note03 - Introduction to Microelectronics Chapter 3 P-N...

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Introduction to Microelectronics Chapter 3 P-N J UNCTION E LECTROSTATICS AND D IODE IV 3.1 P-N Junction in Equilibrium We have gone through the quantitative treatment for the semiconductors with homogeneous doping in the last Chapter. However, the most straightforward way to utilize the changes of large orders of magnitude in carrier concentrations is to bring them from a majority carrier to become a minority carrier. This implies we put a p-type semiconductor adjacent to a n- type semiconductor. The resulted device is called an abrupt p-n junction diode, or simply the junction diode or bipolar diode. We will go through the details of the electrostatics and IV of diodes in this Chapter, not only because diodes are useful nonlinear circuit elements in rectifiers and memory, but also because a detailed understanding of the diode will be essential to understand transistor operations. Both bipolar junction transistors (BJT) and MOSFET can be viewed as two diodes connected back-to-back together, including their IV characteristics. Consider two pieces of semiconductors, one p-type and the other n-type, as shown in Fig. 3.1. Before they interact with each other or exchange mobile carriers, they will achieve equilibrium by their own. When we bring them in contact, and allow exchange of mobile carriers at the interface, in equilibrium due to the difference in carrier concentrations, the holes will diffuse to the n-type side to leave some N A - exposed, and the electrons will diffuse to the p- type side to leave some N D + exposed, as shown in Fig. 3.2. We assume here at room temperature the donor and acceptor atom will not move at all. The abrupt interface where the two types of the semiconductor met (or in gradual cases, N D = N A ) is called the metallurgical junction . For convenience, we will choose x = 0 at the metallurgical junction. Fig. 3.1. A p-n junction in equilibrium before coupling or exchange of carriers. Edwin C. Kan Page 3-1 9/9/2009 p-type, N A =10 17 cm -3 , N D =0 n-type, N D =10 17 cm -3 , N A =0 N A (P-type doping) N D (N-type doping) Hole: majority p p Electron: minority n p Electron: majority n n Hole: minority p n N D + = n p = n i 2 /n – n + N D + =0 N A - = p n = n i 2 /p p – N A - – n=0
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Introduction to Microelectronics Fig. 3.2. The carrier motion immediately after contact of the p-type and n-type materials allows carrier exchange. A new equilibrium will be set up when the current fluxes cease. The hole diffuses from p-type to n-type and becomes a minority carrier, which can recombine with a majority electron (no problem in finding one) or just out of the contact at the far right. Same thing for the electron diffuses from n-type to p-type. This will form a charge dipole of the left-over ionized dopants close to the metallurgical junction, which is called the “depletion” region. We know that the dipole charge will form electric field and hence a potential difference.
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note03 - Introduction to Microelectronics Chapter 3 P-N...

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