- Email: [email protected]
Transport and noise properties of CdTe(Cl) crystals
Microelectronics Reliability 41 (2001) 431±436
www.elsevier.com/locate/microrel
Transport and noise properties of CdTe(Cl) crystals P. Schauer a,*, J. Sikula a, P. Moravec b
a
Faculty of Civil Engineering, Institute of Physics, Brno University of Technology, Zizkova 17, 602 00 Brno, Czech Republic b Institute of Physics, Charles University, Ke Karlovu 3, 121 16 Prague 2, Czech Republic Received 28 April 2000; received in revised form 17 July 2000
Abstract Experimental studies of transport and noise characteristics of CdTe (Cl doped) crystals, prepared by travelling heater method, have been carried out. The basic material is of p-type with p 1:8 1014 m 3 , lh 0:0065 m2 V 1 s 1 , le 0:13 m2 V 1 s 1 . The current and noise spectral density was measured as a function of the sample illumination, voltages across the sample and incident light wavelengths. Two types of eective charge carrier mobility are assumed: namely, the eective transport mobility, which is 0.065 m2 V 1 s 1 and the eective noise mobility, which reaches a value of 0.125 m2 V 1 s 1 , both for high illumination. Under the same conditions, the density of light generated charge carrier pairs is 1:7 1015 m 3 . Experimental results are in a good agreement with the four-level recombination model. The values of 1=f noise parameter a range from 4 10 4 to 2:5 10 3 . The a parameter grows with almost the photocurrent square root. The signal-to-noise ratio improves if the electric ®eld strength in the CdTe detector is set to a higher value. Ó 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction
2. Sample description and experimental setup
Cadmium telluride crystal based detector features some remarkable advantages with respect to lithiumdrifted germanium or silicon. They can operate at room temperatures and have a higher value of photoelectric cross-section as compared with germanium or silicon. For photon energies of 100 keV, the total absorption coecient of CdTe is 20 times as high as that of silicon. Nuclear detectors made on CdTe feature a very low concentration of free electrons and holes, a resistivity of the order of 107 X m and a very low trap concentration. The main application ®eld of CdTe is the high-resolution detection of radiation. A fairly wide gap Eg 1:5 eV makes room operation of these sensors possible, the sensor therefore needs not to be cooled. We have studied transport and noise characteristics, which are related directly to the sensorÕs sensibility.
For this study, a CdTe crystal doped with Cl in an amount 1800 ppm was selected, whose room-temperature parameters were as follows: p-type dark conductivity 1:24 10 7 X 1 m 1 , hole mobility 0:0065 m2 V 1 s 1 , electron mobility 0:13 m2 V 1 s 1 , dark 8 m2 V 1 , hole density 1:8 1014 m 3 , le s e 2 10 9 2 1 lh s 7 10 m V (mobility trapping time prodh uct), sample dark resistance R0 1:9 GX. The sample was of sandwich con®guration with one contact at the bottom (at substrate), and the second one at the upper side of sample. The size of sample: thickness 0.7 mm, cross-section 2 mm2 . The illumination was provided from the upper side of sample through the semitransparent contact. Both contacts were made by coagulation of gold from AuCl3 solution. Our setup allows us to measure the sample current and noise voltage simultaneously. In Fig. 1, a block diagram of the experimental setup is shown. The sample is supplied from Type 314 dry cells connected in series, as this arrangement proved to exhibit a low noise, negligible with respect to the background noise of the lownoise wide-band preampli®er. The noise voltage is measured by a sampler and transformed into the
*
Corresponding author. Tel.: +420-5-4114-7654; fax: +4205-4114-7663. E-mail address: [email protected] (P. Schauer).
0026-2714/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 6 - 2 7 1 4 ( 0 0 ) 0 0 2 0 0 - 6
432
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
Fig. 1. Block diagram of the experimental setup. The sample voltage is supplied by a dry-cell battery. The noise voltage is measured simultaneously by a sampler (transformed by FFT) and by an analog narrow-band voltmeter. The illumination is provided by a mirror monochromator.
corresponding power noise spectral density using FFT ± a method similar to that described in Ref. [1]. In some experiments, an analog noise measurement method is used [2]. The illumination of CdTe sensors is provided by a mirror monochromator in the wavelength range from 670 to 960 nm, which corresponds to photon energies from 1.30 to 1.86 eV. 3. Transport characteristics Our measurements of the I±V characteristics of the illuminated sample (Fig. 2) show that they follow OhmÕs law up to at least 20 V (equivalent electric ®eld strength is 1:8 104 V m 1 ) at any illuminations, which con®rms the applicability of OhmÕs law. Fig. 3 shows the photocurrent versus photon energy plots at two dierent temperatures, the substrate being positive. The photocurrent reaches a maximum for T1 140 K at a photon energy Eph1 1:57 eV and for T2 295 K at Eph2 1:47 eV. Maximum photocurrent for T1 is Im1 2:25 10 6 A and for T2 , it is Im2 1:70 10 6 A, thus Im1 > Im2 . Taking into account that for temperatures T > 80 K, the band gap is given by Eg 1:622 eV 0:00035 eV K 1 T [3], we get the following values: Eg1 1:57 eV for T1 and Eg2 1:52 eV for T2 . The dark I±V characteristics are introduced later in Fig. 5 together with dark noise measurement. The lux±ampere characteristic is in Fig. 4. The sample illumination was monochromatic with Eph 1:50 eV, the applied DC voltage was 10 V (e 1:43 104 V m 1 ) and the temperature T 297 K. The photocurrent versus light intensity plot can be split into two regions. For the intensity of illumination / < 0:028 W m 2 the current is directly proportional to /, whereas for / > 0:028 W m 2 , it holds I U0:55 .
Fig. 2. I±V characteristics for three dierent incident light intensities. The curves follow OhmÕs law up to at least 20 V (29 kV m 1 ) at any incident light intensities.
4. Noise Noise and I±V measurements in the dark were carried out at the room temperature. Fig. 5 shows two plots of the power noise spectral densities versus DC voltage across the CdTe sample and two I±V curves for the same voltage. The measurements were carried out for both electric ®eld directions, curves 1 for positive substrate, curves 2 for negative one. The two noise measurements nearly merge, the in¯uence of the polarity becomes distinct at very high voltages over 80 V. There are two regions in noise curve 1 and three regions in noise curve
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
Fig. 3. Photocurrent versus photon energy plots at two dierent temperatures 140 and 295 K. The substrate is positivebiased. The photocurrent reaches a maximum for 140 K at the photon energy 1.57 eV and for 295 K at 1.47 eV.
Fig. 4. A lux±ampere characteristic for monochromatic sample illumination (Eph 1:50 eV). The applied DC voltage is 10 V (electric ®eld strength 14.3 kV m 1 ) and the temperature is 297 K. For the intensity of illumination under 0.028 W m 2 , the current is directly proportional to incident light intensity, whereas for intensities exceeding this value, it holds I U0:55 .
2. The ®rst two regions are identical for both voltage polarities. The ®rst region follows the quadratic law SP U 2 . Above U > UTFL 19 V, the curve features an extremely steep law, SP U 8 . We suppose that this is
433
Fig. 5. Plots of power noise spectral densities and of sample current versus DC voltage across the CdTe sample in the dark at the room temperature. Curves 1 are for positive substrate, curves 2 for negative one. Full dots belong to noise measurements, hollow ones represent current measurements. The ®rst region of the noise characteristics (under 19 V) obeys a quadratic law, SP U 2 , whereas an extremely steep law SP U 8 holds above 19 V (27 kV m 1 ) and, ®nally, above 80 V, the third region merges with curve 2, which is of SP U 4 type. The I±V curves exhibit the same break point voltages as the noise curves. The positive-substrate I±V curve is approximating OhmÕs law better than that for negative substrate.
due to ®lling the traps, which in turn supports strongly the transitions between the trap levels and the electron band (p-type semiconductor). Above 80 V, the third region begins with curve 2, which is of the type SP U 4 . Occurrence of this region depends on the sample voltage polarity. It is most likely due to a contact noise for which the power noise spectral density versus DC voltage plot can really be fourth power dependence of voltage [4]. The noise behavior is in agreement with I±V measurement. The I±V curve 1, with substrate positive orientation, demonstrates ohmic behavior up to 18 V and also over 80 V. The I±V curve 2 is ohmic up to 18 V only. The power noise spectral density as a function of the sample illumination was measured at two dierent voltages across the sample, the substrate being positive. The measured power noise spectral densities are shown in Fig. 6 as a function of the photocurrent. Curve 1 corresponds to a constant voltage across the sample U1 10 V (electric ®eld strength 1:4 104 V m 1 ), curve 2 to U2 3 V (4:3 103 V m 1 ). The photon energy was in both cases Eph 1:50 eV. The absorption took place in a shallow layer on the surface. Curve 1 is of the type SP I 0:7 within the entire range. Two regions are apparent in curve 2, namely, under 1:3 10 7 A following SP I 0:6 , whereas over 3 10 7 A, the noise starts getting saturated.
434
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
applies. The four levels are the edges of the valence and conduction bands and two trap levels. Blackmore [7] describes this type of recombination by gh /ra Na
Nd
p;
1
where / is the surface intensity of incident photons, ra , the capture coecient, Na , the acceptor density, Nd , the donor density, p, the density of light generated holes and gh , the velocity of generation of holes and is given by p gh : s
2
Here, s is the life time calculated from s
Fig. 6. Power noise spectral densities as a function of the photocurrent at two dierent voltages across the sample, the substrate being positive. The photocurrent was changed by varying the sample illumination. Curve 1 corresponds to a voltage across the sample of 10 V (14.3 kV m 1 ), curve 2 to 3 V (4.3 kV m 1 ). The photon energy was in both cases 1.50 eV. Curve 1 is of the type SP I 0:7 throughout the entire range; two regions are apparent on curve 2, namely, obeying SP I 0:6 law under 0.3 lA and reaching saturation, over 0.3 lA.
5. Discussion First, let us use the peaked behavior of Fig. 3 to discuss the absorption edge of our samples. At low photon energies Eph < Eg , the light absorption is week. As the photon energy gets near the band gap, the absorption coecient increases and the photocurrent goes up. Over a certain energy, the absorption is high and, at the same time, the carriers are generated in a layer on the surface only. The surface recombination plays a higher role in comparison with absorption and the photocurrent decreases. We may therefore conclude that at the room temperature, the surface recombination becomes of importance already at energies lower than those of the band gap Eg . These results are in good agreement accordance with the results given in Ref. [5], where the absorption edge of CdTe was studied. From the in¯ection points of the curves 1 and 2, we may estimate the photon energies at which the absorption coecient gets saturated. Our results show 1.56 eV at T2 295 K and 1.64 eV at T1 140 K. Also these results are in a good agreement with the results presented by other authors [6]. Second, based on the lux±ampere characteristics of our CdTe sample, we may try to predict the model of recombination. Let us assume that the four-level type of nonlinear recombination mechanisms in CdTe crystals
s0 1 ; where s0 : Nd cn 1 Npd
3
Here, cn is the eective capture rate. Using Eqs. (1)±(3) we obtain the relation p p N d cn 1 /ra Na Nd p; 4 Nd and after rearranging Eq. (4), the density of holes generated by light will be 1 /ra Nd p 2 cn s 2 1 /ra /ra Nd Na Nd : 5 4 cn cn The four-level recombination model shows that at low generation, the nonequilibrium concentrations are proportional to the generation (linear recombination), whereas at a higher generation they are proportional to the square root of generation. In Fig. 7, plots of charge carrier density and eective mobility versus illumination intensity of the CdTe crystal are shown. The carrier density and mobility have been calculated in two dierent ways. First, from Eq. (5) of our four-level model of nonlinear recombination, using the following parameters: cn =ra 2 103 m s 1 , Na 1 1013 m 3 , Nd 2:2 1015 m 3 . The second evaluation employs the measurement of lux±ampere characteristics. It is based on the transport equation: I e nle plh p0 lh eS I0 e nle plh eS e n p p0 lt eS;
6
where S is the sample cross-section, e is the electric ®eld strength, le and lh are the electron and hole mobilities, n and p are the densities of electrons and holes generated by light, p0 is the dark hole density and, I0 is the dark current. Mobility lt is the eective transport mobility, which in¯uences the total number of free carriers. Since we assume the light-induced generation to take place in
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
435
Hooge relation separately. To get the total power noise spectral density, we will sum these one-type power noise spectral densities. The cross power noise spectral density that refers to ¯uctuations between the opposite type of carriers is negligible, we suppose. Let us start our considerations with the Hooge formula transformed to power noise spectral density, which has the following form for conduction electrons and holes separately: SP n
Fig. 7. Plots of the light generated charge carrier density, effective transport mobility and eective noise mobility versus the light intensity of the illuminated CdTe crystal. Theoretical values of carrier density and mobilities (Ð) are calculated from the four-level nonlinear recombination model using following parameters: cn =ra 2 103 m s 1 , Na 1 1013 m 3 , Nd 2:2 1015 m 3 . The triangles, circles, and squares have been calculated from experimental lux±ampere characteristic.
pairs, n p, from Eq. (6) we get the density of holes generated by light p
I
I0 : e le lh eS
7
For the same condition, the eective transport mobility may be expressed by lt
ple p p0 lh : 2p p0
8
The eective transport mobility was calculated from Eq. (8) using experimental data p, see Eq. (7), and subsequently using p from Eq. (5) of four-level model. All curves are shown in Fig. 7. Besides, model and experimental data of the eective noise mobility was plotted in Fig. 7 according to Eq. (11), which is introduced below. It is seen that the agreement between the experiment and the model is good. The noise measurements allow us to assess the quality of our CdTe samples. As a quality indicator, we may take the 1=f noise parameter a, which is not constant [8]. Lower as indicate better-quality samples, whereas higher as mean inferior quality. In order to estimate the quality of our crystals, let us assume that the well-known Hooge formula for 1=f noise [9] applies to CdTe crystals in dark as well as under illumination. The sample I±V curve behavior (matching OhmÕs law) and pure 1=f noise characteristics up to 80 V across the sample justify this approach. We suppose that the power noise spectral density for conduction electrons and for conduction holes can be calculated according to the
aIn2 R; Nf
SP p
aIp2 R; Pf
9
where, N is the total number of free electrons and P is the total number of free holes in the sample, In enle eS and Ip e p p0 lh eS are the electron and hole currents through the sample, R is the resistance of the sample and f is the frequency. Using OhmÕs law for the resistance of the sample R U =I d= e nle plh p0 lh S, we get the power noise spectral density as follows: SP
a elN e2 ; f
10
where, e is the electric ®eld strength in the sample (it is constant), e, the elementary charge, f, the frequency and lN , the eective noise mobility, under the condition n p is expressed by lN
pl2e p p0 l2h : p le lh p0 lh
11
The eective noise mobility diers from the eective transport mobility, described by Eq. (8). Using Eq. (11), we can calculate the Hooge parameter a from known values of power noise spectral density using the equation a
SP f : elN e2
12
Fig. 8 shows a versus photocurrent plots for two dierent electric ®eld strengths in the sample. As expected, light illumination causes higher noise and, along with this eect, higher values of a, too. The Hooge parameter grows with nearly the photocurrent square root for both of the electric ®eld strengths. The a is higher at the same photocurrent for lower electric ®eld 4:3 103 V m 1 except for photocurrent over 6 10 7 A where the electric ®eld does not play any role. 6. Conclusion Our experiments show that the four-level recombination mechanisms of light illuminated CdTe crystals is applicable. This allows us to evaluate the donor and acceptor densities by simply ®tting the model. We may conclude that there are two eective carrier mobilities applicable to an illuminated CdTe sample characterization, namely, one for the transport
436
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
the sample at the same photocurrent. In such a way, we can increase the signal-to-noise ratio of the CdTe detectors by applying higher electric ®eld intensities.
Acknowledgements This work was performed as a part of the project Noise and galvanomagnetic spectroscopy of single crystalline materials of type II±VI, GACR no. 102/99/0953, which was ®nancially supported by the Grant Agency of Czech Republic. The authors express their sincere thanks for this support.
References
Fig. 8. 1=f noise parameter a versus photocurrent plots at two dierent electric ®eld strengths in the sample. Parameter a grows with nearly the photocurrent square root for both electric ®eld strengths. At a certain photocurrent value, a is higher at lower electric ®eld intensities.
characterization and the other for the noise characterization. This approach arises from the assumption that the Hooge formula (9) is applicable to one type of charge carriers only, i.e., separately for free holes and separately for free electrons. However, to examine the eective transport mobility, we must include holes and electrons simultaneously into the transport equation. This is the reason, why dierent eective noise and transport mobilities occur. Under the previously mentioned conditions, the 1=f noise parameter, a, ranges from 4 10 4 to 2:5 10 3 for our CdTe crystals, depending on the incident light intensity and electric ®eld strength. It is interesting, that the parameter a is lower for higher electric ®eld across
[1] Karar A, Tanaka R, Vanel JC. APD's excess noise measurements using spectral analysis (FFT). Nucl Instrum Meth Phys Res Sec A 1997;87:205±10. [2] Koktavy B, Sikula J. Method of experimental study of ¯uctuation in semiconductors. J Acta Phys Slovaca 1979;29: 227±36. [3] Strauss AJ. The physical properties of CdTe. Rev Phys Appl 1977;12:167. [4] Nemirovsky Y, Ruzin A, Asa G, Gorelik Y, Li L. Study of contacts to CdZnTe radiation detector. J Electron Mater 1997;26:756±64. [5] Marple DTF. Optical absorption edge in CdTe: experimental. Phys Rev 1966;150:728±33. [6] Wald FV. Rev Phys Appl 1977;12:277. [7] Blakemore JS. Semiconductor statistics, Oxford, London, New York, Paris: Pergamon Press; 1962. [8] Vandamme LKJ. Is the 1=f noise parameter a a constant? In: Seventh International Conference on Noise in Physical Systems and Third International Conference on 1=f Noise, Montpellier, France, 1983 May 17±20, Noise in Physical Systems and 1=f Noise. Amsterdam: Elsevier; 1983. p. 183± 92. [9] Hooge FN. 1=f noise is no surface eect. Phys Lett A 1969;29:139±40.
www.elsevier.com/locate/microrel
Transport and noise properties of CdTe(Cl) crystals P. Schauer a,*, J. Sikula a, P. Moravec b
a
Faculty of Civil Engineering, Institute of Physics, Brno University of Technology, Zizkova 17, 602 00 Brno, Czech Republic b Institute of Physics, Charles University, Ke Karlovu 3, 121 16 Prague 2, Czech Republic Received 28 April 2000; received in revised form 17 July 2000
Abstract Experimental studies of transport and noise characteristics of CdTe (Cl doped) crystals, prepared by travelling heater method, have been carried out. The basic material is of p-type with p 1:8 1014 m 3 , lh 0:0065 m2 V 1 s 1 , le 0:13 m2 V 1 s 1 . The current and noise spectral density was measured as a function of the sample illumination, voltages across the sample and incident light wavelengths. Two types of eective charge carrier mobility are assumed: namely, the eective transport mobility, which is 0.065 m2 V 1 s 1 and the eective noise mobility, which reaches a value of 0.125 m2 V 1 s 1 , both for high illumination. Under the same conditions, the density of light generated charge carrier pairs is 1:7 1015 m 3 . Experimental results are in a good agreement with the four-level recombination model. The values of 1=f noise parameter a range from 4 10 4 to 2:5 10 3 . The a parameter grows with almost the photocurrent square root. The signal-to-noise ratio improves if the electric ®eld strength in the CdTe detector is set to a higher value. Ó 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction
2. Sample description and experimental setup
Cadmium telluride crystal based detector features some remarkable advantages with respect to lithiumdrifted germanium or silicon. They can operate at room temperatures and have a higher value of photoelectric cross-section as compared with germanium or silicon. For photon energies of 100 keV, the total absorption coecient of CdTe is 20 times as high as that of silicon. Nuclear detectors made on CdTe feature a very low concentration of free electrons and holes, a resistivity of the order of 107 X m and a very low trap concentration. The main application ®eld of CdTe is the high-resolution detection of radiation. A fairly wide gap Eg 1:5 eV makes room operation of these sensors possible, the sensor therefore needs not to be cooled. We have studied transport and noise characteristics, which are related directly to the sensorÕs sensibility.
For this study, a CdTe crystal doped with Cl in an amount 1800 ppm was selected, whose room-temperature parameters were as follows: p-type dark conductivity 1:24 10 7 X 1 m 1 , hole mobility 0:0065 m2 V 1 s 1 , electron mobility 0:13 m2 V 1 s 1 , dark 8 m2 V 1 , hole density 1:8 1014 m 3 , le s e 2 10 9 2 1 lh s 7 10 m V (mobility trapping time prodh uct), sample dark resistance R0 1:9 GX. The sample was of sandwich con®guration with one contact at the bottom (at substrate), and the second one at the upper side of sample. The size of sample: thickness 0.7 mm, cross-section 2 mm2 . The illumination was provided from the upper side of sample through the semitransparent contact. Both contacts were made by coagulation of gold from AuCl3 solution. Our setup allows us to measure the sample current and noise voltage simultaneously. In Fig. 1, a block diagram of the experimental setup is shown. The sample is supplied from Type 314 dry cells connected in series, as this arrangement proved to exhibit a low noise, negligible with respect to the background noise of the lownoise wide-band preampli®er. The noise voltage is measured by a sampler and transformed into the
*
Corresponding author. Tel.: +420-5-4114-7654; fax: +4205-4114-7663. E-mail address: [email protected] (P. Schauer).
0026-2714/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 6 - 2 7 1 4 ( 0 0 ) 0 0 2 0 0 - 6
432
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
Fig. 1. Block diagram of the experimental setup. The sample voltage is supplied by a dry-cell battery. The noise voltage is measured simultaneously by a sampler (transformed by FFT) and by an analog narrow-band voltmeter. The illumination is provided by a mirror monochromator.
corresponding power noise spectral density using FFT ± a method similar to that described in Ref. [1]. In some experiments, an analog noise measurement method is used [2]. The illumination of CdTe sensors is provided by a mirror monochromator in the wavelength range from 670 to 960 nm, which corresponds to photon energies from 1.30 to 1.86 eV. 3. Transport characteristics Our measurements of the I±V characteristics of the illuminated sample (Fig. 2) show that they follow OhmÕs law up to at least 20 V (equivalent electric ®eld strength is 1:8 104 V m 1 ) at any illuminations, which con®rms the applicability of OhmÕs law. Fig. 3 shows the photocurrent versus photon energy plots at two dierent temperatures, the substrate being positive. The photocurrent reaches a maximum for T1 140 K at a photon energy Eph1 1:57 eV and for T2 295 K at Eph2 1:47 eV. Maximum photocurrent for T1 is Im1 2:25 10 6 A and for T2 , it is Im2 1:70 10 6 A, thus Im1 > Im2 . Taking into account that for temperatures T > 80 K, the band gap is given by Eg 1:622 eV 0:00035 eV K 1 T [3], we get the following values: Eg1 1:57 eV for T1 and Eg2 1:52 eV for T2 . The dark I±V characteristics are introduced later in Fig. 5 together with dark noise measurement. The lux±ampere characteristic is in Fig. 4. The sample illumination was monochromatic with Eph 1:50 eV, the applied DC voltage was 10 V (e 1:43 104 V m 1 ) and the temperature T 297 K. The photocurrent versus light intensity plot can be split into two regions. For the intensity of illumination / < 0:028 W m 2 the current is directly proportional to /, whereas for / > 0:028 W m 2 , it holds I U0:55 .
Fig. 2. I±V characteristics for three dierent incident light intensities. The curves follow OhmÕs law up to at least 20 V (29 kV m 1 ) at any incident light intensities.
4. Noise Noise and I±V measurements in the dark were carried out at the room temperature. Fig. 5 shows two plots of the power noise spectral densities versus DC voltage across the CdTe sample and two I±V curves for the same voltage. The measurements were carried out for both electric ®eld directions, curves 1 for positive substrate, curves 2 for negative one. The two noise measurements nearly merge, the in¯uence of the polarity becomes distinct at very high voltages over 80 V. There are two regions in noise curve 1 and three regions in noise curve
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
Fig. 3. Photocurrent versus photon energy plots at two dierent temperatures 140 and 295 K. The substrate is positivebiased. The photocurrent reaches a maximum for 140 K at the photon energy 1.57 eV and for 295 K at 1.47 eV.
Fig. 4. A lux±ampere characteristic for monochromatic sample illumination (Eph 1:50 eV). The applied DC voltage is 10 V (electric ®eld strength 14.3 kV m 1 ) and the temperature is 297 K. For the intensity of illumination under 0.028 W m 2 , the current is directly proportional to incident light intensity, whereas for intensities exceeding this value, it holds I U0:55 .
2. The ®rst two regions are identical for both voltage polarities. The ®rst region follows the quadratic law SP U 2 . Above U > UTFL 19 V, the curve features an extremely steep law, SP U 8 . We suppose that this is
433
Fig. 5. Plots of power noise spectral densities and of sample current versus DC voltage across the CdTe sample in the dark at the room temperature. Curves 1 are for positive substrate, curves 2 for negative one. Full dots belong to noise measurements, hollow ones represent current measurements. The ®rst region of the noise characteristics (under 19 V) obeys a quadratic law, SP U 2 , whereas an extremely steep law SP U 8 holds above 19 V (27 kV m 1 ) and, ®nally, above 80 V, the third region merges with curve 2, which is of SP U 4 type. The I±V curves exhibit the same break point voltages as the noise curves. The positive-substrate I±V curve is approximating OhmÕs law better than that for negative substrate.
due to ®lling the traps, which in turn supports strongly the transitions between the trap levels and the electron band (p-type semiconductor). Above 80 V, the third region begins with curve 2, which is of the type SP U 4 . Occurrence of this region depends on the sample voltage polarity. It is most likely due to a contact noise for which the power noise spectral density versus DC voltage plot can really be fourth power dependence of voltage [4]. The noise behavior is in agreement with I±V measurement. The I±V curve 1, with substrate positive orientation, demonstrates ohmic behavior up to 18 V and also over 80 V. The I±V curve 2 is ohmic up to 18 V only. The power noise spectral density as a function of the sample illumination was measured at two dierent voltages across the sample, the substrate being positive. The measured power noise spectral densities are shown in Fig. 6 as a function of the photocurrent. Curve 1 corresponds to a constant voltage across the sample U1 10 V (electric ®eld strength 1:4 104 V m 1 ), curve 2 to U2 3 V (4:3 103 V m 1 ). The photon energy was in both cases Eph 1:50 eV. The absorption took place in a shallow layer on the surface. Curve 1 is of the type SP I 0:7 within the entire range. Two regions are apparent in curve 2, namely, under 1:3 10 7 A following SP I 0:6 , whereas over 3 10 7 A, the noise starts getting saturated.
434
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
applies. The four levels are the edges of the valence and conduction bands and two trap levels. Blackmore [7] describes this type of recombination by gh /ra Na
Nd
p;
1
where / is the surface intensity of incident photons, ra , the capture coecient, Na , the acceptor density, Nd , the donor density, p, the density of light generated holes and gh , the velocity of generation of holes and is given by p gh : s
2
Here, s is the life time calculated from s
Fig. 6. Power noise spectral densities as a function of the photocurrent at two dierent voltages across the sample, the substrate being positive. The photocurrent was changed by varying the sample illumination. Curve 1 corresponds to a voltage across the sample of 10 V (14.3 kV m 1 ), curve 2 to 3 V (4.3 kV m 1 ). The photon energy was in both cases 1.50 eV. Curve 1 is of the type SP I 0:7 throughout the entire range; two regions are apparent on curve 2, namely, obeying SP I 0:6 law under 0.3 lA and reaching saturation, over 0.3 lA.
5. Discussion First, let us use the peaked behavior of Fig. 3 to discuss the absorption edge of our samples. At low photon energies Eph < Eg , the light absorption is week. As the photon energy gets near the band gap, the absorption coecient increases and the photocurrent goes up. Over a certain energy, the absorption is high and, at the same time, the carriers are generated in a layer on the surface only. The surface recombination plays a higher role in comparison with absorption and the photocurrent decreases. We may therefore conclude that at the room temperature, the surface recombination becomes of importance already at energies lower than those of the band gap Eg . These results are in good agreement accordance with the results given in Ref. [5], where the absorption edge of CdTe was studied. From the in¯ection points of the curves 1 and 2, we may estimate the photon energies at which the absorption coecient gets saturated. Our results show 1.56 eV at T2 295 K and 1.64 eV at T1 140 K. Also these results are in a good agreement with the results presented by other authors [6]. Second, based on the lux±ampere characteristics of our CdTe sample, we may try to predict the model of recombination. Let us assume that the four-level type of nonlinear recombination mechanisms in CdTe crystals
s0 1 ; where s0 : Nd cn 1 Npd
3
Here, cn is the eective capture rate. Using Eqs. (1)±(3) we obtain the relation p p N d cn 1 /ra Na Nd p; 4 Nd and after rearranging Eq. (4), the density of holes generated by light will be 1 /ra Nd p 2 cn s 2 1 /ra /ra Nd Na Nd : 5 4 cn cn The four-level recombination model shows that at low generation, the nonequilibrium concentrations are proportional to the generation (linear recombination), whereas at a higher generation they are proportional to the square root of generation. In Fig. 7, plots of charge carrier density and eective mobility versus illumination intensity of the CdTe crystal are shown. The carrier density and mobility have been calculated in two dierent ways. First, from Eq. (5) of our four-level model of nonlinear recombination, using the following parameters: cn =ra 2 103 m s 1 , Na 1 1013 m 3 , Nd 2:2 1015 m 3 . The second evaluation employs the measurement of lux±ampere characteristics. It is based on the transport equation: I e nle plh p0 lh eS I0 e nle plh eS e n p p0 lt eS;
6
where S is the sample cross-section, e is the electric ®eld strength, le and lh are the electron and hole mobilities, n and p are the densities of electrons and holes generated by light, p0 is the dark hole density and, I0 is the dark current. Mobility lt is the eective transport mobility, which in¯uences the total number of free carriers. Since we assume the light-induced generation to take place in
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
435
Hooge relation separately. To get the total power noise spectral density, we will sum these one-type power noise spectral densities. The cross power noise spectral density that refers to ¯uctuations between the opposite type of carriers is negligible, we suppose. Let us start our considerations with the Hooge formula transformed to power noise spectral density, which has the following form for conduction electrons and holes separately: SP n
Fig. 7. Plots of the light generated charge carrier density, effective transport mobility and eective noise mobility versus the light intensity of the illuminated CdTe crystal. Theoretical values of carrier density and mobilities (Ð) are calculated from the four-level nonlinear recombination model using following parameters: cn =ra 2 103 m s 1 , Na 1 1013 m 3 , Nd 2:2 1015 m 3 . The triangles, circles, and squares have been calculated from experimental lux±ampere characteristic.
pairs, n p, from Eq. (6) we get the density of holes generated by light p
I
I0 : e le lh eS
7
For the same condition, the eective transport mobility may be expressed by lt
ple p p0 lh : 2p p0
8
The eective transport mobility was calculated from Eq. (8) using experimental data p, see Eq. (7), and subsequently using p from Eq. (5) of four-level model. All curves are shown in Fig. 7. Besides, model and experimental data of the eective noise mobility was plotted in Fig. 7 according to Eq. (11), which is introduced below. It is seen that the agreement between the experiment and the model is good. The noise measurements allow us to assess the quality of our CdTe samples. As a quality indicator, we may take the 1=f noise parameter a, which is not constant [8]. Lower as indicate better-quality samples, whereas higher as mean inferior quality. In order to estimate the quality of our crystals, let us assume that the well-known Hooge formula for 1=f noise [9] applies to CdTe crystals in dark as well as under illumination. The sample I±V curve behavior (matching OhmÕs law) and pure 1=f noise characteristics up to 80 V across the sample justify this approach. We suppose that the power noise spectral density for conduction electrons and for conduction holes can be calculated according to the
aIn2 R; Nf
SP p
aIp2 R; Pf
9
where, N is the total number of free electrons and P is the total number of free holes in the sample, In enle eS and Ip e p p0 lh eS are the electron and hole currents through the sample, R is the resistance of the sample and f is the frequency. Using OhmÕs law for the resistance of the sample R U =I d= e nle plh p0 lh S, we get the power noise spectral density as follows: SP
a elN e2 ; f
10
where, e is the electric ®eld strength in the sample (it is constant), e, the elementary charge, f, the frequency and lN , the eective noise mobility, under the condition n p is expressed by lN
pl2e p p0 l2h : p le lh p0 lh
11
The eective noise mobility diers from the eective transport mobility, described by Eq. (8). Using Eq. (11), we can calculate the Hooge parameter a from known values of power noise spectral density using the equation a
SP f : elN e2
12
Fig. 8 shows a versus photocurrent plots for two dierent electric ®eld strengths in the sample. As expected, light illumination causes higher noise and, along with this eect, higher values of a, too. The Hooge parameter grows with nearly the photocurrent square root for both of the electric ®eld strengths. The a is higher at the same photocurrent for lower electric ®eld 4:3 103 V m 1 except for photocurrent over 6 10 7 A where the electric ®eld does not play any role. 6. Conclusion Our experiments show that the four-level recombination mechanisms of light illuminated CdTe crystals is applicable. This allows us to evaluate the donor and acceptor densities by simply ®tting the model. We may conclude that there are two eective carrier mobilities applicable to an illuminated CdTe sample characterization, namely, one for the transport
436
P. Schauer et al. / Microelectronics Reliability 41 (2001) 431±436
the sample at the same photocurrent. In such a way, we can increase the signal-to-noise ratio of the CdTe detectors by applying higher electric ®eld intensities.
Acknowledgements This work was performed as a part of the project Noise and galvanomagnetic spectroscopy of single crystalline materials of type II±VI, GACR no. 102/99/0953, which was ®nancially supported by the Grant Agency of Czech Republic. The authors express their sincere thanks for this support.
References
Fig. 8. 1=f noise parameter a versus photocurrent plots at two dierent electric ®eld strengths in the sample. Parameter a grows with nearly the photocurrent square root for both electric ®eld strengths. At a certain photocurrent value, a is higher at lower electric ®eld intensities.
characterization and the other for the noise characterization. This approach arises from the assumption that the Hooge formula (9) is applicable to one type of charge carriers only, i.e., separately for free holes and separately for free electrons. However, to examine the eective transport mobility, we must include holes and electrons simultaneously into the transport equation. This is the reason, why dierent eective noise and transport mobilities occur. Under the previously mentioned conditions, the 1=f noise parameter, a, ranges from 4 10 4 to 2:5 10 3 for our CdTe crystals, depending on the incident light intensity and electric ®eld strength. It is interesting, that the parameter a is lower for higher electric ®eld across
[1] Karar A, Tanaka R, Vanel JC. APD's excess noise measurements using spectral analysis (FFT). Nucl Instrum Meth Phys Res Sec A 1997;87:205±10. [2] Koktavy B, Sikula J. Method of experimental study of ¯uctuation in semiconductors. J Acta Phys Slovaca 1979;29: 227±36. [3] Strauss AJ. The physical properties of CdTe. Rev Phys Appl 1977;12:167. [4] Nemirovsky Y, Ruzin A, Asa G, Gorelik Y, Li L. Study of contacts to CdZnTe radiation detector. J Electron Mater 1997;26:756±64. [5] Marple DTF. Optical absorption edge in CdTe: experimental. Phys Rev 1966;150:728±33. [6] Wald FV. Rev Phys Appl 1977;12:277. [7] Blakemore JS. Semiconductor statistics, Oxford, London, New York, Paris: Pergamon Press; 1962. [8] Vandamme LKJ. Is the 1=f noise parameter a a constant? In: Seventh International Conference on Noise in Physical Systems and Third International Conference on 1=f Noise, Montpellier, France, 1983 May 17±20, Noise in Physical Systems and 1=f Noise. Amsterdam: Elsevier; 1983. p. 183± 92. [9] Hooge FN. 1=f noise is no surface eect. Phys Lett A 1969;29:139±40.