M Pomoni

A Giannopoulou

P Kounavis
email: pkounavis@des.upatras.gr

The role of the recombination centers on the modulated photocurrent: Determination of the gap state parameters of semiconductors

Keywords: semiconductors, photoelectrical, modelling, numerical simulation, thin films PACS numbers: 71.25.M g, 71.55.Jv, 73.50.Gr

Exact expressions of the out of phase modulated photocurrent (MPC), the so-called Y signal, with a clear physical insight for a density of states (DOS) spectroscopy are derived without any approximation. It is found that apart from the capture rate of the majority carriers into the probed gap states, additional mixed contributions from the recombination processes of the free majority carriers with trapped minority carriers may be important for the Y signal of lower frequencies. The above additional contributions prevent the extraction of a reliable DOS. They become important as far as the capture coefficient for the majority carriers of the recombination centers where the minority carriers are trapped is comparable or higher than that of the recombination centers were the majority carriers are trapped. In this case, the recombination rate is relatively high and the mixed contributions from the recombination processes can be detectable in the experimental Y signal and may also induce a phase lead. Taking advantage of this behavior it can be experimentally verified when these recombination processes are negligible in order to safely extract the accurate DOS parameters.

I. INTRODUCTION

The modulated photocurrent (MPC) technique has been applied to determine the density of states (DOS) in the energy gap of various semiconductors including crystalline [1][2][3], amorphous [4][5][6][7][8][9][10], microcrystalline [11], quasicrystalline [12] as well as organic [13,14] semiconductors. This technique is very powerful as it can reveal even very low trap densities, as well as the capture coefficients. The experimental setup as is demonstrated in the sketch of Fig. 1(a) is simple and requires relatively cheap equipment. In this experiment a semiconductor film with ohmic electrodes in coplanar geometry is illuminated by two light emitted diodes (LED's) of band gap light. The one LED provides a relatively weak sinusoidally modulated light (see Fig. 1(b)) of angular modulation frequency ω generating the MPC. The second LED provides a moderate bias light generating a constant photocurrent.

The MPC is amplified by a low noise current amplifier close to the sample to minimize stray capacitance. The output from the amplifier is analyzed by a Lock-in amplifier, which provides the amplitude, i ac , of the MPC and the phase shift, φ, between the MPC and the modulated light (see Fig. 1(b)), which may be a phase lag [1,[5][6][7][8] or a small phase lead [15] . The theoretical analysis of the MPC data is based on the multiple trapping model and the derived basic expressions indicate two different regimes: that at high frequencies (ω) and/or low bias light levels, the so-called high frequency (HF) or emission-limited regime and that at low frequencies and/or high bias light levels, the so-called low frequency (LF) or trapping-limited regime.

Simple theoretical expressions with a physical insight into the MPC data have been originally presented in 1981 by Oheda [1] for the HF regime, which is typically a small portion of the experimental spectra at higher ω. Based on this analysis Bruggemann et al [6] in 1990 proposed a formula for the determination of the so-called reduced DOS (r-DOS), (c/µ)D(E ω ). This formula provides by means of the i ac and φ data the r-DOS at the probe energy level E ω for which the thermal emission rate of the majority carriers equals the modulation frequency ω. Thus by scanning ω [8,[16][17][18]] the DOS at different E ω levels can be obtained. This method is applicable exclusively for the MPC data in the HF regime. Various attempts have been made to extract information about the DOS and to determine the usually unknown ratio of the capture coefficient to the mobility of the predominated carriers, c/µ, by means of the MPC data of lower ω [9,[19][20][21][22][23][24][25][26][27][28][29][30]. However, the general [19] in 1992 and Hattori et al [20] in 1994 are very complicated to extract a simple relation between the MPC of lower ω and the DOS. For this reason an empiric expression was derived by Hattori et al [20] which was applied to determine the DOS parameters of a-Si:H by means of the MPC data obtained upon scanning the bias light level. During this scan the probe energy level (E ω ) was assumed a-priori fixed. Subsequently, in 2001 we presented a general theoretical analysis of the MPC [31] where it was shown that the E ω level can be shifted not only by the modulation frequency, but also by the bias light level. This result invalidates [32] the basic assumption of the method of Hattori et al. In our theoretical analysis [31] a simple approximate expression of the out of phase MPC signal, the so-called Y signal, was extracted. The Y signal was approximated by the capture rate of the majority carriers into the probed gap states for any frequency. This is the basis of our DOS spectroscopy, which has the advantage that it can be used to extract the capture coefficients and the density of the probed states by means of the i ac and φ data of any ω, including those at lower ω which were not utilized before [32][33][34][35][36]. Later, in 2002 Koropecki et al [37] of INTEC group and in 2004 Guenier et al [38] of LGEP group concentrated their analysis on the LF regime in which the expressions of the MPC take a relatively simpler form. They arrived to similar approximate formulas differing in the proportionality constant for the calculation of the DOS.

The above mentioned methods are based on specific assumptions which result to different simplified approximate expressions relating the MPC data with a specific probed DOS. However, the validity and the limitations of these approximations have been not extensively explored. Moreover, it was not specified when a reliable DOS can be extracted from a given set of MPC data. Recently, different studies have been devoted on the accuracy of the DOS determined from the MPC data by means of model simulations [40][41][42]. It was deduced that the capture coefficients of the gap states are important for the MPC, without to exactly understand their role [42].

Moreover, an unexplained phase lead has been obtained both experimentally and by simulations [15]. The expressions of the free electron and hole modulated densities n ac and p ac , respectively, have been extracted in our first analysis and are given by Eqs.(B3) and (B4) of Ref. [31], respectively.

It is proved convenient to express them in the form n ac = G ac /(X n + jY n ) and p ac = G ac /(X p + jY p ), where j is the imaginary unit, Y n,p and X n,p are the imaginary and real parts of the denominators of the Eqs.(B3) and (B4) of Ref. [31] and G ac is the modulated light generation rate. The experimental i ac , φ data, which are expressed in terms of the real and imaginary parts of n ac and p ac (see Eqs.( 24) and ( 25) of Ref. [31]), can be used to directly calculate the Y signal by means of

Y = µeG ac sin φ σ ac , ( 1
)
where µ is the mobility of the predominant carriers and σ ac is the modulated photoconductivity calculated from i ac . The so-calculated Y signal from the experimental data is the essential parameter of the MPC experiment, because it may be directly proportional to the probed DOS (D(E ω )) for any frequency [31].

Specifically, we have shown that the Y signal may coincide with the imaginary part Y n (Y p ), when electrons (holes) dominate. Unlikely, only an approximate expression of the above imaginary part has been obtained in our first analysis [31] relating the Y signal with the probed DOS (D(E ω )). Here the exact expression of this imaginary part is obtained without any approximation. For this purpose several species of monovalent gap state D i (E) distributions are considered with different capture coefficients c i n and c i p for the electrons and holes, respectively. This is because the energy gap consists of gap states of different origin, whereas the charge state of a given localized state is altered following a carrier capture. The electrons are assumed throughout this analysis as the majority carriers. Hence we concentrate on the exact expression of the Y n , which is the imaginary part of the denominator of the exact expression of n ac of Eq.(B3) of Ref. [31] derived without any approximation. For this purpose the factor K, which is given by Eq.(A1) in the Appendix and appears in the exact expression of n ac , is replaced by its imaginary K im and real K re parts. The derived Y n is expressed by three components as where

Y n ∼ = Y 1n + Y 2n + Y 3n , (2)
Y 1n = i E C E V d i n (E)b i ωn (E)c i n D i (E)dE, (3)
Y 2n = i E C E V d i n (E)g i (E)b i ωp (E)c i p D i (E)dE, (4)
Y 3n = i E C E V d i n (E)q i n (E)c i n D i (E)dE. (5)
In Eqs.( 3)-( 5) the following functions appear

b i ωn (E) = ωr i n (E) ω 2 + [S i (E)] 2 , ( 6
) b i ωp (E) = ωr i p (E) ω 2 + [S i (E)] 2 , ( 7
)
d i n (E) = nc i n + r i n (E) S i (E) , ( 8
)
q i n (E) = ωc i p [ng i (E) + p] ω 2 + (S i (E)) 2 , ( 9
)
g i (E) = K im S i (E)/ω -K re . ( 10
)
In the above equations we have

S i (E) = nc i n + pc i p + r i n (E) + r i p (E), where r i n (E) = c i n N C kT exp[-(E C -E)/kT ] and r i p (E) = c i p N V kT exp[-(E -E V )
/kT ] are the thermal emission rates of the electrons and holes, respectively, from a gap energy level E and kT is the thermal energy. E V and E C is the conduction and valence band edge where the effective DOS is N C and N V , respectively. The above exact expressions are appropriate to reveal all the physical processes involved in the Y n and to clarify when it is possible to extract a reliable DOS, as it is explained below.

B. The cases where a DOS spectroscopy is possible

In the present analysis it is assumed a mobility lifetime product of electrons much higher than that of the holes µ n τ n >> µ p τ p and n >> p, such that nc i n >> pc i p . Moreover, it is assumed that Y ∼ = Y n , which is obtained as far as the mobility capture time product of the majority carriers is much higher than that of minority carriers [42]. This way, our analysis is concentrated on the Y n . A similar analysis holds for the Y p as far as holes predominate and Y ∼ = Y p .

The gap states having the higher relative contribution to the Y n for any frequency are defined by the products This is the so-called probe energy level of electrons E i ωn defined by the respective maximum of the sharply peaked b i ωn (E) function of Eq.( 6) and is given by

d i n (E)b i ωn (E), d i n (E)b i ωp (E)
E C -E i ωn = kT ln c i n N C kT ω 2 + {ω i t } 2 1/2 . ( 11
)
The

(E i tp ) = ω i t .
In addition, the Y 2n from Eq.( 4) is proportional to the g i (E) of Eq.( 10), which contains the real and the imaginary parts of K. By considering that both of these parts according to Eqs.(A3) and (A4) of the Appendix are proportional to the p/n ratio and using Eq.( 8), the Y 2n for ω << ω

Y ∼ = Y 1n ∼ = 1 τ ωn = π 2 H(ω, ω t )c n D(E ωn )kT. ( 12
)
This relation is obtained from Eq.( 3) by considering that Eq.( 8) for all the probe E ωn levels gives

d i n (E) ∼ = 1
for nc i n >> pc i p and that the weighting function b i ωn (E) can be replaced by a delta function. Eq.( 12) has been already derived in our first analysis [31] for the Y n using an approximation, as is clarified in Sec.II.D. In Eq.( 12) the so-called universal H function is given by H(ω, ω t ) = 1 -(2/π)arctan(ω t /ω), which presents a step at ω t . This step generates ultimately a step in the Y signal with a characteristic decay at low ω which can be used to verify experimentally Eq.( 12). This decay is due to the fact that the electrons interacting with the probed states at E ωn , which is practically the E tn level at low ω, have an increasingly higher time with decreasing ω to thermal release to the conduction band during a modulation period. This effect results in a decrease of the Y signal and phase shift. The charge neutrality condition states that the density of the trapped electrons above E F equals the density of the trapped holes below E F . By neglecting the thermal emission rates it becomes

Specifically, if Y ∼ = Y 1n , then in the HF regime (ω >> ω t ) we have H(ω, ω t ) ∼ = 1,
nc c n nc c n + pc c p N c r = pc v p nc v n + pc v p N v r , ( 13
)
where

N c r = E c tn E F D c (E)dE and N v r = E F E v tp D v (E)dE.
It is obvious that the free carriers densities n, p are adjusted to fulfil the above condition, depending on the density of the recombination centers, as well as their capture coefficients. This is more evident from n/p = (c v p /c v n )(N v r /N c r ) which results from Eq.( 13) for

nc i n >> pc i p .
An important parameter for the photoelectric properties of a photoconductor is the recombination rate, R, which in steady state equals the dc generation rate, G dc , according to

R = G dc = nc v n pc v p nc v n + pc v p N v r + nc c n pc c p nc c n + pc c p N c r . ( 14
)
The first and second terms in the right hand side of the above relation indicate that R can be expressed by the capture rate, n/τ v n , of the free electrons into the trapped holes below E F and by the capture rate, p/τ c p , of the free holes into the trapped electrons above E F , respectively, as is shown schematically in Fig. taking place through the recombination centers below E F (down arrows in Fig. 3), which is practically governed by the c v n for a given DOS. By incorporating Eq.( 13) in Eq.( 14) the lifetimes of electrons and holes defined by τ n = n/G dc and τ p = p/G dc , respectively, are

τ n = 1 C e c c n N c r , ( 15
)
τ p = 1 c v p N v r . ( 16
)
Thus for a given DOS the capture coefficient, c v n , for electrons of the recombination centers where the minority carriers are trapped determines through the parameter C e = c v n /c c n the lifetime of electrons τ n , the photosensitivity [START_REF] Bube | Photoconductivity of Solids[END_REF] and the recombination rate, which is written as

R = C e nc c n N c r . ( 17
)
Note that although the c v p affects the p density, it has no net effect in the R and Y n , because the changes in the c v p are counteracted by the induced changes in p. Eqs.( 15) and ( 16) agree with the respective lifetimes of Simmons and Taylor theory [43], except from the parameter C e in Eq.( 15). This parameter is absent in the

Y ∼ = Y n ∼ = (1 - C e 2 )Y 1n , ( 18
= c c p /c v p .
Therefore for C e << 2 the recombination rate is sufficiently low and according to Eq.( 18) the recombination processes involved in Y 2n and Y 3n are practically kept negligible to Y n for the LF regime as well. This results in the condition of Eq.( 12), allowing a DOS spectroscopy. By contrast,

for C e > 2 according to Eq.( 18) the negative total contribution from the recombination processes involved in the Y 2n and Y 3n dominates giving rise to a negative sign for the Y n and Y signal and a phase lead (see Fig. 1(b)). A phase lead has been also reported by other authors by means of experimental data [15] and simulations without to clarify the exact underlying mechanism [40].

D. Comparison with previous analysis

The second Y 2n and third Y 3n components of the imaginary part Y n of the majority carriers derived in the present analysis are missing from our first theoretical analysis [31]. This is because it was considered that the factor K defined by Eq.(A1) in the Appendix, which is important only for the expressions of the MPC in the LF regime, can be approximated by the ratio of the free carriers dc densities p/n, whereas its imaginary part was neglected. Note that these approximations are supported by Eqs.(A3) and (A4) of the Appendix. By incorporating the above approximations, K re = p/n and K im = 0, in the exact Eqs.( 4) and ( 5), the Y 2n and Y 3n in LF regime become zero. This way, the Y n is described practically by the Y 1n of Eq.( 12), which also deduced in our first analysis. However, K re according to Eq.(A3) may be slightly higher or lower than the p/n ratio for which Eq.( 5) gives a finite value for Y 3n . In addition, although the K im in the LF regime is negligible compared to the K re , the contribution of the K im in Eqs.( 4) and ( 5) could be not always negligible. This is due to the fact that the K im appears in the above equations as a product with the ratio S i (E)/ω. This product, taking into account the expression of K im of Eq.(A4) in the Appendix, may be not negligible. Hence the above approximations adopted in our first analysis may be not sufficient to provide a negligible contribution

of Y 2n + Y 3n to Y n of low ω.
In fact, as it was deduced above the C e is the crucial parameter and a C e was simulated for C e = 1 and as a first approximation it was taken in agreement with the 1/τ ωn of Eq.( 12), which in fact is a better approximation for C e < 1 according to Eq.( 18) and our recent simulations [42]. In any case Eq.( 12), which is the essential restriction of our DOS spectroscopy, should be verified experimentally, in order to safely extract the accurate DOS by means of the general formula extracted in our previous analysis from Eq.( 12) [31] D

(E ω ) ∼ = 2 π (Y /µ)σ p eω t H(ω, ω t )kT . ( 19
)
The absolute capture coefficient for the majority carriers can be calculated from c = eω t µ/σ p by means of the characteristic frequency ω t , which is extracted according to the procedure described before [31], and the measured dc photoconductivity σ p , by considering that ω t ∼ = nc n (ω t ∼ = pc p ) when electrons (holes) dominate.

The so-derived c can be incorporated in Eq.( 11) to obtain the probed trap depths E ω

E ω = kT ln (eω t /σ p )µN 0 kT ω 2 + [ω t ] 2 1/2 , ( 20
)
for any ω, by introducing the value for the µN 0 product, where N stands for N C or N V .

The analysis originally proposed by the LGEP group [38] and later adopted by the INTEC group for simplicity is based on the hypothesis that the capture coefficients of the gap states for the electrons and holes in the entire energy gap are the same, corresponding to C e = 1. For C e = 1 Eq.( 18) reduces to

Y ∼ = Y n ∼ = Y 1n /2. ( 21
)
In the LF regime after a series expansion of H function to the first order gives H(ω,

ω i t ) ∼ = 2 π ( ω ω i t
). In addition, the phase shift, φ, is small so that tanφ ∼ = sinφ and G ac /G dc ∼ = σ ac /σ dc . By introducing these approximations in our Eq.( 19) and using Eqs.( 1),( 12) and ( 21) we arrive to the simple approximate formula

D(E t ) ∼ = 2 G dc kT tan φ ω , ( 22
)
which was proposed by LGEP group for a DOS spectroscopy. This formula using all the phase shift (φ) data in the LF regime gives a single density, which is the DOS, D(E t ), at the quasi Fermi level of the trapped majority carriers, E t . This density differs from that calculated with our Eq.( 19) using all the i ac and φ data in the LF regime by the factor of 2, due to the factor of 2 in Eq.( 21), which is the essential restriction of this method. However, this restriction (obtained with C e = 1) cannot be tested experimentally and the actual DOS cannot be obtained from Eq.( 22) in the cases of C e < 1 and C e > 1. The simulations were conducted for the fixed temperature of 300 K. Specifically, for a given free electron density n, the respective density p of free holes is numerically obtained by means of the charge neutrality condition [31,43,44]. The exact Y spectrum is calculated from Eq.( 1) and Eqs.( 24), ( 25) and (B3) of Ref. [31] by means of a simulation code. The accuracy of the numerical results is confirmed by another independent code developed for this purpose.

B. Eventual contributions from the minority carriers

For the DOS model of Fig. 4 the DOS above E F is much lower than that below E F such that τ ωn >> τ ωp . In our simulations it is considered µ n = 10µ p so that the mobility capture time product of electrons dominates, namely µ n τ ωn >> µ p τ ωp . This ensures that Y ∼ = Y n , as is evident in Fig. 5(a). It can be experimentally

C. Contributions from the probed and recombination states

The behavior of Y signal according to Eq.( 18) may depend on the parameter C e when electrons dominate. This is confirmed in the examples of Fig. 6(a) calculated for a fixed n = 1 × 10 10 cm -3

and different C e obtained upon introducing different values for c v n . Specifically, for C e < 0.5 the Y signal has a negligible dependence on the C e in agreement with Eq.( 18) and Y practically agrees with the 1/τ ωn rate calculated from Eq.( 12). This is illustrated in Fig. 7(a), which presents Y spectra (solid lines) calculated for C e = 0.1 and generation rates G dc ranging from 2.2 × 10 13 to 2.2 × 10 18 cm -3 s -1 . It can be seen the characteristic light intensity-dependent decay of the Y spectra at low ω. This behavior is also usually observed experimentally (see Fig. 10(a)) and it can be an indication that the trap-limited conduction mechanism predominates over the alternative hopping transport [START_REF] Longeaud | [END_REF]. Each characteristic decay of Y signal in Fig. 7(a) (solid lines) is in excellent agreement with that of 1/τ ωn rate (triangles) calculated from Eq.( 12). As is shown in the example of Fig. 7(a) with n = 10 10 cm -3 , the Y 2n is negative. At low ω the Y 3n is positive and counteracts a significant part of the Y 2n , so that the Y 2n + Y 3n is suppressed at very low negative values (see Fig. 6(b)). This provides that the Y 1n dominates in Y n , in very good agreement with the prediction of Eq.( 18).

Upon increasing C e , the majority carriers lifetime decreases with only a minor change in the minority carriers lifetime, in very good agreement with the predictions of Eqs.( 15) and ( 16), respectively, as is confirmed in Fig. 8(a). This way, as is shown in Fig. 8 free holes increases compared to that of free electrons, which is kept fixed. In addition, the exact K re agrees with the approximate K re and their small difference from the the p/n ratio, which is not detectable in the graphs of Fig. 8(b), is in good agreement with Eq.(A3). In this figure the recombination rate, R, increases with C e , according to the prediction of Eq.( 17). This way, the contributions from the Y 2n and Y 3n components, which are proportional to recombination rates of free electrons with trapped holes, become both negative for C e ≥ 0.5 and increase upon increasing Eq.( 18). This is quantitatively confirmed in Fig. 8(c) where the exact Y signal (solid circles) in the LF regime calculated for ω = 98 rad/s and various C e is in excellent agreement with the prediction of Eq.( 18) (solid line). It is worthy to mention that as C e increases, the restriction nc i n >> pc i p used to derive Eq.( 18) may be not valid, particularly at higher C e . In this case, it was found that only the trend of Y n is qualitatively described by Eq.( 18).

Around C e = 2 a characteristic change in the sign of the Y signal of the LF regime is predicted from Eq.( 18) so that for C e > 2 it becomes negative. A remarkable very similar behavior is also In this case, the i ac is ahead the modulated light (see Fig. 1(b)). This does not mean that the MPC in the output anticipates the modulated light in the input. In fact, as far as the periodic oscillations of the illumination continue unchanged, the MPC is influenced at some finite time in the past by the recombination processes involved in the Y 2n and Y 3n inducing the phase lead.

D. Determination of the relative contributions to the Y signal and of the DOS parameters

The above analysis showed that only for C e < 0.5 the contributions to the Y signal from the recombination are practically negligible so that reliable DOS parameters can be extracted. This possibility, as predicted above, can be experimentally verified by comparing the decay of the experimental Y signal around ω t with that of the 1/τ ωn rate. Therefore the determination of this rate is crucial. It can be calculated from Eq.( 12) by means of the ω t and D(E), which can be reconstructed from the experimental Y spectra, as is illustrated below with the aid of simulations.

The so-calculated rate we call 1/τ ω rate, as it is a reconstruction of the actual 1/τ ωn .

The ω t required for the calculation of the 1/τ ω from Eq.( 12) can be determined according to the procedure earlier presented [31,33,35] which is illustrated with the aid of the simulated example of Fig. 7(b). This procedure takes advantage of the fact that for ω = ω t the H function becomes 1/2. This is experimentally evident as a decay in the Y signal by the factor of 2 (vertical arrow) in respect to the value of the Y 0 spectrum with the same trap depth, which corresponds to a frequency higher than ω t by the factor of √ 2 = 1.41 (horizontal arrow). This is because the trap depth of Y , obtained from Eq.( 20) for ω = ω t , is obtained in the Y 0 spectrum by using ω = √ 2ω t in Eq.( 20), as the characteristic frequency of Y 0 appearing in the denominator of the above equation is practically zero. The so-determined ω t in the example of Fig. Finally, the D(E) parameter required in Eq.( 12) can be obtained from the best fit to the bias light-independent Y 0 spectrum (upper envelope of the Y spectra) using Y 0 ∼ = π 2 c n D(E ωn )kT . This requires to convert the probe trap depths (E ωn ) of the D(E) into the respective frequencies by means of Eq.( 20) as follows. In the denominator of this equation the respective ω t for the Y 0 is negligible. In the numerator the µN 0 product can be assumed if it is unknown. For the parameters ω t and σ p appearing also in the numerator, the respective values of a moderate bias light level can be used. These values are those from which c n is calculated. As D(E) is determined, it can be introduced in Eq.( 12) to calculate the 1/τ ω rate by means of ω t . Specifically, the extracted ω t of a given bias light level is used to determine for any ω the respective probe trap depth E ωn from Eq.( 20) and to specify the respective D(E ωn ), which is introduced in Eq. (12).

Upon applying the above described procedure it is reconstructed the 1/τ ω rates for all the examples of Y spectra of different C e , which can be possibly observed experimentally. These rates are plotted in Fig. 6 significantly underestimates D c (E) and does not overlap for different bias light intensities.

We have also applied the methods of the LGEP and INTEC groups to the respective MPC data of the LF regime obtained with the DOS model of Fig. 4. The characteristic frequency ω t , according to the method proposed by the authors of the above groups [41], is obtained from the frequency where the DOS calculated from Eq.( 22) deviates 10% from the respective constant value of the LF regime. This requires to obtain a single DOS value from Eq.( 22) by means of all the phase shift data in the LF regime. However, such a single DOS value for every energy is only achieved for C e < 2, as is evident from Fig. 9(d). For C e ≥ 2 the Y signal presents a steeper decay than the linear decay (see

IV. COMPARISON WITH EXPERIMENTAL RESULTS

A typical experimental example of Y spectra, which are obtained from the analysis of our MPC data of a-As 2 Se 3 sputtered films taken from Fig. 1 of Ref. [35], is presented in Fig. 10(a).

The two Y signals of weak bias illumination levels (open symbols) and the Y signal at higher ω of the moderate bias light level (solid symbols) merge into a single line, defining the bias light intensity-independent Y 0 spectrum. The decay at lower ω of the experimental Y spectrum of the moderate bias light level agrees with the characteristic decay of the 1/τ ω rate, reconstructed by means of the Y spectra and Eq.( 12) following the procedure described in SecII.D. This agreement is an experimental verification of Eq.( 12) predicted for a low C h,e when a unipolar conduction by the majority carriers dominates. A unipolar conduction is indeed taking place by holes [47] in a-As 2 Se 3 . Moreover, the above films are characterized by a high photosensitivity with a high photo to dark current ratio of the order of 10 3 , which is compatible with a low C h . Therefore the interaction of holes with the probed states dominates in the Y signal of a-As 2 Se 3 and the previously extracted [35] DOS parameters from this signal by applying our methods are reliable.

Another characteristic example of experimental Y signal is presented in Fig. 10(b). This is obtained from the DOS reported by Kleider et al [24], as calculated from the MPC data of a lightly p-type doped a-Si:H sample. Specifically, the Y spectrum is extracted from the DOS presented in Fig. 24(a) of Ref. [24] which was calculated by means of the formula of Bruggenann et al [6]. This formula is equivalent to our Eq.( 19) with H(ω, ω t ) = 1 from which it is evident in SecII.D. This is the predicted behavior for the case where the Y signal is not dominated by the interaction of the majority carriers with the probed states. This conclusion is reasonable for this lightly doped material in which mixed contributions from both carriers are expected, making impossible the extraction of a DOS.

V. CONCLUSIONS

We have obtained general exact expressions for the Y signal without any approximation which clarify all the physical processes involved in the Y signal. It was illustrated how the predominant of these physical processes can be experimentally detected, by means of examples of simulations and experimental data. Specifically, it was found that mixed contributions from the recombination of free majority carriers with trapped minority carriers may dominate in the Y signal of lower ω and may induce a phase lead complicating the extraction of a DOS. This is obtained as far as the capture coefficient for the majority carriers of the recombination centers where the minority carriers are trapped is comparable or higher than that of the recombination centers where the majority carriers are trapped, that is for C e,h ≥ 0.5. This condition for a given DOS favors a relatively lower lifetime for the majority carriers and higher recombination rate. By contrast, for C e,h < 0. The general expression of K appearing in the exact expression of n ac derived in our first analysis [31] (see Eq.(B3)) is given by

K = 1 + i E C E V 1 jω+S i (E) pc i p +r i n (E) S i (E) c i n D i (E)dE 1 + i E C E V 1 jω+S i (E) nc i n +r i p (E) S i (E) c i p D i (E)dE . ( A1
)
This expression is simplified in the LF regime (ω << ω i t ) for the case where the gap state distribution D c (E)

dominates above E F and another gap state distribution D v (E) dominates below E F . In the imaginary parts and the real parts of the numerator and denominator of Eq.(A1) some integrals are obtained which are reduced as follows. Specifically, the obtained integrals

E C E V b v,c ωn,p (E)c v,c n,p D v,
E C E V b v,c ωn,p (E) S v,c (E) c v,c n,p D v,c (E)dE can be approximated by ω 2(ω v,c t ) 2 c v,c n,p N v,c tn,p .
Upon incorporating the charge neutrality condition (Eq.( 13)) presented in Sec.II and defining

g n = N c tn N c r and g p = N v tp N v r , the expression of K becomes K ∼ = -jω( 1 ω v t + 1 2ω c t g n ) + (1 + g n ) -jω( 1 ω v t + 1 2ω v t g p ) + (1 + g p ) p n . ( A2
)
From the above relation the real and imaginary parts of K are obtained for the LF regime in the simple forms

K re ∼ = α re p n , ( A3
)

K im ∼ = ω ω v t α im p n , ( A4)
where

α re = 1 + g n 1 + g p , ( A5
)

α im = (1 + g n )(1 + gp 2 ) -(1 + gn 2 c v n c c n )(1 + g p ) (1 + g p ) 2 . ( A6
)
The parameter α re given by Eq.(A5) is usually close to unity for smooth gap state distributions above and below E F , providing that the quasi Fermi levels are separated by more than a few kT.

  derived by Longeaud and Kleider

  This work concerns a theoretical analysis of the MPC concentrated on the above addressed issues. Specifically, simple exact analytical expressions are derived in Sec.II without any approximation describing all the physical processes contributing to the MPC. It is demonstrated when and how the accurate gap state parameters can be safely extracted from a given set of MPC data. All the theoretical predictions are confirmed by means of model simulations in Sec.III and compared with experimental observations in Sec.IV.

  so that according to Eq.(12) all the experimental Y spectra of different bias light levels should merge in the bias light intensity-independent spectrum of Y 0 ∼ = π 2 c n D(E ωn) kT . The experimental Y signal with decreasing ω should start to drop around ω t from the values of Y 0 following the characteristic decay of the 1/τ ωn rate, due to the step of H function [31]. This prediction can be experimentally verified, parameters c n , ω t and D(E) required to calculate the 1/τ ωn rate from Eq.(12) can be reconstructed from the experimental Y spectra, without any a-priori assumption about the DOS. This is illustrated in Sec.III.D by means of simulation examples. C. The effect of recombination on the Y signal In the previous section it was deduced that the contributions from the recombination processes governing the Y 2n and Y 3n should have a negligible contribution to the Y signal, in order for the condition of Eq.(12) to be valid and to extract the DOS. It is then very important to specify the appropriate DOS parameters of the recombination centers which minimize these recombination processes. The exact role of the recombination centers to the dc photoconductivity and MPC can be better clarified by means of a simple DOS model with one valence band-tail like gap state distribution D v (E) below E F and another conduction band-tail like gap state distribution D c (E) above E F . It is also considered that E F lies on the minimum where the D v (E) and D c (E) overlap, so that these distributions above and below E F , respectively, vanish and are neglected. This way, it is possible to distinguish the exact role of the characteristics of each D v (E) and D c (E).

  respective expression of Simmons and Taylor original theory, because the above authors considered constant capture coefficients (c v n = c c n ) so that C e = 1. The approximate Eqs.(A3) and (A4) of K im and K re , derived in the Appendix for the LF regime, are incorporated in the Eqs.(4) and (5) in order to obtain simplified expressions for the Y 2n and Y 3n . Indeed, by means of the charge neutrality condition of Eq.(13) it is found that the total contribution of the Y 2n and Y 3n can be expressed by the first component Y 1n as Y 2n + Y 3n ∼ = -(C e /2)Y 1n . This relation indicates that the total contribution of the Y 2n and Y 3n is governed by the C e . This is reasonable, because the Y 2n and Y 3n are proportional to the recombination rates of free electrons with trapped holes in recombination centers and these rates according to Eq.(17) are governed by C e . Moreover, the net total Y 2n + Y 3n contribution appears negative, which indicates that the recombination processes involved in the Y 2n and Y 3n are associated to a phase lead. Therefore in the LF regime the Y n depends on the ratio of the capture coefficients for the majority carriers C e = c v n /c c n according to the simple relation

  << 2 is required to minimize the contribution of the recombination processes of Y 2n and Y 3n to Y n and Y . This important role of the C e has been not recognized in our first analysis. For simplicity, the Y signal

  of simulationsIn this section, model simulations are employed in order to verify the theoretical predictions of the previous sections, rather than to fit particular experimental spectra. Moreover, the MPC data generated by the simulations serve as possible experimental data in which our methods are applied to illustrate when and how safe information about the DOS parameters can be extracted. For this purpose we consider the simple DOS model of Fig.4with the D v (E) and D c (E) distributions. These distributions include exponential valence and conduction band-tails with characteristic energies of E ov = 55 and E oc = 35 meV, respectively. In addition, the D v (E) and D c (E) include gaussian distributions, having a maximum density of 3×10 17 cm -3 eV -1 at 0.56 eV and 1×10 16 cm -3 eV -1 at 1.28 eV with half-width at half maxima of 0.15 eV and 0.2, respectively. The energy gap is 1.8 eV and the Fermi level is slightly above midgap at 1.0 eV. In this model, the D v (E) and D c (E) rapidly vanish above and below E F , respectively. This way, it is possible to examine the crucial role of the capture coefficient of the recombination centers below and above E F to the MPC, predicted in Sec.II.C. The capture coefficients are taken asc v p = 10c v n = 1 × 10 -7 cm 3 s -1 and c c n = 10c c p = 1 × 10 -7 cm 3 s -1corresponding to negatively (D v (E)) and positively (D c (E)) charged centers, respectively. This model provides that the electrons are the majority carriers giving n >> p such that nc i n >> pc i p . The effect of the C e parameter on the Y signal predicted in Sec.II is studied by changing the c v n keeping fixed the rest parameters.

  fact that the Y signal at higher ω is independent of the bias light level, because H function is unity. By contrast, the experimental Y signal at higher ω is expected to depend on the bias light level in the cases where the Y signal differs from the imaginary part for the majority carriers Y n for µ n τ ωn ≤ µ p τ ωp , as a result of mixed contributions from the electrons and holes. These are shown in the example of Fig.5(b)obtained upon increasing the mobility of holes at µ p = 10 2 µ n and that of Fig.5(c) obtained upon decreasing both capture coefficients c v p and c v n of the D v (E) by a factor of 10 3 lower than the above introduced values so that τ ωn ≈ τ ωp . Therefore the behavior of the experimental Y spectra at higher ω can be used to conclude whether these spectra are dominated or not by the imaginary part of the majority carriers (Y n ).

  (b), the relative density of

C

  e . This is confirmed in Fig.6(b) where for C e ≥ 0.5 the maximum of the -(Y 2n + Y 3n ) around ω c t = 10 3 rad/s becomes comparable to the Y 1n . Thus the Y signal in Fig.6(a) starts to decay from gradually higher frequencies upon increasing C e and becomes lower than Y 1n according to

  confirmed in the examples of the exact Y signal for C e > 2 of Fig.8(c). In this case, the total negative contribution from the Y 2n + Y 3n exceeds that of the Y 1n around ω c t = 10 3 rad/s and lower ω (see Fig.6(b)). Thus the phase lead from the Y 2n and Y 3n components dominates over the phase lag from the Y 1n at low ω, as is shown in the phase shift spectra of Fig.6(c) with C e = 3 and 6.

  7(b), obtained with C e = 0.1, is in excellent agreement with the actual characteristic frequency ω c t (dotted line). From the so-derived ω t the capture coefficient c n and the H(ω, ω t ) are obtained which are introduced in Eq.(12) to calculate the 1/τ ω rate. It is worth mentioning that for the accurate determination of ω t it is essential to obtain the Y 0 spectrum. The Y 0 in the examples of Figs.7(a) and 7(b) is obtained with an electron density n 0 near dark equilibrium (n 0 = 2.9 × 10 6 cm -3 ). Unlikely, under this condition the Y 0 spectrum experimentally cannot be obtained at sufficiently high frequencies. As it can be seen from Fig.7(a), the Y 0 spectrum coincides with the upper envelope in which the Y spectra of different bias light levels merge, because in this envelope H(ω, ω t ) ∼ = 1. So this envelope can be safely used to experimentally determine the Y 0 .

  (a) (solid lines). In this figure it can be seen that the respective Y signal of Fig.6(a), obtained for C e < 0.5 (open circles and dotted lines) where the total contribution from the Y 2n and Y 3n is practically negligible (see Fig.6(b)), agrees with the respective reconstructed 1/τ ω rate. If such a behavior is experimentally observed, it can be safely concluded that the C e is relatively low, which provides a low recombination rate, such that 1/τ ω ∼ = 1/τ ωn . In this case, by applying our methods the actual characteristic frequency and the actual DOS from Eq.(19) are successfully reconstructed. This is confirmed in the examples of Fig.9(a) and Fig.9(b) with C e < 0.5 where it is found that ω t /ω c t ∼ = 1 and D(E) ∼ = D c (E), respectively. By contrast, the Y signal in the examples of Figs.6(a), obtained for C e ≥ 0.5 (solid circles and dotted lines), systematically differs from the respective reconstructed 1/τ ω rate. Such an experimental behavior can be used to safely conclude that the 1/τ ω differs from the actual 1/τ ωn and our methods cannot provide the actual DOS parameters. This is due to a relatively high C e and recombination rate so that the Y 2n + Y 3n is not negligible (see Fig.6(b)). Indeed, in the examples with C e ≥ 0.5, the ω t in Fig.9(a) significantly overestimates ω c t (ω t /ω c t > 1), whereas in Fig.9(b) the D(E) calculated from Eq.(19)

Fig. 6 ( 17 in

 617 Fig.6(a)). Thus at every energy Eq.(22) gives different values for the DOS by means of the phase shift values of low ω, as in the example of Fig.9(d)for C e = 2. The so-derived DOS parameters

  that the calculated DOS is proportional to Y . Hence this DOS reflects also the Y signal in the energy domain E ω . By adopting the relation E ω = kT ln(ν 0 /ω) with ν 0 = 10 12 s -1 , used by Kleider et al to define the energy scale, the Y signal extracted from the DOS data is converted into the frequency domain ω. The result is presented in Fig.10(b) along with the Y 0 spectrum, which is extracted from the upper envelope of the DOS's of different temperatures. It can be seen that the

FIG. 1 :

 1 photocurrent

FIG. 2 :FIG. 3 : 1 )FIG. 4 :FIG. 5 :

 23145 FIG. 2: Energy dependence of the d i n (E)b i ωn (E) (right axis) and d i n (E)b i ωp (E) (left axis) products above and below midgap, respectively, in (a) and of the ω/(ω 2 + [S i (E)] 2 ) ratio in (b) for various ω indicated by the numbers in units of k = 1000 rad/s. These products define the gap states with the higher relative contribution to each component of the Yn indicated in the parenthesis. The characteristic frequency is at ω i t = 100rad/s and c i n = c i p = 1 × 10 -8 cm 3 s -1 . Arrows above and below midgap indicate the E i ωn and E i ωp levels, respectively. Thinner and thicker lines correspond to ω > ω i t

1 )FIG. 6 :

 16 FIG. 6: (a) Y spectra (circles and dotted lines) calculated for n = 1 × 10 10 cm -3 and the indicated values of Ce in comparison with the respective reconstructed 1/τ ω rates (solid lines). (b) Comparison of the Y 1n spectrum (thick solid line) with the spectra of the total negative Y 2n + Y 3n contribution (thin solid lines) for the indicated C e (numbers). (c) Examples of phase shift lag (φ > 0) and phase shift lead (φ < 0) spectra obtained for the indicated C e (numbers).

1 )FIG. 7 : 1 )FIG. 8 :FIG. 9 :

 17189 FIG. 7: (a) Calculated spectra of Y (solid lines) and 1/τωn (open triangles) of different densities n (2.9 × 10 6 , 10 7 , 10 8 , 10 9 , 10 10 and 10 11 cm -3 from left to right in the figure). Y 1n spectrum (solid circles) in comparison with Y2n (dashed-dotted lines) and Y3n (dashed lines) spectra for the moderate n = 10 10 cm -3 . The signs of the Y2n and Y3n are indicated. The bias light-independent Y 0 spectrum (thick solid line) is obtained with a near dark equilibrium density n0 = 2.9 × 10 6 cm -3 . (b) An example demonstrating the determination of ωt for the Y signal of n = 10 10 cm -3 . The ω t is defined as the frequency where the Y signal decreases by the factor of 2 (vertical double arrow) from the respective value in Y 0 spectrum of the same trap depth that is by a factor of 1.41 (horizontal double arrow) above ω t .

1 )FIG. 10

 110 FIG.10: a) Experimental spectra of Y signal of a-As 2 Se 3 sputtered films taken from our previous publication[35] for light intensities of 8.2 × 10 11 (open triangles), 3.6 × 10 12 (open circles) and 2.8 × 10 13 (solid circles) cm -2 s -1 . (b)Experimental spectra of Y and Y0 spectra extracted from the MPC data of light p-type doped a-Si:H reported by Kleider et al[24]. Each reconstructed 1/τ ω rate (solid line) is also included in (a) and (b) for comparison.

  and ω/(ω 2 +[S i (E)] 2 ) which appear in Y 1n , Y 2n and Y 3n of Eqs.(3)-(5), respectively.As it is demonstrated in Fig.2(a) (right axis), the first Y 1n component is dominated by the capture rate, c i n D i (E)dE, of electrons into the gap states centered at a frequency dependent energy level above midgap.

	6
	These products are illustrated graphically in Figs.2(a) and 2(b), for various modulation frequencies ω by taking
	nc i n = 99 s -1 and pc i p = 1 s -1 , which give a characteristic frequency ω i t = nc i n + pc i p = 100 rad/s.
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

  It is obvious that the above difficulty may be overcome and an absolute DOS can be extracted by utilizing all the MPC data, as far as the Y 1n component predominates in the Y n and Y signal not only for the HF regime

	rate of free electrons with the trapped holes in the gap states around the E i tp level. Similarly,
	in Eq.(5) by taking into account Eq.(9) and Eqs.(A3) and (A4) of the Appendix, the Y 3n for the
	LF regime is also found proportional to the c i n pc i p /S i (E)D i (E)dE rate. The above rate indicates
	that the Y 3n is proportional to the recombination rate of free electrons with trapped holes in the
	recombination centers of the D i (E) distributions between the E i tp and E i tn . These centers as is
	evident from Fig.2(b) (thick lines) are selected by the ω/(ω 2 + [S i (E)] 2 ) ratio in Eq.(9) and they
	have the largest contribution to the Y 3n . This way, the recombination processes involved in Y 2n
	r o F and Y 3n may complicate the extraction of a DOS from the data in the LF regime.
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	i t is
	found proportional to the c i n pc i p /S i (E)D i (E)dE rate. Since the pc i p /S i (E) ratio gives the fraction of
	the unoccupied states, the above rate indicates that the Y 2n is proportional to the recombination

but also for any ω. This way, the probed D(E ωn ) dominating in the Y 1n can be extracted directly from the Y signal. It is worthy to mention that this possibility can be tested experimentally, because the Y 1n has the well defined frequency dependence of the capture rate 1/τ ωn of electrons into the probe E ωn level according to

  by means of simulations in Sec.III.C for nc i n >> pc i p . Similar arguments can be made for the Y p , as far as holes are the majority carriers. In this case, the crucial parameter is the C h

	10
	which is verified
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	)

  5 the mixed contributions from the recombination are negligible, so that the contribution from the capture rate of the majority carriers into the probed states dominates in the Y signal. This can be verified experimentally, because the above capture rate can be reconstructed from the experimental Y spectra. If the reconstructed 1/τ ω rate agrees with the Y signal, then this rate dominates in the Y signal and the accurate DOS parameters can be obtained with confidence by our DOS spectroscopy. It was shown that the methods reported byLGEP and INTEC groups are reliable exclusively for C e,h = 1, which unlikely cannot be verified experimentally.

	APPENDIX: APPROXIMATE EXPRESSION OF K
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters


Gráinne O'keeffe

THE 2001 CENSUS -TO TICK OR NOT TO TICK THE EXISTENCE OF AN IRISH ETHNIC IDENTITY IN ENGLAND?

Keywords: deuxième génération, ethnicité, identité, invisibilité, recensement second-generation, ethnicity, identity, invisibility, census

Le recensement britannique de 2001 inclut pour la première fois la catégorie « Irlandais » sous la rubrique « groupe ethnique ». Le nombre de personnes qui opta pour cette catégorie fut moins important que prévu, surtout pour la deuxième génération irlandaise. Ceci remet en cause l'existence d'une véritable identité « ethnique » irlandaise et l'utilité de garder cette catégorie dans le prochain recensement. Cet article propose d'examiner si une identité ethnique irlandaise est revendiquée par la communauté irlandaise en Angleterre et comment on peut expliquer le faible taux de réponse à la question sur l'ethnicité dans le recensement national.

The Irish were included for the first time under the "Ethnic Group" category in the 2001 Census. The number of people in England who chose to tick this box was much lower than originally anticipated. The existence of an Irish "ethnic" identity has thus been called into question. This article will discuss whether or not the Irish community in England recognises an "Irish" ethnicity and the reasons why a greater number did not choose to tick this box. Particular attention will be paid to the second-generation Irish who had, for the first time in a national census, the chance to express their Irish identity and who did not do so in the anticipated numbers.

Firstly, the construction of the Irish migrant generation as an "invisible" minority in the period following the Second World War will be analysed. This meant that an Irish dimension was often missing in regard to central and local government policymaking and in official discourse concerning England's ethnic minorities. The Irish migrant generation and their children were subject to a "forced inclusion" into mainstream white society where their difference and identity were often ignored. This invisibility did not necessarily mean that the Irish did not suffer from many of the same problems as the "visible" minorities such as discrimination or unequal access to benefits or that an Irish identity ceased to exist on English soil. This did signify however that Irish immigrants and their children lacked recognition. The Irish-born were first "invisible" as an immigrant population and subsequently, with their children, as an ethnic group. An ethnic identity came to be constructed in official discourse as something only "visibly" different groups -i.e. non-white groups -possessed.

The second-generation Irish will then be examined in order to ascertain if they feel a particular affinity for their Irish background and heritage and if they see this part of their identity as a positive attribute and something to embrace. The second-generation Irish, being white and having English accents, have the option to choose which part of their identity they wish to make public. We will examine how they negotiate the various dimensions of their identity in English society.

The final part of this article will analyse the census question on ethnicity. Some explanations will be advanced as to why the second-generation did not take the opportunity given by the census to express the existence of their Irish heritage and background in the numbers that were hoped for by the Irish lobby. This lobby, made up mainly of the Irish voluntary sector, had worked for more than ten years for the inclusion of this category in the national census. It will be concluded that a number of different factors are at play, not least the years of "invisibility" of the Irish community as a separate and distinct ethnic group in official discourse in England.

The creation of the myth of a British white homogenous society

In the period following the Second World War, the British government began to discuss the possibility of introducing immigration controls to control the large influx of immigrants into Great Britain, especially those from the Commonwealth. The case of Irish immigrants became problematic as the British government was reluctant to introduce controls between the Republic of Ireland and Great Britain and in 1955, a Working Party gave the following arguments to support the continuing freedom of movement of Irish immigrants between both countries:

Citizens of the Irish Republic present a very difficult problem in that their exclusion from the scope of a Bill applying restrictions to the entry of British subjects would be open to obvious criticism on political grounds. However, the Irish not only provide much-needed labour but have always done so, and any restoration of the immigration control on traffic between GB and Ireland would be tiresome to the hundreds of thousands of passengers who travel each way during the year and would mean a considerable increase of the Immigration Service and the carrying of passports or other identity documents by citizens of Northern Ireland who would much resent it. The Working Party have previously pointed out that the only way out of this dilemma would appear to be to argue boldly along the lines that the population of the whole British Isles is for historical and geographical reasons essentially one and, except during the special circumstances of the war when Eire was a neutral state though still within the Commonwealth, has always been treated as such and that there is every reason on grounds of common sense and expediency for no departing from that principle in the present connection. 1 This citation gives many reasons for exclusion of the Irish from possible immigration controls but what is particularly noteworthy however is the argument that, "the Irish and the British are, unlike Commonwealth citizens, essentially the same". The Working Party continued by declaring that, "the Irish are not, whether they like it or not, a different race from the ordinary inhabitants of Great Britain" 2 . The Irish were constructed as the "same" as "not different" from ordinary British citizens and their shared skin colour played a significant role in this construction.

Consequently, when the British government finally introduced legislation to control immigration, the 1962 Commonwealth Immigration Bill, the Irish were excluded 3 . They were not to be treated "any differently than British citizens" and could travel to and from Britain without hindrance. According to Mary Hickman, the exclusion of the Irish from controls on entry at this time directly contributed to their subsequent forced inclusion in British society 4 . The non-inclusion of the Irish in immigration controls meant they were not officially recognised as immigrants unlike those from the Commonwealth. These immigrants and their children subsequently became England's "ethnic minorities". The Irish, already not officially considered an immigrant population group, were not, as a consequence, constructed as an "ethnic minority" group in England. Therefore an Irish dimension was subsequently ignored in debates surrounding harmonious race relations.

On the one hand, Irish immigrants were officially told that they were not different from the dominant white, British population for historical and geographical reasons but, on the other hand, they experienced discrimination and anti-Irish prejudice in their day-to-day lives. They were often forced to be discreet about their identity, not speaking to avoid revealing an Irish accent or instead anglicising it, not mentioning any clearly Irish name or by not making reference to Ireland or Irish culture 5 .

For Irish emigrants, who came over in the 1950s or the 1960s, playing down their Irishness became a feature of their lives in England. Many of them saw signs on doors, when they were looking for accommodation or employment, saying, "No blacks. No dogs. No Irish" 6 . For many expressing their Irishness was limited to the home or to times when they were with other Irish people. The Commission for Racial Equality (CRE) report on the discrimination of the Irish in Britain, the first of its kind concerning the problems the Irish community faced in Britain, cited numerous examples of Irish discrimination and stereotyping in the workplace, when accessing benefits, when looking for accommodation and in relation to the problems in Northern Ireland 7 . Sixty-five per cent of respondents stated clearly that they had seen or heard things directed against the Irish in Britain, which they had rejected, either openly or privately 8 . During the 1980s, the Irish began to mobilise, members of the Irish community no longer wanted to remain "invisible". Their mobilisation was helped by the societal changes taking place in Britain where "difference" and "diversity" were becoming familiar terms. Britain was becoming a multicultural society and all sorts of groups were gaining recognition so why not the Irish? Irish voluntary organisations began to flourish with as their principle demand -recognition of the Irish as an ethnic group.

Recognition of Irish diversity

In this new British multicultural society immigrants were becoming "ethnic minorities". This term includes both the migrant generation and the second and 4 Ibid, pp. 288-307. 5 subsequent generations. An ethnic group has been defined as a community whose heritage offers important characteristics in common between its members and which makes them distinct from other communities9 . According to Tariq Modood, ethnicity is a multi-faceted phenomenon based on physical appearance, subjective identification, cultural and religious affiliation, stereotyping and social exclusion 10 . In British society, having an "ethnic identity" became synonymous with having a different skin colour, with being "visible". How could the Irish then, who were not officially considered as immigrants in the first place and had remained invisible as such since the Second World War, hope to be recognised as an ethnic minority? Many decided to become "ethnically assertive", following the example of the lobbying of other minority groups.

Many minority groups began to exercise "ethnic assertiveness" during this period and the Irish were no different. This "ethnic assertiveness" arose from: "feelings of not being respected or of lacking access to public space, consisting of setting 'positive' images against traditional or dominant stereotypes"11 . Members of the Irish community decided to organise themselves and were no longer willing to be excluded. They called for the Irish to be recognised in their own right as a distinct group with its own unique identity.

The Irish voluntary sector and members of the Irish community began to mobilise throughout England but particularly in London which became the epicentre of change at this time. They were principally effective at the local level and much lobbying was carried out in several London local authorities. Their main demand was recognition -recognition of the Irish experience in Britain, recognition of Irish cultural difference, recognition of an Irish ethnic identity. A number of local authorities, traditional enclaves for Irish immigration, reacted in favour of Irish demands, employing Irish Liaison Officers, organising conferences to discuss Irish issues, consulting with the local Irish community and recognising the Irish as having a distinct ethnic identity.

A citation from a report, published in Camden by the Irish present at one of these conferences, states that:

For us, the question of Irish ethnicity is a fait accompli. Our Irishness is our ethnicity. Our ethnicity is our Irishness. As a singular national group we share history, religions, traditions and experience, values and norms-social and political-that are unique and distinct; and in Britain and Camden we are minority.

[…] By demanding of Camden to include "Irish" as a separate category in ethnic classification we want to be counted. It is estimated that approx 15% (1 st and 2 nd generation) of the borough's population is Irish. Officially, in the Council's eyes, we are invisible, but we are only invisible because they do not consider us to be a distinct group 12 .

In this citation, the Irish in Camden explain how they define their ethnicity. It is made up of many different elements but which are, according to them, unique and distinct. They want to be counted and to be included in ethnic classification systems for both the migrant generation but also for their second-generation children.

The Greater London Council (GLC) proved to be an important ally at this time. It was headed by Ken Livingstone, a Labour MP and a fervent advocate of the Irish in England. The GLC recognised the problems that the Irish community could encounter. It published a policy report on the Irish community in London in the early 1980s which was also the first official report recognising anti-Irish discrimination and racism 13 . At this time nearly 30% of the Irish population lived in this region 14 . This report was significant as the GLC acknowledged the importance of more funding for Irish community needs. It concluded that the Irish community was disadvantaged in many areas such as housing, employment and mental health. More importantly, it also recognised that the expression of Irish culture and identity should be promoted as it had been denigrated in the past in British society and called for recognition of the Irish as an ethnic minority. The report stated that:

The Irish should be recognised unequivocally as an ethnic minority with a unique and identifiable cultural heritage and should be included in all initiatives to improve the quality of life of London's ethnic minorities. [......] Historically, it was necessary to denigrate the Irish as treacherous, stupid and intractable in order to justify the British occupation of Ireland whilst at the same time covering over the massive exploitation of Ireland in economic terms 15 .

The report went on to speak about how the negative imaging concerning Ireland and Irishness undoubtedly did not encourage an open articulation of an Irish heritage or identity in English society:

It is evident in the way children of Irish parents feel that it is best to deny or refuse to acknowledge Irish origins because they know little of those origins, Irish History and Heritage, except what comes through the media. It is evident in innumerable subtle ways in social life where Irish born prefer to keep a low profile especially during high points and crises in Anglo-Irish relations.

12 Camden Irish Conference Planning, The Voice of the Irish in Camden -Conference Report, Londres, Camden Irish Conference Planning Group, août 1990, p. 2. 13 The GLC was abolished in 1986, under the Thatcher government, before significant progress could be made but it greatly contributed to increasing the visibility of Irish issues and problems. Following its abolition, the onus was then on the local authorities to include an Irish dimension in ethnic monitoring procedures. However, because of the overwhelming association of ethnicity and "blackness" in Britain, the Irish were not automatically included in these procedures. The Irish voluntary sector continued its lobbying on local authorities, calling for them to recognise an Irish ethnic identity, but achieved limited success. According to the CRE report on the Irish community, only about half of the local authorities in London did some kind of monitoring of the Irish in the early 1990s 17 .

At the time of the abolition of the GLC, the CRE itself did not monitor the Irish as a distinct ethnic group so official bodies, which used the ethnic categories recommended by this organism, did not include the Irish in their monitoring procedures. Due to the years of "invisibility" on an official level as an ethnic minority in Britain, the Irish were subsequently excluded from the "Ethnic Group" category when it was first introduced in the 1991 Census. This meant that the second-generation Irish who wished to express their Irish identity and heritage did not have the option to do so in this census.

Let us now turn our attention to this second-generation (those with one or two Irish-born parents) and look at what identity they perceive themselves as having. Do they see themselves as different from the English mainstream population? Do they recognise an Irish dimension to their identity or do they see themselves as simply English? It was during the 1980s that the first studies were carried out as to how these second-generation Irish children expressed their identity in England.

The second generation -which identity?

The first studies on second-generation Irish children that we are going to examine in this section were carried out in Catholic secondary schools in the 1980s and early 1990s. The majority of children of Irish descent are educated in these schools 18 . The analyses that follow relate therefore to the identities expressed by second-generation Irish Catholic children 19 .

In the early 1980s research was carried out in four Catholic secondary schools in London where 176 second-generation Irish children and thirty teachers, 16 Ibid., p. 12. 17 Mary Hickman et Bronwen Walter, op. cit., p. 64. 18 Bronwen Walter, Sarah Morgan, Mary Hickman et Joseph Bradley, "Family Stories, Public Silence: Irish Identity Construction amongst the Second-generation Irish in England", Scot. Geog. J. 118(3), p. 202. 19 To date no large-scale survey has been carried out on the ethnic identity of second-generation Irish Protestant children.

who were mostly of Irish origin, were interviewed [START_REF] Inglis | The Irish in Britain -A Question of Identity[END_REF] . It was discovered that the children were aware of negative stereotyping of the Irish in Britain especially related to the situation in Northern Ireland. The problems or the "Troubles" in Northern Ireland were particularly serious at this time; the hunger strikes were taking place there. In addition, IRA bombings on mainland Britain, especially London, contributed significantly to experiences of prejudice and discrimination against the Irish in England.

These types of events undermined the confidence of the Irish and caused many people to play down their Irishness. It may not be surprising therefore that the teachers interviewed in this study preferred to ignore their students' Irish backgrounds and did not encourage them to discuss their Irish heritage at school. One teacher said that, "children and teachers would avoid any mention of the 'Troubles', to all intents and purposes, the children are English, they've assimilated into the British teenage culture" 21 .

Another teacher remarked that, "Once people come to England, they become English, to imply anything else makes it more difficult for them to integrate. They should merge with the host community" 22 . One teacher was afraid that if the differences were brought out the barriers would be heightened. This survey showed that for those second-generation children who wanted to openly express a cultural difference were not encouraged to do. This fear of heightening barriers, expressed by some of the teachers in the early 1980s, shows that they did not believe that the second-generation Irish children could both express Irishness as part of their identity and remain part of British society.

Other second-generation Irish children, 142 in total, were interviewed in Catholic schools in London and Birmingham in the mid-1980s [START_REF] Ullah | Second-generation Irish Youth: Identity and Ethnicity[END_REF] . Approximately 56% of the children interviewed when asked to state their identity replied, "half English, half Irish", thus favouring a hybrid identity 24 .

It was discovered that ethnic prejudice was a significant issue for many of them and that they were well aware of anti-Irish prejudice. The research revealed that responses to this problem of prejudice were very closely linked to the different ethnic identities adopted by these people. Thirteen per cent adopted a "mainly English" identity and 8.5% a "completely English" one 25 . The adoption of an English identity was a way of denying one's Irish origins in order to avoid the stigma attached to having Irish roots and the "Troubles" in Northern Ireland.

The children were asked how much pride they felt being of Irish descent. In most cases this source of pride was closely linked to their involvement in the Irish community and the many social and cultural activities that it generated. Their upbringing had led them to appreciate the close family atmosphere that could be found at such venues, and the sense of togetherness, which was so important for the development of a collective and positive sense of identity. The results of the interviews showed the relationship between the chosen identity and the degree of pride in one's Irish origins. It was found that they would feel Irish in situations in which this identity was salient and English in situations where that identity was most salient, thus, favouring a "situational identity" 26 .

Mary Hickman looked more extensively at the role of Catholic schools in the formation of an Irish identity. She interviewed pupils in Catholic schools in London and Liverpool in the early 1990s. Eighty-one per cent of respondents claimed either "Irish" or "of Irish descent" in London whereas 65% preferred a local or Liverpudlian identity in Liverpool27 . This survey showed a marked change in the articulation of Irishness. In London, there seems to have been a change in the early 1990s towards a more positive perception of Irishness and a willingness to embrace this identity.

However, she noted that the Catholic education system favoured a Catholic rather than an Irish identity and there was an absence of teaching about Ireland from the curriculum leaving cultural expression to the family and community. Those second-generation who struggled not to reject their Irishness were encouraged by their experience of Catholic schooling to maintain a low public profile for their identity.

These studies show that second-generation Irish children were aware of their Irish roots and heritage. Nevertheless, the negative stereotypes of the Irish and the "Troubles" in Northern Ireland did not encourage them to openly celebrate this part of their identity. Many of them went to Catholic schools where they were not encouraged to discuss their Irish background or Ireland in general. It was even felt by some teachers that they could not be both "Irish" and "British", nevertheless more than half the children in one study favoured a hybrid identity.

It is clear from these studies that the encouragement for these second-generation children to recognise and celebrate their Irishness came from the "inside" (family and community) and not from the "outside" (their education or English society). The inclusion of an Irish ethnic category in the 2001 Census was therefore the opportunity for recognition from the "outside". Irish community activists and the Irish voluntary sector had worked hard to gain this public recognition but results were disappointing.

The 2001 Census

When the "Ethnic Group" category was included for the first time in the 1991 Census, the argument used for its inclusion was that it would make statistical data available which would allow the Government to better meet the needs of ethnic minorities 28 . The Irish would have to wait for the publication of an official report by the CRE in 1997, which gave official recognition of Irish discrimination and disadvantage, and much lobbying from voluntary groups, especially the Federation of Irish Societies, before they were to be included in this category.

It was felt the Irish should be included under the "Ethnic Group" category for the following reasons: the situation of the Irish and other "visible" minorities was similar; benefits accorded to "visible" minorities were now needed by Irish people because of the similarity of their socio-economic position; the contribution of the Irish as migrant labour was not acknowledged and Irish cultural difference was not understood by the British. After more than ten years of lobbying by members of the Irish community and the Irish voluntary sector, the Office for National Statistics (ONS) finally included an Irish category under the "Ethnic Group" question in the 2001 Census

The CRE report had calculated the size of the Irish community in Britain at 2.5 million. This figure includes the migrant generation and the second-generation 29 . The number of people who ticked the "Ethnic Group" box was 641,804 or 1.21% of the British population 30 . When the figures are broken down 149,586 people who ticked the Irish "Ethnic Group" box were born in Britain 31 . If we take this figure as the second-generation Irish, it is a long way off the figure calculated by the CRE at over one and a half million.

Possible reasons for this small figure were put forward in the initial findings of the Irish2 Project, which was the first large-scale project on second-generation Irish adults 32 . While the project organisers were interviewing second-generation Irish participants before the Census, it was discovered there was a lot of confusion surrounding the category on ethnicity and many had taken it to be a question on nationality. Most people had not read the explanatory text which said: "indicate your cultural background" 33 .

Furthermore, as we have seen from the studies on second-generation Irish children, many favoured a hybrid identity. This also applied to the second-generation adults interviewed for the Irish2 Project. Even though some second-generation Irish people described themselves as simply "Irish", over half favoured a mixed description of their identity, for example, "Anglo-Irish", 28 Nada Afiouni, La gestion de la différence en France et en Grande-Bretagne : discours et pratiques, (thèse non-publiée), l'Université Aix-Marseille, décembre 2001, p. 99. 29 32 The Irish2 Project is the first large-scale research project about the children of Irish migrants to Britain. The project involved 12 discussion groups and 120 interviews with a wide range of people of Irish parentage, both professional and manual workers, people with one or two Irish-born parents from North and South, a balance of women and men with a broad age range in London, Glasgow, Manchester, Coventry and Banbury. Newsletters and the first findings of this project can be found at-http://www.apu.ac.uk/geography/progress/irish2/index.html. 33 Bronwen Walter, "Making Sense of the Irish Census Question", Irish Post, 22/1/06, p. 12. "London Irish", "English and Irish", "Irish-Italian" or "Irish-Pakistani"34 . This would mean that the choice of "Irish" alone on the census form was too restrictive for those with hyphenated identities. The "visible" ethnic minorities had more choice in this category, and a "mixed" heading was included. Under this heading the following categories could be found: "white and black Caribbean"; "white and black African"; "white and Asian" and "other mixed".

However, it must not be forgotten that the Irish, either first or second-generation had not been accustomed to asserting their Irish identity on official documents in the past. It was also the first time people of Irish descent had been asked about their ethnicity in a national census. May of them did not realise what was being asked of them. The years of invisibility as an ethnic group in England may have gone some way in explaining the poor take-up of this category.

This low response rate for the question on ethnic identity by the Irish community has made official bodies doubt the usefulness of keeping this category in the future census of 2011. The ONS had been discussing possible exclusion of this category in late 2005 but lobbying by Irish voluntary organisations managed to avoid this for the moment. It was felt by Irish activists that the question on ethnicity in the 2001 Census was unclear and that the Census provided no guidance on what ethnicity was and to whom it applied and that the simple category "Irish" was too restrictive for those with mixed identities. For the 2011 Census, an expanded Irish category is being called for to allow for other mixed Irish backgrounds.

Conclusion

For much of the post World War II period, the Irish have been constructed as "invisible" in official discourse concerning ethnic minorities. They have been conspicuously absent from ethnic monitoring procedures and have been largely excluded from all official reports on ethnic minorities. In the 1980s, the research carried out on second-generation Irish children has shown that they have never been particularly encouraged to express their cultural difference or their Irish identity in English society. It may not be surprising then that these second-generation Irish children, now adults, were not aware that they were being asked to express their ethnicity in the 2001 census as they had not been accustomed to or encouraged to express their Irish identity in the public domain.

Research on the second-generation has shown that many are conscious of their Irish background but that a large majority favour a hybrid identity. The choice of simply "Irish" on the 2001 census form did not therefore suit the identities expressed by many of the second-generation. The low response rate of those of Irish decent to the ethnicity question in the 2001 Census should therefore be interpreted with caution. It should not be taken to mean that an Irish ethnic identity simply does not exist.

Due to the low response rate, the inclusion of an "Irish" heading under the "Ethnic Group" question in the 2011 census remains uncertain. The Irish voluntary sector is now lobbying for the inclusion of a category that reflects more accurately the identities expressed by the Irish community.

  Nessa Winston, Between Two Places: A Case Study of Irish-born People Living in England, Dublin, The Irish National Committee of the European Cultural Foundation, 2000, p. 31. 6 Ibid, p. 32. 7 Mary Hickman et Bronwen Walter, Discrimination and the Irish Community in Britain, Londres, Commission for Racial Equality, 1997, p. 213.

8

Idem.

  Greater London Council, Policy Report on the Irish Community -Ethnic Minorities in London, Londres, Greater London Council, 1983, p. 14. 14 Liam Greenslade et al., Irish Migrants in Britain -Socio-economic and Demographic Conditions, Liverpool, The Institute of Irish Studies, 1991, p. 6. 15 Greater London Council, op. cit., p. 11. [...] It is evident in the PTA 16 .

  Mary Hickman et Bronwen Walter, op. cit., p. 21. 30 2001 Census, Key Statistics, (Table KS06-Ethnic Group). 31 2001 Census, Standard Tables, (Table S102-Sex and Country of Birth by Ethnic Group).

Tariq Modood et al., Ethnic Minorities in Britain: Diversity and Disadvantage, Londres, Policy Studies Institute, 1997, p. 13.

Idem.

Ibid, p. 290.

Robin Cohen, Frontiers of Identity: the British and the Others, New York, Longman Group ltd., 1994, p. 205.

Mary Hickman, Religion, Class and Identity, Hants, Ashgate Publishing Company, 1995, p. 245.

Idem.