has a sheet resistance of 125 H/square. If the P material has a conductivity of 200{) Spurn, find thickness of the layer in microns. Solution. From equation 2-6, p = 1/2000 = 5 X \0′: U· m. From equation 6-37. 5 X \0-4.E.. = 4 X 10-6 m = 4 p,m R.\ 125 • Integrated Circuits 227 The ratio of the length of a diffused resistor to its width, IIW (see Figure 6-19), is called its aspect ratio, a. From equation 6-36, we have (6-38) Since the sheet resistance R, is generally fixed by the requirements for base and emitter diffusion, it is the aspect ratio that designers control to obtain a resistance of desired value.It is desired to fabricate a 1.5-kO resistor using a diffused P layer having sheet resistance 200 O/square. 1. What aspect ratio should the resistor have? 2. What should be the total length of the diffused region if its width is 30 p.,m? Solution 1. From equation 6-38. ( = 1500/200 = 7.5. 2. From the definition of aspect ratio, a I = W= 7.5 1= 7.5W = 7:5(30 p.,m) = 225 p.,m = O.~5 mm For a diffused resistor to have a large resistance, it is clear’ that it must have a large aspect ratio, /IW. This can’ be accomplished by using a zigzag or meandering pattern to increase its length, such as shown in Figure 6-20. In general, very large resistance values arc difficult to obtain in integrated circuits and are avoided where possible. In some cases, large resistance values are obtained using ion implantation, which makes possible a very thin impurity layer (small value of r ), and a corresponding large value for R; One advantage of this method is, the saving of chip space that would otherwise be needed to obtain a large aspect ratio. A resistor can be isolated from other IC components by connecting a suitable reverse-biasing potential around it. For example, the N material in Figure 6-20 could be connected to the highest positive voltage in the circuit. An alternative structure for an integrated-circuit resistor is the double-diffused resistor illustrated in Figure 6-21. To produce this structure, a layer of P material is diffused into the
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epithelial layer at the same time that the base diffusion occurs, and the resistor is then formed as an N-type layer diffused into the P material when the emitter diffusion occurs. It ‘is difficult to obtain precise resistance values in integrated circuits. Tolerances are typically :!::20%. On the other hand. two or more resistors of nearly equal value can be obtained with less difficulty. The production of components having equal or very similar characteristics is called matching, and resistors can be matched to within :!::5% or better. Good matching is possible because resistors are created at the same time using the same diffusion material. In general, integrated-circuit designers avoid design procedures that require precise resistor values and take advantage of techniques that depend on matched values.
