The figure I recollect is that urbanisation accounts for 1% or 3% of Earth's total land area. That's in line with requirements for direct solar power.
In practice, that's not entirely appropriable (people and urban environments have some demand for sunlight other than solar PV), and you'd want some geographic distribution to account for weather, seasonality, and power demand variability (daily, weekly, monthly, seasonal), as well as other forms of interruption.
Solar is in theory largely sufficient, and with addition of wind, hydro (both power and storage), and geothermal, affords one possible route to a reasonably-sustainable, reasonably technological future, for a largish population. I suspect it still presents challenges and would probably fall below levels presently experienced in the US and Western Europe, especially at higher latitudes.
In practice, that's not entirely appropriable (people and urban environments have some demand for sunlight other than solar PV), and you'd want some geographic distribution to account for weather, seasonality, and power demand variability (daily, weekly, monthly, seasonal), as well as other forms of interruption.
Solar is in theory largely sufficient, and with addition of wind, hydro (both power and storage), and geothermal, affords one possible route to a reasonably-sustainable, reasonably technological future, for a largish population. I suspect it still presents challenges and would probably fall below levels presently experienced in the US and Western Europe, especially at higher latitudes.