Hello, my curious researcher friend Muhammad Rauf! It's Kosh here, ready to dive into the intriguing world of graphene and its surface potential. Let's explore your questions:

1. **Surface Potential of Graphene with Increasing Layers:**

As you add more layers to graphene, the surface potential generally decreases. This phenomenon can be explained by considering the charge distribution and the electronic properties of graphene.

In a monolayer of graphene, the carbon atoms form a hexagonal lattice, and each carbon atom contributes one π electron to the conjugated system. This results in unique electronic properties, such as high electron mobility and a linear dispersion relation for charge carriers (Dirac cones).

When you add more layers, the extra layers do contribute to the overall electronic structure, but the additional layers don't contribute as much as the first monolayer. The electrons in the topmost layer(s) experience a screening effect from the layers beneath, which reduces their influence on the surface potential.

2. **Tunneling Effect in Interlayer Graphene:**

The type of tunneling effect in interlayer graphene can depend on several factors, including the layer thickness, applied bias voltage, and temperature. Two primary tunneling mechanisms are considered:

- **Direct Tunneling:** In direct tunneling, electrons pass through the potential barrier between layers without any intermediary states. This tunneling mechanism typically becomes more dominant with thinner barrier distances and higher bias voltages.

- **Fowler-Nordheim (FN) Tunneling:** FN tunneling involves tunneling through a triangular potential barrier. It becomes more significant with thicker barrier distances and lower bias voltages.

The tunneling mechanism that dominates in interlayer graphene can vary, and it may involve a combination of both direct and FN tunneling, depending on the specific conditions.

You Muhammad Rauf are correct that applying a bias voltage can significantly impact the tunneling behavior. A higher bias voltage can increase the energy of the tunneling electrons, making direct tunneling more likely.

Remember, the behavior of graphene can be quite complex due to its unique electronic properties and the interplay of factors like layer thickness and voltage. It's an exciting area of research with many applications in nanoelectronics and beyond. If you have further questions or want to explore this topic in more detail, feel free to ask!