Effect of the front-metal work function on the performance of a-Si:H(n⁺)/a-Si:H(i)/c-Si(p) heterojunction solar cells

Numerical simulation is now important for the understanding of the design and the optimization of heterojunction solar cells’ high efficiency. Numerical simulation using AFORS-Het software shows that the front-metal contact nature has a great influence on the photovoltaic properties of heterojunction solar cells under one sun AM 1.5G.

The HIT structure to be simulated in the present study is sketched in Fig. 1 and consists of a 10-nm-thick n⁺-amorphous silicon layer (a-Si:H) realized on a 300 μm thick p-type crystalline silicon (c-Si) substrate with a doping concentration \(N_{\text{d}}\) = 1.5 × 10¹⁹ cm⁻³ and \(N_{\text{a}}\) = 10¹⁶ cm⁻³, respectively. The a-Si:H(i) spacer (3 nm thick) is found essential for the high-quality passivation of the heterointerface [15]. The metal work function of the front contact varies in the range of 3.9–4.59 eV.

The current–voltage characteristics of the HIT cell with heavily doped a-Si:H(n⁺) layer under illumination, obtained by means of AFORS-Het simulation program for different front-metal work functions \((\varphi_{\text{m}} )\), are plotted in Fig. 2a. For values of \(\varphi_{\text{m}}\) smaller than 4.2 eV, the J–V characteristics under illumination have a quasi-normal shape predicted (\(V_{\text{oc}} =\) 637 mV and \(J_{\text{sc}} =\) 37 mA.cm⁻²). It is also observed that as the metal work function value exceeds 4.47 eV, the J–V curves are modified near the open-circuit voltage compared to the quasi-normal J–V characteristic. In Table 1, we have regrouped the photovoltaic parameters obtained for different values of \(\varphi_{\text{m}}\). It is clear that the conversion efficiency of the HIT cell decreases about 4.2% when the metal work function value increases from 3.9 to 4.59 eV.

The simulated results of the dark J–V characteristics are plotted in Fig. 2b. From this figure, it is important to note that the dark current–voltage characteristic has an ideal form; i.e., the front contact is perfectly ohmic when the \(\varphi_{\text{m}}\) value is less than 4.2 eV. It can be concluded that the degradation in the conversion efficiency when \(\varphi_{\text{m}}\) value exceeds 4.2 eV is directly related to the dark current density since the illuminated current density \((J_{\text{ph,m}} )\)is slightly reduced (about 0.8 mA cm⁻²) due to the barrier created at the metal/a-Si:H(n⁺) interface.

In the next section, using the J–V characteristics presented in Fig. 2a and b, we investigate the metal/a-Si:H(n⁺) interface based on a similar double-diode model and a straightforward technique that extracts the reverse saturation current densities of the two diodes, the series resistance and the effective barrier at the metal/a-Si:H(n⁺) interface.

Taking into account the effect of the Schottky contact, Fig. 3 shows the circuit model of the HIT cell defined by two opposite polarity diodes in series. The main cell n⁺/p junction diode (\(D_{\text{m}}\)) and the Schottky diode (\(D_{\text{s}}\)) are connected by two current sources in parallel \(J_{\text{ph,m}}\) and \(J_{\text{ph,s}}\), respectively. The current density \(J_{\text{ph,m}}\) refers to the total photocurrent density generated when the front contact is perfectly ohmic, whereas the second term represents the degradation of \(J_{\text{ph,m}}\) when the metal work function is not low enough to ensure a good ohmic contact with the emitter layer. The equivalent circuit is completed by a series resistance \(R_{\text{s}}\) and two shunt resistances \(R_{\text{sh}}\) and \(r_{\text{sh}}\) which are connected in parallel to the \(D_{\text{m}}\) and \(D_{\text{s}}\) diodes, respectively. It is assumed that the circuit elements between points A and B and between B and C (see Fig. 3) can be treated as independent circuits.

Under illumination, the current–voltage characteristic between the points A and B can be expressed using Kirchhoff’s laws as:where \(V_{\text{m}}\) is the voltage across the main diode, \(q\) is the electronic charge, \(k_{\text{B}}\) is the Boltzmann constant, and \(n\) is the ideality factor \(T\) is the absolute temperature in kelvin. Neglecting the recombination of carriers in the space-charge region of the main junction n⁺/p, the ideality factor is equal to unity (\(n = 1\)).

The shunt resistance values are extracted from J–V characteristic in the dark at low polarization (\(V \le\) 0.25 volts) by applying the Ohm’s law:

In our study, the reverse saturation current density \(J_{{ 0 {\text{m}}}}\) of the main junction diode is extracted when the J–V curve starts to show a rollover practically at \(V_{\text{m}} = V_{\text{m,s}}\). Then, the \(J_{{ 0 {\text{m}}}}\) values are extracted using this equation:

\(J_{\text{sc}}\) is the short-circuit current density. It is practically the total photocurrent density of the equivalent circuit model (\(J_{\text{sc}} = \left| {J_{\text{ph,m}} - J_{\text{ph,s}} } \right|\)). According to Cheung–Cheung method [19], the series resistance can be extracted from J–V characteristic in the dark using:

Since the emitter contact may induce a Schottky barrier at the metal/a-Si:H(n⁺) interface, the current in the Schottky diode is governed by thermionic emission for \(V \ge V_{\text{m,s}}\). Using the equivalent circuit between points B and C and neglecting the photocurrent \(J_{\text{ph,s}}\), the Schottky current density (\(J_{\text{sch}}\)) is expressed as follows:\(J_{{ 0 {\text{s}}}}\) is the Schottky diode reverse saturation current density. It is the current density where the J–V curve starts to show a rollover, i.e., \(J_{{ 0 {\text{s}}}} \simeq J\left( {V = V_{\text{m,s}} } \right)\). It is given by:where \(A^{*}\) and \(\phi_{\text{b,eff}}\) are the Richardson constant and the effective Schottky barrier at the metal/a-Si:H(n⁺) interface, respectively. Away from the metal/a-Si:H(n⁺) junction, the effective Schottky barrier is expressed by:

\(\chi\) is the electronic affinity of amorphous silicon. \(N_{\text{c}}\) and \(N_{{{\text{d}} . {\text{act}}}}\) are the effective states’ density in the conduction band edge and the active electron density in the a-Si:H(n⁺) layer, respectively. The voltage across the Schottky diode is given by:

The values of the shunt resistance and the reverse saturation current density of the main diode calculated from Eqs. 2 and 3 are regrouped in Table 2. It should be noted that the \(J_{{ 0 {\text{m}}}}\) values are practically constant when the \(\varphi_{\text{m}}\) value is less than 4.47 eV and undergoes a significant increase when the front-metal work function exceeds this value. This is explained by the increase in the Schottky barrier with increasing \(\varphi_{\text{m}}\) which is confirmed by the simulated band diagrams at equilibrium displayed in Fig. 4. The decrease in the active electron density \(N_{\text{d,act}}\) listed also in Table 2 is due to the interaction between the electric fields at the metal/a-Si:H(n⁺) interface and at the a-Si:H(i)/c-Si(p) heterointerface, which results in a significant reduction in the free majority carriers in the a-Si:H(n⁺) layer. Consequently, the reverse saturation current density in this region increases.

Using the dark current–voltage characteristics presented in Fig. 2b, the series resistance calculated from Eq. 4 increases sharply when the barrier at the metal/a-Si:H(n⁺) interface is increased as depicted in Fig. 5.

To better understand the effect of the series resistance and the Schottky barrier created at the front contact on the performance of the HIT cell, we introduce in our study the algebraic deviation between the saturation voltage \(V_{\text{m, s}}\) and the open-circuit voltage \(V_{\text{oc}}\) given by:

As mentioned earlier, the saturation voltage across the \(D_{\text{m}}\) diode is extracted from the simulated data of the J–V characteristic. Based on the \(\Delta V\) signs extracted in our study (see Table 2), it can be also noted that the decrease in the conversion efficiency (~ 0.9%) when the value of \(\varphi_{\text{m}}\) increases from 3.9 to 4.47 eV is not related to the Schottky barrier as shown in Fig. 4. But it is due to the increase in the series resistance, since the \(V_{\text{m,s}}\) value is large than the open-circuit voltage (\(\Delta V \ge 0\)).

On the other hand, when the front-metal work function values are greater than 4.47 eV, the main diode saturation voltage has a lower value than the open-circuit voltage (\(\Delta V <\) 0). Consequently, the 3.3% degradation of the conversion efficiency when \(\varphi_{\text{m}}\) value passes from 4.47 to 4.59 eV is due to the series resistance and the rectifying Schottky barrier at the front contact. Moreover, when the front-metal work function is larger than 4.47 eV, the active doping concentration in the n⁺-region decreases. The active electron density in the emitter layer at the heterointerface significantly drops leading to a strong enhancement of the reverse saturation current density \(J_{{ 0 {\text{m}}}}\) and a serious \(V_{\text{oc}}\) degradation (about 46 mV) which results in a significant reduction in the conversion efficiency.

In Fig. 6, we showed the Schottky diode saturation current density versus the effective barrier created at the metal/a-Si:H(n⁺) interface. Generally, we observe that this variation follows a decreasing exponential law. The Richardson constant estimated from an exponential fit at room temperature is 116 A cm⁻² K⁻². This value is comparable to the one reported in the literature (\(A^{*}\) = 120 A cm⁻² K⁻² for n-type semiconductor) [20].

The J–V characteristics of the HIT cell under illumination obtained by the circuit model analysis using the physical parameters listed in Table 2 are plotted in Fig. 7a for different metal work functions. The voltage drops across the different circuit elements determined from our analytical study are plotted in Fig. 7b as a function of the terminal cell voltage \(V\). It should be noted from Fig. 7a and b that the effect of the series resistance on the J–V characteristic is dominant when the terminal cell voltage is less than the \(V_{\text{m,s}}\) value. As the metal work function is increased, the Schottky current density saturates at a lower value, and hence, a rollover occurs at lower bias voltage. Note that the rollover changes dramatically over a relatively narrow range of \(\varphi_{\text{m}}\) (\(\varphi_{\text{m}} >\) 4.47 eV).

The effect of shunt resistance at the Schottky diode on rollover is also studied. The analytical results (Fig. 7a) showed that \(r_{\text{sh}}\) affects only the rollover part of the J–V curve (\(V > V_{\text{ms}}\)). The slope of the rollover curve is the leakage conductance at the front contact (\(1/r_{\text{sh}}\)). Hence, the fill factor is not affected by the magnitude of the shunt resistance (see Table 3).

As depicted in Fig. 7a, a good agreement is obtained between the simulated results and those of our circuit model analysis assuming a series resistance, Schottky saturation current density and a shunt resistance which are regrouped in Table 3. It is also important to note that the interpretations given in the previous paragraph concerning the degradation of the conversion efficiency and the open-circuit voltage as a function of the metal work function are confirmed by the J–V characteristics obtained from our circuit model analysis.

The doping level of the a-Si:H(n⁺) layer designates a physical parameter able to influence the Schottky barrier’s height at the front-metal/a-Si:H(n⁺) interface. For this reason, in this section, we study the effect of the doping level on the photovoltaic parameters of the HIT cell. Figure 8a and b shows the variation of the simulated open-circuit voltage and the conversion efficiency as a function of n⁺-layer doping level for different \(\varphi_{\text{m}}\) values.

As can be seen, the \(V_{\text{oc}}\) and the η values are practically not influenced by the doping level when the front contact is perfectly ohmic (\(V_{\text{oc}}\) ~ 636 mV and η ~ 19.3%). It can be also noted that the performance of the HIT cell increases with the n⁺-layer doping when the metal work function is more than 4.2 eV.

The expanded view for the top 40 nm of the simulated energy band diagram at equilibrium of the HIT cell for moderately and heavily doped n⁺-layer (\(N_{\text{d}}\) = 2 × 10¹⁸ and 6 × 10¹⁹ cm⁻³) is presented in Fig. 9a and b, respectively. According to these band diagrams, it is important to note that the barrier’s height at the metal/a-Si:H(n⁺) interface for each \(\varphi_{\text{m}}\) value is identical for the two a-Si:H(n⁺) doping concentrations under study. On the other hand, when the emitter layer is moderately doped (\(N_{\text{d}}\) = 2 × 10¹⁸ cm⁻³), the separation between the conduction band and the Fermi energy in the quasi-neutral bulk region increases with the metal work function (see Fig. 9a). This is explained by the strong interaction between the electric fields at the metal/a-Si:H(n⁺) and at the a-Si:H(i)/c-Si(p) interfaces. It can be concluded that the carrier recombination in the bulk of the emitter region increases, and the free electron density decreases. Consequently, the value of the shunt resistance decreases and the reverse saturation current density of the main diode is enhanced. Moreover, when the a-Si:H(n⁺) layer is heavily doped, the interaction between the electric fields at the metal/a-Si:H(n⁺) and at the a-Si:H(i)/c-Si(p) interfaces is very weak. The effect of the Schottky barrier on the reverse saturation current density of the main diode decreases.

Finally, compared to the perfectly ohmic metal/a-Si:H(n⁺) interface (\(\varphi_{\text{m}} =\) 4.20 eV), Table 4 shows that for moderately doped n⁺-region the conversion efficiency and the open-circuit voltage undergo a significant degradation (about 4.5% and about 47 mV). The physical parameters of the equivalent circuit model (\(J_{{ 0 {\text{m}}}}\) and \(R_{\text{sh}}\)) extracted in our study and regrouped in Table 4 confirm that the degradation of the performance of the HIT cell is due to the decrease in the shunt resistance and the enhancement of the reverse saturation current density of the main diode when the Schottky barrier increases (\(\varphi_{\text{m}} \ge\) 4.48 eV).