Transcript 슬라이드 1

Chapter 8. pn Junction Diode:
Transient Response
Turn-Off Transient
vA = 0
Fwd-biased
vA > 0
 Assumption: VF & VR ≫ VON
IF 
VR  v A 0t ts VR
VF  VON VF

, IR 

RF
RF
RR
RR
 Storage (delay) time: ts → constant IR
 Reverse recovery time: trr → decay to 10%
 Recovery time: tr = trr － ts
Minority Carrier Storage
 Why is there delay in going from onstate to off-state?
 How is it forward-biased for 0< t < ts ?
 Forward bias: storage of excess
minority carrier in QNR
 Reverse bias: deficit of minority
carriers in QNR
 To progress from on-state to off-state,
excess minority carriers must be
removed.
 The majority of the stored charge is
removed during the storage time ts.
Removal of Excess Minority Carrier Charge
Two mechanisms that operate to remove the excess minority carrier charge
① Recombination
• It takes several minority carrier lifetimes (τs) to die out.
② Reverse current flow
• When the sustaining external bias is reversed, the minority carriers flow
back to the other side of the junction ⇒ very rapid!
• Time required to drift back across the depletion region: W/vd ≒ 10-10 s
• Limitation on the minority carrier removal rate ← maximum reverse current
determined by external circuitry
IR 
VR
RR
Forward Bias due to Excess Minority Carrier
During t < ts,
pn(x=xn, t) > pn0
⇒ Junction is
forward-biased.
Why positive slope
with same value? ⇒
⇒ Residual carrier excess at the edges and
inside the depletion region maintains the
forward bias across the junction.
Exercise 8.1
(a)
(b)
(c)
Charge Control Approach
 Basic carrier variable: charge associated with the minority carrier excess (or deficit)
within an entire QNR.
 Total excess hole charge in the n-side QNR of a forward biased p+-n junction diode.

QP (t )  qA pn ( x, t )dx
xn
 From the minority carrier diffusion equation we can obtain
dQP (t )
Q (t )
 iDIFF  P
dt
p
 In the steady state we can equate QP to the product of Δpn(xn) and ALP giving
I DIFF 
QP
p




2
2
LP ni
DP ni
qVA / kT
 qA
e
 1  qA
e qVA / kT  1
 p ND
LP N D
⇒ Expression for the diffusion current in the p+-n junction diode.
Storage Delay Time
For an ideal p+-n step junction diode,
dQP (t )
Q (t )
i P
dt
p
i = -IR = constant for times 0+≤ t ≤ ts, where t =0+ is an instant after switching.


dQP (t )
Q
(
t
)
P

  I R 

dt
 p 

Integration over time from t =0+ to t = ts yields
 IF 
t s   p ln1  
 IR 
⇒ compare with Exercise 8.1
More precise analysis gives
 t 
1
erf  s  
 p 
I

 1 R
IF
where erf x  
2

x  2
0 e
d
Measured Storage Delay Time
 IF 
 ln1  
p
 IR 
ts
 t 
1
erf  s  
 p 
I

 1 R
IF
⊙ 1N4002 Si diode
■ 1N91 Ge diode
How to reduce ts?

Storage delay time ts is the primary figure of merit used to characterize the
transient response of pn junction diodes.

As a general rule, ts ~ τp (or τn) ( τ = 10-4 s ~ 10-9 s )

ts depends on the number of initially stored carriers QP(0) (=IF×τp) and the rate of
carrier removal by the reverse current IR.

IR/IF ratio↑⇒ ts decreases below τp (or τn).

τp (or τn) ↓⇒ rapid switching
•
Intentional introduction of R-G centers ⇒ NT↑ ⇒ τp (or τn) ↓
•
Typical method to reduce τp (or τn): diffusion of Au into Si.
⇒ R-G current↑ (Off-state current increase to unacceptable level.)

For faster switching, BJT or MOS devices with fewer stored carriers are available.
Turn-On Transient


We consider the case where a current pulse is used to switch the diode into the
on state.
The voltage drop across the diode, vA(t) increases from the VOFF at t =0 to VON at
t =∞.
vA(t) = ?
Build-Up of Stored Hole Charge during TurnOn Transient
For an ideal p+-n step junction diode,
same negative
slope related to
constant IF ⇒
dQP (t )
QP (t )
i
dt
p
Since i = IF throughout the turn-on transient,
dQP (t )
Q (t )
Q (t )
 i  P  IF  P
dt
p
p
⇒ Growth of the stored n-side hole charge
with time leads to the rise in vA(t).
Diode Voltage during Turn-On Transient
For an ideal p+-n step junction diode in turn-on transient,
dQP (t )
Q (t )
 IF  P
dt
p
Integration over time from t =0 when QP=0 to an arbitrary time t when QP=QP(t) gives

QP (t )  I F p 1  e
t  p

(8.13)

Let’s assume the steady state relationship, QP  I DIFF  p  I 0 p eqVA
applicable in the turn-on transient as


QP (t )  I 0 p eqvA (t ) kT 1
kT

 1 is
(8.15)
Equating (8.13) and (8.15) for QP(t) , and solving for vA(t) , we arrive at the solution,


kT  I F
t  p 
v A (t ) 
ln 1 
1 e

q  I0

τp↑⇒ overall length of the transient ↑
slow final approach
rapid initial rise
HW #5
8.1 (except (h) & (j)), 8.2, 8.4,