If you look up diodes in a physics book you'll probably find an explanation which finishes up telling you that current through a diode varies exponentially with the applied voltage. The shape of this exponential curve depends upon various factors which include a 'fiddle factor' called the saturation current . There are two problems with this result. One is that the equation is fairly complicated and quite difficult to use for analysing some circuits. Being simple souls who like a quiet life, electronic engineers deal with these problems by simplifying things and using whichever of the following three models of the diode suits them.
V d represents the height of the diode barrier when no voltage is applied.
The 'square law' model assumes that the current, when forward biassed, is proportional to the square of the applied voltage. The 'corner' model assumes that the current is zero for any voltage below V d but rises when we try to apply a voltage greater than this. In effect, the diode is viewed as a sort of 'switch' which is open when we apply low or negative voltages but which closes when we try to apply a voltage equal to or greater than V d . This means that it is impossible to get a voltage larger than this across the diode. In this way of looking at things, V d is called the corner voltage .