Q1. This question has four parts. Credit for each sub-part appears in brackets.In this question, you are asked to consider mobility and scattering processes. In an n-channel metal-oxide-semiconductor transistor, current flow in the device is associated with a charge sheet (electrons) formed at the surface of the semiconductor. In this layer, a "universal" mobility relationship is observed - as illustrated in the graph shown below. The roll-off with increasing electric field is attributed to interface roughness scattering (at the semiconductor/oxide interface). Note that the electric field in this figure is the field perpendicular to the charge sheet - for low electric fields, one would expect that the reported value would correspond to a "bulk" value. The current flow is driven by a different field- namely one applied along the length of the channel.

a.       Consider the 77 K curves in the figure - note that curves are shown for a number of background doping concentrations. Qualitatively explain why the mobility generally decreases with increasing doping density. [5]

b) Consider the low-field region (E < 0.1 MV/cm) -- again at 77K. Based on the value in the graph, what scattering time would you estimate for this regime?

c) What scattering mechanism likely dominates in the regime considered in part (b)? 

d) There are two key trends in the graph: i) the mobility at 77K is higher than  that at 300K and ii) the mobility decreases with increasing vertical electric field. Qualitatively explain these trends in terms of relative contributions to net scattering time from various scattering mechanisms and

increasing/decreasing values as a given parameter changes.