#### Transcript Chapter 6 pn Junction Diodes: I-V Characteristics

Semiconductor Device Physics Lecture 8 Dr.-Ing. Erwin Sitompul President University http://zitompul.wordpress.com President University Erwin Sitompul SDP 8/1 Chapter 6 pn Junction Diodes: I-V Characteristics Qualitative Derivation Majority carriers Majority carriers President University Erwin Sitompul SDP 8/2 Chapter 6 pn Junction Diodes: I-V Characteristics Current Flow in a pn Junction Diode When a forward bias (VA > 0) is applied, the potential barrier to diffusion across the junction is reduced. Minority carriers are “injected” into the quasi-neutral regions Δnp > 0, Δpn > 0. Minority carriers diffuse in the quasi-neutral regions, recombining with majority carriers. President University Erwin Sitompul SDP 8/3 Chapter 6 pn Junction Diodes: I-V Characteristics Ideal Diode: Assumptions Steady-state conditions. Non-degenerately doped step junction. One-dimensional diode. Low-level injection conditions prevail in the quasi-neutral regions. No processes other than drift, diffusion, and thermal R–G take place inside the diode. President University Erwin Sitompul SDP 8/4 Chapter 6 pn Junction Diodes: I-V Characteristics Current Flow in a pn Junction Diode Current density J = JN(x) + JP(x) dn d (n) J N ( x) qn nE qDN q n nE qDN dx dx dp d (p ) J P ( x) qp pE qDP q p pE qDP dx dx JN(x) and JP(x) may vary with position, but J is constant throughout the diode. President University Erwin Sitompul SDP 8/5 Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentrations at –xp, xn Consider the equilibrium carrier concentrations at VA = 0: p-side n-side pp0 ( xp ) N A nn0 ( xn ) N D ni2 np0 ( xp ) NA ni2 pn0 ( xn ) ND If low-level injection conditions prevail in the quasi-neutral regions when VA 0, then: pp ( xp ) NA President University nn ( xn ) ND Erwin Sitompul SDP 8/6 Chapter 6 pn Junction Diodes: I-V Characteristics “Law of the Junction” The voltage VA applied to a pn junction falls mostly across the depletion region (assuming that low-level injection conditions prevail in the quasi-neutral regions). Two quasi-Fermi levels is drawn in the depletion region: p ni e( Ei FP ) kT n ni e( FN Ei ) kT np ni2e( Ei FP ) kT e( FN Ei ) kT ni2e( FN FP ) kT np ni2eqVA kT for xp x xn President University Erwin Sitompul SDP 8/7 Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Concentrations at –xp, xn p-side n-side nn ( xn ) ND pp ( xp ) NA ni2 e qVA pn ( xn ) ND 2 qVA kT i ne np ( xp ) NA np0 e President University pn0 e qVA qVA kT ni2 qVA np ( xp ) (e NA kT kT 1) ni2 qVA pn ( xn ) (e ND Erwin Sitompul kT kT SDP 8/8 1) Chapter 6 pn Junction Diodes: I-V Characteristics Example: Carrier Injection A pn junction has NA=1018 cm–3 and ND=1016 cm–3. The applied voltage is 0.6 V. a) What are the minority carrier concentrations at the depletion-region edges? np (xp ) np0eqVA pn ( xn ) pn0eqVA kT kT 100 e0.6 0.02586 1.192 1012 cm3 104 e0.6 0.02586 1.192 1014 cm3 b) What are the excess minority carrier concentrations? np (xp ) np (xp ) np0 1.192 1012 100 1.192 1012 cm3 pn ( xn ) pn ( xn ) pn0 1.192 1014 104 1.192 1014 cm3 President University Erwin Sitompul SDP 8/9 Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Distribution From the minority carrier diffusion equation, d 2 pn pn 0 DP , 2 dx p x 0 We have the following boundary conditions: pn ( xn ) pn0 (eqVA pn () 0 kT 1) For simplicity, we develop a new coordinate system: x 0 0 Then, the solution is given by: x LP x LP pn ( x) Ae A e 1 2 for x 0 LP DP p • LP : hole minority carrier diffusion length President University x Erwin Sitompul SDP 8/10 Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Distribution x '/ LP x '/ LP pn ( x) Ae A e 1 2 New boundary conditions pn ( x 0) pn0 (eqVA pn ( x ) 0 kT 1) From the x’ → ∞, A2 0 From the x’ → 0, A1 pn0 (e qVA / kT 1) x LP Therefore qVA pn ( x ) pn0 (e kT 1)e Similarly, np ( x) np0 (eqVA kT 1)ex LN , x 0 President University Erwin Sitompul , x 0 SDP 8/11 Chapter 6 pn Junction Diodes: I-V Characteristics pn Diode I–V Characteristic n-side d pn ( x) DP J P ( x) qDP q pn0 (eqVA dx LP d np ( x) DN q np0 (eqVA p-side J N ( x) qDN dx LN J JN x xp JP x xn JN x 0 JP DN DP qVA J qn (e LN N A LP N D 2 i President University Erwin Sitompul kT kT kT 1)e x LP 1)e x LN x 0 1) SDP 8/12 Chapter 6 pn Junction Diodes: I-V Characteristics pn Diode I–V Characteristic DN DP qVA I AJ Aqn (e LN N A LP N D 2 i I I 0 (e 1) DP 2 DN I 0 Aqni LN N A LP N D qVA kT President University kT 1) • Shockley Equation, for ideal diode • I0 can be viewed as the drift current due to minority carriers generated within the diffusion lengths of the depletion region Erwin Sitompul SDP 8/13 Chapter 6 pn Junction Diodes: I-V Characteristics Diode Saturation Current I0 DP DN I 0 Aqni L N L N N A P D 2 I0 can vary by orders of magnitude, depending on the semiconductor material, due to ni2 factor. In an asymmetrically doped pn junction, the term associated with the more heavily doped side is negligible. If the p side is much more heavily doped, DP I 0 Aqni L N P D 2 If the n side is much more heavily doped, DN I 0 Aqni L N N A 2 President University Erwin Sitompul SDP 8/14 Chapter 6 pn Junction Diodes: I-V Characteristics Diode Carrier Currents • Total current density is constant inside the diode • Negligible thermal R-G J J N JP throughout depletion region dJN/dx = dJP/dx = 0 J N ( xp x xn ) J N ( xp ) J P ( xp x xn ) J P ( xn ) President University Erwin Sitompul SDP 8/15 Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentration: Forward Bias Law of the Junction np ni2eqVA kT Low level injection conditions pp0 nn0 pp N A nn N D pn0 np0 Excess minority carriers np ( x) np0 (e qVA kT President University x LN 1)e Erwin Sitompul Excess minority carriers pn ( x) pn0 (eqVA kT SDP 8/16 1)e x LP Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentration: Reverse Bias Deficit of minority carriers near the depletion region. Depletion region acts like a “sink”, draining carriers from the adjacent quasineutral regions President University Erwin Sitompul SDP 8/17 Chapter 6 pn Junction Diodes: I-V Characteristics Deviations from the Ideal I-V Behavior Si pn-junction Diode, 300 K. Forward-bias current Reverse-bias current “Slope over” No saturation “Breakdown” Smaller slope President University Erwin Sitompul SDP 8/18 Chapter 6 pn Junction Diodes: I-V Characteristics Empirical Observations of VBR VBR decreases with increasing N, 1 VBR 0.75 NB VBR decreases with decreasing EG. • VBR : breakdown voltage President University Dominant breakdown mechanism is tunneling Erwin Sitompul SDP 8/19 Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Voltage, VBR If the reverse bias voltage (–VA) is so large that the peak electric field exceeds a critical value ECR, then the junction will “break down” and large reverse current will flow ECR 2q N A N D Vbi VBR S NA ND • At breakdown, VA=–VBR Thus, the reverse bias at which breakdown occurs is VBR SECR 2 N A N D Vbi 2q N A N D President University Erwin Sitompul SDP 8/20 Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Mechanism: Avalanching High E-field: High energy, enabling impact ionization which causing avalanche, at doping level N < 1018 cm–3 E 2 CR Small E-field: 2q N A N D VBR S NA ND • ECR : critical electric field in the depletion region Low energy, causing lattice vibration and localized heating President University Erwin Sitompul SDP 8/21 Chapter 6 pn Junction Diodes: I-V Characteristics Breakdown Mechanism: Zener Process Zener process is the tunneling mechanism in a reverse-biased diode. Energy barrier is higher than the kinetic energy of the particle The particle energy remains constant during the tunneling process Barrier must be thin dominant breakdown mechanism when both junction sides are heavily doped Typically, Zener process dominates when VBR < 4.5V in Si at 300 K and N > 1018 cm–3. President University Erwin Sitompul SDP 8/22 Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region R–G in the depletion region contributes an additional component of diode current IR–G. n qA dx t thermal xp xn I R-G R G The net generation rate is given by np ni 2 n t thermal p (n n1 ) n ( p p1 ) R-G ( ET Ei ) kT n1 nie p1 ni e( Ei ET ) kT President University • ET: trap-state energy level Erwin Sitompul SDP 8/23 Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region Continuing, np ni 2 qA dx (n n1 ) n ( p p1 ) xp p xn I R-G For reverse bias, with the carrier concentrations n and p being negligible, • Reverse biases with VA< – few kT/q I R-G qAnW i 2 0 p 1 n where 0 p 1 n 1 2 ni ni President University Erwin Sitompul SDP 8/24 Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region Continuing, np ni 2 qA dx (n n1 ) n ( p p1 ) xp p xn I R-G For forward bias, the carrier concentrations n and p cannot be neglected, qVA IR-G qAnWe i President University 2kT Erwin Sitompul SDP 8/25 Chapter 6 pn Junction Diodes: I-V Characteristics Effect of R–G in Depletion Region I I DIFF I R G Diffusion, ideal diode I DIFF I R-G DN DP qVA Aqn (e LN N A LP N D 2 i kT qVA kT qAnW ( e 1) i 2 0 V V n p 1 bi A eqVA kT q 2 0 President University Erwin Sitompul 1) 2 kT SDP 8/26 Chapter 6 pn Junction Diodes: I-V Characteristics Effect of Series Resistance VJ VA IRS q (VA IRS ) kT I I 0e I 0eqVJ kT , VA Vbi Voltage drop, significant for high I RS can be determined experimentally V IRS slope=RS President University Erwin Sitompul SDP 8/27 Chapter 6 pn Junction Diodes: I-V Characteristics Effect of High-Level Injection As VA increases and about to reach Vbi, the side of the junction which is more lightly doped will eventually reach high-level injection: nn nn0 (for a p+n junction) pp pp0 (for a pn+ junction) This means that the minority carrier concentration approaches the majority doping concentration. Then, the majority carrier concentration must increase to maintain the neutrality. This majority-carrier diffusion current reduces the diode current from the ideal. President University Erwin Sitompul SDP 8/28 Chapter 6 pn Junction Diodes: I-V Characteristics High-Level Injection Effect Perturbation of both minority and majority carrier President University Erwin Sitompul SDP 8/29 Chapter 6 pn Junction Diodes: I-V Characteristics Summary Deviations from ideal I-V Forward-bias current Reverse-bias current Due to high-level injection and series resistance in quasineutral regions Due to thermal recombination in depletion region President University Erwin Sitompul Due to thermal generation in depletion region Due to avalanching and Zener process SDP 8/30 Chapter 5 pn Junction Electrostatics Homework This time no homework. Prepare well for Quiz 2. President University Erwin Sitompul SDP 8/31