Simulation of Current Filaments in
Photoconductive Semiconductor
Switches
K. Kambour, H. P. Hjalmarson, F. J. Zutavern and A. Mar
Sandia National Laboratories*
Charles W. Myles**
Texas Tech University
15th International IEEE Pulsed Power Conference
June 16, 2005
* Sandia is a multiprogram laboratory operated by Sandia Corporation, a
Lockheed Martin company, for the United States Department of Energy
under contract DE-AC04-94AL85000.
** Supported in part by an AFOSR MURI Contract
Outline
 Photoconductive Semiconductor Switches
(PCSS's)
 Lock-on
 Collective Impact Ionization Theory
 Monte Carlo Calculations
 Continuum Calculations
 Conclusions
A PCSS
Lock-on
 Characterized by a persistent or 'locked-on'
electric field (~5 kV/cm) after laser turn off.
 High conductivity state
 Always accompanied by the formation of
current filaments.
 The lock-on field is much lower than the bulk
breakdown field for GaAs.
Current Filaments
Bistable Switch
Carrier Distribution Function
Collective Impact Ionization Theory
Explains highly conductive filaments sustained
by a lock-on field lower than the breakdown field.
 Inside (high carrier density): the carrier-carrier
scattering increases the efficiency of impact
ionization for the hot carriers.
 Outside (low carrier density): the electric field is
too low to create carriers by impact ionization.
Monte Carlo Calculations
Calculating the rate of change of particle number
dn
  f k1i (rii  rAuger  rdefects )d 3 k
dt
Determining the distribution function
Ensemble Monte Carlo
Maxwellian
Evolution to a Steady State Solution
(no carrier-carrier scattering)
dn
 R0 ( F , n)n
dt
R0 ( F , n)  Cii ( F )  C Auger n  Cdefects
2
n( F ) 
Cii ( F )  Cdefects
C Auger
Steady State Solution
(no carrier-carrier scattering)
Evolution to Steady State Solutions
(carrier-carrier scattering included)
dn
 R ( F , n) n
dt
R0 ( F , n)  Cii ( F , n)  C Auger n  Cdefects
2
 Cii0 ( F )  Cii1 ( F )n  C Auger n  Cdefects
2
Steady State Solutions
(carrier-carrier scattering)
GaAs
Continuum Calculations
Continuity equations for electrons n(r , t ), holes p (r , t ), and intrinsic n i (r , t ) carrier densities :
n / t  g  B (ni2  np )( n  p )  A(ni2  np )  1 / qJ n
p / t  g  B (ni2  np )( n  p )  A(ni2  np )  1 / qJ n
Current equations for electron and hole currents :
J n  qnv n (E)  Dnn
J p  qpv p (E)  D p p
Poisson' s equation for the electric field :
q
E = - ( p  n )

Load line equation for the switch vol tage V (t ) in terms of a power supply vol tage V0 and resistance R0 :
V(t)/ t = V0  V (t )  R0 I (t )
Total carrier current :
I (t ) 
1
(J n (r , t )  J p (r , t )) dr
L
Continuum Results
Continuum Results
V0
(KV)
50
50
50
50
t
(sec)
0
1x10-9
1x10-10
1x10-11
VLO
(KV)
30
40
no lock-on
no lock-on
200
200
0
1x10-11
40
60
Conclusions
 Collective Impact ionization Theory (CIIT)
predicts that lock-on will occur in GaAs at a
field much less than the intrinsic breakdown
field in GaAs, in qualitative agreement with
experiment.
 CIIT also predicts that the lock-on field will be
independent of rise time and that the lock-on
current will flow in stable current filaments in
agreement with experiment.