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ECE344_2 - p-n junctions Intuitive description What are p-n...

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p-n junctions Intuitive description. What are p-n junctions? p - n junctions are formed by starting with a Si wafer (or ’substrate’) of a given type (say: B-doped p -type, to fix the ideas) and ‘di ff using’ or ‘implanting’ impurities of opposite type (say: n -type, as from a gas source of P – such as phosphine – or implanting As ions) in a region of the wafer. At the edge of the di ff used (or implanted) area there will be a ‘junction’ in which the p -type and the n -type semiconductor will be in direct contact. Refer to the Streetman-Banerjee text, section 5.1, for a description of semiconductor processing. We will review this topic later on, before dealing with metal-oxide-semiconducor (MOS) fied-e ff ect transisitors (FET). What happens to the junction at equilibrium? Consider the idealized situation in which we take an n -type Si crystal and a p -type Si crystal and bring them together, while keeping them ‘grounded’, that is, attached to ‘contacts’ at zero voltage. At first, the conduction and valence band edges will line up, while the Fermi level will exhibit a discontinuity at the junction. But now electrons are free to di ff use from the n -region to the p -region, ‘pushed’ by the di ff usion term D n n in the DDE. Similarly, holes will be free to di ff use to the n region. As these di ff usion processes happen, the concentration of extra electrons in the p -region will build up, as well as the density of extra holes in the n region. These charges will grow until they will build an electric field which will balance and stop the di ff usive flow of carriers. Statistical mechanics demands that at equilibrium the Fermi level of the system is unique and constant. Therefore, the band-edges will ‘bend’ acquiring a spatial dependence. This is illustrated in the left frame of the figure on page 97. Note: 1. Deep in the n -type region to the right and in the p -type region to the left the semiconductor remains almost neutral: The contacts have provided the carriers ‘lost’ during the di ff usion mentioned above, so that n = N D in the ‘quasi-neutral n region and p = N A in the quasi-neutral p region. 2. There is a central region which is ‘depleted’ of carriers: Electrons have left the region 0 x x n 0 , holes have left the region - x p 0 x < 0 , so that for x p 0 x x n 0 we have np < n 2 i . This is called the ‘transition region’ or, more often, the ‘depletion region’ of the junction. Its total width is W = x n 0 + x p 0 . ECE344 Fall 2009 95
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3. The voltage ‘barrier’ built by the difusion of carriers upon putting the n and p regions in contact with each other is called the ‘built-in’ potential, V bi (denoted by eV 0 in the textbook). Streetman and Banerjee present one possible way to calculate it. But an alternative, easier approach is based on the observation that V bi will be given by the di ff erence between the equilibrium Fermi levels in the the two regions: V bi = E F n 0 - E F p 0 = E i + k B T ln N D n i - E i + k B T ln N A n i = k B T ln N D N A n 2 i .
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