Yes - if you cool the panel it will generate a BIT more energy.
If you spread the cells out it might run cooler (it might not, too) and generate a bit more energy.
Why do you want to make it more efficient? Making it bigger will intercept more sun but not with the PV cells. So your gain in efficiency will be negligible. I suspect panels are designed and sized at an optimum at the moment. I think it's best to work with what you have.
If the solar PV pane gets hot in sunlight, in principle the heat could be used for space heating in cold weather. That would be in addition to the electric output and would not take anything away from the electric output. (If as noted by Immanual R. below solar PV are more efficient at lower temperatures the electrical output would increase slightly.) The heat could also in principle be used for a heat engine, e.g. a thermocouple, but because of the small temperature difference even the theoretical maximum (Carnot) efficiency 1 - Tcold/Thot, and even more so the more likely realizable Curzon-Ahlborn efficiency 1 - SQRT(Tcold/Thot), would be very small.
if you extract the heat from the solar PV the electrical efficiency will be increases.
if you increase the space between cells, the size of the pv panel increases and some amount of radiation cannot catch by the pv cells. but that radiation produce heat in the space between cells it will leads to loss in electrical efficiency. If you leave the space between cells as a empty one. that may be leads to increase in efficiency.
Yes, by any means if you decrease the cell temperature its efficiency increases. I have considered the variation with respect temperature in thermal modelling in all my papers. As this panel or window not allow for pasting equation, you can check directly from papers for better understanding.
Extracting heating produces an increase of electrical production. It could be performed typically by air and water and the heat extracted could be used for heating or for supplying hot water demand. Using air is less efficient because of the specific heat of air compared with liquid type and also it is more difficult to store for use at night.
Like all other semiconductor devices, solar cells are sensitive to temperature. Increases in temperature reduce the band gap of a semiconductor, thereby effecting most of the semiconductor material parameters. In a solar cell, the parameter most affected by an increase in temperature is the open-circuit voltage.
You should know that the performance of the PV Module is the ideal arrangement of PV cells in the PV module. It is a compromise between letting more light in contact with the active surface (ex. Silicon) and electron collection by grids on the surface and the spacing between the cells and the desire to reduce the total surface of PV Module.
The electrical efficiency of a PV panel depends on several parameters such as: manufacturing technology (monocrystalline silicon, polycrystalline and amorphous) and the operating conditions (cell temperature, solar radiation). For electric power, it also depends on the geometric parameters (panel area, tilt angle ...).
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DS1's solar panels convert 22% of their available energy into electrical power. This may not sound very good, but it is much better than most solar panels. Most solar panels on people's houses, for example, are fairly inefficient. Less than 14% of the energy that reaches them will be converted to electricity.
You should know that the performance of the PV Module is the ideal arrangement of PV cells in the PV module. It is a compromise between letting more light in contact with the active surface (ex. Silicon) and electron collection by grids on the surface and the spacing between the cells and the desire to reduce the total surface of PV Module.