- Email: [email protected]
Thermal diffusion of Cr2+ in bulk ZnSe
Journal of Crystal Growth 240 (2002) 176–184
Thermal diffusion of Cr2+ in bulk ZnSe J.-O. Ndapa, K. Chattopadhyaya, O.O. Adetunjia, D.E. Zelmonb, A. Burgera,* a
Department of Physics, Center for Photonic Materials and Devices, Fisk University, Nashville, TN 37208-3051, USA b Air Force Research Laboratory, WPAFB, OH 45433-7707, USA Received 26 July 2001; accepted 15 January 2002 Communicated by R. James
Abstract Cr2+:ZnSe is now known as a room-temperature widely tunable solid-state mid-infrared laser material. Optimization of laser performance requires first and foremost optimization of the Cr2+-doping level in the crystals. A simple theoretical model has been developed for evaluation of the thermal diffusivity of Cr2+ ions in bulk ZnSe single crystals and polycrystalline window materials, from optical absorption measurements in the 1200–2800 nm spectral region. Sputtered metallic chromium and powders have been used as dopant sources. Diffusion appears to be faster in polycrystalline materials than in single crystals for annealing temperatures below 9101C. The activation energy, which is lower in polycrystals, depends on the nature of the dopant source. For mid-IR laser application, the model predicts for example, non-negligible optical losses due to passive self-absorption in the 2000–3000 nm spectral region for chromiumdoped polycrystalline materials after annealing at temperatures above 9001C for 1.75 days. r 2002 Elsevier Science B.V. All rights reserved. Keywords: A1. Diffusion; A1. Doping; A1. Impurities; B1. Inorganic compounds; B1. Zinc compounds; B2. Semiconducting II–VI materials; B3. Solid state lasers
1. Introduction ZnSe has a variety of applications in optical devices such as light-emitting diodes and waveguides. The bulk polycrystalline compound is used for infrared optical components such as lenses and windows for IR detectors and high-power lasers. It was recently reported that the incorporation of transition metal ions (Cr2+,Co2+,Fe2+,Ni2+, W2+) gives rise to properties [1–13] that make this material particularly attractive for applications in *Corresponding author. Tel.: +1-615-329-8516; fax: +1615-329-8634. E-mail address: aburger@fisk.edu (A. Burger).
room-temperature solid-state laser devices, tunable in the mid-IR [14–17]. Laser action was demonstrated in Cr2+:ZnSe [14,17]. Chromium, as well as the other transition metals, substitutes for the cation in ZnSe. EPR measurements [18,19] have revealed two charge states of chromium in ZnSe:Cr1+ and Cr2+. The second state appears to be the most stable and the most probable for concentrations p4 1019 atoms/cm3 [1]. The acceptor state Cr1+ can be induced by a chargetransfer using a below band-gap photo-excitation (16900–22000 cm1), with ejection of an electron from the valence band to the Cr2+ energy level [11,12]. A crystal field splits the ground state 5D of the Cr2+ free ion into an excited state 5E and a
0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 2 ) 0 0 8 7 2 - 2
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
ground state 5T2. Laser operations exploit the intra-center absorption and emission transitions between these two multiplets (5T2 and 5E are further split due to Jahn-Teller distortions), where the 5 T2 -5 E absorption broadband peaks at near 1.8 mm (5500 cm1) and the 5 E-5 T2 photoluminescence band covers the 2–3 mm spectral region. Rablau et al. [13] report in Cr2+:ZnSe optical losses due to self-absorption in the emission spectral range for heavily doped materials. Bulk Cr2+:ZnSe crystals can be obtained from melt [1] or vapor [20] growth techniques by including the dopant in the starting charge. However, uncontrolled contamination during high-temperature melt growth can mask optical effects expected from Cr2+ ions by inducing undesired absorptions. On the other hand, the control of the amount of Cr2+ ions incorporated in the crystals is difficult using vapor growth techniques. Thermally activated post-growth diffusion of Cr2+ in ZnSe wafers (single crystals or polycrystalline window materials) is another alternative used. Diffusion appears to be important in both material and device technology through for example, control of stoichiometry, impurity doping and compositional interdiffusion. In impurity diffusion, which is of interest to us, the impurity can be achieved in the crystal lattice by ion implantation or from an external phase that can be a vapor or a surface layer. This process is generally complex. The impurity diffusivity varies with both the deviation from stoichiometry in the crystal lattice and the initial concentration of this impurity. Various methods are used to measure the diffusivity. Most of them relate to a concentration profile. Techniques such as capacitance profiling, resistivity profiling have been applied in semiconductors [21,22]. In these techniques, it is necessary for the diffusant to be ionized, and the only ionized species in the material. Photoluminescence based on exciton emission has been used to measure the compositional interdiffusivity in II– VI alloys [23]. Laser emission of Cr2+:ZnSe bulk crystals relies basically upon optimum doping of the materials. The thermal diffusion doping technique needs
177
optimization of the annealing temperature and duration. In this report, we present a simple theoretical model based on Fick’s second diffusion law, used for calculation of the thermal diffusivity of Cr2+ ions in bulk undoped ZnSe, from optical absorption measurements in the 1.2–2.8 mm absorption band of Cr2+.
2. Theoretical model Consider an absorbing medium with a nonhomogeneous distribution of the absorbing species. The intensity of light passing through this medium, along direction (x) (cf. Fig. 1(a)) is generally defined as Z x2 I ¼ I0 exp aðxÞ dx ; ð1Þ x1
aðxÞ; the absorption coefficient at position x in the medium is defined as aðxÞ ¼ sa CðxÞ;
ð2Þ
Fig. 1. Absorption of light by a diffusion-doped sample. (a) The diffusion is supposed to have occurred though the plane (x1 ). (b) A layer of thickness d1 ¼ x01 x1 has been removed from plane (x1 ).
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
178
where sa is the absorption cross section of the absorbing species, and CðxÞ is the concentration along the (x) direction. For diffusing species in the medium, Fick’s second diffusion equation can be written as qCðx; tÞ q2 Cðx; tÞ D ¼ 0; qt qx2
ð3Þ
where t is the time and D the diffusion coefficient considered independent of the position (x) and the time (t). For the following initial and boundary conditions: Cðx; 0Þ ¼ CðN; tÞ ¼ 0; Cð0; tÞ ¼ C0 ;
ð4aÞ
the solution of the above one-dimensional equation in a semi-infinite medium is given as ! x Cðx; tÞC0 erfc pffiffiffiffiffiffi : ð4bÞ 2 Dt Eq. (1) can then be written as " Z x2
I ¼ I0 exp
x1
! # x sa C0 erfc pffiffiffiffiffiffi dx : 2 Dt
The absorbance is defined as
I : A ¼ log I0
ð5Þ
ð6Þ
Therefore, 1 A¼ lnð10Þ
Z
!
x2
sa C0 erfc x1
x pffiffiffiffiffiffi dx; 2 Dt
ð7Þ
The absorption cross-section sa can be expressed as a Gaussian function of the wavelength: 2 !2 3 l l0 pffiffiffiffiffiffiffiffiffiffi 5; sa ðlÞ ¼ s0 exp44 ð8Þ w= lnð2Þ where l0 is the center, w is the full-width at half-maximum (FWHM), and s0 is the height (sa ðl ¼ l0 Þ ¼ s0 ) of the Gaussian. The above approach gives, for the case of Cr2+:ZnSe, a good match between theory and experiment. Since s0 and C0 do not depend on the depth x; the absorbance given in Eq. (7) can be expressed as
a function of the wavelength: 2 !2 3 s0 C0 l l 0 pffiffiffiffiffiffiffiffiffiffi 5 exp44 AðlÞ ¼ lnð10Þ w= lnð2Þ ! Z x2 x erfc pffiffiffiffiffiffi dx: x1 2 Dt
ð9Þ
Eqs. (8) and (9) show that sa ðlÞ and AðlÞ can be expressed as a Gaussian with the same FWHM (w) and center (l0 ). Its numerical fit to the optical density measured in the 5 T2 -5 E Cr2+-transition spectral region should lead to the determination of D; C0 ; l0 ; w and l0 : l0 and w can directly be obtained from the measured absorbance spectra, and s0 from the literature or other types of experiments. If a layer of thickness d1 ¼ x01 x1 is removed from the diffusion face (Fig. 1(b)), this reduces the amplitude of the absorbance for the remaining crystal. A second equation can therefore be written by changing the integration limits in relation (9). D and C0 can then be calculated by solving a system of two equations with two unknowns for each annealing temperature. The activation energy of diffusion can then be determined from the following expression of the diffusion coefficient:
Ead DðTÞ ¼ D0 exp ; ð10Þ kB T where Ead is the activation energy, T is the temperature, D0 is the diffusion coefficient for 1=TE0 and kB is the Boltzmann constant.
3. Experiments Thermal diffusion experiments have been performed, for comparison, on bulk single crystals and microcrystalline window materials of ZnSe purchased from Eagle-Picher and II–VI Inc., respectively. The crystals were respectively grown by physical vapor transport (PVT) and chemical vapor deposition (CVD). Note that these growth techniques, obviously different, produce materials that could be of different stoichiometry. Prior to diffusion-annealing, wafers of dimension 0.9 0.9 0.2 and 0.9 0.9 0.5 cm3 were
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
179
polished off. The wafers were mechanically polished using a 0.1 mm alumina suspension and a corresponding cloth (from Buehler), then cleaned in trichloroethylene and rinsed in methanol. A CARY 500 spectrometer was used for the absorbance measurements. At least two sets of measurements were performed for each sample: the first was conducted on the as-doped sample, and the second was completed after polishing off 120–920 mm from the diffusion face.
4. Results and discussion
mechanically polished on a P4000 Silicon Carbide grinding paper from Buehler, ultrasonically cleaned in acetone, then rinsed in methanol. A 2–3 mm film of metallic chromium 4 N was deposited on one face of each wafer using a Kurt Lesker RF sputtering system. The samples were then placed in clean quartz square tubes that were then positioned in clean quartz ampoules as shown in Fig. 2. The ampoules were evacuated at 4 107 Torr and then sealed off. Chromium powders (4 N) purchased from Atomergic Chemical Corp. were also used in a different set of experiments. For each of these, a wafer prepared in the same manner was placed in a cleaned quartz ampoule with chromium powders, in a way so as to promote the diffusion only through one face. A direct contact between the crystal and the powders was avoided, preventing the formation of spots on the surface. The ampoule was evacuated at B4 107 Torr and sealed off. The annealing process was performed at four different temperatures for durations varying between 1 and 6 days, so as to minimize diffusion throughout the whole crystal, hence, satisfying the semi-infinite medium condition. A very small diffusion could occur through lateral diffusion or along opposite faces when using chromium powders. Those areas were
1.4
(A) 1.2
RT spectra o Diff. 906 C - 1.75 days
1.0
Absorbance
Fig. 2. Design of an ampoule used for thermal diffusion of chromium in ZnSe crystals.
The application of the above model assumes no lateral diffusion of the dopant in the crystals (a one-dimensional problem). Fig. 3 presents two room-temperature optical absorption spectra in the 1300–2400 nm spectral region for a diffusion-doped ZnSe crystal with 4 N chromium powders. The diffusion was performed at 9061C for 1.75 days. The band peaking at B1770 nm is associated with the 5 T2 -5 E internal transition of Cr2+ ions; it is the excitation band for mid-IR laser emission. Spectra (A) and (B) characterize, respectively, the as-doped crystal and after polishing-off 150 mm from the diffusion layer. The calculations of the diffusion coefficient D and
(B)
0.8 0.6 0.4 0.2 0.0 1400
1600
1800
2000
2200
2400
Wavelength (nm)
Fig. 3. Room-temperature optical absorption spectra of a diffusion-doped ZnSe crystal with 4 N chromium powders. Spectra (A) and (B) correspond, respectively, to the as-doped crystal and to the crystal after polishing off 150 mm of the diffusion layer.
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
180
the concentration C0 were performed using Eq. (9), with the following integration limits: (i) x1 ¼ 0; x2 ¼ L (thickness of the wafer) for spectrum (A), (ii) x01 ¼ d1 ; x2 ¼ L for spectrum (B). This results in solving, for each annealing temperature, a system of two non-zero equations with D and C0 as unknowns. The FWHM (w) and the center (l0 ) were obtained from the above spectra, s0 ¼ 1:15 1018 cm2 (for l0 ¼ 1770 nm) was obtained from data reported by Vallin et al. [1]. A new set of data (spectrum (Q)) was generated as spectrum ðQÞ ¼
spectrum ðAÞ baseline : spectrum ðBÞ baseline
The relation GðlÞ ¼ AðlÞ=A0 ðlÞ was used to fit the so-generated data for evaluation of the diffusion o
Temperature ( C) 950
850
800
Sputtered Cr single crystal Window material
-8
Cr powders Single crystal Window material
2
Diffusion coefficient (cm /s)
10
900
10
-9
8.0x10
-4
8.4x10
-4
8.8x10
-4
9.2x10
-4
9.6x10
-4
-1
1/T (K )
Fig. 4. Arrhenius plot of the thermal diffusion coefficient of Cr2+ ions in bulk. 4 N sputtered chromium and 4 N chromium powders were used on single crystals (solid circles and solid squares) and on polycrystalline window materials (open circles and open squares). The lines represent the theory.
coefficient, D: AðlÞ and A0 ðlÞ are, respectively, the absorbance as given in relation (9), for integration limits (i) and (ii). C0 can then be calculated from either AðlÞ or A0 ðlÞ: For the case of the absorbance presented in Fig. 3, the best fit was obtained for D ¼ 4:06 109 cm2 =s and C0 ¼ 7:40 1019 ions=cm3 : The values of D and C0 were calculated for each temperature with a relative error of B75%. Fig. 4 summarizes the temperature dependence of the diffusion coefficient of Cr2+ ions in single crystals and window materials of ZnSe, from two different sources of chromium. The lines represent relation (10), using the calculated values of D0 and Ead summarized in Table 1. The faster diffusion of Cr2+ in polycrystalline window materials than in single crystals for temperatures below B9101C could arise from faster diffusion along grain boundaries than through the grains. The behavior above 9101C could be explained by the enhancement of the grain growth process (solid state recrystallization) that we have observed in polycrystalline materials. For temperatures above B8501C, the diffusion is faster when using chromium powders than sputtered metallic chromium. This is likely the result of a higher flux of chromium through the diffusion face from the powders. This higher flux could be due to the presence of a volatile element in the 4 N chromium powders, allowing its easier transport throughout the ampoule. The more scattered diffusion coefficient values obtained for chromium powders on single crystals could be a consequence of the relatively small thickness of the wafers (0.2 cm). Overall, it should be noted that doping with CrSe powders as a Cr2+ source gives
Table 1 Calculated thermal diffusion coefficient (D0 ) and the activation energy for diffusion of Cr2+ ions in single crystals and polycrystalline window materials of ZnSe. Two sources of chromium were used Crystalline structure
Chromium source
D0 (cm2/s)
Ead (eV) 5
Polycrystal
Sputtering Powders
(1.0270.20) 10 (1.9770.10) 103
0.8270.13 1.4370.01
Single crystal
Sputtering Powders
(2.0170.10) 103 2677
1.3670.03 2.3170.20
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
3
Co (ions/cm )
7x10 6x10 5x10 4x10 3x10 2x10 1x10
19
3
19
8x10
Single cryst. - sputtered Cr Window mat. - sputtered Cr Single cryst. - Cr powders Window mat. - Cr powders
19 19 19 19 19
2+
8x10
19
Cr concentration (ions/cm )
9x10
19
7x10 6x10 5x10 4x10 3x10 2x10 1x10
181
19
Predicted Average
19 19 19 19 19 19 19
0 1050
1100
1150
1200
1250
0.0
0.1
Temperature (K)
0.4
ð11Þ
where A0 is the amplitude of the absorbance at l ¼ l0 and d is the total thickness of the sample. Fig. 6 shows an example that compares the Cr2+ concentration obtained from diffusion profile to that calculated using Eq. (11), for diffusion
Fig. 6. Cr2+ ions concentration profile, predicted in a 0.44 cm thickness Cr2+:ZnSe polycrystalline window material, doped by thermal diffusion at 9071C for 1.75 days, with D ¼ 4:06 109 cm2 =s and C0 ¼ 7:40 1019 ions=cm3 : The dashed line corresponds to the average concentration calculated from Eq. (11).
FWHM of the 1770-nm absorption band (nm)
results that differ for CrSe reagent powders obtained from different vendors. One can see in Fig. 5 that the concentration C0 depends not only on the amount of chromium used, but also on the annealing temperature. The value of C0 is smaller than the atomic density of ZnSe (B2.2 1022 atoms/cm3), and the total number of Cr2+ ions incorporated should be smaller than the number of chromium atoms contained in the amount used for each experiment. We summarize that the number of chromium atoms contained in the sputtered films varied between 1.0 1019 and 6.5 1019 atoms, which leads to C0 in the range of 7.0 1018– 5.7 1019 ions/cm3. This number varied, for the cases where powders were used, between 3:0 1021 and 5:0 1021 atoms; which corresponds to C0 in the range of 2:8 1019 27:4 1019 ions=cm3 : The average concentration Cav of Cr2+ ions, even in diffusion-doped ZnSe crystals, is usually calculated from the expression A0 lnð10Þ; s0 d
0.3
x (cm)
Fig. 5. Concentration (C0 ) of Cr2+ ions at the origin (x ¼ 0), calculated from the model in Cr2+:ZnSe single crystals and polycrystalline window materials doped by diffusion from sputtered metallic chromium and chromium powders.
Cav ¼
0.2
390 Room Temperature
Sputtered Cr single crystal Window material
385 380
Cr powders Single crystal Window material
375 370 365 360 355 350 1050
1100
1150
1200
1250
Temperature (K)
Fig. 7. Temperature dependence of the mid-IR optical absorbance’s FWHM of Cr2+:ZnSe crystals doped by thermal diffusion from 4 N Cr powders and 4 N sputtered Cr. The measurements were performed at room temperature.
performed at 906.51C for 1.75 days through two opposite faces of a thick ZnSe wafer. The average Cr2+ concentration (9.5 1018 ions/cm3) calculated from the above relation underestimates that concentration (2.5 1019 ions/cm3) in the actually doped volume, where laser transitions occur. The FWHM (w) of the 1770 nm absorption band plotted in Fig. 7 shows a linear variation
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
182
Table 2 Coefficients w0 and w1 of the FWHM ðwðTÞ ¼ w0 þ w1 TÞ at room temperature of the 1800 nm absorption band of Cr2+:ZnSe crystals doped by thermal diffusion. T is the annealing temperature Crystalline structure
Chromium source
w0 (nm)
W1 (nm/K)
Polycrystal
Sputtering Powders
41973 39374
0.05670.002 0.03670.003
Single crystal
Sputtering Powders
28574 438731
0.06070.004 0.05970.027
The reflection coefficient RðlÞ is defined as RðlÞ ¼
ðnðlÞ 1Þ2 þ k2 ðlÞ : ðnðlÞ þ 1Þ2 þk2 ðlÞ
ð13Þ
The extinction coefficient kðlÞ is assumed to be negligible in the spectral range of our study. nðlÞ is the refractive index of ZnSe. The following relation fits very well the values of refractive index of Cr2+:ZnSe that we measured, or others have reported in the literature [24–26]: 4:59498 n2 ðlÞ ¼ 1 þ 2 1 0:04319 103 =l 0:33176 þ 2 1 0:16619 103 =l 2 þ ð1:33952 103 Þ 103 =l : ð14Þ Here l is expressed in units of nanometers. Fig. 8 compares the predicted and experimentally measured absorbance for a Cr2+:ZnSe polycrystalline flat window material doped
1.2
(a)
Experiment Theory
Absorbance
1.0 0.8 0.6 0.4 0.2 0.0 1.4 1.2
Absorbance
with the annealing temperature in the range considered in this study, and the slopes are o10%. Table 2 compiles the FWHM coefficients. Light losses due to multiple reflections in the crystal contribute to the total absorbance. They can be accounted for in a first approximation by the following expression: s0 C0 ðTÞ ATot ðl; TÞ ¼ log ð1 RðlÞÞ2 þ lnð10Þ 2 !2 3 l l 0 pffiffiffiffiffiffiffiffiffiffi 5 exp44 wðTÞ= lnð2Þ ! Z x2 x erfc pffiffiffiffiffiffiffiffiffiffiffiffiffi dx: ð12Þ 2 DðTÞt x1
(b)
Experiment Theory
1.0 0.8 0.6 0.4 0.2 0.0 1000
1200
1400
1600
1800
2000
2200
2400
Wavelength (nm)
Fig. 8. Comparison between the predicted and the experimentally measured room-temperature absorbance, for the case of a Cr2+:ZnSe polycrystalline window material doped by diffusion at 906.51C for 1.75 days using chromium powders. (a) The baseline has been subtracted from the experimental data, and relation (9) is used. (b) The baseline has not been subtracted; relation (12) is used. The solid black line corresponds to the theory, while the doted line represents the experiments.
through one face by thermal diffusion at 906.51C for 1.75 days using chromium powders. In Fig. 8(a) the baseline has been subtracted from the data points, and Eq. (9) produces a good match between the experiment and the predicted values. In Fig. 8(b), the baseline is not subtracted, and relation (12) is used. The slight mismatch here could arise from the non-consideration in relation (12) of the contribution of light scattered on structural defects. Fig. 9 shows the prediction of the total absorbance of polycrystalline ZnSe window materials diffusion-doped through one face with 4 N
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184 1.25 o
800 C o 850 C o 900 C o 950 C
Absorbance
1.00
0.75
0.50
0.25
0.00 1000
1500
2000
2500
3000
Wavelength (nm)
Fig. 9. Predicted room-temperature total absorbance for polycrystalline window materials of Cr2+:ZnSe doped with chromium powders for 1.75 days at different temperatures: 8001C, 8501C, 9001C and 9501C. C0 is chosen to be equal, respectively, to 4.77 1019, 4.91 1019, 7.07 1019, and 7.47 1019 ions/cm3.
chromium powders for 1.75 days at different temperatures (8001C, 8501C, 9001C and 9501C). The values of Co used for the computation were, respectively, equal to 4.77 1019, 4.91 1019, 7.07 1019, and 7.47 1019 ions/cm3. One can see that Cr2+:ZnSe polycrystals diffusion-doped at temperatures above 9001C for 1.75 days in the conditions presented in this report will present non-negligible self-absorption in the 2000– 3000 nm spectral range, overlapping the spectral range for laser emission and therefore being detrimental to laser performance. However, self-absorption losses in heavily diffusion-doped thick materials could be reduced by mechanically polishing off a layer from the diffusion face(s). This decreases the concentration of dopant in the diffusion volume.
183
polycrystalline materials than in single crystals for temperatures lower than 9101C, which is likely due to the presence of grain boundaries. Above 9101C, the increasing rate of the grain growth process could explain the relatively slower diffusion. The activation energy for diffusion was found to depend on the nature of the chromium source, and varies from 0.82 to 2.31 eV. The FWHM of the 1770 nm absorption band in the as-doped crystals appeared to be a linear function of the annealing temperature with a slope less than 10%. It was demonstrated from the concentration profile of Cr2+ in a thick crystal that the average concentration usually calculated throughout the whole crystal underestimated the average concentration in the actually doped volume. For laser application, the model predicts, for doping performed at temperatures above 9001C for 1.75 days on polycrystalline window materials using Cr powder, significant self-absorption in the 2000– 3000 nm spectral region. This self-absorption will be detrimental to laser performance.
Acknowledgements The authors at Fisk University acknowledge the support of the NASA through the Center for Photonic Materials and Devices under NASA Grant NCC5-286, Dr. Kennedy Reed for his support through the Research Collaborations Program for HBCU/MIs under Grant DE-FG0394SF20368 and NSF grants DMR0097272 and EHR-0090526. The summer student intern acknowledges the support of NSF and the REU program through Grant DUE-9987224.
References 5. Conclusions The thermal diffusion coefficients of Cr2+ ions in ZnSe single crystals and polycrystalline window materials were evaluated by fitting a theoretical model to optical absorption data in the midinfrared. The diffusion appears to be faster in
[1] J.T. Vallin, G.A. Slack, S. Roberts, A.E. Hughes, Phys. Rev. B 2 (11) (1970) 4313. [2] E.M. Wray, J.M. Allen, J. Phys. C 4 (1971) 512. [3] M. Kaminska, J. Baranowski, S.M. Uba, J.T. Vallin, J. Phys. C 12 (1979) 2197. [4] H. Pradalla, U.W. Pohl, Phys. Stat. Sol. B 141 (1987) K143. [5] G. Goetz, H.-J. Schulz, J. Lumin. 40/41 (1988) 415.
184
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
[6] A.I. Belogorokhov, M.I. Kulakov, V.A. Kremerman, A.L. Natadze, Yu.B. Rozenfel’d, A.I. Ryskin, Sov. Phys. JETP 67 (6) (1988) 1184. [7] V.V. Ushakov, A.A. Gippius, J. Crystal Growth 101 (1990) 458. [8] A. Hoffman, U. Scherz, J. Crystal Growth 101 (1990) 358. [9] G. Goetz, H. Zimmermann, H.-J. Schulz, Z. Phys. B 91 (1993) 429. [10] M.U. Lehr, P. Pekat, A. Klimakow, H.-J. Schulz, J. Phys.: Condens. Matter 8 (1996) 3477. [11] V.Yu. Ivanov, Yu.G. Semenov, M. Surma, M. Godlewski, Phys. Rev. B 54 (7) (1996) 4696. [12] M.U. Lehr, B. Litzenburger, J. Kreissl, U.W. Pohl, H.R. Selbert, H.-J. Schulz, A. Klimakow, L. Worschech, J. Phys.: Condens. Matter 9 (1997) 753. [13] C.I. Rablau, J.-O. Ndap, X. Ma, A. Burger, N.C. Giles, J. Electron. Matter 28 (6) (1999) 678. [14] L. Deloach, R.H. Page, G.D. Wilke, S.A. Payne, W.F. Krupke, IEEE J. Quantum Electron. 32 (1996) 885. [15] R.H. Page, K.I. Schaffers, L.D. Deloach, G.D. Wilke, F.D. Patel, J.B. Tassano, S.A. Payne, F. Krupke, K.T. Chen, A. Burger, IEEE J. Quantum Electron. 33 (1997) 609.
[16] M. Birnbaum, M.B. Camargo, S. Lee, F. Unlu, R.D. Stultz, OSA TOPS, Vol. 10, Advanced Solid State Lasers, 1997. [17] G.J. Wagner, T.J. Carrig, R.H. Page, K.I. Schaffers, J.-O. Ndap, X. Ma, A. Burger, Opt. Lett. 24 (1) (1999) 19. [18] R.S. Title, Phys. Rev. 133 (1964) A1613. [19] M. Dewit, A.R. Reinberg, W.C. Holton, T.L. Estle, Bull. Am. Phys. Soc. 10 (1965) 329. [20] C-H. Su, S. Feth, M.P. Volz, R. Matyi, M.A. George, K. Chattopadhyay, A. Burger, S.L. Lehoczky, J. Crystal Growth 207 (1999) 35. [21] T.H. Yeh, Diffusion in Semiconductors, In: D. Shaw (Ed.), Plenium, London, 1973, Chapter 4. [22] B. Tuck, Atomic Diffusion in III–V Semiconductors, Hilger, Bristol, 1988, Chapter 2. [23] H.F. Taylor, V.N. Smiley, S.S. Pawka, Phys. Rev. B 5 (1972) 1467. [24] II–VI Inc. database, Web address: http://www.ii.vi.com/ pages/prod-iivi-materials-znse.html [25] A.J. Moses, Hughes Aircraft Company, Culver City, California AD-704 555, 1970. [26] R. Dahmani, L. Salamanca-Riba, N.V. Nguyen, D. Chandler-Horowitz, B.T. Jonker, J. Appl. Phys. 76 (1) (1994) 514.
Thermal diffusion of Cr2+ in bulk ZnSe J.-O. Ndapa, K. Chattopadhyaya, O.O. Adetunjia, D.E. Zelmonb, A. Burgera,* a
Department of Physics, Center for Photonic Materials and Devices, Fisk University, Nashville, TN 37208-3051, USA b Air Force Research Laboratory, WPAFB, OH 45433-7707, USA Received 26 July 2001; accepted 15 January 2002 Communicated by R. James
Abstract Cr2+:ZnSe is now known as a room-temperature widely tunable solid-state mid-infrared laser material. Optimization of laser performance requires first and foremost optimization of the Cr2+-doping level in the crystals. A simple theoretical model has been developed for evaluation of the thermal diffusivity of Cr2+ ions in bulk ZnSe single crystals and polycrystalline window materials, from optical absorption measurements in the 1200–2800 nm spectral region. Sputtered metallic chromium and powders have been used as dopant sources. Diffusion appears to be faster in polycrystalline materials than in single crystals for annealing temperatures below 9101C. The activation energy, which is lower in polycrystals, depends on the nature of the dopant source. For mid-IR laser application, the model predicts for example, non-negligible optical losses due to passive self-absorption in the 2000–3000 nm spectral region for chromiumdoped polycrystalline materials after annealing at temperatures above 9001C for 1.75 days. r 2002 Elsevier Science B.V. All rights reserved. Keywords: A1. Diffusion; A1. Doping; A1. Impurities; B1. Inorganic compounds; B1. Zinc compounds; B2. Semiconducting II–VI materials; B3. Solid state lasers
1. Introduction ZnSe has a variety of applications in optical devices such as light-emitting diodes and waveguides. The bulk polycrystalline compound is used for infrared optical components such as lenses and windows for IR detectors and high-power lasers. It was recently reported that the incorporation of transition metal ions (Cr2+,Co2+,Fe2+,Ni2+, W2+) gives rise to properties [1–13] that make this material particularly attractive for applications in *Corresponding author. Tel.: +1-615-329-8516; fax: +1615-329-8634. E-mail address: aburger@fisk.edu (A. Burger).
room-temperature solid-state laser devices, tunable in the mid-IR [14–17]. Laser action was demonstrated in Cr2+:ZnSe [14,17]. Chromium, as well as the other transition metals, substitutes for the cation in ZnSe. EPR measurements [18,19] have revealed two charge states of chromium in ZnSe:Cr1+ and Cr2+. The second state appears to be the most stable and the most probable for concentrations p4 1019 atoms/cm3 [1]. The acceptor state Cr1+ can be induced by a chargetransfer using a below band-gap photo-excitation (16900–22000 cm1), with ejection of an electron from the valence band to the Cr2+ energy level [11,12]. A crystal field splits the ground state 5D of the Cr2+ free ion into an excited state 5E and a
0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 2 ) 0 0 8 7 2 - 2
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
ground state 5T2. Laser operations exploit the intra-center absorption and emission transitions between these two multiplets (5T2 and 5E are further split due to Jahn-Teller distortions), where the 5 T2 -5 E absorption broadband peaks at near 1.8 mm (5500 cm1) and the 5 E-5 T2 photoluminescence band covers the 2–3 mm spectral region. Rablau et al. [13] report in Cr2+:ZnSe optical losses due to self-absorption in the emission spectral range for heavily doped materials. Bulk Cr2+:ZnSe crystals can be obtained from melt [1] or vapor [20] growth techniques by including the dopant in the starting charge. However, uncontrolled contamination during high-temperature melt growth can mask optical effects expected from Cr2+ ions by inducing undesired absorptions. On the other hand, the control of the amount of Cr2+ ions incorporated in the crystals is difficult using vapor growth techniques. Thermally activated post-growth diffusion of Cr2+ in ZnSe wafers (single crystals or polycrystalline window materials) is another alternative used. Diffusion appears to be important in both material and device technology through for example, control of stoichiometry, impurity doping and compositional interdiffusion. In impurity diffusion, which is of interest to us, the impurity can be achieved in the crystal lattice by ion implantation or from an external phase that can be a vapor or a surface layer. This process is generally complex. The impurity diffusivity varies with both the deviation from stoichiometry in the crystal lattice and the initial concentration of this impurity. Various methods are used to measure the diffusivity. Most of them relate to a concentration profile. Techniques such as capacitance profiling, resistivity profiling have been applied in semiconductors [21,22]. In these techniques, it is necessary for the diffusant to be ionized, and the only ionized species in the material. Photoluminescence based on exciton emission has been used to measure the compositional interdiffusivity in II– VI alloys [23]. Laser emission of Cr2+:ZnSe bulk crystals relies basically upon optimum doping of the materials. The thermal diffusion doping technique needs
177
optimization of the annealing temperature and duration. In this report, we present a simple theoretical model based on Fick’s second diffusion law, used for calculation of the thermal diffusivity of Cr2+ ions in bulk undoped ZnSe, from optical absorption measurements in the 1.2–2.8 mm absorption band of Cr2+.
2. Theoretical model Consider an absorbing medium with a nonhomogeneous distribution of the absorbing species. The intensity of light passing through this medium, along direction (x) (cf. Fig. 1(a)) is generally defined as Z x2 I ¼ I0 exp aðxÞ dx ; ð1Þ x1
aðxÞ; the absorption coefficient at position x in the medium is defined as aðxÞ ¼ sa CðxÞ;
ð2Þ
Fig. 1. Absorption of light by a diffusion-doped sample. (a) The diffusion is supposed to have occurred though the plane (x1 ). (b) A layer of thickness d1 ¼ x01 x1 has been removed from plane (x1 ).
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
178
where sa is the absorption cross section of the absorbing species, and CðxÞ is the concentration along the (x) direction. For diffusing species in the medium, Fick’s second diffusion equation can be written as qCðx; tÞ q2 Cðx; tÞ D ¼ 0; qt qx2
ð3Þ
where t is the time and D the diffusion coefficient considered independent of the position (x) and the time (t). For the following initial and boundary conditions: Cðx; 0Þ ¼ CðN; tÞ ¼ 0; Cð0; tÞ ¼ C0 ;
ð4aÞ
the solution of the above one-dimensional equation in a semi-infinite medium is given as ! x Cðx; tÞC0 erfc pffiffiffiffiffiffi : ð4bÞ 2 Dt Eq. (1) can then be written as " Z x2
I ¼ I0 exp
x1
! # x sa C0 erfc pffiffiffiffiffiffi dx : 2 Dt
The absorbance is defined as
I : A ¼ log I0
ð5Þ
ð6Þ
Therefore, 1 A¼ lnð10Þ
Z
!
x2
sa C0 erfc x1
x pffiffiffiffiffiffi dx; 2 Dt
ð7Þ
The absorption cross-section sa can be expressed as a Gaussian function of the wavelength: 2 !2 3 l l0 pffiffiffiffiffiffiffiffiffiffi 5; sa ðlÞ ¼ s0 exp44 ð8Þ w= lnð2Þ where l0 is the center, w is the full-width at half-maximum (FWHM), and s0 is the height (sa ðl ¼ l0 Þ ¼ s0 ) of the Gaussian. The above approach gives, for the case of Cr2+:ZnSe, a good match between theory and experiment. Since s0 and C0 do not depend on the depth x; the absorbance given in Eq. (7) can be expressed as
a function of the wavelength: 2 !2 3 s0 C0 l l 0 pffiffiffiffiffiffiffiffiffiffi 5 exp44 AðlÞ ¼ lnð10Þ w= lnð2Þ ! Z x2 x erfc pffiffiffiffiffiffi dx: x1 2 Dt
ð9Þ
Eqs. (8) and (9) show that sa ðlÞ and AðlÞ can be expressed as a Gaussian with the same FWHM (w) and center (l0 ). Its numerical fit to the optical density measured in the 5 T2 -5 E Cr2+-transition spectral region should lead to the determination of D; C0 ; l0 ; w and l0 : l0 and w can directly be obtained from the measured absorbance spectra, and s0 from the literature or other types of experiments. If a layer of thickness d1 ¼ x01 x1 is removed from the diffusion face (Fig. 1(b)), this reduces the amplitude of the absorbance for the remaining crystal. A second equation can therefore be written by changing the integration limits in relation (9). D and C0 can then be calculated by solving a system of two equations with two unknowns for each annealing temperature. The activation energy of diffusion can then be determined from the following expression of the diffusion coefficient:
Ead DðTÞ ¼ D0 exp ; ð10Þ kB T where Ead is the activation energy, T is the temperature, D0 is the diffusion coefficient for 1=TE0 and kB is the Boltzmann constant.
3. Experiments Thermal diffusion experiments have been performed, for comparison, on bulk single crystals and microcrystalline window materials of ZnSe purchased from Eagle-Picher and II–VI Inc., respectively. The crystals were respectively grown by physical vapor transport (PVT) and chemical vapor deposition (CVD). Note that these growth techniques, obviously different, produce materials that could be of different stoichiometry. Prior to diffusion-annealing, wafers of dimension 0.9 0.9 0.2 and 0.9 0.9 0.5 cm3 were
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
179
polished off. The wafers were mechanically polished using a 0.1 mm alumina suspension and a corresponding cloth (from Buehler), then cleaned in trichloroethylene and rinsed in methanol. A CARY 500 spectrometer was used for the absorbance measurements. At least two sets of measurements were performed for each sample: the first was conducted on the as-doped sample, and the second was completed after polishing off 120–920 mm from the diffusion face.
4. Results and discussion
mechanically polished on a P4000 Silicon Carbide grinding paper from Buehler, ultrasonically cleaned in acetone, then rinsed in methanol. A 2–3 mm film of metallic chromium 4 N was deposited on one face of each wafer using a Kurt Lesker RF sputtering system. The samples were then placed in clean quartz square tubes that were then positioned in clean quartz ampoules as shown in Fig. 2. The ampoules were evacuated at 4 107 Torr and then sealed off. Chromium powders (4 N) purchased from Atomergic Chemical Corp. were also used in a different set of experiments. For each of these, a wafer prepared in the same manner was placed in a cleaned quartz ampoule with chromium powders, in a way so as to promote the diffusion only through one face. A direct contact between the crystal and the powders was avoided, preventing the formation of spots on the surface. The ampoule was evacuated at B4 107 Torr and sealed off. The annealing process was performed at four different temperatures for durations varying between 1 and 6 days, so as to minimize diffusion throughout the whole crystal, hence, satisfying the semi-infinite medium condition. A very small diffusion could occur through lateral diffusion or along opposite faces when using chromium powders. Those areas were
1.4
(A) 1.2
RT spectra o Diff. 906 C - 1.75 days
1.0
Absorbance
Fig. 2. Design of an ampoule used for thermal diffusion of chromium in ZnSe crystals.
The application of the above model assumes no lateral diffusion of the dopant in the crystals (a one-dimensional problem). Fig. 3 presents two room-temperature optical absorption spectra in the 1300–2400 nm spectral region for a diffusion-doped ZnSe crystal with 4 N chromium powders. The diffusion was performed at 9061C for 1.75 days. The band peaking at B1770 nm is associated with the 5 T2 -5 E internal transition of Cr2+ ions; it is the excitation band for mid-IR laser emission. Spectra (A) and (B) characterize, respectively, the as-doped crystal and after polishing-off 150 mm from the diffusion layer. The calculations of the diffusion coefficient D and
(B)
0.8 0.6 0.4 0.2 0.0 1400
1600
1800
2000
2200
2400
Wavelength (nm)
Fig. 3. Room-temperature optical absorption spectra of a diffusion-doped ZnSe crystal with 4 N chromium powders. Spectra (A) and (B) correspond, respectively, to the as-doped crystal and to the crystal after polishing off 150 mm of the diffusion layer.
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
180
the concentration C0 were performed using Eq. (9), with the following integration limits: (i) x1 ¼ 0; x2 ¼ L (thickness of the wafer) for spectrum (A), (ii) x01 ¼ d1 ; x2 ¼ L for spectrum (B). This results in solving, for each annealing temperature, a system of two non-zero equations with D and C0 as unknowns. The FWHM (w) and the center (l0 ) were obtained from the above spectra, s0 ¼ 1:15 1018 cm2 (for l0 ¼ 1770 nm) was obtained from data reported by Vallin et al. [1]. A new set of data (spectrum (Q)) was generated as spectrum ðQÞ ¼
spectrum ðAÞ baseline : spectrum ðBÞ baseline
The relation GðlÞ ¼ AðlÞ=A0 ðlÞ was used to fit the so-generated data for evaluation of the diffusion o
Temperature ( C) 950
850
800
Sputtered Cr single crystal Window material
-8
Cr powders Single crystal Window material
2
Diffusion coefficient (cm /s)
10
900
10
-9
8.0x10
-4
8.4x10
-4
8.8x10
-4
9.2x10
-4
9.6x10
-4
-1
1/T (K )
Fig. 4. Arrhenius plot of the thermal diffusion coefficient of Cr2+ ions in bulk. 4 N sputtered chromium and 4 N chromium powders were used on single crystals (solid circles and solid squares) and on polycrystalline window materials (open circles and open squares). The lines represent the theory.
coefficient, D: AðlÞ and A0 ðlÞ are, respectively, the absorbance as given in relation (9), for integration limits (i) and (ii). C0 can then be calculated from either AðlÞ or A0 ðlÞ: For the case of the absorbance presented in Fig. 3, the best fit was obtained for D ¼ 4:06 109 cm2 =s and C0 ¼ 7:40 1019 ions=cm3 : The values of D and C0 were calculated for each temperature with a relative error of B75%. Fig. 4 summarizes the temperature dependence of the diffusion coefficient of Cr2+ ions in single crystals and window materials of ZnSe, from two different sources of chromium. The lines represent relation (10), using the calculated values of D0 and Ead summarized in Table 1. The faster diffusion of Cr2+ in polycrystalline window materials than in single crystals for temperatures below B9101C could arise from faster diffusion along grain boundaries than through the grains. The behavior above 9101C could be explained by the enhancement of the grain growth process (solid state recrystallization) that we have observed in polycrystalline materials. For temperatures above B8501C, the diffusion is faster when using chromium powders than sputtered metallic chromium. This is likely the result of a higher flux of chromium through the diffusion face from the powders. This higher flux could be due to the presence of a volatile element in the 4 N chromium powders, allowing its easier transport throughout the ampoule. The more scattered diffusion coefficient values obtained for chromium powders on single crystals could be a consequence of the relatively small thickness of the wafers (0.2 cm). Overall, it should be noted that doping with CrSe powders as a Cr2+ source gives
Table 1 Calculated thermal diffusion coefficient (D0 ) and the activation energy for diffusion of Cr2+ ions in single crystals and polycrystalline window materials of ZnSe. Two sources of chromium were used Crystalline structure
Chromium source
D0 (cm2/s)
Ead (eV) 5
Polycrystal
Sputtering Powders
(1.0270.20) 10 (1.9770.10) 103
0.8270.13 1.4370.01
Single crystal
Sputtering Powders
(2.0170.10) 103 2677
1.3670.03 2.3170.20
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
3
Co (ions/cm )
7x10 6x10 5x10 4x10 3x10 2x10 1x10
19
3
19
8x10
Single cryst. - sputtered Cr Window mat. - sputtered Cr Single cryst. - Cr powders Window mat. - Cr powders
19 19 19 19 19
2+
8x10
19
Cr concentration (ions/cm )
9x10
19
7x10 6x10 5x10 4x10 3x10 2x10 1x10
181
19
Predicted Average
19 19 19 19 19 19 19
0 1050
1100
1150
1200
1250
0.0
0.1
Temperature (K)
0.4
ð11Þ
where A0 is the amplitude of the absorbance at l ¼ l0 and d is the total thickness of the sample. Fig. 6 shows an example that compares the Cr2+ concentration obtained from diffusion profile to that calculated using Eq. (11), for diffusion
Fig. 6. Cr2+ ions concentration profile, predicted in a 0.44 cm thickness Cr2+:ZnSe polycrystalline window material, doped by thermal diffusion at 9071C for 1.75 days, with D ¼ 4:06 109 cm2 =s and C0 ¼ 7:40 1019 ions=cm3 : The dashed line corresponds to the average concentration calculated from Eq. (11).
FWHM of the 1770-nm absorption band (nm)
results that differ for CrSe reagent powders obtained from different vendors. One can see in Fig. 5 that the concentration C0 depends not only on the amount of chromium used, but also on the annealing temperature. The value of C0 is smaller than the atomic density of ZnSe (B2.2 1022 atoms/cm3), and the total number of Cr2+ ions incorporated should be smaller than the number of chromium atoms contained in the amount used for each experiment. We summarize that the number of chromium atoms contained in the sputtered films varied between 1.0 1019 and 6.5 1019 atoms, which leads to C0 in the range of 7.0 1018– 5.7 1019 ions/cm3. This number varied, for the cases where powders were used, between 3:0 1021 and 5:0 1021 atoms; which corresponds to C0 in the range of 2:8 1019 27:4 1019 ions=cm3 : The average concentration Cav of Cr2+ ions, even in diffusion-doped ZnSe crystals, is usually calculated from the expression A0 lnð10Þ; s0 d
0.3
x (cm)
Fig. 5. Concentration (C0 ) of Cr2+ ions at the origin (x ¼ 0), calculated from the model in Cr2+:ZnSe single crystals and polycrystalline window materials doped by diffusion from sputtered metallic chromium and chromium powders.
Cav ¼
0.2
390 Room Temperature
Sputtered Cr single crystal Window material
385 380
Cr powders Single crystal Window material
375 370 365 360 355 350 1050
1100
1150
1200
1250
Temperature (K)
Fig. 7. Temperature dependence of the mid-IR optical absorbance’s FWHM of Cr2+:ZnSe crystals doped by thermal diffusion from 4 N Cr powders and 4 N sputtered Cr. The measurements were performed at room temperature.
performed at 906.51C for 1.75 days through two opposite faces of a thick ZnSe wafer. The average Cr2+ concentration (9.5 1018 ions/cm3) calculated from the above relation underestimates that concentration (2.5 1019 ions/cm3) in the actually doped volume, where laser transitions occur. The FWHM (w) of the 1770 nm absorption band plotted in Fig. 7 shows a linear variation
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
182
Table 2 Coefficients w0 and w1 of the FWHM ðwðTÞ ¼ w0 þ w1 TÞ at room temperature of the 1800 nm absorption band of Cr2+:ZnSe crystals doped by thermal diffusion. T is the annealing temperature Crystalline structure
Chromium source
w0 (nm)
W1 (nm/K)
Polycrystal
Sputtering Powders
41973 39374
0.05670.002 0.03670.003
Single crystal
Sputtering Powders
28574 438731
0.06070.004 0.05970.027
The reflection coefficient RðlÞ is defined as RðlÞ ¼
ðnðlÞ 1Þ2 þ k2 ðlÞ : ðnðlÞ þ 1Þ2 þk2 ðlÞ
ð13Þ
The extinction coefficient kðlÞ is assumed to be negligible in the spectral range of our study. nðlÞ is the refractive index of ZnSe. The following relation fits very well the values of refractive index of Cr2+:ZnSe that we measured, or others have reported in the literature [24–26]: 4:59498 n2 ðlÞ ¼ 1 þ 2 1 0:04319 103 =l 0:33176 þ 2 1 0:16619 103 =l 2 þ ð1:33952 103 Þ 103 =l : ð14Þ Here l is expressed in units of nanometers. Fig. 8 compares the predicted and experimentally measured absorbance for a Cr2+:ZnSe polycrystalline flat window material doped
1.2
(a)
Experiment Theory
Absorbance
1.0 0.8 0.6 0.4 0.2 0.0 1.4 1.2
Absorbance
with the annealing temperature in the range considered in this study, and the slopes are o10%. Table 2 compiles the FWHM coefficients. Light losses due to multiple reflections in the crystal contribute to the total absorbance. They can be accounted for in a first approximation by the following expression: s0 C0 ðTÞ ATot ðl; TÞ ¼ log ð1 RðlÞÞ2 þ lnð10Þ 2 !2 3 l l 0 pffiffiffiffiffiffiffiffiffiffi 5 exp44 wðTÞ= lnð2Þ ! Z x2 x erfc pffiffiffiffiffiffiffiffiffiffiffiffiffi dx: ð12Þ 2 DðTÞt x1
(b)
Experiment Theory
1.0 0.8 0.6 0.4 0.2 0.0 1000
1200
1400
1600
1800
2000
2200
2400
Wavelength (nm)
Fig. 8. Comparison between the predicted and the experimentally measured room-temperature absorbance, for the case of a Cr2+:ZnSe polycrystalline window material doped by diffusion at 906.51C for 1.75 days using chromium powders. (a) The baseline has been subtracted from the experimental data, and relation (9) is used. (b) The baseline has not been subtracted; relation (12) is used. The solid black line corresponds to the theory, while the doted line represents the experiments.
through one face by thermal diffusion at 906.51C for 1.75 days using chromium powders. In Fig. 8(a) the baseline has been subtracted from the data points, and Eq. (9) produces a good match between the experiment and the predicted values. In Fig. 8(b), the baseline is not subtracted, and relation (12) is used. The slight mismatch here could arise from the non-consideration in relation (12) of the contribution of light scattered on structural defects. Fig. 9 shows the prediction of the total absorbance of polycrystalline ZnSe window materials diffusion-doped through one face with 4 N
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184 1.25 o
800 C o 850 C o 900 C o 950 C
Absorbance
1.00
0.75
0.50
0.25
0.00 1000
1500
2000
2500
3000
Wavelength (nm)
Fig. 9. Predicted room-temperature total absorbance for polycrystalline window materials of Cr2+:ZnSe doped with chromium powders for 1.75 days at different temperatures: 8001C, 8501C, 9001C and 9501C. C0 is chosen to be equal, respectively, to 4.77 1019, 4.91 1019, 7.07 1019, and 7.47 1019 ions/cm3.
chromium powders for 1.75 days at different temperatures (8001C, 8501C, 9001C and 9501C). The values of Co used for the computation were, respectively, equal to 4.77 1019, 4.91 1019, 7.07 1019, and 7.47 1019 ions/cm3. One can see that Cr2+:ZnSe polycrystals diffusion-doped at temperatures above 9001C for 1.75 days in the conditions presented in this report will present non-negligible self-absorption in the 2000– 3000 nm spectral range, overlapping the spectral range for laser emission and therefore being detrimental to laser performance. However, self-absorption losses in heavily diffusion-doped thick materials could be reduced by mechanically polishing off a layer from the diffusion face(s). This decreases the concentration of dopant in the diffusion volume.
183
polycrystalline materials than in single crystals for temperatures lower than 9101C, which is likely due to the presence of grain boundaries. Above 9101C, the increasing rate of the grain growth process could explain the relatively slower diffusion. The activation energy for diffusion was found to depend on the nature of the chromium source, and varies from 0.82 to 2.31 eV. The FWHM of the 1770 nm absorption band in the as-doped crystals appeared to be a linear function of the annealing temperature with a slope less than 10%. It was demonstrated from the concentration profile of Cr2+ in a thick crystal that the average concentration usually calculated throughout the whole crystal underestimated the average concentration in the actually doped volume. For laser application, the model predicts, for doping performed at temperatures above 9001C for 1.75 days on polycrystalline window materials using Cr powder, significant self-absorption in the 2000– 3000 nm spectral region. This self-absorption will be detrimental to laser performance.
Acknowledgements The authors at Fisk University acknowledge the support of the NASA through the Center for Photonic Materials and Devices under NASA Grant NCC5-286, Dr. Kennedy Reed for his support through the Research Collaborations Program for HBCU/MIs under Grant DE-FG0394SF20368 and NSF grants DMR0097272 and EHR-0090526. The summer student intern acknowledges the support of NSF and the REU program through Grant DUE-9987224.
References 5. Conclusions The thermal diffusion coefficients of Cr2+ ions in ZnSe single crystals and polycrystalline window materials were evaluated by fitting a theoretical model to optical absorption data in the midinfrared. The diffusion appears to be faster in
[1] J.T. Vallin, G.A. Slack, S. Roberts, A.E. Hughes, Phys. Rev. B 2 (11) (1970) 4313. [2] E.M. Wray, J.M. Allen, J. Phys. C 4 (1971) 512. [3] M. Kaminska, J. Baranowski, S.M. Uba, J.T. Vallin, J. Phys. C 12 (1979) 2197. [4] H. Pradalla, U.W. Pohl, Phys. Stat. Sol. B 141 (1987) K143. [5] G. Goetz, H.-J. Schulz, J. Lumin. 40/41 (1988) 415.
184
J.-O. Ndap et al. / Journal of Crystal Growth 240 (2002) 176–184
[6] A.I. Belogorokhov, M.I. Kulakov, V.A. Kremerman, A.L. Natadze, Yu.B. Rozenfel’d, A.I. Ryskin, Sov. Phys. JETP 67 (6) (1988) 1184. [7] V.V. Ushakov, A.A. Gippius, J. Crystal Growth 101 (1990) 458. [8] A. Hoffman, U. Scherz, J. Crystal Growth 101 (1990) 358. [9] G. Goetz, H. Zimmermann, H.-J. Schulz, Z. Phys. B 91 (1993) 429. [10] M.U. Lehr, P. Pekat, A. Klimakow, H.-J. Schulz, J. Phys.: Condens. Matter 8 (1996) 3477. [11] V.Yu. Ivanov, Yu.G. Semenov, M. Surma, M. Godlewski, Phys. Rev. B 54 (7) (1996) 4696. [12] M.U. Lehr, B. Litzenburger, J. Kreissl, U.W. Pohl, H.R. Selbert, H.-J. Schulz, A. Klimakow, L. Worschech, J. Phys.: Condens. Matter 9 (1997) 753. [13] C.I. Rablau, J.-O. Ndap, X. Ma, A. Burger, N.C. Giles, J. Electron. Matter 28 (6) (1999) 678. [14] L. Deloach, R.H. Page, G.D. Wilke, S.A. Payne, W.F. Krupke, IEEE J. Quantum Electron. 32 (1996) 885. [15] R.H. Page, K.I. Schaffers, L.D. Deloach, G.D. Wilke, F.D. Patel, J.B. Tassano, S.A. Payne, F. Krupke, K.T. Chen, A. Burger, IEEE J. Quantum Electron. 33 (1997) 609.
[16] M. Birnbaum, M.B. Camargo, S. Lee, F. Unlu, R.D. Stultz, OSA TOPS, Vol. 10, Advanced Solid State Lasers, 1997. [17] G.J. Wagner, T.J. Carrig, R.H. Page, K.I. Schaffers, J.-O. Ndap, X. Ma, A. Burger, Opt. Lett. 24 (1) (1999) 19. [18] R.S. Title, Phys. Rev. 133 (1964) A1613. [19] M. Dewit, A.R. Reinberg, W.C. Holton, T.L. Estle, Bull. Am. Phys. Soc. 10 (1965) 329. [20] C-H. Su, S. Feth, M.P. Volz, R. Matyi, M.A. George, K. Chattopadhyay, A. Burger, S.L. Lehoczky, J. Crystal Growth 207 (1999) 35. [21] T.H. Yeh, Diffusion in Semiconductors, In: D. Shaw (Ed.), Plenium, London, 1973, Chapter 4. [22] B. Tuck, Atomic Diffusion in III–V Semiconductors, Hilger, Bristol, 1988, Chapter 2. [23] H.F. Taylor, V.N. Smiley, S.S. Pawka, Phys. Rev. B 5 (1972) 1467. [24] II–VI Inc. database, Web address: http://www.ii.vi.com/ pages/prod-iivi-materials-znse.html [25] A.J. Moses, Hughes Aircraft Company, Culver City, California AD-704 555, 1970. [26] R. Dahmani, L. Salamanca-Riba, N.V. Nguyen, D. Chandler-Horowitz, B.T. Jonker, J. Appl. Phys. 76 (1) (1994) 514.