CONVENIOS VIGENTES PARA LA REALIZACIÓN DE PRÁCTICAS

One can calculate the theoretical upper limit for Voc as a function of the material bandgap

Eg in the case of an ideal p-n junction [Shah 1995b]. Such limits calculated from Kiess theory

both cases, Voc linearly increases as Eg increases, with a similar slope. 0 0.5 1 1.5 2 1 1.2 1.4 1.6 1.8 2

theoretical limit (Kiess) semi-empirical limit (Green) experimental µc-Si:H V oc [V] E* g [eV]

†

V

†

V

Fig. 4.29: Upper limits (black dotted lines) calculated from Kiess theory [Kiess 1995] and from Green semi-empirical values [Green 1998] for the open-circuit voltage (Voc) as a

function of the material bandgap Eg; Voc-values measured on various p-i-n and n-i-p solar

cells (triangles), as well as a linear fit, as a function of the weighted bandgap Eg* as defined

in (equ. 4.4) (the data are those of Fig. 4.26). Typical Voc-values obtained for state-of-the-art

c-Si and a-Si:H solar cells are also given (grey rectangles). Note that the linear fit to the experimental data obtained on mc-Si:H solar cells (full black line) has roughly the same slope as the line linking the typical Voc-values for c-Si and a-Si:H solar cells (grey dotted line).

In Fig. 4.26, we demonstrated an experimental linear relation between the Voc-values and

the crystallinity of various mc-Si:H solar cells. In order to compare our experimental results with such theoretical limits, we have calculated an "equivalent average bandgap" value Eg*,

by somewhat arbitrarily weighting the bandgap of a-Si:H (Ega-Si:H = 1.75 eV) and c-Si

(Egc-Si = 1.1 eV) materials with the Raman crystallinity measured on the samples:

† E_g* =fc A ⋅1.1+ (1-fc A_{) ⋅1.75 . (equ. 4.4)}

In Fig. 4.29 is also represented the evolution of the Voc-values measured on the solar cells as a

function of Eg* calculated from (equ. 4.4), for all the p-i-n and n-i-p solar cells analysed in

this work (see data of Fig. 4.26). Since Voc vs. fcA gave rise to a linear relation (Fig. 4.26), it is

1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 Eg* (equ. 4.4) Tauc gap, layers

E g

[eV]

f_cA (514nm)

Fig. 4.30: Weighted bandgap value Eg* calculated by weighting the respective gaps of a-Si:H

and c-Si with the fraction of each phase present in the solar cells (equ. 4.4) (crosses and full line), as well as experimental optical bandgap evaluated by the Tauc method from CPM data measured on the SC series of single layers (see § 4.4.3.5) (diamond) as a function of fcA

measured on these layers.

Before discussing the results of Fig. 4.29, one can wonder if the weighted gap defined by (equ. 4.4) has an actual meaning. The best way for that would be to evaluate the optical gap of the solar cells studied here, and to compare it with the data obtained from (equ. 4.4). Such evaluation would be possible from CPM (constant photocurrent method) measurements performed directly on the solar cells [Poruba 1997]. However, we do not have such measurements for our solar cells. On the other hand, we have evaluated in Chapter 3 the optical gap Eg by the Tauc method from CPM measurements performed on the SC series of

single i-layers (see § 3.4.3.5). From Fig. 4.30, one sees that these values of Eg, when

represented as a function of fcA at 514 nm evaluated on the same layers, are well in

accordance with the relation between fcA and Eg* given by (equ. 4.4) and used in Fig. 4.29.

Such a linear relation between the crystallinity and optical properties could seem surprising. Indeed, we do observe that the optical properties suddenly change as the silane concentration (SC) used for the deposition increases. However, the crystallinity also decreases abruptly with increasing SC [Houben 1998, Lambertz 2003]. Such a sharp decrease has indeed been observed for the SC series of layers in Fig. 3.15. Therefore a linear relation between optical properties and fc should not be a priori excluded. It turns out that best mc-Si:H solar cells are

those with the i-layer deposited near the transition to amorphous material. However, such mc-Si:H material has not been extensively studied as yet and the values for optical parameters as are generally attributed to mc-Si:H material are mostly those of "highly microcrystalline" material (as deposited for low values of SC).

In Fig. 4.29 are also given the range for experimental Voc-values obtained for state-of-

the-art crystalline silicon (Vocc-Si) and amorphous silicon (Voca-Si:H) solar cell technology.

Whereas Vocc-Si is nearly attaining the semi-empirical limit given by Green, Voca-Si:H, although

higher than Vocc-Si, is still quite lower than the theoretical or semi-empirical limit. The limits

of Fig. 4.29 consider a p-n junction formed with a crystalline material having a given bandgap value (x-axis value), which corresponds to c-Si solar cell technology. On the other hand, the technology of a-Si:H solar cells consists in p-i-n (or n-i-p) structure and amorphous material. These both aspects are explanations for lower Voc-values as compared to the theoretical limits.

a-Si:H material contains an important quantity of localised states in the bandtails. Therefore, compared to a crystalline material with a bandgap value equal to that of a-Si:H (Eg ≈ 1.75 eV), one can expect lower Voc-values due to the localisation of carriers that do no

longer contribute to the built-in field, i.e. to the Voc.

From Fig. 4.29, one can observe that the slope of Voc vs. Eg from theoretical values is

about 2.5 times higher than that of the linear fit to our experimental data. (Note that this difference holds if fcp-i or fcn-i is used in (equ. 4.4) instead of fcA). The variation of the gap in

our samples as evaluated by (equ. 4.4) is due to the incorporation of a certain quantity of amorphous phase. Fig. 4.29 shows that this incorporation of a-Si:H material in mc-Si:H does not enable to increase the Voc in a similar way as for crystalline material (as observed in the

theoretical limit evolution with Eg).

One observes from Fig. 4.29 that, surprisingly, the slope of the fit to our experimental data measured on various mc-Si:H solar cells is roughly the same as the slope between Vocc-Si

and Voca-Si:H. Indeed, one can note on Fig. 4.29 that for both extreme cases (i.e. Eg*

approaching Egc-Si and Eg* approaching Ega-Si:H), our experimental Voc-values are about 0.3 V

lower than Vocc-Si and Voca-Si:H, respectively. Note that such comparison between Voc obtained

for our mc-Si:H solar cells and for state-of-the-art c-Si and a-Si:H cells can also be done on the basis of Fig. 4.26 (that uses fcA as x-axis). This comparison and the following discussion

are therefore independent of the weighted gap Eg* introduced with (equ. 4.4). Although a

difference of 0.3 mV is indeed observed for both extreme values of the crystallinity (fcA ≈ 1

and fcA ≈ 0, respectively, see Fig. 4.26), it is probably not due to the same reasons in both

cases. We will try to give below some possible explanations for each case:

- Comparison with c-Si cells (Fig. 4.26: fcA ≈ 1; Fig. 4.29: Eg* ≈ 1.1 eV): in this case,

the lower Voc obtained for our mc-Si:H solar cells can be due to two factors. First, our

mc-Si:H samples have a p-i-n (or n-i-p) structure, whereas c-Si cells have a p-n structure. Second, mc-Si:H material compared to c-Si material contains a lot of disordered material at the grain boundaries. Indeed, already for the case of poly-Si solar cells (which have a p-n structure), the presence of the grain boundaries (and,

thus of localised states) reduces the value of Voc as compared to c-Si cells [Ghosh

1980].

- Comparison with a-Si:H cells (Fig. 4.26: fcA ≈ 0; Fig. 4.29: Eg* ≈ 1.75 eV): one of

the main difference, in this case is the thickness between state-of-the-art a-Si:H solar cells (i-layer: 0.2 - 0.3 µm) and cells grown with mc-Si:H characteristics (i-layer: 1 - 3 µm). On the other hand, for a series of a-Si:H solar cells fabricated by reducing the SC for the i-layer deposition (thickness ≈ 0.25 µm), it has been observed that the

Voc-value is kept about constant around 890 - 900 mV for SC = 100% down to 20%,

whereas it suddenly falls to 700 mV for SC = 10% [Niquille 2003]. The interface between the doped layers and the i-layer is also crucial for high Voc-values. Here, we

are comparing state-of-the-art a-Si:H solar cells (with optimized interfaces), and a kind of "hybrid" solar cells (non-optimized) that have some characteristics of mc-Si:H cells (doped layers, thickness of the i-layer), but an intrinsic layer material close to that of an a-Si:H cell.