figs. Since thefollows intensities the(1) twoand bands havena different dependence on 4 and 5) it fromofeqs. (2) that 2 and n3 depend on ‘L with a different power law, i.e. n2 must have an exponent smaller than n3. \ ___ ________ _______ 0.02 — —3 0.35 2 2.58 2,40 2.05 1 S — lo ~ ///////)/// vap•nc. •V I ban //////// Fig. 6. Energy band diagram. 468 4.1. F. Corno!ti et al., Two-photon absorption Balance equations For the population of level 2, in the stationary case, the equation dn 2 0 = -~- n2 = —-— + 72n4(N2— /12) — y2n2N4 exp(—z~2E/kT) (3) holds, where ~2E = E2 0.35 eV, 12 is the mean life related to the 2-to-grourn level decay process, ‘y2n4 is the non-radiative capture probability from the conduction band to trap 2, and ‘y2n2N4 exp (-.-L~2E/kT)is a temperature dependent transition rate from level 2 to level 4. For level 3 a similar equation holds: dn3 fl3 +-y3n4(N3--n3)—y3n3N4 exp(—~3E/kT), = (4) where the symbols are now obvious. We discuss eqs. (3) and (4) first omitting the term 1 /T, for simplicity. We have /12/14 _____________ N2 N4 n4/N4 - + exp (—~2E/kT)’ (5) 1 N4 n4/N4 +exp(—~3E/kT)~ 6 n3n4 N3 () For low population density (n4o~ N4 exp (—~E/kT)),these equations give the Boltzmann distribution and both n2 and n3 should be proportional to n4. Furthermore, since n4 ~ I~,n2 and n3 should also show the same dependence on ‘L But this is not the case; indeed we have shown in the previous section that the luminescence intensity from level 2 has a smaller exponent than from level 3. So we can infer that at least level 2 must be partially saturated, i.e. its dependence on n4 is a sub-linear one, and hence n4 must be n4 ~N4exp(—~2E/kT). (7) If we consider the term l/r in eqs. (3) and (4), we have a similar conclusion. Eq. (7) becomes n4y2 1/12 + N4 exp(—~2E/kT)y2 - (8) Relation (8) and our experimental data allow us to evaluate 72 and the capture cross section 02. Indeed the electron state density NkT whose energy is included in the range from E4 toE4 + kT can be calculated as follows: 469 F. Corno!ti et aL, Two-photon absorption E~+kT f NkT= 2ir 2 (2~*~ h E 3, (E—E4)~dE~ 1018 cm (9) 4 where m* is the electron effective mass (about 0.2 me in our case) [14], ~2E 0.35 eV and T 300°K,we have 3 (10) N4 exp(—~2E/kT)‘—‘5 X 10’’ cm Previously we had evaluated the conduction band population and we found n 4 3, then relation (8) will be satisfied for 1011 cm . — ~fl (11) 472. As seen before, ~2 102 s, then from eq. (11) we have ~ io~s~cm 3. (12) For about 1 eV energy electrons, eq. (12) gives a lower limit of capture cross-section: 02 ~ 10—16 cm2, (13) which is a typical value for processes of this kind. While we need to suppose a partial saturation for level 2, the sub-quadratic dependence of 13 versus ‘L does not need a similar assumption for level 3: this behaviour can result from an electron pile.up in level 1. Moreover, the level 3 saturation assumption would be questionable, indeed arguments like the previous ones lead to the following requirements: 73 ~ 10—6 s~cm3 from which 03 10_13 cm2 which is a too high value; N 3 (notice that Boltzmann factor 4 c~1011 would be e08). This value disagrees withcm eq. (13) which leads to 1018 cm3 for the conduction band density of states entering in thermal equilibrium between levels 3 and 4 at 300°K.Therefore, it is reasonable to suppose that level 3 is not saturated, but eq. (6) holds in an approximate form ~‘ n.~ n~ 10_6 N 3 N4 — — while for level 2 it is n2 N2. This also explains the higher intensity of the 6100 A band compared with the 5200 A band. Indeed, if we put N2 N3, we obtain n3 106 n2. Since the final state densities are the same for both processes, the ratio of the two intensities is 470 F. Cornolti et aL, Two-photon absorption I~(22’~ /(2.~lo3 13 \~2/ I \13/ Our results show that ‘2 is at least 500 times higher than 13. 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