Appl. Phys. A 71, 695–700 (2000) / Digital Object Identifier (DOI) 10.1007/s003390000506 Applied Physics AMaterialsScience & Processing

Impedance spectroscopic study of Si/HF-electrolyte systemduring Si dissolutionB.K. Patel, S.N. Sahu∗

Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India

Received: 10 December 1999/Accepted: 12 February 2000/Published online: 13 September 2000 – Springer-Verlag 2000

Abstract. Porous silicon (PS) has been synthesized by anodicetching in HF and ethanol electrolyte. The in situ current–voltage characteristic clearly identify the pore formation,transition and electropolishing regimes. The experimentallyobserved impedance and phase as a function of frequency(Bode plots) reasonably agree with theoretically simulatedBode plots drawn by considering the equivalent circuit forPS/electrolyte.

PACS: 98.80.Cq; 61.30.Jf; 12.39.Dc

In recent years, there has been considerable interest in thestudy of porous silicon [1–15] vis-a-vis the in situ character-ization [16–29] of Si/HF electrolyte system in order to iden-tify the potential distribution across the interface and porousSi formation mechanisms. Porous Si formation and the oc-currence of electropolishing under anodic bias depend uponvarious process parameters viz. crystal orientation, conduc-tivity type, dopant concentration and electrolyte stirring rate,etc. Under forward bias, porous silicon formation is asso-ciated with divalent Si dissolution whereas a tetravalent Sidissolution leads to an electropolishing effect. The overallelectrochemical reaction at the electrode/electrolyte interfaceis given by [24]

Si+4OH−ad+nh+ −→ SiO2 +2H2O+ (4−n)e− (n ≤ 4)

|+6HF

−→ H2SiF6 +2H2O , (1)

Si+2F−ad+4HF+nh+ −→ H2SiF6 +2H2O (n ≤ 2) , (2)

where OH−ad and F−ad are the adsorbed ions, and h+ and e−

represent hole and electron, respectively. Reaction (1) clearlysuggest that electropolishing proceeds through an intermedi-ate oxide layer present at the silicon surface [30, 31]. Despite

∗Corresponding author. (E-mail: sahu@iopb.res.in)

enormous work on porous Si, controversies still exist as topotential distribution across the electrode/electrolyte inter-face in low forward bias (porous silicon formation) regimewhere one group advocates the dominant contribution is fromthe space charge [20], and another group suggests it to befrom the Helmholtz layer [21]. Although different techniqueshave been used to study porous Si and its formation mech-anism, useful information in general is obtained from the insitu current(I)−voltage(V ) studies. However, theI − V studyalone will not be sufficient to indicate the oxide formation.Hence, theI −V studies in conjunction with impedance spec-troscopic measurements are expected to provide useful infor-mation as to the porous Si formation, the oxide growth andin general characterize in detail the Si/HF-electrolyte inter-face under bias. In fact, impedance spectroscopy is a pow-erful tool to identify the potential distribution across theelectrode/electrolyte interface as well as it throw light on theeffective reactance arising due to the inductive, capacitive andresistive elements of the system. Application of the ac biasgenerally changes the reactance of the inductance and cap-acitance which influence the impedance spectra with respectto its frequency and give clear information of the depletion,inversion and accumulation conditions.

The present work reports the in situ study of p-Si/HFelectrolyte interface by in situI − V and impedance measure-ments.

1 Experimental

p-type (10−2 Ω cm) silicon with (100) orientation was used.After standard chemical cleaning, the back sides of the waferswere vacuum coated with aluminum to provide an ohmicelectrical back contact and were covered by an acid-proofwax. The electrolyte consisted of ethanol and HF(49%) mix-ture (1: 1). Anodization was carried out at 22C using a stan-dard electrochemical cell as shown in Fig. 1a. The elec-trode potential was controlled with a EG&G PAR Model273 potentiostat and the current was plotted with an X−Y

696

−1.5 0.5 2.5 4.5Voltage vs SCE (V)

−5.0

45.0

95.0

145.0

J (

mA

/cm

2)

VReferenceElectrode

PotentiostatStirrer

(a) (b)

Fig. 1. a Schematic of an electrochemical cell. b J − V characteristic ofp-Si/HF-electrolyte junction under different applied potential. Dashed linescorresponds to the applied potential at which impedance has been measured

recorder. For impedance measurements a variable-frequencyLCR meter was used in conjunction with a galvanostat. Thepertubating signal was a sine wave of 5 mV rms ampli-tude. Experiments were generally carried out by immers-ing a sample and monitoring the open-circuit potential untila steady-state value was recorded. At this time the poten-tial was stepped incrementally in the positive direction andimpedance spectra were measured at the steady-state currentconduction.

2 Results and discussion

2.1 Current–voltage (I − V) analysis

Shown in Fig. 1b is the I − V characteristic of p-type siliconin aqueous HF-electrolyte system. The characteristic showssome basic similarities to the normal Schottky diode behav-ior[18] where in the reverse bias, there is very low currentflow through the junction and at forward bias it increases ex-ponentially along with two peak structures. In the absenceof the two peak structures of the forward-biased I − V char-acteristic the spectra look more like the shape of a normalSchottky diode. The two peak structures we ascribe to thecharge trapping/de-trapping when two localized surface stategenerated by oxide growth cross over the Fermi level (Thedetails will be published elsewhere).

In order for a current to flow across the Si/HF electrolytejunction, the electronic charge carrier should change to ionic.In the reverse bias condition silicon does not dissolve, hencea cathodic charge transfer is mediated at the Si/HF systemby the reduction of the H+ [18]. However, under anodic biasa complex phenomena for such Si/HF electrolyte system oc-curs where one visualizes both silicon dissolution and oxideformation. Based on the above, we divide the I − V charac-teristic shown in Fig. 1 tentatively into three regions. At verylow anodic potential generally pore formation occurs whereasa high anodic potential leads to electropolishing. The poten-tial regime (0.0 to 1.0 V(SCE)) below the 1st current peakcan be identified as pore formation regime whereas above2.4 V(SCE) (2nd current peak) can be identified as electropol-ishing regime. The intermediate regime (1.0 to 2.4 V(SCE)) isthe transition region where simultaneously pore, oxide forma-tion and electropolishing occur.

3 Impedance analysis

Figure 2a shows the frequency dispersion of impedanceof p-Si/HF+ethanol electrolyte interface as a function ofapplied potential. In the low-frequency regime (0.1 kHzto 5 kHz) the impedance of the interface decreases from4 MΩ to 80 kΩ when the applied potential is increasedfrom −0.3 to 4.0 V(SCE); except for −1.0 V(SCE) a devi-ation is clearly seen. At intermediate frequency (5 kHz to60 kHz) the impedance spectra are linear but shift with fre-quency as a function of applied potential. For example, for−1.0 V(SCE) the impedance spectra shifts to the lower fre-quency side whereas for higher forward bias (4.0 V(SCE))the spectra shift to the higher frequency side as a function ofapplied potential. Note that for all the applied potentials, theimpedance spectra appear to converge to a common point andthen deviate from their linearity at about 100 kHz frequency.The inset shows the magnified version of the impedance spec-tra in the frequency range 10 kHz to 15 kHz. The shifting ofthe impedance curve with applied bias is clearly resolvable.

Figure 2b shows the frequency dispersion of phase asa function of applied potential for the same p-Si/HF+ethanolelectrolyte interface. At low frequencies of about 0.1 kHz to5 kHz the phase decreases with increasing forward bias as inFig. 2a but deviation is seen for −1.0 V(SCE) as is the casewith Fig. 2a. The phase spectra too at all potentials mergeto a common point and deviate from the linearity at about100 kHz as is the case with the impedance spectra shownin Fig. 2a.

In order to understand the above features as shown inFig. 2 we have to understand first the semiconductor elec-trolyte interface. PS growth is normally associated with Sidissolution, oxide formation and electropolishing. In anycase the interface is mainly between the PS/electrolyte andPS/SiOx/electrolyte under forward bias as shown in Fig. 3a,bwhere a space-charge layer inside the semiconductor con-sisting of ionized acceptors and dense positively chargedions forming a Helmholtz layer is formed towards the elec-trolyte. For sufficiently concentrated solution the potentialdrops across the Helmholtz layer can be neglected and the

Fig. 2. a a Impedance diagram (Bode plots) in both reverse and forwardbias conditions. Closed circle, square and triangle are, respectively, −1.02,−0.15, 0.63 V(SCE) whereas open circle, square and triangle are 0.93, 2.13and 4.0 V(SCE), respectively. b Phase spectra as a function of frequencyunder different potentials as given in a

697

voltage drops across the system are almost completely sup-ported by the depletion layer alone whose thickness and cor-responding electric field depend upon the carrier concentra-tion of the semiconductor. Figure 3c,d represents the chargedistribution of the above semiconductor/electrolyte systemunder forward bias, which demonstrates the charge neutralityconditions for the two types of interfaces.

Shown in Fig. 3e,f is the energy band scheme of thePS/HF-electrolyte and PS/oxide/HF+ethanol electrolyteunder a small reverse bias (depletion condition) where a smalldownward band bending has been taken into account. Increas-ing the reverse bias, one attains the inversion region and theforward bias give the accumulation condition.

In order to have a detailed understanding of the en-ergy band scheme, one need to discuss the equivalentcircuits [29, 32] for the two interfaces shown in Fig. 3g,h.Note that the capacitance arising due to the surface state (Css)and oxide (Cox) layer are in parallel and series with space-charge capacitance (Csc). The other quantities Rsc, Rss, Rox,and Rel are, respectively, the resistances arising from spacecharge, surface state, oxide layer, electrolyte and their com-binations are shown in equivalent circuit Fig. 3g,h. In thepresence of surface state the inverse of Helmholtz layercapacitance is very low (see Fig. 3g,h). Similarly the bulksemiconductor resistances being negligible due to high dop-

ω ω

+++

+++++

++

+++

−

− −−−

−

− −−−

−

−−

−− −

− −−−

−

−−−−

−−−

−−

−−

++

++++++

+++++++

++++

+ +--

X X

ρ ρ

\/\/\/\

\/\/\/\

\/\/\/\)|

)|

\/\/\/\

)|

\/\/\/\\/\/\/\

)|

\/\/\/\

)|SS

a b

c d

E S E O S

HF:Eth Solution HF:Eth SolutionP-Si P-Si

LayerGauy-HelmholtzLayer Oxide

Space chargeLayer

e

g

f

h

F

EEEv

Fi

VOX

RelC RSS

RSC RR

RSSCSS

SC

elROX

C CCOX

SCSC

EF,el

Ec

FiE

FEvE

E c

Gauy-Helmholtz Space chargeLayer

Layer

F,elE

Fig. 3a–h. Schematic of the HF-ethanol electrolyte/p-Si interface (a),charge distribution (c), energy band scheme (e), and the equivalent circuit(g) without an insulating layer. Whereas (b), (d), (f) and (h) are the samein the presence of an insulating layer. Ec, Ev, EF, EFi and EF, el are, re-spectively, conduction band edge, valance band edge, Fermi level, intrinsicFermi level of semiconductor and pseudo-Fermi level of electrolyte. Vox ispotential drops across oxide layer

ing compared to electrolyte resistance Rel are also neglected.The total equivalent capacitance Ceq is given by [29]

1

Ceq= 1

Csc+ 1

Cox, (3)

with

Cox = A fRεε0

dox, (4)

where A, fR, ε, ε0, dox are, respectively, the area, surfaceroughness factor, dielectric constant, permitivity of the freespace and the thickness of the oxide layer.

Since in most cases the measured electrode/electrolyte in-terfaces do not represent ideal capacitive behavior, the equiva-lent circuit is modified by describing the system capacitancein terms of a constant-phase element (CPE).

The model [32] describing the frequency-dependentimpedances for an electrolytic oxide growth takes account ofRel, Rox, Cox, Css, Rss, Cdl and Rdl. The impedance of theabove-mentioned equivalent circuit as shown in Fig. 4 can beexpressed as [29, 32, 33]

Z(ω) = Rel +[

1

Rct+ω0

(jω

ω0

)α

Ceq

]−1

, (5)

where ω = 2π f is angular frequency of the ac voltage. Z de-notes the complex system impedance, j = (−1)0.5, and α isthe exponent of the CPE which becomes 1 for an ideal ca-pacitor and ω0 was set to 2π f0 ( f0 = 1000). The real andimaginary part of the complex impedance, Z(ω) was decon-voluted using De Moivers theorem and expressed as

Zre(ω) = Rel + a(ω)

a(ω)2 +b(ω)2(6)

and

Z img(ω) = − b(ω)

a(ω)2 +b(ω)2, (7)

where

a(ω) = 1

Rct+ω1−α

0 cos

(απ

2

)Ceqω

α (8)

and

b(ω) = ωα0 sin

(απ

2

)Ceqω

α . (9)

The magnitude and phase of the impedance can be describedby

Z(ω) =(

Zre(ω)2 + Z img(ω)2) 1

2

(10)

and

φ = tan−1(

Z img(ω)

Zre(ω)

). (11)

To know the impedance behavior as a function of frequency,(11) was theoretically simulated with varied parameter such

698

as Rct, Rel and Ceq. The simulated Bode plot is shown inFig. 4. Firstly, Rct, Rel and α are kept constant and Ceqwas varied from 100 nF (dashed line) to 300 nF (thick solidline). Note that the impedance curve for 100 nF shifts to-wards the higher frequency side in the frequency range 2 kHzto 80 kHz (a similar feature also observed in the experi-mental impedance curve as shown in Fig. 2a (inset)). Sec-ondly, by varying the Rct and keeping other parameters con-stant, for 100-nF Ceq one can note that the impedance curveshifts to a higher value in the frequency range 2 kHz to0.1 kHz. On the other hand when Rel is varied alone for thesame 100-nF Ceq, the impedance curve shifts downward withdecreasing Rel.

Fig. 4. Theoretical impedance plot using (11). Inset: Simplified model as-suming nonideal capacitive behavior

-100

-50

0

50

100 -Phase (D

egree)

10-1

100

101

102

103

Frequency (kHz)

100

101

102

103

104

Impe

danc

e (O

hm)

-100

-50

0

50

100 -Phase (D

egree)

10-1

100

101

102

103

Frequency (kHz)

100

101

102

103

104

Impe

danc

e (O

hm)

-100

-50

0

50

100 -Phase (D

egree)

10-1

100

101

102

103

Frequency (kHz)10

0

101

102

103

Impe

danc

e (O

hm)

-100

-50

0

50

100 -Phase (D

egree)

10-1

100

101

102

103

Frequency (kHz)

100

101

102

103

104

Impe

danc

e (O

hm)

-100

-50

0

50

100 -Phase (D

egree)

10-1

100

101

102

103

Frequency (kHz)

100

101

102

103

104

Impe

danc

e (O

hm)

-100

-50

0

50

100 -Phase (D

egree)

10-1

100

101

102

103

Frequency (kHz)

100

101

102

103

Impe

danc

e (O

hm)

a b

c d

e f

Fig. 5a–f. Impedance spectrum (Bode plots) forp-Si/HF-electrolyte at a −1.02, b −0.15, c 0.63,d 0.93, e 2.13, f 4.0 V(SCE) with a fit according tothe model presented in Fig. 4 (inset). The continuouslines are theoretical plots

In order to explain the details of the experimental Bodeplot (Fig. 2) the data were fitted to estimate various parame-ters viz. Rct, Rel, Ceq and α etc. at different applied bias asmarked by arrows shown in Fig. 1 of the I − V curve and theplots are shown in Fig. 5a–f. Note from Fig. 5 the slope ofthe impedance Bode plots decreases when one goes from rela-tively low reverse bias to higher forward bias conditions inthe low-frequency regime (0.1 to 1.0 kHz). However, a devia-tion is clearly marked for higher reverse bias (−1.0 V(SCE))which may result due to the inversion layer as explained inFig. 1 of the I − V curve.

The charge transfer resistance, Rct estimated from Fig. 5ain the inversion layer is found to be 13 MΩ whereas that ob-tained for −0.15 V(SCE) (depletion regime) was ≈ 100 MΩwhich fast decreases initially and attains a saturation asone goes towards accumulation region (higher forward bias).A similar feature has been observed in the theoretical simu-lated Bode plots as shown in Fig. 4.

The decrease of the charge transfer resistance from de-pletion to accumulation regime can be understood as fol-lows. A higher charge transfer resistance implies a low elec-tron transfer rate normally associated in the pore-formationregime (≈ 2 electrons transfer). Now, with increase in for-ward bias one attains the transition and electropolishingregime which implies a higher electron transfer rate (≈ 4electrons transfer) [17]. This suggests that the charge trans-fer resistance should decrease and attains a saturation in theelectropolishing regime. This is in consistent with our experi-mental Bode plots.

699

The equivalent capacitance, Ceq obtained by fitting (11)was found to be potential dependent. It decreases from 300 nFat high reverse bias (inversion regime) to 100 nF at higherforward bias (≈ 4.0 V (SCE) (accumulation regime). The in-termediate capacitance corresponds to the depletion regime(−0.15 to 0.83 V(SCE)) for which the Bode plots are shownin Fig. 5b,c. However, as the forward potential is increasedone would expect an oxide growth [20, 30, 31] which wouldbe responsible for distributing the applied potential across itas well as across the depletion layer [34, 35].

Further, note that the impedance data (Fig. 2 Bode plots)meet at a common point ( f ≈ 300 kHz), which suggests theelectrolyte resistance, Rel for all potentials are to be nearlythe same. However, with increasing frequency (from 300 kHzto 1000 kHz) the impedance again increases which is in-consistent with our theoretical prediction (Fig. 4) and needsexplanation. At very high frequency the system impedanceis mainly controlled by the electrolyte resistance and alongwith it the imaginary part of the impedance which becomessmall such that other errors such as parasitic impedance ofthe electrolytic cell become important. Hence, the experi-mentally observed impedance at higher frequency does notmatch with the theoretical prediction. So far, we are dis-cussing the impedance alone. This and the phase, which wasmeasured simultaneously along with the impedance for dif-ferent bias and frequencies, are shown in Fig. 2b and sepa-rately the fit in Fig. 5 with fitting parameters the same as usedin impedance data.

From the Bode plots the phase behavior as a functionof frequency follows a similar trend as that of impedanceso the interpretation remains the same as that discussed forthe impedance spectra. However, in any case the phase angledoes not reach 90 which suggests the capacitance to benon-ideal nature, which is also confirmed from the CPE (α)value ≈ 0.8 (< 1). Interestingly, the experimental phase datadoes not match with that of the fitted one in the frequencyrange 300 kHz to 1000 kHz as is the case with impedanceand yields a negative phase value. The above clearly suggestsa dominant parasitic impedance contribution to the system asdiscussed earlier. The fitted parameters obtained from the ex-perimental Bode plots are summarized in Table 1.

Figure 6 shows the Ceq − V and Rct − V plots extractedfrom the experimental impedance data of Fig. 5a–f. From theCeq − V plots a rapid rise in the capacitance in the voltageregime −0.3 to −1.0 V(SCE) clearly suggests the contri-bution from the inversion layer whereas a slow increase incapacitance in the voltage regime −0.2 to 0.7 V(SCE) is thecontribution from the depletion layer. On the other hand theconstant decrease in capacitance with increasing forward biasis solely due to the contribution from the oxide layer. The in-

Table 1. Fitted parameters obtained from experimental Bode plots

Bias/V (SCE) Rct/MΩ Ceq/nF α Rel/kΩ

−1.02 14 300 0.8 70−0.15 100 210 0.8 750.63 30 200 0.8 760.93 14 210 0.8 902.13 3 120 .62 964.0 1.5 80 .52 120

−1.5 −0.5 0.5 1.5 2.5 3.5 4.50

20

40

60

80

100

120

Rct (

MΩ

)

−1.5 −0.5 0.5 1.5 2.5 3.5 4.5Voltage vs SCE (V)

50

150

250

350

Capaci

tance

(nF

)

−1.5 −0.5 0.5 1.5 2.5 3.5 4.5Voltage vs SCE (V)

50

150

250

350

Capaci

tance

(nF

)

−1.5 −0.5 0.5 1.5 2.5 3.5 4.50

20

40

60

80

100

120

Fig. 6. Rct − V and Ceq − V plots of the p-Si/HF electrolyte system. Datapoints are collected by fitting the experimental Bode plots

version layer effect is also reflected in the low Rct value in theRct − V plot. The nature of change in Rct in the depletion andaccumulation regimes are explained earlier.

4 Conclusions

The non-ideal porous silicon/electrolyte system shows Schot-tky behavior characteristics. The theoretically simulated Bodeplots reasonably agree with the experimental results. It hasbeen found that decrease of the charge transfer resistance,Rct with increasing forward bias suggests a different elec-tron transfer resulting in the pore, oxide formation and Sidissolution. The capacitance derived from the experimen-tal Bode plots clearly identifies the inversion around (1.0 to−0.2 V(SCE)), depletion (−0.2 to 1.2 V(SCE)), and accumu-lation (1.2 to 4.0 V(SCE)) regime.

Acknowledgements. Thanks are due to Prof. S.N. Behera and Prof. V.S. Ra-mamurthy for their helpful discussion and constant encouragement. Partialfinancial support received from IFC PAR project No. 1508-4 is gratefullyacknowledged.

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