APPLICATION NOTE PIN Diode Basics Introduction Under steady conditions the mobile charge density in the I region is constant, i. e., Basic Theory—Variable Resistance dQ S A PIN diode is essentially a variable resistor. To determine the value = 0, so tha t of this resistance, consider a volume comparable to a typical PIN dt QS diode chip, say 20 mil diameter and 2 mils thick. This chip has a IF = I dc = DC resistance of about 0.75 M Ω. Note: 1 mil = 0.001 inches. TL In real diodes there are impurities, typically boron, which cannot We can next proceed to calculate the forward resistance of a PIN be segregated out of the crystal. Such impurities contribute car - diode of cylindrical geometry with a thickness, W 1, and an area, riers, holes or electrons, which are not very tightly bound to the A. We can ignore some details of analysis not critical to this note. lattice and therefore lower the resistivity of the silicon. The forward current I F was given before as The resistivity of the I region and thus the diode resistance is determined by the number of free carriers within the I region. The IF = Q/T L where Q = Charge per unit volume and resistivity of any semiconductor material is inversely proportional Q = q (N+P) WI A therefore to the conductivity of the material. q (N+P) WI A IF = Expressed mathematically the resistivity of the I region is TL I/ P = q ( µ N+ µ P) 1 N P If there is not unneutralized charge in the I region, P= N and then -19 where q is the electronic charge (q = 1.602 x 10 coul.), µ N and µ P are the mobilities of electrons and holes respectively. 2q NWI A IF = Consider electrons and holes travelling in opposite directions TL within the I region under the impetus of an applied, positive elec - tric field. The I region will fill up and an equilibrium condition will and the resistivity of the I region, given previously, will now be be reached. In non-equilibrium conditions excess minority car - µ + µ µ –1 µ ( N P ) riers exist, and recombination between holes and electrons PI (2q N) where = 2 proceed to restore equilibrium. Recombination often occurs because of interactions between mobile charge carriers and The resistance of the I region will then be: imperfections in the semiconductor crystalline structure, either P I W I –1 W I structural defects or dopant atoms. The rate of recombination of RF = = (2q µN) holes and electrons is proportional to the carrier concentrations A A and inversely proportional to a property of the semiconductor Combining equations yields: called the LIFETIME, T L, of the minority carriers. [2] 2 In the case of applied forward bias, the equation governing WI RF = mobile charges in the I region is 2I F µTL dQ S QS = IF – The above relation is a fundamental equation of PIN diode theory dt TL and design. [3] Rigorous analysis such as reported by Chaffin [4] shows: where Q S is the stored charge and Q S = q(N+P). Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 200823 Rev. A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • August 15, 2008 1 APPLICATION NOTE • PIN DIODE BASICS In simplest form the capacitance of a PIN is determined by the 2kT W I –1 R F = sinh ( ) tan area and width of the I region and the dielectric constant of sil - qI F 2 DT L icon. This minimum capacitance is obtained by the application of W a reverse bias in excess of V PT , the voltage at which the depletion [sinh ( I )] region occupies the entire I layer. 2 DT L CU Where k = Boltzmann’s constant, 1. 38044 x 10 -23 joule/kelvin T = Temperature in degrees kelvin Contacts C D = Diffusion constant D Typical data on R S as a function of bias current are shown in RC Figure 1. A wide range of design choices is available, as the data Depleted indicate. Many combinations of W and T have been developed to L RU satisfy the full range of applications. 500 Undepleted A A Low T L Thick Attenuator Diode B Thick High T L Switching Diode 100 C Low T L Thin Attenuator Diode B D High T L Thin Switching Diode Figure 2. Equivalent Circuit of I Region Before Punch-Through E Beam Lead 0.2 µF C E ) 10 Consider the undepleted region: this is a lossy dielectric con - Ω ( D S sisting of a volume (area A, length L) of silicon of permittivity 12 R E and resistivity ρ. The capacitance is A C 1 12E 0 A 24 π12E 0 A D , and the admittance is B L L 0.1 The resistance is proportional to L/A and the conductance to A/L. 0.1 1 10 100 At voltages below V PT , C J will increase and approach ∞ capaci - Bias Current (mA) tance at a forward bias of 0.7 V in silicon and 0.9 V in GaAs. Skyworks measures junction capacitance at 1 MHz; this is a Figure 1. Typical Series Resistance measure of the depletion zone capacitance. as a Function of Bias (1 GHz) For I region thickness of W and a depletion width X d, the unde - pleted region is (W-X d). Breakdown Voltage Capacitance, Q Factor The capacitance of the depleted zone is, proportionally, The previous section on R S explained how a PIN can become a 1 1 low resistance, or a “short.” This section will describe the other , of the undepleted, Xd W–X d state—a high impedance, or an open. Silicon has a dielectric strength of about 400 V per mil, and all The 1 MHz capacitance decreases with bias until “punch- through” where X = W. At microwave frequencies well above PIN diodes have a parameter called V B, breakdown voltage, d which is a direct measure of the width of the I region. Voltage in the crossover, the junction looks like two capacitors in series. excess of this parameter results in a rapid increase in current C d C U C T = , which is proportional to 1/W flow (called avalanche current). When the negative bias voltage is Cd + C U below the breakdown of the I region, a few nanoamps will be drawn. As V B is approached, the leakage current increases. i. e., the microwave capacitance tends to be constant, Typically leakage current occurs at the periphery of the I region. independent of X d and bias voltage. For this reason various passivation materials (silicon dioxide, sil - However, since the undepleted zone is lossy, an increase icon nitride, hard glass) are deposited to protect and stabilize this in reverse bias to the punch-through voltage reduces the surface and minimize leakage. These techniques have been well RF power loss. advanced at Skyworks and provide a reliable PIN diode. VB is usually specified at a reverse current of 10 microamps. Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 2 August 15, 2008 • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • 200823 Rev. A APPLICATION NOTE • PIN DIODE BASICS 10 CJ A = Zero Punch-Through PIN, Thin Low Voltage B = 200 V PIN C = Thick PIN ) F p ( e c n 1 a t i c Punch-Through a Capacitance p 0.5 a Values from C C 0.05–1.0 pF B Generally Available for A All Types RP 0.1 0 10 100 Reverse Bias (V) Figure 6. Simplified Equivalent Circuit, Shunt Figure 3. Typical Capacitance 10K B 10 GHz C 10 GHz RC CJ RSR A 10 GHz C 18 GHz B 18 GHz A 18 GHz ) Ω ( 1K Figure 4. Simplified Equivalent Circuit, Series P R A = Thin PIN C J = 0.15 pF B = 200 V PIN C J = 0.15 pF C = Thick PIN C J = 0.15 pF 500 A = 200 V PIN C J = 0.15 pF 0.1K A B = Thin PIN 0 10 100 C J = 0.15 pF 100 Reverse Bias (V) A ) Ω ( Figure 7. Reverse Shunt Resistance V 500 MHz R 10 B 3 GHz 0.5 3 GHz 0.4 1 0 10 100 ) A: 10 V B 0.3 d Reverse Bias (V) ( s s B: 100 V o L 0.2 Figure 5. Reverse Series Resistance A = Thin PIN 0.1 C J = 0.15 pF B = Thick PIN A good way to understand the effects of series resistance is C J = 0.15 pF to observe the insertion loss of a PIN chip series mounted in a 50 Ω line. 1 10 18 Frequency (GHz) Figure 8. Insertion Loss vs. Frequency Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 200823 Rev. A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • August 15, 2008 3 APPLICATION NOTE • PIN DIODE BASICS An accepted way to include reverse loss in the figure of merit of a PIN is to write the switching cutoff frequency Diode Impedance R S 1 High R S FCS = 2πC T R S RV Forward Bias Current Current t = 0 Time Charge where R S and R V are measured under the expected forward and Storage reverse bias conditions at the frequency of interest.