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Role of parasitics in humidity sensing by porous silicon
Sensors and Actuators A 94 (2001) 44±52
Role of parasitics in humidity sensing by porous silicon J. Das, S.M. Hossain, S. Chakraborty, H. Saha* Department of Electronics and Telecommunication Engineering, IC Design and Fabrication Center, Jadavpur University, Kolkata 700032, India Received 7 February 2001; received in revised form 25 May 2001; accepted 21 June 2001
Abstract Humidity sensing by porous silicon (PS) layer is commonly reported either by capacitive sensing or by conductive sensing. A critical analysis of both capacitive and conductive sensing by microporous PS layer is presented here. The in¯uences of parasitic capacitances and resistances unavoidably associated with the active porous layer on the measured changes in capacitance and resistance of the humidity sensor with variation of humidity are analysed. The role of contact geometry, signal frequency and porosity of PS layer are also discussed. It is shown that capacitive sensing is more sensitive in low frequency range owing to the relative contributions of parasitic components. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Porous silicon; Humidity sensor
1. Introduction Porous silicon (PS), which is essentially crystalline silicon with nanostructured pores preferentially etched into it to give it a sponge-like structure, is a well-known material for sensing layer in different gas and humidity sensors [1±3]. Owing to its very large surface area to volume ratio (>500 m2/cm3), PS can absorb large amounts of foreign molecules on its surface. With the presence of these molecules, many properties associated with PS will change. For example, photoluminescence (PL) ef®ciency decreases when PS is exposed to various chemicals and the ®nal PL ef®ciency depends on the dipole moment of the physically absorbed molecules [4]. Likewise, the effective dielectric constant and conductivity of PS layer will change if the PS surface is saturated with some other molecules. Therefore, a capacitance-based [5] or conductance-based [6] humidity sensor can be realised using the relative change of dielectric constant or conductivity, respectively, when moisture is adsorbed on the surface of a PS layer. For humidity sensing with ceramic layer, it is well known that both capacitance and conductance variation of a porous ceramic layer depends very much on the porosity of layer and the applied frequency [7,8]. The size and distribution of
*
Corresponding author. Tel.: 91-33-4732217/4721833; fax: 91-33-4732217. E-mail address: [email protected] (H. Saha).
pores of the ceramic humidity sensors also play very important role in determining the sensitivity and response time of a humidity sensor. Computer simulations for ceramic sensors indicate that micropores below 10 nm in diameter are slow in response while pore sizes between 1 and 30 nm are desirable for good sensitivity [9]. In a similar manner, the pore size and distribution of porous silicon humidity sensor can be varied considerably by simply controlling its formation parameters, like formation current density (J), HF concentration, illumination level, etc. [10]. Also, porous silicon is a nanostructured porous semiconductor having both capacitance and conductance that is signi®cantly dependent on applied frequency of measurement. This is further aggravated by the unavoidable presence of parasitic capacitances and resistances arising out of the contacts between different layers and interconnects of the humidity sensor. The change in the measured capacitance and conductance of a PS humidity sensor would thus depend on the selection of the frequency of the signal source and the pore size and pore distribution of the PS layer. The contact geometry on the PS surface is also important and may in¯uence considerably the measurements. These considerations have not been emphasised in some of the earlier reports [5,6,9]. The present paper aims at studying the role of the parasitic components of the PS humidity sensor in¯uencing the measured changes of the capacitance and conductance with reference to variations in its porosity and pore size, applied frequency of measurement as well as geometry of contact structure.
0924-4247/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 ( 0 1 ) 0 0 6 8 4 - 7
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52 1=t
2. Sensing principle
PS layer undergoes a change in its dielectric constant and conductivity when exposed to humid atmosphere owing to the adsorption of the water vapour molecules in its micropores. Thus, PS humidity sensor has been studied either by monitoring the change in capacitance or conductance of the PS layer under humidity exposure. 2.1. Capacitive sensing In order to explain the change in dielectric constant of PS layer and provide a theoretical basis for optimising the structure of the capacitive sensor, a simple theoretical model considering PS layer as a uniform network of partly oxidised Si nanowires and voids has been chosen following Rittersma and Benecke [11] (Fig. 1). A generalised effective medium approximation (GEMA) describes the effective dielectric constant of an n-phase mixture (Em) of dispersed spherical particles as [12±14] n X i1
1=t
vi
1=t
Ei
1=t
Em
0
1=t
Ei jP = 1
jP Em
(1)
where Ei is the dielectric constant of phase i with volume fraction vi , jP the percolation volume fraction and t is the non-linearity correction factor. Applying GEMA in case of PS dielectric layer, we can express the effective dielectric constant of the layer (EPS) as vSi
1=t ESi
1=t
1=t EPS
ESi jP = 1
1=t
jP EPS
1=t
vP
1=t
vox
1=t Eox 1=t
Eox jP = 1
1=t EPS
1=t
jP EPS
1=t
EP
EPS
EP jP = 1
1=t
jP EPS
0
(2)
where ESi, Eox and EP refer to statistical average values of dielectric constants while vSi , vox and vP refer to fractional volumes of silicon, silicon oxide and air in the pore, respectively. Again, if P be the porosity and r be the volume ratio of SiO2 and Si, one can write, vox r 1 P= 1 r and vSi 1 P= 1 r so that, 1=t
1=t
ESi EPS 1 P 1 r E1=t jP = 1 jP E1=t Si
45
PS
1=t
r 1 P Eox EPS 1=t 1 r Eox jP = 1 jP E1=t PS
1=t
P
1=t
EP
1=t
EPS
EP jP = 1
1=t
jP EPS
0
(3)
When PS layer is exposed to humid atmosphere, the pores get soaked with water vapour resulting in change of effective dielectric constant of the PS layer (EPSw) as vapour molecules diffuse into the pores until an equilibrium moisture content (EMC) inside the porous dielectric is reached. Water vapour condenses in all pores having radii less than Kelvin radius rK defined as rK
2gMw cos y rw RT ln pw =ps
(4)
where g is the surface tension, y the contact angle, rw the density of water, Mw the molecular mass of water, pw the water vapour pressure and ps is the saturation pressure at a specified temperature. Let jw represent the volume fraction of pores filled with condensed water vapour in the porous dielectric with pore radii less than rK. The response time of the sensor is dependent on the EMC, which in turn depends upon the relative humidity and the pore radius distribution (morphology) of the porous silicon layer. The effective dielectric constant of the porous silicon layer changes to EPSw in this situation so that Eq. (3) is modi®ed to 1=t
1=t
ESi EPSw 1 P 1=t 1 r E jP = 1 jP E1=t
PSw 1=t
Si
1=t
r 1 P Eox EPSw 1=t 1 r Eox jP = 1 jP E1=t
PSw
jw P 1
1=t Ew 1=t
1=t EPSw
Ew jP = 1 jw P
1=t
jP EPSw 1=t
1=t
1=t
EP
EPSw
EP jP = 1
1=t
jP EPSw
(5)
where Ew refers to the dielectric constant of water. EPSw undergoes change with relative humidity through the dependence of jw with relative humidity. 2.2. Conductive sensing In case of conductive sensing also, GEMA describes the effective conductivity of the PS layer (sPSw) as 1=t
1=t
sSi sPSw 1 P 1 r s1=t jP = 1 jP s1=t
PSw 1=t
Si
1=t
r 1 P sox sPSw 1=t 1 r sox jP = 1 jP s1=t
PSw
Fig. 1. PS layer as a uniform network of partly oxidised Si nanowires and voids.
0
jw P
1=t
sw 1=t
sw jP = 1
1=t
sPSw
1=t
jP sPSw
46
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
1
jw P
1=t
1=t sP
sP
jP = 1
1=t
sPSw
1=t jP sPSw
0
(6)
where sSi, sox and sP refer to statistical average values of conductivity of silicon, silicon oxide and air in the pore, respectively. The effective conductivity is determined by the relative contributions of the oxide, Si nanowires, pores and of course jw, which is dependent on relative humidity. Eqs. (5) and (6) clearly indicate that changes in both capacitance and conductance of the porous layer with changes in relative humidity will depend signi®cantly on the porosity and the volume ratio of the porous layer which are again determined by the pore size and pore distribution as discussed earlier. The conductivity modulation is further accentuated by the nanostructures of the pores (<5 nm) which cause band gap widening due to quantum con®nement of mobile carriers. 2.3. Parasitic capacitances and resistances Parasitic resistances and capacitances, which are usually much less sensitive to changes in relative humidity are invariably associated with the active resistances and capacitances of the porous silicon layer. The origin of these parasitic resistances and capacitances are (i) contact resistance and contact capacitance, (ii) bulk silicon layer resistance and capacitance, (iii) inter-connecting metal layer resistance and capacitance and (iv) diffusion and depletion capacitance and resistance of the heterojunction interface between PS layer and bulk silicon layer. It is extremely dif®cult to separate out the contributions of each of these parasitic components. In order to assess the overall impact of the parasitic resistances and capacitances that are invariably associated with the porous silicon humidity sensor, a simple model of an equivalent lumped parallel combination of parasitic resistance (R2) and parasitic capacitance (C2) have been assumed to be connected in series with the parallel combination of active layer resistance (R1) and active layer capacitance (C1) of the porous silicon layer as shown in Fig. 2. Similar models have in fact been used for the analysis of thin ®lm devices [15].
In Fig. 2, C1 and R1 represent the capacitance and resistance of the active porous silicon device while C2 and R2 represent the associated parasitic capacitances and resistances. If R1, C1 and R2, C2 are replaced in the equivalent circuit by Req and Ceq, the admittances of the equivalent circuit is Y Geq joCeq where Y
Y1 Y2 ; Y1 Y2
Geq
Y1 G1 joC1
and
Y2 G2 joC2
G1 G2 G1 G2 o2 C12 G2 C22 G1 G1 G2 2 o2 C1 C2 2
(7)
and Ceq
G21 C2 G22 C1 o2 C1 C2 C1 C2 G1 G2 2 o2 C1 C2 2
(8)
2.4. Signal frequency optimisation It is interesting to note that both Req (1/Geq) and Ceq are frequency dependent. Thus, the relative contributions of the parasitic and active components on Req and Ceq depend signi®cantly on the choice of the signal frequency. For example, for very low frequency (o ! 0), Req G1 G2 =G1 G2 R1 R2 and hence for dc measurements, the measured resistance actually indicates the sum of the active device resistance (R1) and the parasitic resistance (R2). If R2 is signi®cant with respect to R1, the conductive perturbation is reduced considerably assuming that the parasitic resistance (R2) is much less sensitive to change in relative humidity than the active porous layer resistance (R1). This is often overlooked in earlier reports on conductive humidity sensors [6]. In the high frequency range, on the other hand, Geq ! C12 G2 C22 G1 = C1 C2 2 , which is constant and independent of frequency. For capacitive sensing again, in the high frequency range, Ceq ! C1 C2 = C1 C2 . Since the active capacitance C1 is usually much larger than the parasitic capacitance C2, C eq C2 and thus, at high frequency, the measured capacitance is principally determined
Fig. 2. (a) Circuit diagram for measurement of response characteristics of the device. (b) Equivalent circuit diagram for measurement of response characteristics of the device.
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
47
by the parasitic capacitance rather than the active capacitance. This leads to reduced capacitance changes of the device at high frequency. At relatively low frequency, on the other hand, Ceq ! G21 C2 G22 C1 = G1 G2 2 . Under normal circumstances, i.e. assuming R1 @ R2 or G1 ! G2, C eq C1 and hence the measured capacitance (Ceq) truly represents the active capacitance (C1) of the PS sensing device. This implies that the capacitive changes of the humidity sensor would be much higher in the low frequency range. 3. Contact geometry Usually, for PS humidity sensor, one contact has been taken from the top PS surface and the other contact has been taken from the bulk Si surface at the bottom [3±6]. Recently, however, a mesh electrode has been used at the top PS surface for better performance of the sensor [11]. For Fig. 3a this type of sandwich structure, the relatively small capacitance of the bulk Si, which is in series with the much larger capacitance of the PS layer may dominate the equivalent capacitance of the device, and thus reduces the sensitiveness of the PS layer to humidity changes. On the other hand, if both the contacts are taken from surface membrane of the PS layer [16] (Fig. 3b), the effective capacitance is dictated by the capacitance of the PS layer which is in parallel with that of the bulk Si and thus any change in the effective dielectric constant of the PS layer will readily be detected in this contact structure. Fig. 4 shows the theoretical computations of changes of capacitances for different porosity values for both the sandwich and the membrane structure. One observes that the relative change in capacitance of the membrane structure is far greater than that of the usual sandwich structure. The basic structure of the humidity sensor based on PS dielectric membrane reported in this paper is shown in Fig. 5. An additional advantage of using a membrane is that, it allows the placement of a heating resistor or microhotplate underneath the membrane. This microhotplate plays a signi®cant role for resetting the device as refresh resistor [5,11].
Fig. 4. Theoretical computations of sensitivity of capacitances with respect to porosity. Both the contacts are taken from top surface of PS layer: (a) neglecting the effect of bulk silicon; (b) considering the effect of bulk silicon. (c) Contacts are taken from top surface of PS layer and bottom surface of bulk silicon (sandwich structure).
4. Experiment Silicon wafers of p-type (1 0 0) orientation and 7 cm2 area having resistivity in the range of 1±2 O cm were anodised in a cell specially developed for the purpose [17]. The wafers actually act as a seal between the front and rear regions of the cell. The front region of the cell was ®lled with the mixture of HF and CH3OH [17,18] while the rear portion was immersed in KCl solution. The back contact metallisation was done by screen printing of silver±aluminium paste and its subsequent ®ring. The anodisation current density was varied from 2 to 50 mA/cm2 and HF concentration in methanol was varied from 24 to 48%. 4.1. Estimation of porosity and nanocrystallite dimensions The porosity of the samples were estimated gravimetrically [19]. Samples before and after anodisation were weighed by a precision microbalance. Then the porous layers were removed by dipping in dilute NaOH solution and the wafers were weighed again. The porosity was then determined by using the relation: m1 m2 Pm m1 m3 where m1 is the mass of the sample before anodisation, m2 the mass of the sample after anodisation and m3 is the mass
Fig. 3. (a) Contacts are taken from top surface of PS layer and bottom surface of bulk silicon (sandwich structure). (b) Contacts are taken from the top surface of PS layer.
Fig. 5. Schematic diagram of PS humidity sensor.
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J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
of the sample after complete dissolution of the porous layer. The masses were measured with the help of a microbalance with a maximum error of 0.1 mg and the maximum percentage error is found to be 5% in the measurement of porosity for the lowest porosity sample. For higher porosity samples this error reduces to 1%. To estimate the sizes of the nanocrystallites in the PS layer, X-ray powder diffraction pattern of three different samples with different anodisation parameters were measured. From the broadening of the X-ray diffraction peak at diffraction angle 28.68 of porous silicon, the nanocrystal diameter has been estimated [18]. An alternative method to estimate the nanocrystallite diameters by measuring the peak wavelength (lp) of the photoluminescence spectra of the various samples with different anodisation parameters has also been employed [20]. PL spectra of the samples were measured in a standard photoluminescence measurement setup using ORIEL-7070 under UV excitation wavelength 350 nm. 4.2. Device fabrication As stated earlier, the device structure for the PS humidity sensor developed in this work has a membrane structure as shown in Fig. 5. The membrane structure has been realised using porous silicon sacri®cial layer. The porous silicon absorbing layer was formed on the top surface by usual anodic etching method. Contacts on the top surface were formed by vacuum evaporation of aluminium and its subsequent heat treatment. The microheater at the back side for resetting the device was also formed by vacuum evaporation
technique of thin aluminium layer on to the back of the membrane after sacri®ce of the PS layer through a patterned shadow mask. 4.3. Humidity sensing In order to study the sensitiveness of the fabricated sensor to humidity of the environment, an experimental arrangement has been developed as shown in Fig. 6a and b. The sample is kept in a chamber which can be ®rst evacuated to <10 2 Torr by a rotary suction pump and then exposed to water vapour in a controlled manner as shown in the ®gure. The pressure inside the chamber for the entire range of humidity variation is maintained at a constant level of 1 atm by allowing the in¯ow of dry nitrogen in the chamber in a controlled manner. This is essential for eliminating the effect of change in the partial pressure of the environment with varying humidity level. The temperature of the sensor has been maintained constant at room temperature (258C). Humidity level inside the chamber is determined by a standard digital hygrometer (QC24ACC, China). To avoid the noises and error caused by the stray capacitances and resistances of the circuit, a lock-in-ampli®er (Stanford Research 530) driven by a precision signal generator (Aplab 2004) fed through an isolation transformer is used for measurements of amplitude (A) and phase (j) of the signal output across the sample. The equivalent resistance and capacitance of the porous silicon samples at different humidity levels are then computed through a software developed for this purpose from the measured values of A and j. The software is based on Newton±Raphson technique for two
Fig. 6. (a) Experimental setup for measurement of response characteristics of PS humidity sensor. (b) Block diagram of the experimental setup for measurement of response characteristics of the device.
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
dimensions which yields only real values of Req and Ceq. The software is very fast and leads to precision >0.01%. Samples of different porosity are measured in this setup at different signal frequencies ranging from a few Hertz to a few hundred kiloHertz. 5. Results and discussions Fig. 7a and b show the dependence of the porosity of the PS samples on the anodisation current density (J) and HF concentration (C) in the HF:CH3OH mixture, respectively. One observes that the porosity of the samples can be varied considerably over a wide range of 40±85% by controlling either J or C or both. In this paper, C was kept constant at 24% while J was varied over the range of 2±50 mA/cm2 leading to a porosity variation from 60 to 85%. The concentration was intentionally kept at 24% instead of the usual 48% in order to improve the uniformity parameter of the PS layer [17]. Table 1 shows the typical estimated and XRD measured values of the diameters of the Si nanocrystallites of the PS layer formed at different anodisation current density and HF concentration. One observes that the PS layers formed under these given conditions (porosity in the range of 40±80%), the nanocrystallites are in the range of 3±5 nm. The nanocrystallite size can be related to the pore diameter for a given porosity for an idealised geometry of pore distribution that leads to pore sizes 1±3 nm [21], which is similar to the
Fig. 7. Dependence of the porosity of PS layer on (a) anodisation current density (J) and (b) HF concentration (C).
49
Table 1 Estimated and measured values of the Si nanocrystallite diameter C (%)
J (mA/cm2)
lp (nm) (measured)
Si nanocrystallite diameter (nm) Computed
From XRD
48 48 48 48 36 30 30 24
10 15 20 30 20 20 30 20
680 670 660 650 640 630 620 620
4.10 3.91 3.95 3.83 3.88 3.72 3.55 3.59
4.5 ± ± 3.5 ± ± 3.3 ±
values reported by O'Halloran et al. using HF:Triton X-100 surfactant solution for very good samples [9]. The volume of small micropores accounts for the very increased sensitiveness of capacitors based on these layers. 5.1. Frequency optimisation The importance of the selection of signal frequency for the measurements of conductance or capacitance changes can be realised from Figs. 8±10. In Fig. 8, one notes that, for signal frequencies below 10 kHz, the equivalent resistance of the sample changes very rapidly while it changes very slowly thereafter. This behaviour can be understood from the expression Geq of the equivalent circuit where as o ! 1, Geq becomes independent of frequency. The curves in Fig. 9 clearly depict the sensitiveness of the resistance variation with the changes in humidity corresponding to different signal frequencies ranging from 170 Hz to 103 kHz. The relative changes with humidity are more pronounced at high frequencies (>50 kHz) than that at lower frequencies (<1 kHz). At low frequencies, Eq. (7) implies that Req involves only R1 and R2, which are not so sensitive to humidity changes as can be seen from Eq. (5). But at high
Fig. 8. Variation of equivalent resistance with frequency for a 70% porosity sample at 70% relative humidity.
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J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
Fig. 11. Variation of normalised equivalent capacitance with relative humidity for various samples having different porosity. Fig. 9. Variation of equivalent resistance with relative humidity for various frequency ranges for a 70% porosity sample.
frequencies, Req is determined by C1 and C2 as can be seen from Eq. (7). Since, C1 is strong function of humidity, Req also undergoes much greater relative changes with humidity in this frequency range. In the case of capacitive sensors, relative changes in capacitance are much more pronounced at low frequencies (<1 kHz) than that at high frequencies (>10 kHz) as indicated clearly by the different curves of Fig. 10. This behaviour can be readily understood from the equivalent circuit expression (8) and earlier discussions in Section 2.4. At low frequencies, Ceq is determined by C1 since G1 ! G2 usually. On the other hand, at high frequencies, Ceq is dominated by C2, which is much smaller than C1 and relatively insensitive to humidity changes. Thus, the presence of parasitic components in the humidity sensor and the nature of sensing, whether capacitive or conductive, determine the range of signal frequencies to be selected
Fig. 10. Variation of equivalent capacitance with relative humidity for various frequency ranges for a 70% porosity sample.
for maximum sensitiveness of the sensor. It is also interesting to note that, at low frequency range, relative changes in capacitance with humidity variation is much greater than the relative changes in resistance with humidity at high frequency. Thus, capacitive sensing appears to be more desirable than conductive sensing for porous silicon humidity sensors, provided proper signal frequencies are chosen. 5.2. Porosity dependence Fig. 11 shows the variation of normalised capacitance with the variation of relative humidity in the range of 20± 85% for various samples having different porosities. One readily observes that the sensitivity initially increases with increasing porosity from 60 to 85% (curves P1±P3) but then starts decreasing as the porosity exceeds 85%. The increase in capacitive sensitiveness with increasing porosity is expected from Eq. (5). However, when the porosity reaches 85% level or more, the PS layer becomes mechanically unstable and may loose its inter-connected network structure
Fig. 12. Variation of normalised equivalent resistance with relative humidity for various samples having different porosity.
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
51
leading to a loss in sensitiveness. Thus, it appears that, porosity in the range of 80% is most desirable for highest capacitive sensitiveness. Similarly, in the case of conductive sensing, the relative response increases with increasing porosity up to the range of 85% (Fig. 12). Further increase in porosity to 90% and above, will lead to sudden increase in the resistance value perhaps due to loss of the inter-connected network structure, thereby decreasing the sensitiveness.
Germany. Thanks are also for Prof. Middelhoek and his group, Delft University of Technology, The Netherlands for promptly providing us the relevant literatures essential for this work. All India Council for Technical Education and University Grants Commission, Government of India ®nancially supported this work.
6. Conclusions
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The role of parasitic resistances and capacitances in determining the sensitiveness of PS humidity sensor with reference to applied frequency of the signal source, pore size and pore distribution of PS layer and geometry of contact structure has been studied. It is observed that, though for conductive sensing, contact structure is not so important, for capacitive sensing, it may play a key role, and the most desirable structure is the membrane structure where both the contacts are taken from the top PS surface. For both types of sensors, capacitive and conductive, it is observed that the sensitiveness of the device increases with increasing porosity from 60 to 85%. But for very high porosity (when porosity exceeds 85%), the device becomes insensitive. So, porosity in the range of 80% is the most desirable for both types of sensors. Finally, as because, at low frequency range, the measured capacitance truly represents the active capacitance of the device, whereas at high frequency range it is mainly governed by the parasitic capacitance, low frequency range is desirable for capacitive type sensors. For conductive sensing, at high frequency range, Req is determined by both R1, R2 and C1, C2 and since C1 is strongly dependent on humidity, the relative changes in Req with humidity is greater in the high frequency range. But for low frequency range (o ! 0), Eq. (8) indicates that the capacitive contributions are relatively small and the measured resistance represents primarily the sum of the active resistance and the parasitic resistance, which are not so sensitive to humidity changes. Thus, one can conclude that capacitive sensing at low frequencies is the most desirable situation for porous silicon humidity sensors. Acknowledgements The authors wish to acknowledge with gratitude the help and cooperation received from Dr. S.K. Dutta of the Department of Physics, City College, Calcutta and Dr. Gautam Bhattacharyya of Belur Ramakrishna Mission Residential College, Calcutta. Thanks are due to Dr. Utpal Gangopadhyay of IC Design and fabrication Centre, Jadavpur University for his cooperation in this work. We must also acknowledge our thanks to Dr. Z.M. Rittersma, University of Bremen, Faculty of Physics and Electrical Engineering Institute for Microsensors, Actuators and Systems (IMSAS),
References
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J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
[20] H. Saha, S. Chakraborty, S.M. Hossain, U. Gangopadhyay, A simple model to explain visible PL from porous silicon, in: Proceedings of the International Conference on Computers and Devices for Communication, Calcutta, India, 14±17 January 1998, p. 620. [21] G. Amato, C. Delerue, H.-J. von Bardeleben, Structural and Optical Properties of Porous Silicon Nanostructures, Overseas Publishers Association, Amsterdam, 1997, pp. 502±503.
Syed Minhaz Hossain was born in 1973 in India and received his MSc degree in physics in 1996 from Jadavpur University, Kolkata. He is now going to submit his PhD thesis on porous silicon-based optoelectronic devices.
Biographies
Hiranmay Saha was born in 1946 and received his MTech degree in radio physics and electronics in 1967 and PhD on solar cells and system in 1977. He is a professor in the Department of Electronics and Telecommunication Engineering and Coordinator of the IC Design and Fabrication Centre, Jadavpur University. His present research interest covers silicon solar cells, porous silicon-based devices, smart sensors and VLSI design.
Jayoti Das was born in 1974 in India and received her MSc degree in physics from Jadavpur University, Kolkata in 1998. She is now working on porous silicon-based humidity sensors as her PhD work at the Department of E.T.C.E., Jadavpur University.
Sanchita Chakraborty was born in 1972 and received her MSc degree in electronic sciences from University of Calcutta in 1996. She is now doing her PhD on device applications of porous silicon.
Role of parasitics in humidity sensing by porous silicon J. Das, S.M. Hossain, S. Chakraborty, H. Saha* Department of Electronics and Telecommunication Engineering, IC Design and Fabrication Center, Jadavpur University, Kolkata 700032, India Received 7 February 2001; received in revised form 25 May 2001; accepted 21 June 2001
Abstract Humidity sensing by porous silicon (PS) layer is commonly reported either by capacitive sensing or by conductive sensing. A critical analysis of both capacitive and conductive sensing by microporous PS layer is presented here. The in¯uences of parasitic capacitances and resistances unavoidably associated with the active porous layer on the measured changes in capacitance and resistance of the humidity sensor with variation of humidity are analysed. The role of contact geometry, signal frequency and porosity of PS layer are also discussed. It is shown that capacitive sensing is more sensitive in low frequency range owing to the relative contributions of parasitic components. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Porous silicon; Humidity sensor
1. Introduction Porous silicon (PS), which is essentially crystalline silicon with nanostructured pores preferentially etched into it to give it a sponge-like structure, is a well-known material for sensing layer in different gas and humidity sensors [1±3]. Owing to its very large surface area to volume ratio (>500 m2/cm3), PS can absorb large amounts of foreign molecules on its surface. With the presence of these molecules, many properties associated with PS will change. For example, photoluminescence (PL) ef®ciency decreases when PS is exposed to various chemicals and the ®nal PL ef®ciency depends on the dipole moment of the physically absorbed molecules [4]. Likewise, the effective dielectric constant and conductivity of PS layer will change if the PS surface is saturated with some other molecules. Therefore, a capacitance-based [5] or conductance-based [6] humidity sensor can be realised using the relative change of dielectric constant or conductivity, respectively, when moisture is adsorbed on the surface of a PS layer. For humidity sensing with ceramic layer, it is well known that both capacitance and conductance variation of a porous ceramic layer depends very much on the porosity of layer and the applied frequency [7,8]. The size and distribution of
*
Corresponding author. Tel.: 91-33-4732217/4721833; fax: 91-33-4732217. E-mail address: [email protected] (H. Saha).
pores of the ceramic humidity sensors also play very important role in determining the sensitivity and response time of a humidity sensor. Computer simulations for ceramic sensors indicate that micropores below 10 nm in diameter are slow in response while pore sizes between 1 and 30 nm are desirable for good sensitivity [9]. In a similar manner, the pore size and distribution of porous silicon humidity sensor can be varied considerably by simply controlling its formation parameters, like formation current density (J), HF concentration, illumination level, etc. [10]. Also, porous silicon is a nanostructured porous semiconductor having both capacitance and conductance that is signi®cantly dependent on applied frequency of measurement. This is further aggravated by the unavoidable presence of parasitic capacitances and resistances arising out of the contacts between different layers and interconnects of the humidity sensor. The change in the measured capacitance and conductance of a PS humidity sensor would thus depend on the selection of the frequency of the signal source and the pore size and pore distribution of the PS layer. The contact geometry on the PS surface is also important and may in¯uence considerably the measurements. These considerations have not been emphasised in some of the earlier reports [5,6,9]. The present paper aims at studying the role of the parasitic components of the PS humidity sensor in¯uencing the measured changes of the capacitance and conductance with reference to variations in its porosity and pore size, applied frequency of measurement as well as geometry of contact structure.
0924-4247/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 ( 0 1 ) 0 0 6 8 4 - 7
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52 1=t
2. Sensing principle
PS layer undergoes a change in its dielectric constant and conductivity when exposed to humid atmosphere owing to the adsorption of the water vapour molecules in its micropores. Thus, PS humidity sensor has been studied either by monitoring the change in capacitance or conductance of the PS layer under humidity exposure. 2.1. Capacitive sensing In order to explain the change in dielectric constant of PS layer and provide a theoretical basis for optimising the structure of the capacitive sensor, a simple theoretical model considering PS layer as a uniform network of partly oxidised Si nanowires and voids has been chosen following Rittersma and Benecke [11] (Fig. 1). A generalised effective medium approximation (GEMA) describes the effective dielectric constant of an n-phase mixture (Em) of dispersed spherical particles as [12±14] n X i1
1=t
vi
1=t
Ei
1=t
Em
0
1=t
Ei jP = 1
jP Em
(1)
where Ei is the dielectric constant of phase i with volume fraction vi , jP the percolation volume fraction and t is the non-linearity correction factor. Applying GEMA in case of PS dielectric layer, we can express the effective dielectric constant of the layer (EPS) as vSi
1=t ESi
1=t
1=t EPS
ESi jP = 1
1=t
jP EPS
1=t
vP
1=t
vox
1=t Eox 1=t
Eox jP = 1
1=t EPS
1=t
jP EPS
1=t
EP
EPS
EP jP = 1
1=t
jP EPS
0
(2)
where ESi, Eox and EP refer to statistical average values of dielectric constants while vSi , vox and vP refer to fractional volumes of silicon, silicon oxide and air in the pore, respectively. Again, if P be the porosity and r be the volume ratio of SiO2 and Si, one can write, vox r 1 P= 1 r and vSi 1 P= 1 r so that, 1=t
1=t
ESi EPS 1 P 1 r E1=t jP = 1 jP E1=t Si
45
PS
1=t
r 1 P Eox EPS 1=t 1 r Eox jP = 1 jP E1=t PS
1=t
P
1=t
EP
1=t
EPS
EP jP = 1
1=t
jP EPS
0
(3)
When PS layer is exposed to humid atmosphere, the pores get soaked with water vapour resulting in change of effective dielectric constant of the PS layer (EPSw) as vapour molecules diffuse into the pores until an equilibrium moisture content (EMC) inside the porous dielectric is reached. Water vapour condenses in all pores having radii less than Kelvin radius rK defined as rK
2gMw cos y rw RT ln pw =ps
(4)
where g is the surface tension, y the contact angle, rw the density of water, Mw the molecular mass of water, pw the water vapour pressure and ps is the saturation pressure at a specified temperature. Let jw represent the volume fraction of pores filled with condensed water vapour in the porous dielectric with pore radii less than rK. The response time of the sensor is dependent on the EMC, which in turn depends upon the relative humidity and the pore radius distribution (morphology) of the porous silicon layer. The effective dielectric constant of the porous silicon layer changes to EPSw in this situation so that Eq. (3) is modi®ed to 1=t
1=t
ESi EPSw 1 P 1=t 1 r E jP = 1 jP E1=t
PSw 1=t
Si
1=t
r 1 P Eox EPSw 1=t 1 r Eox jP = 1 jP E1=t
PSw
jw P 1
1=t Ew 1=t
1=t EPSw
Ew jP = 1 jw P
1=t
jP EPSw 1=t
1=t
1=t
EP
EPSw
EP jP = 1
1=t
jP EPSw
(5)
where Ew refers to the dielectric constant of water. EPSw undergoes change with relative humidity through the dependence of jw with relative humidity. 2.2. Conductive sensing In case of conductive sensing also, GEMA describes the effective conductivity of the PS layer (sPSw) as 1=t
1=t
sSi sPSw 1 P 1 r s1=t jP = 1 jP s1=t
PSw 1=t
Si
1=t
r 1 P sox sPSw 1=t 1 r sox jP = 1 jP s1=t
PSw
Fig. 1. PS layer as a uniform network of partly oxidised Si nanowires and voids.
0
jw P
1=t
sw 1=t
sw jP = 1
1=t
sPSw
1=t
jP sPSw
46
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
1
jw P
1=t
1=t sP
sP
jP = 1
1=t
sPSw
1=t jP sPSw
0
(6)
where sSi, sox and sP refer to statistical average values of conductivity of silicon, silicon oxide and air in the pore, respectively. The effective conductivity is determined by the relative contributions of the oxide, Si nanowires, pores and of course jw, which is dependent on relative humidity. Eqs. (5) and (6) clearly indicate that changes in both capacitance and conductance of the porous layer with changes in relative humidity will depend signi®cantly on the porosity and the volume ratio of the porous layer which are again determined by the pore size and pore distribution as discussed earlier. The conductivity modulation is further accentuated by the nanostructures of the pores (<5 nm) which cause band gap widening due to quantum con®nement of mobile carriers. 2.3. Parasitic capacitances and resistances Parasitic resistances and capacitances, which are usually much less sensitive to changes in relative humidity are invariably associated with the active resistances and capacitances of the porous silicon layer. The origin of these parasitic resistances and capacitances are (i) contact resistance and contact capacitance, (ii) bulk silicon layer resistance and capacitance, (iii) inter-connecting metal layer resistance and capacitance and (iv) diffusion and depletion capacitance and resistance of the heterojunction interface between PS layer and bulk silicon layer. It is extremely dif®cult to separate out the contributions of each of these parasitic components. In order to assess the overall impact of the parasitic resistances and capacitances that are invariably associated with the porous silicon humidity sensor, a simple model of an equivalent lumped parallel combination of parasitic resistance (R2) and parasitic capacitance (C2) have been assumed to be connected in series with the parallel combination of active layer resistance (R1) and active layer capacitance (C1) of the porous silicon layer as shown in Fig. 2. Similar models have in fact been used for the analysis of thin ®lm devices [15].
In Fig. 2, C1 and R1 represent the capacitance and resistance of the active porous silicon device while C2 and R2 represent the associated parasitic capacitances and resistances. If R1, C1 and R2, C2 are replaced in the equivalent circuit by Req and Ceq, the admittances of the equivalent circuit is Y Geq joCeq where Y
Y1 Y2 ; Y1 Y2
Geq
Y1 G1 joC1
and
Y2 G2 joC2
G1 G2 G1 G2 o2 C12 G2 C22 G1 G1 G2 2 o2 C1 C2 2
(7)
and Ceq
G21 C2 G22 C1 o2 C1 C2 C1 C2 G1 G2 2 o2 C1 C2 2
(8)
2.4. Signal frequency optimisation It is interesting to note that both Req (1/Geq) and Ceq are frequency dependent. Thus, the relative contributions of the parasitic and active components on Req and Ceq depend signi®cantly on the choice of the signal frequency. For example, for very low frequency (o ! 0), Req G1 G2 =G1 G2 R1 R2 and hence for dc measurements, the measured resistance actually indicates the sum of the active device resistance (R1) and the parasitic resistance (R2). If R2 is signi®cant with respect to R1, the conductive perturbation is reduced considerably assuming that the parasitic resistance (R2) is much less sensitive to change in relative humidity than the active porous layer resistance (R1). This is often overlooked in earlier reports on conductive humidity sensors [6]. In the high frequency range, on the other hand, Geq ! C12 G2 C22 G1 = C1 C2 2 , which is constant and independent of frequency. For capacitive sensing again, in the high frequency range, Ceq ! C1 C2 = C1 C2 . Since the active capacitance C1 is usually much larger than the parasitic capacitance C2, C eq C2 and thus, at high frequency, the measured capacitance is principally determined
Fig. 2. (a) Circuit diagram for measurement of response characteristics of the device. (b) Equivalent circuit diagram for measurement of response characteristics of the device.
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
47
by the parasitic capacitance rather than the active capacitance. This leads to reduced capacitance changes of the device at high frequency. At relatively low frequency, on the other hand, Ceq ! G21 C2 G22 C1 = G1 G2 2 . Under normal circumstances, i.e. assuming R1 @ R2 or G1 ! G2, C eq C1 and hence the measured capacitance (Ceq) truly represents the active capacitance (C1) of the PS sensing device. This implies that the capacitive changes of the humidity sensor would be much higher in the low frequency range. 3. Contact geometry Usually, for PS humidity sensor, one contact has been taken from the top PS surface and the other contact has been taken from the bulk Si surface at the bottom [3±6]. Recently, however, a mesh electrode has been used at the top PS surface for better performance of the sensor [11]. For Fig. 3a this type of sandwich structure, the relatively small capacitance of the bulk Si, which is in series with the much larger capacitance of the PS layer may dominate the equivalent capacitance of the device, and thus reduces the sensitiveness of the PS layer to humidity changes. On the other hand, if both the contacts are taken from surface membrane of the PS layer [16] (Fig. 3b), the effective capacitance is dictated by the capacitance of the PS layer which is in parallel with that of the bulk Si and thus any change in the effective dielectric constant of the PS layer will readily be detected in this contact structure. Fig. 4 shows the theoretical computations of changes of capacitances for different porosity values for both the sandwich and the membrane structure. One observes that the relative change in capacitance of the membrane structure is far greater than that of the usual sandwich structure. The basic structure of the humidity sensor based on PS dielectric membrane reported in this paper is shown in Fig. 5. An additional advantage of using a membrane is that, it allows the placement of a heating resistor or microhotplate underneath the membrane. This microhotplate plays a signi®cant role for resetting the device as refresh resistor [5,11].
Fig. 4. Theoretical computations of sensitivity of capacitances with respect to porosity. Both the contacts are taken from top surface of PS layer: (a) neglecting the effect of bulk silicon; (b) considering the effect of bulk silicon. (c) Contacts are taken from top surface of PS layer and bottom surface of bulk silicon (sandwich structure).
4. Experiment Silicon wafers of p-type (1 0 0) orientation and 7 cm2 area having resistivity in the range of 1±2 O cm were anodised in a cell specially developed for the purpose [17]. The wafers actually act as a seal between the front and rear regions of the cell. The front region of the cell was ®lled with the mixture of HF and CH3OH [17,18] while the rear portion was immersed in KCl solution. The back contact metallisation was done by screen printing of silver±aluminium paste and its subsequent ®ring. The anodisation current density was varied from 2 to 50 mA/cm2 and HF concentration in methanol was varied from 24 to 48%. 4.1. Estimation of porosity and nanocrystallite dimensions The porosity of the samples were estimated gravimetrically [19]. Samples before and after anodisation were weighed by a precision microbalance. Then the porous layers were removed by dipping in dilute NaOH solution and the wafers were weighed again. The porosity was then determined by using the relation: m1 m2 Pm m1 m3 where m1 is the mass of the sample before anodisation, m2 the mass of the sample after anodisation and m3 is the mass
Fig. 3. (a) Contacts are taken from top surface of PS layer and bottom surface of bulk silicon (sandwich structure). (b) Contacts are taken from the top surface of PS layer.
Fig. 5. Schematic diagram of PS humidity sensor.
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J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
of the sample after complete dissolution of the porous layer. The masses were measured with the help of a microbalance with a maximum error of 0.1 mg and the maximum percentage error is found to be 5% in the measurement of porosity for the lowest porosity sample. For higher porosity samples this error reduces to 1%. To estimate the sizes of the nanocrystallites in the PS layer, X-ray powder diffraction pattern of three different samples with different anodisation parameters were measured. From the broadening of the X-ray diffraction peak at diffraction angle 28.68 of porous silicon, the nanocrystal diameter has been estimated [18]. An alternative method to estimate the nanocrystallite diameters by measuring the peak wavelength (lp) of the photoluminescence spectra of the various samples with different anodisation parameters has also been employed [20]. PL spectra of the samples were measured in a standard photoluminescence measurement setup using ORIEL-7070 under UV excitation wavelength 350 nm. 4.2. Device fabrication As stated earlier, the device structure for the PS humidity sensor developed in this work has a membrane structure as shown in Fig. 5. The membrane structure has been realised using porous silicon sacri®cial layer. The porous silicon absorbing layer was formed on the top surface by usual anodic etching method. Contacts on the top surface were formed by vacuum evaporation of aluminium and its subsequent heat treatment. The microheater at the back side for resetting the device was also formed by vacuum evaporation
technique of thin aluminium layer on to the back of the membrane after sacri®ce of the PS layer through a patterned shadow mask. 4.3. Humidity sensing In order to study the sensitiveness of the fabricated sensor to humidity of the environment, an experimental arrangement has been developed as shown in Fig. 6a and b. The sample is kept in a chamber which can be ®rst evacuated to <10 2 Torr by a rotary suction pump and then exposed to water vapour in a controlled manner as shown in the ®gure. The pressure inside the chamber for the entire range of humidity variation is maintained at a constant level of 1 atm by allowing the in¯ow of dry nitrogen in the chamber in a controlled manner. This is essential for eliminating the effect of change in the partial pressure of the environment with varying humidity level. The temperature of the sensor has been maintained constant at room temperature (258C). Humidity level inside the chamber is determined by a standard digital hygrometer (QC24ACC, China). To avoid the noises and error caused by the stray capacitances and resistances of the circuit, a lock-in-ampli®er (Stanford Research 530) driven by a precision signal generator (Aplab 2004) fed through an isolation transformer is used for measurements of amplitude (A) and phase (j) of the signal output across the sample. The equivalent resistance and capacitance of the porous silicon samples at different humidity levels are then computed through a software developed for this purpose from the measured values of A and j. The software is based on Newton±Raphson technique for two
Fig. 6. (a) Experimental setup for measurement of response characteristics of PS humidity sensor. (b) Block diagram of the experimental setup for measurement of response characteristics of the device.
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
dimensions which yields only real values of Req and Ceq. The software is very fast and leads to precision >0.01%. Samples of different porosity are measured in this setup at different signal frequencies ranging from a few Hertz to a few hundred kiloHertz. 5. Results and discussions Fig. 7a and b show the dependence of the porosity of the PS samples on the anodisation current density (J) and HF concentration (C) in the HF:CH3OH mixture, respectively. One observes that the porosity of the samples can be varied considerably over a wide range of 40±85% by controlling either J or C or both. In this paper, C was kept constant at 24% while J was varied over the range of 2±50 mA/cm2 leading to a porosity variation from 60 to 85%. The concentration was intentionally kept at 24% instead of the usual 48% in order to improve the uniformity parameter of the PS layer [17]. Table 1 shows the typical estimated and XRD measured values of the diameters of the Si nanocrystallites of the PS layer formed at different anodisation current density and HF concentration. One observes that the PS layers formed under these given conditions (porosity in the range of 40±80%), the nanocrystallites are in the range of 3±5 nm. The nanocrystallite size can be related to the pore diameter for a given porosity for an idealised geometry of pore distribution that leads to pore sizes 1±3 nm [21], which is similar to the
Fig. 7. Dependence of the porosity of PS layer on (a) anodisation current density (J) and (b) HF concentration (C).
49
Table 1 Estimated and measured values of the Si nanocrystallite diameter C (%)
J (mA/cm2)
lp (nm) (measured)
Si nanocrystallite diameter (nm) Computed
From XRD
48 48 48 48 36 30 30 24
10 15 20 30 20 20 30 20
680 670 660 650 640 630 620 620
4.10 3.91 3.95 3.83 3.88 3.72 3.55 3.59
4.5 ± ± 3.5 ± ± 3.3 ±
values reported by O'Halloran et al. using HF:Triton X-100 surfactant solution for very good samples [9]. The volume of small micropores accounts for the very increased sensitiveness of capacitors based on these layers. 5.1. Frequency optimisation The importance of the selection of signal frequency for the measurements of conductance or capacitance changes can be realised from Figs. 8±10. In Fig. 8, one notes that, for signal frequencies below 10 kHz, the equivalent resistance of the sample changes very rapidly while it changes very slowly thereafter. This behaviour can be understood from the expression Geq of the equivalent circuit where as o ! 1, Geq becomes independent of frequency. The curves in Fig. 9 clearly depict the sensitiveness of the resistance variation with the changes in humidity corresponding to different signal frequencies ranging from 170 Hz to 103 kHz. The relative changes with humidity are more pronounced at high frequencies (>50 kHz) than that at lower frequencies (<1 kHz). At low frequencies, Eq. (7) implies that Req involves only R1 and R2, which are not so sensitive to humidity changes as can be seen from Eq. (5). But at high
Fig. 8. Variation of equivalent resistance with frequency for a 70% porosity sample at 70% relative humidity.
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J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
Fig. 11. Variation of normalised equivalent capacitance with relative humidity for various samples having different porosity. Fig. 9. Variation of equivalent resistance with relative humidity for various frequency ranges for a 70% porosity sample.
frequencies, Req is determined by C1 and C2 as can be seen from Eq. (7). Since, C1 is strong function of humidity, Req also undergoes much greater relative changes with humidity in this frequency range. In the case of capacitive sensors, relative changes in capacitance are much more pronounced at low frequencies (<1 kHz) than that at high frequencies (>10 kHz) as indicated clearly by the different curves of Fig. 10. This behaviour can be readily understood from the equivalent circuit expression (8) and earlier discussions in Section 2.4. At low frequencies, Ceq is determined by C1 since G1 ! G2 usually. On the other hand, at high frequencies, Ceq is dominated by C2, which is much smaller than C1 and relatively insensitive to humidity changes. Thus, the presence of parasitic components in the humidity sensor and the nature of sensing, whether capacitive or conductive, determine the range of signal frequencies to be selected
Fig. 10. Variation of equivalent capacitance with relative humidity for various frequency ranges for a 70% porosity sample.
for maximum sensitiveness of the sensor. It is also interesting to note that, at low frequency range, relative changes in capacitance with humidity variation is much greater than the relative changes in resistance with humidity at high frequency. Thus, capacitive sensing appears to be more desirable than conductive sensing for porous silicon humidity sensors, provided proper signal frequencies are chosen. 5.2. Porosity dependence Fig. 11 shows the variation of normalised capacitance with the variation of relative humidity in the range of 20± 85% for various samples having different porosities. One readily observes that the sensitivity initially increases with increasing porosity from 60 to 85% (curves P1±P3) but then starts decreasing as the porosity exceeds 85%. The increase in capacitive sensitiveness with increasing porosity is expected from Eq. (5). However, when the porosity reaches 85% level or more, the PS layer becomes mechanically unstable and may loose its inter-connected network structure
Fig. 12. Variation of normalised equivalent resistance with relative humidity for various samples having different porosity.
J. Das et al. / Sensors and Actuators A 94 (2001) 44±52
51
leading to a loss in sensitiveness. Thus, it appears that, porosity in the range of 80% is most desirable for highest capacitive sensitiveness. Similarly, in the case of conductive sensing, the relative response increases with increasing porosity up to the range of 85% (Fig. 12). Further increase in porosity to 90% and above, will lead to sudden increase in the resistance value perhaps due to loss of the inter-connected network structure, thereby decreasing the sensitiveness.
Germany. Thanks are also for Prof. Middelhoek and his group, Delft University of Technology, The Netherlands for promptly providing us the relevant literatures essential for this work. All India Council for Technical Education and University Grants Commission, Government of India ®nancially supported this work.
6. Conclusions
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The role of parasitic resistances and capacitances in determining the sensitiveness of PS humidity sensor with reference to applied frequency of the signal source, pore size and pore distribution of PS layer and geometry of contact structure has been studied. It is observed that, though for conductive sensing, contact structure is not so important, for capacitive sensing, it may play a key role, and the most desirable structure is the membrane structure where both the contacts are taken from the top PS surface. For both types of sensors, capacitive and conductive, it is observed that the sensitiveness of the device increases with increasing porosity from 60 to 85%. But for very high porosity (when porosity exceeds 85%), the device becomes insensitive. So, porosity in the range of 80% is the most desirable for both types of sensors. Finally, as because, at low frequency range, the measured capacitance truly represents the active capacitance of the device, whereas at high frequency range it is mainly governed by the parasitic capacitance, low frequency range is desirable for capacitive type sensors. For conductive sensing, at high frequency range, Req is determined by both R1, R2 and C1, C2 and since C1 is strongly dependent on humidity, the relative changes in Req with humidity is greater in the high frequency range. But for low frequency range (o ! 0), Eq. (8) indicates that the capacitive contributions are relatively small and the measured resistance represents primarily the sum of the active resistance and the parasitic resistance, which are not so sensitive to humidity changes. Thus, one can conclude that capacitive sensing at low frequencies is the most desirable situation for porous silicon humidity sensors. Acknowledgements The authors wish to acknowledge with gratitude the help and cooperation received from Dr. S.K. Dutta of the Department of Physics, City College, Calcutta and Dr. Gautam Bhattacharyya of Belur Ramakrishna Mission Residential College, Calcutta. Thanks are due to Dr. Utpal Gangopadhyay of IC Design and fabrication Centre, Jadavpur University for his cooperation in this work. We must also acknowledge our thanks to Dr. Z.M. Rittersma, University of Bremen, Faculty of Physics and Electrical Engineering Institute for Microsensors, Actuators and Systems (IMSAS),
References
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[20] H. Saha, S. Chakraborty, S.M. Hossain, U. Gangopadhyay, A simple model to explain visible PL from porous silicon, in: Proceedings of the International Conference on Computers and Devices for Communication, Calcutta, India, 14±17 January 1998, p. 620. [21] G. Amato, C. Delerue, H.-J. von Bardeleben, Structural and Optical Properties of Porous Silicon Nanostructures, Overseas Publishers Association, Amsterdam, 1997, pp. 502±503.
Syed Minhaz Hossain was born in 1973 in India and received his MSc degree in physics in 1996 from Jadavpur University, Kolkata. He is now going to submit his PhD thesis on porous silicon-based optoelectronic devices.
Biographies
Hiranmay Saha was born in 1946 and received his MTech degree in radio physics and electronics in 1967 and PhD on solar cells and system in 1977. He is a professor in the Department of Electronics and Telecommunication Engineering and Coordinator of the IC Design and Fabrication Centre, Jadavpur University. His present research interest covers silicon solar cells, porous silicon-based devices, smart sensors and VLSI design.
Jayoti Das was born in 1974 in India and received her MSc degree in physics from Jadavpur University, Kolkata in 1998. She is now working on porous silicon-based humidity sensors as her PhD work at the Department of E.T.C.E., Jadavpur University.
Sanchita Chakraborty was born in 1972 and received her MSc degree in electronic sciences from University of Calcutta in 1996. She is now doing her PhD on device applications of porous silicon.