The Americans gave credit to themselves for something invented before Hall -rediscovered it.
Gus Hall (Gus Hall, 1910-2000)
Holzer (A.H.Hall, 1855 - 1938)
In 1879, physicist Holzer found Holzer effect when Hall was a rookie 24 yr old and Americans made it their own invention, now called by the Hall Effect. ( ! )
I see three things that are hurting your charge pump circuit.
The capacitors are aluminum electrolytic instead of ceramic, so they have very high dissipation factor and low self-resonant frequency. These charge pumps really do require ceramic capacitors.
Second, they are radial-leaded and axial-leaded capacitors instead of surface-mount. That adds some series inductance, which tends to defeat the capacitance.
Third, the whole thing is built on a white solderless breadboard, which adds even more inductance. You'd be better off using a PCB breakout board (like a Surfboard) and solder capacitors with trimmed short leads, or better yet, surface-mount capacitors.
Not all capacitors are created equal, and not even all ceramic capacitors are created equal. The X7R and X5R types give fairly large capacitance values stable over a good temperature range. The cheaper Y5V, Y5U, and Z5V types can lose a lot of their capacitance over temperature, so sometimes we have to compensate for that loss by using higher nominal starting capacitance. (The NP0 and C0G types are highly stable over temperature, but usually are only available in very low capacitance values.)
Back in the day, ceramic capacitors were only available up to about 10uF, but nowadays there are 100uF ceramic capacitors. So the need for using tantalum and aluminum electrolytics is somewhat diminished; now it's driven by a cost vs performance trade-off.
The self-resonant frequency (SRF) is important in switching circuits, because at frequencies higher than SRF, the capacitor stops behaving like a capacitor and starts behaving like an inductor. Surface-mount ceramic capacitors are usually higher SRF and thus closer to "ideal" capacitors.
Aluminum electrolytic capacitors are great for providing a large amount of capacitance and accepting large inrush current, these are typically seen on power supply inputs. But they don't work well for the "flying capacitor" of a charge pump.
Take a look at MAX619EVKIT http://datasheets.maximintegrated.com/en/ds/MAX619EVKIT.pdf for an example of a good charge pump layout, using surface-mount ceramic capacitors.
Disclosure: I am a Maxim employee and designed the MAX619EVKIT way back when great lizards roamed the earth.
Best Answer
Cf and Rf form a first-order low-pass filter with a cutoff frequency \$f_C = \frac {1}{2\pi R C}\$. The response will be reduced to 0.707 (1/2 power) at that frequency. A first-order filter response only drops by -6dB/octave, so attenuation only increases gently.
The maximum value of Rf is determined by the requirements of whatever it is connected to, and perhaps the leakage of the capacitor. The minimum value is determined by the capability of the part, and 4.7K is specified. If you were to try to use, say, 10M ohm you'd need a very low leakage capacitor and a very low input bias current/input impedance input on whatever its connected to. Often you can only go to a few K ohms if you're going directly into a micro.
There is no maximum or minimum for the capacitance value, provided you keep the resistance more than 4.7K. You could use a 10uF capacitor and a 100K resistor (if whatever it's connected to is okay with 100K) and get a 0.16Hz cutoff if you want. The trade-off is that the response will be sluggish and it will take many seconds to settle to a stable value (a bit less than 5 time constants or 5 seconds in this case to get within 1% of the final value).