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

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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 Fx the ideas) and ‘di±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±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) Fed-e±ect transisitors (²ET). – 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 Frst, the conduction and valence band edges will line up, while the ²ermi level will exhibit a discontinuity at the junction. But now electrons are free to di±use from the n -region to the p -region, ‘pushed’ by the di±usion term D n n in the DDE. Similarly, holes will be free to di±use to the n region. As these di±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 Feld which will balance and stop the di±usive ³ow of carriers. Statistical mechanics demands that at equilibrium the ²ermi 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 Fgure 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±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 ²all 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 diFerence between the equilibrium ±ermi levels in the the two regions: V bi = E Fn 0 - E Fp 0 = E i + k B T ln ± N D n i ² - E i + k B T ln ± N A n i ² = k B T ln ³ N D N A n 2 i ´ .
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This note was uploaded on 09/13/2010 for the course ECE ECE344 taught by Professor Polizinni during the Spring '10 term at University of Massachusetts Boston.

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

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