Half wave rectifier at high frequency and small amplitude ac signal 
This is the picture taken from my oscilloscope where I was just checking how a standard half wave rectifier properties. The yellow one is input signal of frequency 20.5KHz and peak to peak value is 100mV(less than 700mV. I know!). In this case the whole of the input signal passes through, there is no rectification. I am trying to find explanations for this.
I have observed that the output signal lags behind the input, so it must be capacitive effect. But I want to get a clearer idea of how the circuit works in this region. What is the source of the capacitance? Is it only the depletion region? How is the negative portion also passing through diode?
 A: 
I've developed a half wave rectifier circuit in LTspice and I've got the result as shown in figures. In first figure, the input voltage(V(n001)) is 400mV(frequency 20.5kHz), which is grater than the threshold voltage of the diode and the output voltage gives a half rectified pattern. But when I give the input voltage value 200mV, which is less than the threshold voltage, I get a  sine wave which indicates the capacitave effect of the diode.
Now when the input voltage is less than threshold voltage of the diode then majority carriers of the diode can not cross the potential barrier of the diode. As a result the space charge region of the diode here acts like a dielectric of a capacitor where the charge in the both side of this region acts like a charge on capacitor plates.So in low input voltage(below threshold voltage) diode acts like a capacitor.
When the frequency of the input voltage is very small then we get a very low amplitude of output voltage as shown in fig. below.

we know that the reactantce of a capacitor is $\frac{1}{j \omega}$ i.e. at low frequency the reactance of the diode capacitance becomes very high. As a result we get a very low output amplitude in low frequency.
And the peak of the output voltage pattern at low frequency due to quantum tunneling effect of the semiconductor carriers. When the positive peak of the input voltage comes across the diode, some carriers get some energy form that and cross the potential barrier. Of course those  carriers had energy less than the potential barrier.
