Tunnel junction simulation of all-perovskite tandem solar cells

Abstract

All-perovskite tandem solar cells are a promising photovoltaic technology, but their efficiency is strongly limited by the tunnel junction. The tunnel junction enables carrier tunneling and recombination, which depend on the interfacial band alignment. Through quantitative simulations using Silvaco Technology Computer Aided Design (TCAD), we find that hole tunneling is intrinsically more difficult than electron tunneling in the tunnel junction. Efficient tunnel junctions require minimizing the barrier for holes while maintaining a moderate barrier for electrons to balance tunneling. For the SnO₂/metal/PEDOT:PSS tunnel junction in all-perovskite tandem solar cells, tuning the metal work function achieves balanced electron and hole tunneling, reduces junction resistance, and directly enhances performance of tandem solar cells. This work provides quantitative design rules for tunnel junction optimization, offering a clear pathway toward high-performance all-perovskite tandem solar cells.

Graphical abstract

Keywords

Tunnel junction / Perovskite / Tandem solar cell / Work Function / TCAD simulation

1 Introduction

All-perovskite tandem solar cells (TSCs) have reached efficiencies above 30% and still show room for improvement toward the theoretical limit (~45%) [1–3]. Advancing toward this limit requires not only high-quality absorbers but also efficient electrical connection between sub-cells [4,5]. The tunnel junction is essential, as it connects the sub-cells in series and controls carrier recombination at the interface [6–8].

In most cases, the tunnel junction contains a thin metal layer between SnO₂ electron transport layer (ETL) and PEDOT:PSS hole transport layer (HTL) [1,2,9]. Charge transport involves tunneling across SnO₂/metal and PEDOT:PSS/metal interfaces [7]. Small changes in interfacial band alignment can strongly influence tunneling because the probability depends exponentially on barrier height [10]. Conventional III–V TSCs use heavily doped p⁺/n⁺ tunnel junction, enabling efficient band-to-band tunneling with weak sensitivity to interfacial band alignment [11]. In contrast, tunnel junctions of all-perovskite TSCs exhibit lower tunneling probabilities and are more prone to interfacial mismatch [7]. Progress on tunnel junctions of all-perovskite TSCs so far has mostly relied on empirical choices, such as using Au or Cu/Au composite as the interlayer metal [12–14], but understanding on the tunneling mechanism remains unclear.

In this work, we conducted fundamental analysis and simulations of the tunnel junction in all-perovskite TSCs. First, we examined the characteristics of the tunnel junction and found that hole tunneling is intrinsically more difficult than electron tunneling. Both electron and hole tunneling are strongly affected by the barrier height, which is determined by the metal work function (Φ_M) in the tunnel junction. We then systematically tuned the Φ_M to modify interface band alignment, which affects tunneling current and equivalent series resistance. We find that achieving an efficient tunnel junction requires minimizing the barrier at the PEDOT:PSS/metal interface to enable hole tunneling, while keeping a moderate barrier at the SnO₂/metal interface to allow electron tunneling. Finally, we evaluated the effect of the tunnel junction on performance of TSCs and found that device-level trends follow analysis of the tunnel junction. The highest efficiency appears when hole and electron tunneling are balanced and efficient. These results provide quantitative design rules for tunnel junction engineering, offering clear guidance for advancing high-efficiency all-perovskite TSCs.

2 Results and discussion

2.1 Characteristics of tunneling junction in all-perovskite TSCs

A two-terminal tandem solar cell (TSC) consists of a wide-bandgap (~1.78 eV) top sub-cell, a tunnel junction, and a narrow-bandgap (~1.2 eV) bottom sub-cell (Fig. 1a). The tunnel junction conducts opposite to the sub-cells, so it operates under reverse bias when the TSCs work at maximum power point (Fig. 1b). Tunnel junctions typically use highly doped semiconductors to enable rapid carrier recombination and a low equivalent resistance. In III–V TSCs (Fig. 1c), n⁺⁺/p⁺⁺ tunnel junctions with doping ~10²⁰ cm⁻³ allow efficient interband tunneling [15]. The resulting J–V curve exhibits a “S-shape” with valley current density (J_valley) exceeding the sub-cell photocurrent by more than an order of magnitude, ensuring unimpeded current flow (Fig. 1d) [11].

In all-perovskite TSCs, the SnO₂ ETL and PEDOT:PSS HTL are lightly doped, typically below 10¹⁸ cm⁻³ [16,17]. Such low doping is insufficient to achieve interband tunneling. To achieve efficient tunneling in all-perovskite TSCs, a composite tunnel junction uses an ultrathin metal layer between the ETL and HTL to assist tunneling [8,12,18]. The metal forms a near-Ohmic contact with the HTL while creating a Schottky junction with the ETL (Fig. 1e and 1f). In this configuration, charge transport across the tunnel junction is governed primarily by electron tunneling, thereby maintaining current conduction. The tunneling current density through the Schottky junction can be described by Eq. (1) [19],

(1)J\propto \exp \left(-\frac{2}{q\hslash }{\left(\frac{m^{\ast }{\epsilon }_{\mathrm{r}}{\epsilon }_0}{N_{\mathrm{D}}}\right)}^{\frac{1}{2}}q\left(V_{\mathrm{D}}-V\right)\right),

where J is the saturation current density, q is the elementary charge, ℏ is the reduced Planck constant, m* is the electron or hole effective mass, ε_r is the relative permittivity of the semiconductor, ε₀ is the vacuum permittivity, N_D is the doping concentration, V_D is barrier height, and V is the applied bias voltage. From Eq. (1), tunneling probability depends strongly on both barrier height and carrier effective mass. In SnO₂, electrons have an effective mass of ~0.2 m₀ [20], while in PEDOT:PSS, holes reach ~4.8 m₀ [21]. Thus, the tunneling probability of holes is four orders of magnitude lower than electrons. Therefore, minimizing the HTL/metal barrier while keeping electron tunneling at the ETL/metal interface efficient is crucial. From Eq. (1), tunneling barriers for electrons and holes can be tuned by adjusting the Φ_M. The following section will focus on the role of the Φ_M in tailoring the barrier properties of the tunnel junction and its impact on performance of TSCs.

2.2 Simulation of tunnel junction in all-perovskite TSCs

Simulations of tunnel junction were performed using the Atlas module of Silvaco Technology Computer Aided Design (TCAD). Silvaco TCAD is a widely used commercial tool for semiconductor device modeling. It uses finite-element methods to solve the full set of semiconductor equations, including the Poisson equation, continuity equations, and drift-diffusion or carrier-transport models. Atlas is a physics-based semiconductor simulator that solves the Poisson equation along with the electron and hole continuity equations under steady-state conditions [22]. To accurately model tunneling transport across the Schottky barrier, the universal Schottky tunneling model was implemented [23]. Carrier transport at the tunnel-junction interface is modeled using the Schottky tunneling model. The tunneling probability is calculated via the WKB approximation. Image-force corrections are included in the calculation of the effective barrier height. We use the standard image-potential formulation as follows [24,25]:

(2)E_{\mathrm{e}\mathrm{f}\mathrm{f}}=V_{\mathrm{D}}-\sqrt{\frac{qE}{4\pi {ϵ}_{\mathrm{s}}}},

where E_eff is the effective barrier height, V_D is the ideal barrier height, q is the elementary charge, E is the interfacial electric field, and ϵ_s is the semiconductor dielectric constant. This treatment ensures that the computed tunneling current reflects realistic interfacial physics.

The work functions of ETL and HTL are approximately 4.6 eV and 5.3 eV, respectively, estimated from their doping levels and effective density of states (Table S1). To evaluate the impact of band alignment, Φ_M was scanned from 4.2 eV to 5.6 eV, covering common electrode materials such as Ag (4.3 eV) and Au (5.1 eV) [26]. Based on the position of Φ_M relative to the ETL and HTL work functions, the tunnel junction can be divided into three situations, as shown in Fig. 2a–c.

When Φ_M ranges from 4.2 eV to 4.6 eV, the tunnel junction enters the regime shown in Fig. 2a. An Ohmic contact forms with the ETL, while the HTL/metal interface has a large barrier exceeding 0.7 eV. This high barrier can strongly suppress hole tunneling. The simulated J–V characteristics indicate that the forward tunneling current is limited (Fig. 2d), resulting in an extracted equivalent series resistance exceeding 100 Ω cm² (Fig. 2g). In typical tandem sub-cells, intrinsic series resistance ranges from 30 to 40 Ω cm² [27]. The additional resistance from the tunnel junction can be more than four times the total, significantly lowering the fill factor (FF) and efficiency of TSCs.

When Φ_M ranges from 4.6 eV to 5.1 eV, the tunnel junction transitions to the regime illustrated in Fig. 2b. The turn-on voltage of tunnel junction gradually decreases from above 0.4 V to nearly 0 V (Fig. 2e). Consequently, the equivalent series resistance drops sharply from over 100 Ω cm² to below 10⁻² Ω cm² (Fig. 2g), due to the reduction of the HTL/metal barrier from ~0.7 eV to ~0.2 eV. According to Eq. (1), lowering the hole barrier height by ~0.5 eV greatly increases the hole tunneling probability by over ten orders of magnitude, overcoming the intrinsic disadvantage of the larger hole effective mass. As a result, holes can efficiently tunnel and recombine with electrons in the metal, sharply reducing the equivalent resistance of the tunnel junction. At a representative Φ_M of 5.1 eV, the HTL/metal barrier is reduced to ~0.2 eV, while the ETL/metal barrier remains moderate at ~0.5 eV. Under these barrier conditions, holes and electrons tunnel with balanced efficiency, reducing the tunnel junction series resistance to about 10⁻² Ω cm². This balance is crucial because electrons and holes have different effective masses in SnO₂ and PEDOT:PSS, and the tunneling current depends on both the barrier height and carrier effective mass. The configuration balances hole and electron tunneling for optimal tunnel junction.

When Φ_M ranges from 5.1 eV to 5.6 eV, the HTL/metal interface forms an Ohmic contact (Fig. 2c), while the ETL/metal barrier rises from ~0.5 eV to ~1.0 eV. The increasing ETL barrier suppresses electron tunneling, making carrier recombination progressively limited by electron tunneling (Fig. 2f). As a result, the tunnel junction series resistance increases sharply from ~10² Ω cm² to ~10⁵ Ω cm² (Fig. 2g), reflecting the reduced electron conduction.

We further assessed the robustness of the optimal intermediate-metal work-function range under realistic material and device variations. Sensitivity studies on SnO₂ doping (10¹⁰–10¹⁷ cm⁻³) and the hole effective mass of PEDOT:PSS (4.0–5.5 m₀) all show that the minimum equivalent series resistance consistently appears at Φ_M = 5.0–5.2 eV (Fig. S1). Temperature-dependent simulations from 25°C to 125°C also preserve this optimal range (Fig. S2), despite possible changes in carrier effective masses, metal work functions, and barrier heights. These results confirm that the identified optimal Φ_M range remains stable against realistic variations in material parameters and operating temperature, supporting the general applicability of our conclusions. In addition, we validated our simulation results experimentally using SnO₂/metal/PEDOT:PSS tunnel junctions with Au (5.1 eV), Cu (4.7 eV), and Ag (4.3 eV) as intermediate metals. The measured J–V characteristics and series resistances follow the trends predicted by simulations, with metals near the optimal Φ_M range (5.0–5.2 eV) showing the best conduction and lowest resistance (Fig. S3).

2.3 Effect of Φ_M on device performance

Simulations show that achieving balanced and efficient tunneling of holes and electrons is essential for a high-performance tunnel junction. The next step involves investigating the impact of the optimized tunnel junction on the performance of all-perovskite TSCs.

The J–V characteristics of the wide-bandgap sub-cell, narrow-bandgap sub-cell, and the all-perovskite TSCs were simulated (Fig. 3a–c). The tandem simulation first uses Au as the interlayer metal to verify the validity of the tandem model [8]. The simulated device parameters of the wide-bandgap sub-cell, narrow-bandgap sub-cell, and the TSC are summarized in Table 1. The simulation results indicate that the TSC achieves an open-circuit voltage (V_OC) of 2.29 V, which is nearly the sum of the V_OC values of the wide-bandgap (1.39 V) and narrow-bandgap (0.94 V) sub-cells, demonstrating effective series connection. The short-circuit current density (J_SC) is 17.38 mA cm⁻², limited by the lower-generating wide-bandgap sub-cell, in line with current-matching requirements. The FF reaches 85.4%, slightly higher than the wide-bandgap (85.0%) and narrow-bandgap (80.1%) sub-cells. The overall power conversion efficiency (PCE) achieves 34.01%, indicating efficient carrier recombination across the optimized tunnel junction. These results demonstrate that the Silvaco TCAD model accurately captures behavior of TSCs, providing a solid basis to analyze the effect of Φ_M on TSCs.

When Φ_M is low (4.2–4.6 eV), the TSC shows poor performance. The J–V curve (Fig. 3d) shows a slow increase of current density near the V_OC, indicating hindered carrier transport. The FF drops to ~68% and the V_OC is limited to ~1.78 V (Fig. 3f and 3g). Based on the previous tunnel junction analysis, a shallow Φ_M creates a large barrier (> 0.7 eV) at the HTL/metal interface. The high barrier suppresses hole tunneling and recombination, preventing effective series connection between the two sub-cells.

As Φ_M increases from 4.6 eV to 5.1 eV, the TSC performance improves. The J–V curve (Fig. 3d) becomes steeper near the V_OC, indicating more efficient carrier transport. FF rises from 68% to 85% and V_OC increases from 1.78 V to 2.29 V (Fig. 3f and 3g). At Φ_M between 4.6 eV and 5.1 eV, the HTL/metal barrier reduces to ~0.1–0.2 eV while the ETL/metal barrier remains moderate (< 0.5 eV). Both holes and electrons tunnel efficiently. The tunnel junction provides minimal additional resistance, enabling effective series connection between the two sub-cells. At Φ_M = 5.1 eV, the TSC reaches a maximum FF of ~85%, consistent with tunnel junction simulations showing the lowest equivalent series resistance (10⁻² Ω cm²).

When Φ_M exceeds 5.1 eV, the TSC performance declines slightly (Fig. 3e), with the FF dropping from 85% to 72% (Fig. 3g). The HTL forms an Ohmic contact, but the ETL/metal barrier rises above 0.5 eV. The higher barrier reduces electron tunneling and limits recombination in the tunnel junction. The tunnel junction no longer provides a low-resistance pathway, preventing further performance gains.

The J_SC of TSCs remains nearly constant across the Φ_M range (Fig. 3h). Under short-circuit or reverse-bias conditions of the TSCs, the tunnel junction operates at a substantial forward bias, allowing efficient tunneling. This forward tunneling maintains carrier flow, keeping the J_SC nearly unchanged. The PCE of TSCs exhibits a clear maximum around Φ_M ≈ 5.1 eV (Fig. 3i), following the trends in FF. The FF of TSCs varies significantly with the Φ_M, consistent with the change in equivalent series resistance of the tunnel junction. The open-circuit voltage remains nearly unchanged in the range of 4.8 eV to 5.4 eV. These results show that tunnel junction performance directly controls efficiency of TSCs through barrier engineering. We further studied the effect of metal thickness on tunnel junction performance. Varying thickness from 5 nm to 10 nm has minimal impact on series resistance (Fig. S4a), as tunneling is controlled by interface barriers. Thicker metals mainly increase optical losses, reducing photon flux to the bottom sub-cell and lowering short-circuit current, while open-circuit voltage and fill factor remain nearly unchanged (Fig. S4b−e).

Device simulations reveal that the interlayer Φ_M affects performance parameters of all-perovskite TSCs by dictating the recombination efficiency and equivalent series resistance of the tunnel junction. Adjusting Φ_M to 5.0−5.2 eV establishes a small barrier at the HTL/metal interface and a moderate barrier at the ETL/metal interface, enabling efficient tunneling of both holes and electrons and minimizing the equivalent series resistance of the tunnel junction to ~10⁻² Ω cm². Under these conditions, the TSCs achieve a FF of 85% and a peak efficiency of 34%, demonstrating that careful tuning of the tunnel junction is essential for maximizing device performance. The simulated efficiency of 34.01% is higher than typical experimental values due to the use of a near-ideal device model. Bulk recombination is included using representative minority-carrier lifetimes [12,13] (1 μs for wide-bandgap perovskite and 5 μs for narrow-bandgap perovskite), while interface defects and non-radiative recombination are excluded. This efficiency represents an upper theoretical limit and serves as a benchmark for determining the optimal interlayer metal work-function range of 5.0–5.2 eV.

Our method optimizes interface energy alignment via the intermediate-layer work function Φ_M to achieve balanced tunneling and minimal series resistance. It is general and can analyze any metal-based tunnel junction. The framework predicts energy alignment with adjacent charge transport layers (e.g., SnO₂ and PEDOT:PSS or alternatives) and identifies metals or alloys for optimal conduction.

3 Conclusion

Through Silvaco TCAD simulations, we systematically elucidated the tunneling processes within the tunnel junction of all-perovskite TSCs. The study highlights that carrier transport across the junction is predominantly dictated by the energy barriers at the SnO₂/metal and PEDOT:PSS/metal interfaces, which are in turn controlled by the Φ_M. Optimal tunneling occurs when Φ_M ≈ 5.1 eV, yielding a small ~0.2 eV barrier at the HTL side and a moderate ~0.5 eV barrier at the ETL side. This balanced alignment enables efficient bidirectional tunneling of holes and electrons, reduces the equivalent junction resistance of tunnel junction to ~10⁻² Ω cm², and ensures effective carrier recombination within the interlayer. These results establish Φ_M-driven band alignment as the key design principle for engineering high-performance tunnel junctions in all-perovskite TSCs.

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