ELEC 254 SEMICONDUCTOR (PN JUNCTION) DIODES Physically, diodes are formed by the interface between two regions of oppositely doped semiconductor (i.e., pn junction) and are thus, structurally, the simplest semiconductor devices used in electronics. 1. Ideal Diode An ideal diode is a two-terminal device defined by the following non-linear (current- voltage) iv-characteristic: + v - i Anode Cathode Circuit Symbol "brick wall""arrowhead" 0 Reverse Bias Forward Bias i v "electronic check valve" "FB""RB" Forward Biased Regime (v>0): Zero voltage drop occurs across a forward-biased ideal diode (i.e., the diode behaves like an ideal short circuit). Reverse Bias Regime (v≤0): Zero current flows in a reverse-biased ideal diode (i.e., the diode behaves like an open circuit). Note: From the above, it follows that zero power dissipation occurs in an ideal diode. 2. Real Diode The physics of real pn junctions leads to the following (non-ideal) iv-characteristics: (see Figs. 3.7, 3.8 in S&S 4th ed. - Real Diode current-voltage characteristics) Forward Bias Regime (v>0): The iv-characteristic in this region is closely approximated by i = I s e v/ nV T − 1 ( ) where I s =Reverse Saturation Current (also called Scale Current in S&S text, since I s ∝A). Typically, I s is very small: pA for small Si diodes, fA for IC diodes. 1 Sedra & Smith,  4th Ed. Sedra & Smith,  4th Ed. 2 I s = Aq D p L p N D + D n L n N A       n i 2 =constant for a given diode at a given temperature. n=empirical constant (typically 1≤n≤2, depending on the type of diode and its physical structure), which accounts for carrier gen/recomb in the depletion region (higher J's and fewer centers in IC's, so n is closer to 1, cf. 2 for discrete devices). Actually n depends on the magnitude of v & so is not strictly constant. V T =Volt-Equivalent of Temperature or Thermal Voltage. The Thermal Voltage can also be written explicitly as V T =kT/q where k=Boltzmann's constant (also written k B )=1.38x10 -23 J/K T=Absolute Temperature (K) q=Electronic Charge=1.602x10 -19 C. e.g. At 20 ˚C, V T =25.2 mV ≈25 mV (used throughout S&S text and this course). Clearly, for larger currents (where i>>I s or v>10nV T ) i ≅I s e v / nV T which has been found to hold over several (≈7) decades of current. The diode equation has 2 parameters and hence 2 measurements are required to determine I s and n empirically. Consider the change in diode voltage drop due to a change in diode current: Let I 1 = I s e V 1 /nV T and I 2 = I s e V 2 /nV T , then I 1 /I 2 = e V 1 − V 2 ( ) /nV T or V 1 − V 2 = 2.303nV T log(I 1 /I 2 ) - so slope of log plot yields value of n i.e., the diode voltage changes by ≈2.3nV T for every decade change in diode current (e.g., ≈60 mV for n=1 @20 ˚C). In practice, if n is unknown, a common "rule of thumb" is to assume V 1 -V 2 ≈100 mV/decade @ 20 ˚C, which yields n≈1.7 (in this course, if n is unknown, use n=1). Reverse Bias Regime (V ZK ≤ v≤0): The reverse diode current is also described by i = I s e v/ nV T − 1 ( ) 3 but, since e v/nV T → 0 when v<<0, this expression reduces to i≈-I s so the current "saturates" at -I s when the diode is significantly reverse biased (and hence the name Reverse Saturation Current). Note that the actual reverse current may be mA due to leakage over the surface of the diode and additional carriers generated by collisions in the depletion region. Breakdown Regime (v≤V ZK ): A reversible breakdown occurs when v<V ZK , which gives rise to the steep gradient in the iv-characteristic in this region. There are actually two distinct breakdown mechanisms: 1. Zener breakdown (predominates if -5≤V ZK ≤-2 V) - does not involve collisions (direct disruption of covalent bonds due to E across depletion region; occurs in heavily doped semiconductors, since higher doping results in narrower depletion region 2. Avalanche Breakdown (predominates if V ZK <-7 V) - lightly doped semiconductors A combination of these mechanisms is usually responsible in diodes where -7≤V ZK ≤-5 V. Diodes specifically designed to be operated in this breakdown regime are typically called Zener diodes, regardless of which mechanism dominates. (see Fig. 3.31 in S&S 4th ed. - Zener diode characteristic & circuit symbol - note "reverse" polarity compared to signal diodes) Temperature Dependence: Forward Bias Regime: At a given (constant) diode current, v exhibits a linear temperature dependence due to the dependence of I s and V T on temp. Rule of Thumb: Typically, the iv-characteristic shifts approx. -2 mV/˚C. i v -2 mV/˚C T2 T1 T2>T1 Reverse Bias Regime: The temp. dependence of the reverse current is that of I s . Rule of Thumb: Typically, I s approx. doubles for every 10 ˚C increase in Temp. Sedra & Smith,  4th Ed. 4 Breakdown Regime: The temperature coefficient of Zener diodes depends on both voltage and current. Note: sometimes "TC" is called "Temco". TC mV/˚C i Vz=6.8 V Vz=5.1 V 0 Note: A 6.8 V Zener diode exhibits a TC≈+2 mV/˚C, which is complementary to a forward biased diode! 0.7 V 6.8 V ≈7.5 V+ - ← nearly independent of T (over a useful range of i) 3. Diode Models & Analysis of Diode Circuits e.g. Consider the following circuit: R 10 kΩ V + - 10 V V I V DD = IR + V (1) I = I S (e V/nVT −1) (2) DD Exact Solution: If I s and n for the diode are known, then (1) and (2) can be solved simultaneously to obtain I and V. Graphical Solution: If data are available, then (1) and (2) could be plotted and I and V could be obtained from the intersection. /R v i 0 I V Load Line Quiescent (Operating) Point, Q a similar graphical method is used for the analysis of transistors - later V DD V DD 5 Approximate Solution: If an exact solution is not required, an approximation can be found using an iterative approach: e.g. Suppose the diode is specified as exhibiting a 0.7 V drop at 1 mA (in the text, this is sometimes called "a 1-mA diode" for short), with n=1.8. step 0) Assume that the diode can be adequately described by I ≅ I s e V/nV T (2') Substitute I=1 mA and V=0.7 V (from specs.) to calculate I s I s = 10 −3 e −0.7/nV T which yields I =10 −3 e (V−0.7)/nV T or V = nV T ln(I /10 −3 ) + 0.7 (2'') step 1) As a first guess/approximation, assume V=0.7 V, then I = V DD − V R = 10 V - 0.7 V 10 kW = 0.93 mA The accuracy can be improved by iterating between (1) and (2'') as follows: step 2) Substitute the value of I found in step 1 into (2'') to calculate a new value for V V = (1.8)(0.025)ln(0.93) + 0.7 = 696.7 mV step 3) Substitute this value back into (1), to calculate a new value for I I = 10 V - 0.697 V 10 kW = 0.9303 mA step 4) Continue iterating between (1) and (2'') until (I n − I n−1 ) I n ≤ 1% (arbitrary precision) Graphical representation of iterative method: V /R V v i 0 Load Line (1) 1 2 3 4 5 .7.697 .93 .9303 (2) DD DD 6 Alternatively, appropriate simplifying assumptions can yield an approximate solution. Diode Models (for approximate analyses): 1. Exponential Model (I D = I s e V D /nV T ) 2. Ideal Diode Model  3. Constant-Voltage-Drop Model  Linearized Models 4. Piecewise-Linear (or Battery-plus-Resistance) Model  5. Small-Signal Model (later) (see Figs. 3.1, 3.24, 3.21 of S&S 4th ed. - linearized "Large-Signal" diode models) The choice of which model to apply in a given design/analysis depends on the operating point of the diode and the magnitude of the other voltages and currents in the circuit. e.g. Ideal Diode: may be adequate if V D is negligible compared to other voltages & currents in the circuit. Constant-Voltage-Drop: gives a reasonable approximation at higher currents Piecewise-Linear: is useful at smaller currents (gives significant error at higher currents) Small-Signal Model: Consider the following prototype circuit: v (t) + - V i (t) v (t) v D ( t ) = V D + v d ( t ) i D (t)= I S e v D (t)/ nV T D D d D The expression for i D (t) can be expanded in a Taylor series about the operating point to obtain i D (t) ≈ I D 1 + v d (t) nV T       Small-Signal Approximation (Recall: f (x) = f(x o ) 0! + (x − x o ) 1! f '(x o ) + (x− x o ) 2 2! ′ ′ f (x o ) + L) where I D = I s e V D /nV T = diode current when v d (t)≡0, which remains a good approximation provided [...]...7 vd . 254 SEMICONDUCTOR (PN JUNCTION) DIODES Physically, diodes are formed by the interface between two regions of oppositely doped semiconductor (i.e., pn junction) . Small-Signal Model: Consider the following prototype circuit: v (t) + - V i (t) v (t) v D ( t ) = V D + v d ( t ) i D (t)= I S e v D (t)/ nV T D D d D The expression