Electrical behaviour of fresh and stored porous silicon films

Thin Solid Films 325 (1998) 271–277

Electrical behaviour of fresh and stored porous silicon films M.L. Ciurea a ,*, I. Baltog a, M. Lazar a, V. Iancu b, S. Lazanu a, E. Pentia a a

National Institute of Materials Physics, Institute of Physics, P.O. Box MG-7, 76900 Bucharest-Magurele, Romania Physics Department, University ‘Politehnica’ of Bucharest, 33 Splaiul Independentei, 77206 Bucharest, Romania

b

Received 22 September 1997; accepted 2 January 1998

Abstract We have measured I–V and C–V characteristics, the temperature dependence of dark currents, and thermally stimulated depolarisation currents on fresh and stored samples of photoluminescent porous silicon. By storage in ambient, the low rectifying I–V curves become strong rectifying, and C–V curves become MIS-like. I–T characteristics for fresh samples have only one activation energy, in the 0.49–0.55 eV range. After storage, a slightly modified value, of about 0.50–0.60 eV is observed at low temperatures only. At about 280 K, the activation energy suddenly changes to 1.20–1.80 eV. Also, both the number and the positions of maxima in thermally stimulated depolarisation currents change by storage. The annealing at about 50°C induces small reversible changes in I–T characteristics and strong irreversible ones in thermally stimulated depolarisation currents, both for fresh and stored samples. A simplified quantum confinement model is proposed to explain the main aspects of the electrical behaviour of porous silicon films. The surface and/or interface contributions are observed especially in thermally stimulated depolarisation currents. The changes induced by storage are attributed to the oxidation process of the internal surface of porous silicon films.  1998 Elsevier Science S.A. All rights reserved Keywords: Electrical properties and measurements; Quantum effects; Silicon

1. Introduction The preparation of porous silicon (PS) films with efficient photoluminescence (PL) in the visible range at room temperature (RT) [1,2] has aroused a great interest in this material, because the main objective is to fabricate high quality optoelectronic devices that can be integrated with silicon microtechnology. Photoluminescent PS films obtained by anodization consist of an interconnected network of small Si crystallites with sizes of few nm. The quantum efficiency of the PL of PS films is quite high (≅1%–10%) [3], while the efficiency of the electroluminescence (EL) is less than 0.01%. This low value reported on metal/PS [4], ITO/PS [5] and on p–n junction devices [6] has been previously attributed to a poor contact at the surface of PS. Later, the use of conductive polymers has not led to a significant improvement in the EL efficiency [7]. An already accepted model for the PL of PS films is that * Corresponding author. Fax: +40 1 4203700; e-mail: [email protected]

0040-6090/98/$19.00  1998 Elsevier Science S.A. All rights reserved PII S0040-6090 (98 )0 0429-5

of quantum confinement of carriers inside crystallites that results in an increased band gap [1,2]. It has not been clear up to now whether this model is necessary to explain the electrical transport properties. Besides, PS films have a very large specific surface (≅1000 m2/cm3) and thus the surface contribution in electrical as well as optical properties must be taken into consideration [3,8–10]. The electrical properties of PS films were investigated using sandwich configurations such as Schottky devices and p–n junctions. Different results, depending on the preparation conditions, were reported in the literature [11–15]. Thus the electrical conduction of a self-supporting PS film shows a hopping behaviour at low temperatures and a thermal-activation process at high temperatures [11]. In Ref. [12] the observed electric-field-enhanced conduction is explained by a Poole–Frenkel type mechanism. The analysis of the frequency dependence of the conductivity and of the dielectric constant strongly suggests that the low-frequency regime is governed by the fractal properties of PS and the high-frequency dispersion is due to a broad distribution of activation energies [13]. The reverse current, dependent on humidity in a M/PS structure, is discussed

272

M.L. Ciurea et al. / Thin Solid Films 325 (1998) 271–277

considering the generation-recombination process in the PS depletion region [14]. In the present paper, the electrical behaviour of fresh samples, as well as those stored under ambient conditions is investigated. The current–voltage (I–V) characteristics, the temperature dependence of the dark current, and thermally stimulated depolarisation currents (TSDC) are analysed. All data were taken on capacitance–voltage (C–V) characterised samples. A simplified quantum confinement model is proposed. It provides a good explanation for the electrical properties of our fresh and stored PS films.

2. Experimental aspects PS layers of approximately 25–35 mm thickness were prepared on (100) p-type wafers of crystalline Si (c-Si) with resistivity of 5–10 Q cm. To improve the homogeneity of PS films, Al ohmic electrodes were prepared on the backside of the wafers by thermal evaporation followed by a sinterisation process at 450°C for 30 min. The wafers were electrochemically etched in dark, in an HF (49%)– C2H5OH electrolyte (with a volume ratio of 1:1) using a current density of 5–10 mA/cm2. After the etching, the samples either do not present PL or the PL intensity is very low. Hence, the samples were submitted to an activation process of PL [16]. Immediately after the preparation, the samples were washed in a double-distilled water and dried in air. The top electrodes were deposited by thermal evaporation at an angle of 20–25° to the film surface, to prevent the appearance of short-circuits into the samples. All the samples were then stored for different durations, ranging from 1 month to 2 years, in ambient conditions (no special precautions were taken). Measurements were performed on sandwich configuration, Al/PS/c-Si/Al, using a Keithley 2000 multimeter and

Fig. 1. Current–voltage characteristic for fresh sample; T = 300 K.

Fig. 2. Temperature dependence of the dark current for fresh sample: B, Ua = −1 V (‘+’ on PS); W, Ua = 1 V (‘+’on c-Si).

a Keithley 642 electrometer. I–V and C–V characteristics were taken in vacuum, in darkness, at room temperature (RT). The temperature dependence of the dark current (I– T characteristic) was measured for both bias polarities, at 1 V. To perform TSDC measurements, the samples had to be polarised. To do this, an external electric field was applied on the sample at RT and then the sample was cooled down to 150 K, in the dark. Then, the sample was connected with an electrometer and heated up at RT with a constant rate of approximately 0.1 K/s. The fresh and stored samples were also annealed in vacuum and in the dark for 20 min at 50°C. Some changes in electrical properties were observed.

3. Results 3.1. Fresh samples At RT, our samples present a slow rectifying behaviour in the −30– + 30 V range (Fig. 1), the I–V characteristics being practically linear in the −5– + 5 V interval, in good agreement with the literature [12]. The I–T characteristic was recorded in the temperature range 150–300 K (Fig. 2) and exhibits only one activation f whose value lies in the interval 0.49–0.55 eV. energy Edl The value obtained for the activation energy is independent of the bias polarity at low voltage. At low bias, the injected carrier concentration is small compared to the thermally generated concentration and the sample has an ohmic behaviour. We have to point out that all the values of the different kinds of activation energies (see below) are characterised by dispersion, i.e. different values were obtained for different samples prepared, stored and measured in the same conditions. A typical TSDC curve presents two maxima, a broad one at low temperatures and another one, well-defined, at high

273

M.L. Ciurea et al. / Thin Solid Films 325 (1998) 271–277 Table 1

Activation energies of the dark current and TSDC, on fresh samples, before and after annealing

Fig. 3. TSDC (fractional heating) Ua = −2 V.

temperatures. The activation energy for the high temperatures maximum, Ehf (whose value is 0.47–0.53 eV) was calculated from the slope of the increasing part, that behaves like an Arhennius curve: I = I0 exp( − Ea =kT). We have also tried the Meyer–Neldel relation: I0 = I00 exp(Ea =E0 ), where the activation energy Ea is characterised by dispersion, while I00 and E0 must have the same value for all samples, but this model did not fit our data. By performing a fractional heating, we have resolved the low temperature maximum into two peaks, having the activation energies of f f f ≅0.28 eV and El2 ≅0.35 eV (see Fig. 3). The El2 value El1 f was calculated in the same way as Eh . Because the discharging current is very low, it was not possible to calculate the f . However, we slope for the maximum corresponding to El1 f can determine El1 , if we consider the Bube formula [17] f ≅nkTm1 (where Tm1 is the temperature position of the El1 peak and k the Boltzmann constant). The used value for n f = 0.35 eV≅nkTm2. Because the two is obtained from El2 maxima are very near, the introduced error is small. After the annealing of the samples at 50°C, small changes were observed. They are listed in Table 1. Although the annealing temperature is low, it causes the irreversible disappearance of low temperature maxima in TSDC curves and a small reversible decrease in the value of the other activation energies.

Activation energy before annealing

Activation energy after annealing

Dark current

f Edl ≅ 0.49–0.55 eV

fa Edl ≅ 0.43–0.51 eV

TSDF

f El1 ≅ 0.28 eV, f ≅ 0.35 eV El2 Ehf ≅ 0.47–0.53 eV

Low T maxima disappeared Ehfa ≅ 0.41–0.48 eV

have a strong rectifying behaviour (Fig. 4). It can be observed that, for the forward bias, the current-voltage curve presents an usual exponential behaviour for low voltages 0–2.2 V and then an approximately linear dependence in the range 2.2–30 V. The temperature dependence of the dark current measured in the range 150–300 K on stabilised samples strongly differs from that of the fresh samples. Thus, the I–T curve presents two activation energies, one at low temperatures, s Edl ≅0.50–0.60 eV, independent of the bias polarity in the −2– + 2 V range and the other at high temperatures, s ≅1.20–1.80 eV, that has different values for opposite Edh bias polarities (see Fig. 5 and Table 2). However, these differences are small, so we neglect them in the following. As it can be seen in Fig. 5, the change of the activation energy takes place abruptly at about 280 K. This temperature also has slightly different values for opposite bias polarities. We have also to remark that, after storage, the current is diminished with approximately two orders of magnitude. The TSDC curve for stabilised PS samples displays only one maximum for the whole temperature range, characterised by the activation energy Ehs ≅ 0.81–0.87 eV (Table 2). Thermal annealing at 50°C induces small increases in the activation energies of the dark current. These changes are

3.2. Stored samples It is well known that photoluminescent properties (the shape of the spectral dependence and the position of the maximum) are changed by storage in ambient due to natural oxidation and controlled thermal oxidation. It is therefore normal to expect some changes in electrical properties of PS films due to the storage, too. We observed that, after approximately 1.5 years, the electrical parameters become practically constant. In the following, only the results obtained on the stabilised samples are presented. The current–voltage characteristics taken on sandwich configuration, Al/PS/c-Si/Al, in the range −30– + 30 V,

Fig. 4. Current–voltage characteristic on stored sample; T = 300 K.

274

M.L. Ciurea et al. / Thin Solid Films 325 (1998) 271–277

to explain the main aspects of the electrical behaviour of PS films. If we consider our PS samples, the length of wires is 103 –104-times greater than their diameter. Under these conditions, the electron Hamiltonian can be separated into a longitudinal part, describing the carrier motion along the wire, and a transversal one. In spite of the fact that this separation is not exact, due to the tetrahedral symmetry of the silicon, it represents a good first approximation. The solution of the longitudinal equation is an onedimensional (1D) Bloch function, that determines a band structure with an increased band gap compared to that of the bulk silicon (see Ref. [20]). To evaluate the transversal part of the Hamiltonian, it is reasonable to choose a cylindrical symmetry for the wire description and to use the model of a 2D infinite quantum well. Under these conditions, the expression for the electron energy is: Fig. 5. Temperature dependence of the dark current for stored sample. B, Ua = 2 V (‘+’ on c-Si); A, Ua = −2 V (‘+’ on PS).

reversible if the samples are stored again in ambient for 3–4 weeks. At the same time, the activation energy of the discharging current in TSDC measurements is increased up to the value Ehsa ≈ 1.0–1.1 eV. This change is irreversible. Even after a long storage time in ambient conditions, this activation energy does not come back to the initial value. We have to remark that C–V characteristics in the −5– + 5 V range are metal-insulator-semiconductor (MIS)like curves (Fig. 6). The high-frequency characteristic that appears practically flat at about 70% of the maximum values of the capacitance is due to the ionic contamination (mostly with Na) during the aging.

4. Analysis and discussion PS films with high PL are formed by a network of small crystallites, wires and/or dots. The main crystallite size at the surface of our films, evaluated from transmission microscopy measurements [18] is of the order of 2.5–7 nm (Fig. 7). As we already mentioned in Section 1, the main contributions to the characteristics of the electrical transport properties in crystallites having the size in this range are determined by the quantum confinement and surface effects. In the following, we will present a simplified model [19]



2"2 2"2 E = enkz + p 2 x2mp = enkz + p 2 x2o1 md md



2"2 2 (xmp − x2o1 ) ≡ esnkz + Emp (1) mp d 2 where esnkz is the shifted band energy corresponding to the longitudinal motion, Emp the discrete energy levels corresponding to the transversal motion (by definition, E01 ≡ 0), m* the effective mass of the electron, d the wire diameter, and xmp is the p-th zero of the Bessel function Jm, m being the orbital magnetic quantum number. Therefore, the quantum confinement produces both an increase of the band gap and the introduction of a number of discrete energy levels into the gap. This means that the Fermi level is pinned on the first discrete level until this one is fully occupied, then it jumps on the following one, while the longitudinal conduction is supported by the holes formed in the valence band. Then Emp represents the values for the activation energy of the dark current. In our simplified model, the activation energies Ea = Emp are proportional with d−2, typical for the effective mass approximation. However, the calculation of the electronic band structure of Si nanocrystallites, using the linear combination of atomic orbitals technique [20], showed that the band gap follows approximately a d − 1.39 dependence. If we accept this exponent, the variation of the activation energy values for our diameter range is quite small, in agreement with Tables 1 and 2. At the same time, the degeneracy of the levels is proportional with the number of atoms in a given transversal sec+

Table 2 The changes induced by annealing in the activation energies obtained on stored samples

Dark current TSDC

Activation energy before annealing

Activation energy after annealing

Low T

High T

Low T

s Edl ≅ 0.50–0.60 eV Ehs ≅ 0.81–0.87 eV

s Edh

≅ 1.20–1.80 eV

sa Edl Ehsa

≅ 0.58–0.66 eV ≅ 1.0–1.1 eV

High T sa Edh ≅ 1.35–1.80 eV

275

M.L. Ciurea et al. / Thin Solid Films 325 (1998) 271–277 Table 3

The energy values, Emp (in eV) for some of the first discrete levels introduced by the 2D quantum well m

p

0 1 2 a

1

2

3

0 0.21 0.48

0.58 1.02 1.53

1.62 2.29a 3.03b

E13 = 2.29 eV is close to the highest value of the band gap. E23 = 3.03 eV is definitely located in the conduction band.

b

f, s Edh

≈ f, s

Edl Fig. 6. Capacitance–voltage curves for stored sample. W, n = 2 kHz; B, n = 2 MHz.

tion, that is, with d2. Consequently, the decrease of the diameter of the silicon wire by oxidation will produce a f, s = E02, but a small increase of the activation energy Edl strong decrease of the degeneracy. At a given temperature, corresponding to the saturation of the first level, the Fermi level will jump on the second one, and the value of the f, s = E03. Their ratio is: activation energy will become Edh

Fig. 7. Transmission electron micrograph of our PS films: surface part.

E03 x203 − x201 = ≈ 2: 8 E02 x202 − x201

(2)

in excellent agreement with our experimental results (see Table 2 and Fig. 5). We have to mention that, even if E11 and E21 are smaller than E02 (see Table 3), the corresponding levels cannot be excited by the applied electric field, because of the angular momentum conservation. To excite them, we would have to measure the dark current at low temperatures, in a strong longitudinal magnetic field. We can also use the Emp expression to evaluate the s ≈ 0:58 crystallite diameter. Using the activation energy Edl * eV from the Fig. 4, we obtain with m = m0e, a diameter d ≈ 2.55 nm, and with mp = mpt = 0:66m0e a diameter d ≈ 3.14 nm, in good agreement with our data [18]. Under these conditions, if the first activation energy E02 becomes equal to the band gap (≥2 eV), the diameter reduces below 1.3–1.6 nm, less than 6–7 interatomic distances, equivalent with three lattice parameters, so the wire is no longer a proper 3D crystallite. Let us review our experimental results in the light of the previous model. The discrete energy levels in quantum wells practically exclude the presence of a depletion region inside the crystallites and of an accumulation layer at the metal/PS interface. Therefore an ideal contact Al/PS is not rectifying. However, both the spread of the levels into narrow bands and the deposition of Al contact at a small angle (allowing the electrode to reach larger crystallites) can introduce a low rectifying behaviour. At the same time, the PS/c-Si is a rectifying contact, due to the band bending in c-Si. The large specific surface of PS films can introduce supplementary localised states with lower energies than those due to the quantum confinement and it can produce small shifts of the quantum well energy levels. The I–V characteristic for fresh samples (Fig. 1) shows their low rectifying behaviour, due to the high (series) resistance of the thick PS films. The existence of only one activation energy of the dark current (Fig. 2) over the whole investigated temperature range shows that the first discrete level (E02≅0.5 eV) does not saturate up to 300 K. Thermoelectric probe measurements have shown that photoluminescent PS does exhibit n-

276

M.L. Ciurea et al. / Thin Solid Films 325 (1998) 271–277

type or p-type conductivity, depending on the conduction type of the substrate [15]. This supposition is also sustained by the fact that the activation energy for the high-temperature maximum in TSDC measurements, Ehf , has practically the same value in all fresh samples. This shows that the same carriers and the same mechanism produce the sample polarisation as a capacitor [21]. The two low-temperature maxima in TSDC measurements on fresh samples, which irreversibly disappear either by annealing (Table 1) or by aging (Table 2) can be attributed to some species (H, OH, etc.) adsorbed at the internal surface of the PS films during the preparation process. These adsorbed species act as trapping centres. Annealing also produces small reversible changes of the activation energies (Table 1), due to the surface desorption–adsorption processes (e.g. H2O), which influence the bulk (i.e. the quantum well) energy levels. Storage of PS samples in the ambient oxidises the surface of Si crystallites, reducing their size [22]. As a result, the small changes in the low temperatures activation energy f s to Edl ) and the appearance of the high-tempera(from Edl s ) at about 280 K (Fig. 1; Table 1 ture activation energy (Edh and Table 2) in the temperature dependence of the dark current can be understood in the frame of our model. MIS-like behaviour of the stored samples in C–V measurements at low frequencies (Fig. 6) suggests that the oxide layer could be formed even under the top Al contact. The C–V curve taken at high frequencies (Fig. 6) corresponds to the shifted characteristic induced by ionic contamination (mostly with Na) of the oxide. Due to the natural oxidation of our samples in the ambient, it can be expected that the oxide layer (SiOx) to be strongly contaminated. As a result, the SiOx layer behaves like a very high resistivity semiconductor and forms a strongly rectifying heterojunction with PS (Fig. 4). The very high SiOx resistivity limits the current at forward bias, giving an ohmic behaviour. This is also supported by the fact that currents measured on aged samples are reduced by 1–2 orders of magnitude in comparison with those measured on fresh samples. As the activation energy of the ohmic current through the oxide is practically equal with that of the substrate (PS in our case) [23], the temperature dependence of the dark current is controlled by the PS film, while I–V and C–V characteristics are determined by the oxide layer. One can observe that the value of the activation energy in TSDC measurements seems to be correlated with the values s s − Edl of the discrete energy levels discussed above: Ehs ≈ Edh sa sa sa and Eh ≈ Edh − Edl . Because the first of these relations is not as precise as the second one, another possibility would be the existence of a trapping level at the SiOx/PS interface, irreversibly influenced by annealing. The reversible changes induced by the annealing in the dark current activation energies correspond to the weak influence of the interface SiOx/PS upon the bulk energy levels in PS.

5. Conclusions In this paper we have shown that the main contribution to the electrical transport mechanism is given by the quantum confinement effects. The experimental data are well described by a 2D infinite quantum well model. This permits to explain the activation energies of dark and TSD currents by means of the discrete energy levels introduced into the longitudinal band gap. The surface effects are particularly observed in TSDC. The stabilisation of the electrical properties of stored PS films is due to the oxidation of their surfaces. The oxidation produces a decreasing crystallites size, which determines the appearance of a new activation energy in the dark current and changes the activation energy in TSDC. It also determines a strong rectifying heterojunction SiOx/PS and a MIS-like behaviour of the samples.

Acknowledgements The authors wish to thank Prof. R. Grigorovici (Romanian Academy), Prof. A. Goldenblum (National Institute of Materials Physics, Bucharest) and Prof. A. Yelon (Ecole Polytechnique de Montreal) for helpful discussions. Prof. V. Teodorescu and Prof. L. Nistor from the National Institute of Materials Physics, Bucharest, are also acknowledged for measurements and discussions regarding TEM.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

L.T. Canham, Appl. Phys. Lett. 57 (1990) 1046. V. Lehmann, V. Go¨sele, Appl. Phys. Lett. 58 (1991) 826. B. Hamilton, Semic. Sci. Technol. 10 (1995) 1187. N. Koshida, H. Koyama, Nanotechnology 3 (1992) 192. F. Namavar, H.P. Maruska, N.M. Kalkhoran, Appl. Phys. Lett. 60 (1992) 2514. P. Steiner, F. Kozlovski, W. Lang, Appl. Phys. Lett. 62 (1993) 2700. N. Koshida, H. Koyama, Y. Yamamoto, G.J. Collins, Appl. Phys. Lett. 63 (1993) 2655. F. Koch, T. Petrova-Koch, T. Muschik, A. Nicolov, V. Gavrilenko, Mater. Res. Soc. Symp. Proc. 283 (1992) 197. V. Petrova-Koch, T. Muschik, A. Kux, B.K. Meyer, F. Koch, Appl. Phys. Lett. 61 (1992) 943. F. Koch, Mater. Res. Soc. Symp. Proc. 298 (1993) 319. N. Koshida, H. Koyama, Mater. Res. Soc. Symp. Proc. 283 (1993) 337. M. Ben-Chorin, F. Mo¨ller, F. Koch, Phys. Rev. B 49 (1994) 2981. M. Ben-Chorin, F. Mo¨ller, F. Koch, Phys. Rev. B 51 (1995) 2199. D.B. Dimitrov, Phys. Rev. B 51 (1995) 1562. C. Peng, K.D. Hirschmann, P.M. Fauchet, J. Appl. Phys. 80 (1996) 295. M.L. Ciurea, E. Pentia, A. Manea, A. Belu-Marian, I. Baltog, Phys. Stat. Sol. (b) 195 (1996) 637. R.H. Bube, Photoconductivity of Solids, John Wiley, New York, 1960. M.L. Ciurea, V. Teodorescu, L. Nistor, submitted.

M.L. Ciurea et al. / Thin Solid Films 325 (1998) 271–277 [19] [20] [21] [22]

V. Iancu, M.L. Ciurea, Solic State Electron., in press. C. Delerue, G. Allan, M. Lanoo, Phys. Rev. B 48 (1993) 11024. P. Mu¨ller, Phys. Stat. Sol. (a) 23 (1974) 165. M.L. Ciurea, E. Pentia, M. Lazar, A. Belu-Marian, F. Zavaliche, R.

277

Manaila, Proc. Int. Conf. Semic. (CAS), 1, Sinaia, Romania, 1996, p. 233. [23] S.M. Sze, Physics of Semiconductor Devices, John Wiley, New York, 1969.